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

Percentage Accurate: 73.0% → 84.3%

Time: 36.9s

Alternatives: 26

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: 73.0% 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: 84.3% accurate, 0.2× speedup

Math

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

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* x (- (* y z) (* t a))) (* b (- (* t i) (* z c)))))
        (t_2 (- (* a c) (* y i))))
   (if (<= (+ t_1 (* j t_2)) INFINITY)
     (fma j t_2 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 * ((t * i) - (z * c)));
	double t_2 = (a * c) - (y * i);
	double tmp;
	if ((t_1 + (j * t_2)) <= ((double) INFINITY)) {
		tmp = fma(j, t_2, t_1);
	} else {
		tmp = 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(t * i) - Float64(z * c))))
	t_2 = Float64(Float64(a * c) - Float64(y * i))
	tmp = 0.0
	if (Float64(t_1 + Float64(j * t_2)) <= Inf)
		tmp = fma(j, t_2, t_1);
	else
		tmp = Float64(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[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$1 + N[(j * t$95$2), $MachinePrecision]), $MachinePrecision], Infinity], N[(j * t$95$2 + t$95$1), $MachinePrecision], N[(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 89.8%

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

      1. +-commutative 89.8%

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

      2. fma-define 89.8%

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

      3. *-commutative 89.8%

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

      4. *-commutative 89.8%

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

   3. Simplified 89.8%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in y around -inf 26.3%

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

   5. Simplified 32.4%

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

   6. Taylor expanded in t around inf 49.5%

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

      1. associate-/l* 54.0%

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

      2. +-commutative 54.0%

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

      3. mul-1-neg 54.0%

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

      4. unsub-neg 54.0%

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

      5. *-commutative 54.0%

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

   8. Simplified 54.0%

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

4. Final simplification 80.7%

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

Alternative 2: 84.3% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (+ (* x (- (* y z) (* t a))) (* b (- (* t i) (* z c))))
          (* 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 * ((t * i) - (z * c)))) + (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 * ((t * i) - (z * c)))) + (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 * ((t * i) - (z * c)))) + (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(t * i) - Float64(z * c)))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(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 * ((t * i) - (z * c)))) + (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[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(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 89.8%

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

   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 26.3%

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

   5. Simplified 32.4%

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

   6. Taylor expanded in t around inf 49.5%

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

      1. associate-/l* 54.0%

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

      2. +-commutative 54.0%

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

      3. mul-1-neg 54.0%

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

      4. unsub-neg 54.0%

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

      5. *-commutative 54.0%

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

   8. Simplified 54.0%

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

4. Final simplification 80.7%

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

Alternative 3: 57.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := a \cdot \left(c \cdot j\right) + t\_1\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_4 := y \cdot \left(x \cdot z + \frac{t \cdot \left(b \cdot i - x \cdot a\right)}{y}\right)\\ \mathbf{if}\;x \leq -8.2 \cdot 10^{+25}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(z - a \cdot \frac{t}{y}\right)\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-91}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-171}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-270}:\\ \;\;\;\;t\_1 - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-141}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-70}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x \leq 3900:\\ \;\;\;\;t\_3 - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+140}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c))))
        (t_2 (+ (* a (* c j)) t_1))
        (t_3 (* j (- (* a c) (* y i))))
        (t_4 (* y (+ (* x z) (/ (* t (- (* b i) (* x a))) y)))))
   (if (<= x -8.2e+25)
     (* (* x y) (- z (* a (/ t y))))
     (if (<= x -3.4e-91)
       t_2
       (if (<= x -4.2e-171)
         t_3
         (if (<= x 1.6e-270)
           (- t_1 (* i (* y j)))
           (if (<= x 4.1e-141)
             t_2
             (if (<= x 1.05e-70)
               t_4
               (if (<= x 3900.0)
                 (- t_3 (* b (* z c)))
                 (if (<= x 6e+140) t_4 (* x (- (* y z) (* t a)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = (a * (c * j)) + t_1;
	double t_3 = j * ((a * c) - (y * i));
	double t_4 = y * ((x * z) + ((t * ((b * i) - (x * a))) / y));
	double tmp;
	if (x <= -8.2e+25) {
		tmp = (x * y) * (z - (a * (t / y)));
	} else if (x <= -3.4e-91) {
		tmp = t_2;
	} else if (x <= -4.2e-171) {
		tmp = t_3;
	} else if (x <= 1.6e-270) {
		tmp = t_1 - (i * (y * j));
	} else if (x <= 4.1e-141) {
		tmp = t_2;
	} else if (x <= 1.05e-70) {
		tmp = t_4;
	} else if (x <= 3900.0) {
		tmp = t_3 - (b * (z * c));
	} else if (x <= 6e+140) {
		tmp = t_4;
	} else {
		tmp = x * ((y * z) - (t * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = (a * (c * j)) + t_1
    t_3 = j * ((a * c) - (y * i))
    t_4 = y * ((x * z) + ((t * ((b * i) - (x * a))) / y))
    if (x <= (-8.2d+25)) then
        tmp = (x * y) * (z - (a * (t / y)))
    else if (x <= (-3.4d-91)) then
        tmp = t_2
    else if (x <= (-4.2d-171)) then
        tmp = t_3
    else if (x <= 1.6d-270) then
        tmp = t_1 - (i * (y * j))
    else if (x <= 4.1d-141) then
        tmp = t_2
    else if (x <= 1.05d-70) then
        tmp = t_4
    else if (x <= 3900.0d0) then
        tmp = t_3 - (b * (z * c))
    else if (x <= 6d+140) then
        tmp = t_4
    else
        tmp = x * ((y * z) - (t * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = (a * (c * j)) + t_1;
	double t_3 = j * ((a * c) - (y * i));
	double t_4 = y * ((x * z) + ((t * ((b * i) - (x * a))) / y));
	double tmp;
	if (x <= -8.2e+25) {
		tmp = (x * y) * (z - (a * (t / y)));
	} else if (x <= -3.4e-91) {
		tmp = t_2;
	} else if (x <= -4.2e-171) {
		tmp = t_3;
	} else if (x <= 1.6e-270) {
		tmp = t_1 - (i * (y * j));
	} else if (x <= 4.1e-141) {
		tmp = t_2;
	} else if (x <= 1.05e-70) {
		tmp = t_4;
	} else if (x <= 3900.0) {
		tmp = t_3 - (b * (z * c));
	} else if (x <= 6e+140) {
		tmp = t_4;
	} else {
		tmp = x * ((y * z) - (t * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = (a * (c * j)) + t_1
	t_3 = j * ((a * c) - (y * i))
	t_4 = y * ((x * z) + ((t * ((b * i) - (x * a))) / y))
	tmp = 0
	if x <= -8.2e+25:
		tmp = (x * y) * (z - (a * (t / y)))
	elif x <= -3.4e-91:
		tmp = t_2
	elif x <= -4.2e-171:
		tmp = t_3
	elif x <= 1.6e-270:
		tmp = t_1 - (i * (y * j))
	elif x <= 4.1e-141:
		tmp = t_2
	elif x <= 1.05e-70:
		tmp = t_4
	elif x <= 3900.0:
		tmp = t_3 - (b * (z * c))
	elif x <= 6e+140:
		tmp = t_4
	else:
		tmp = x * ((y * z) - (t * a))
	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(Float64(a * Float64(c * j)) + t_1)
	t_3 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_4 = Float64(y * Float64(Float64(x * z) + Float64(Float64(t * Float64(Float64(b * i) - Float64(x * a))) / y)))
	tmp = 0.0
	if (x <= -8.2e+25)
		tmp = Float64(Float64(x * y) * Float64(z - Float64(a * Float64(t / y))));
	elseif (x <= -3.4e-91)
		tmp = t_2;
	elseif (x <= -4.2e-171)
		tmp = t_3;
	elseif (x <= 1.6e-270)
		tmp = Float64(t_1 - Float64(i * Float64(y * j)));
	elseif (x <= 4.1e-141)
		tmp = t_2;
	elseif (x <= 1.05e-70)
		tmp = t_4;
	elseif (x <= 3900.0)
		tmp = Float64(t_3 - Float64(b * Float64(z * c)));
	elseif (x <= 6e+140)
		tmp = t_4;
	else
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = (a * (c * j)) + t_1;
	t_3 = j * ((a * c) - (y * i));
	t_4 = y * ((x * z) + ((t * ((b * i) - (x * a))) / y));
	tmp = 0.0;
	if (x <= -8.2e+25)
		tmp = (x * y) * (z - (a * (t / y)));
	elseif (x <= -3.4e-91)
		tmp = t_2;
	elseif (x <= -4.2e-171)
		tmp = t_3;
	elseif (x <= 1.6e-270)
		tmp = t_1 - (i * (y * j));
	elseif (x <= 4.1e-141)
		tmp = t_2;
	elseif (x <= 1.05e-70)
		tmp = t_4;
	elseif (x <= 3900.0)
		tmp = t_3 - (b * (z * c));
	elseif (x <= 6e+140)
		tmp = t_4;
	else
		tmp = x * ((y * z) - (t * a));
	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[(N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y * N[(N[(x * z), $MachinePrecision] + N[(N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8.2e+25], N[(N[(x * y), $MachinePrecision] * N[(z - N[(a * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.4e-91], t$95$2, If[LessEqual[x, -4.2e-171], t$95$3, If[LessEqual[x, 1.6e-270], N[(t$95$1 - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.1e-141], t$95$2, If[LessEqual[x, 1.05e-70], t$95$4, If[LessEqual[x, 3900.0], N[(t$95$3 - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6e+140], t$95$4, N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if x < -8.19999999999999933e25

   1. Initial program 58.0%

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

   3. Taylor expanded in y around -inf 52.9%

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

   5. Simplified 56.6%

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

   6. Taylor expanded in x around inf 59.2%

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

      1. associate-*r* 59.3%

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

      2. *-commutative 59.3%

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

      3. mul-1-neg 59.3%

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

      4. unsub-neg 59.3%

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

      5. associate-/l* 60.3%

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

   8. Simplified 60.3%

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

   if -8.19999999999999933e25 < x < -3.40000000000000027e-91 or 1.59999999999999994e-270 < x < 4.10000000000000002e-141

   1. Initial program 67.6%

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

   3. Taylor expanded in x around 0 72.6%

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

   4. Taylor expanded in y around 0 69.7%

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

   if -3.40000000000000027e-91 < x < -4.2e-171

   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 j around inf 80.7%

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

   if -4.2e-171 < x < 1.59999999999999994e-270

   1. Initial program 67.5%

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

   3. Taylor expanded in x around 0 78.6%

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

   4. Taylor expanded in a around 0 78.8%

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

   if 4.10000000000000002e-141 < x < 1.0500000000000001e-70 or 3900 < x < 5.99999999999999993e140

   1. Initial program 61.7%

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

   3. Taylor expanded in y around -inf 54.3%

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

   5. Simplified 59.4%

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

   6. Taylor expanded in t around inf 75.7%

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

      1. associate-/l* 70.1%

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

      2. +-commutative 70.1%

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

      3. mul-1-neg 70.1%

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

      4. unsub-neg 70.1%

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

      5. *-commutative 70.1%

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

   8. Simplified 70.1%

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

   9. Taylor expanded in j around 0 69.8%

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

   if 1.0500000000000001e-70 < x < 3900

   1. Initial program 93.8%

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

   3. Taylor expanded in x around 0 72.7%

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

   4. Taylor expanded in c around inf 72.9%

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

   if 5.99999999999999993e140 < x

   1. Initial program 65.8%

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

   3. Taylor expanded in x around inf 76.7%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+25}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(z - a \cdot \frac{t}{y}\right)\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-91}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-171}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-270}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-141}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-70}:\\ \;\;\;\;y \cdot \left(x \cdot z + \frac{t \cdot \left(b \cdot i - x \cdot a\right)}{y}\right)\\ \mathbf{elif}\;x \leq 3900:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+140}:\\ \;\;\;\;y \cdot \left(x \cdot z + \frac{t \cdot \left(b \cdot i - x \cdot a\right)}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -7.2 \cdot 10^{+88}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-8}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -9.4 \cdot 10^{-222}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-142}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-103}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-25}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 8.4 \cdot 10^{+58}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j))))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (* a (- (* c j) (* x t)))))
   (if (<= a -7.2e+88)
     t_3
     (if (<= a -1.4e-8)
       t_2
       (if (<= a -9.4e-222)
         (* b (- (* t i) (* z c)))
         (if (<= a 9e-142)
           (* y (- (* x z) (* i j)))
           (if (<= a 1.4e-103)
             t_1
             (if (<= a 5.6e-25)
               t_2
               (if (<= a 8.2e+58)
                 t_1
                 (if (<= a 8.4e+58) (* x (* y z)) 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 = i * ((t * b) - (y * j));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -7.2e+88) {
		tmp = t_3;
	} else if (a <= -1.4e-8) {
		tmp = t_2;
	} else if (a <= -9.4e-222) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 9e-142) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= 1.4e-103) {
		tmp = t_1;
	} else if (a <= 5.6e-25) {
		tmp = t_2;
	} else if (a <= 8.2e+58) {
		tmp = t_1;
	} else if (a <= 8.4e+58) {
		tmp = x * (y * z);
	} 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 = i * ((t * b) - (y * j))
    t_2 = x * ((y * z) - (t * a))
    t_3 = a * ((c * j) - (x * t))
    if (a <= (-7.2d+88)) then
        tmp = t_3
    else if (a <= (-1.4d-8)) then
        tmp = t_2
    else if (a <= (-9.4d-222)) then
        tmp = b * ((t * i) - (z * c))
    else if (a <= 9d-142) then
        tmp = y * ((x * z) - (i * j))
    else if (a <= 1.4d-103) then
        tmp = t_1
    else if (a <= 5.6d-25) then
        tmp = t_2
    else if (a <= 8.2d+58) then
        tmp = t_1
    else if (a <= 8.4d+58) then
        tmp = x * (y * z)
    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 = i * ((t * b) - (y * j));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -7.2e+88) {
		tmp = t_3;
	} else if (a <= -1.4e-8) {
		tmp = t_2;
	} else if (a <= -9.4e-222) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 9e-142) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= 1.4e-103) {
		tmp = t_1;
	} else if (a <= 5.6e-25) {
		tmp = t_2;
	} else if (a <= 8.2e+58) {
		tmp = t_1;
	} else if (a <= 8.4e+58) {
		tmp = x * (y * z);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	t_2 = x * ((y * z) - (t * a))
	t_3 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -7.2e+88:
		tmp = t_3
	elif a <= -1.4e-8:
		tmp = t_2
	elif a <= -9.4e-222:
		tmp = b * ((t * i) - (z * c))
	elif a <= 9e-142:
		tmp = y * ((x * z) - (i * j))
	elif a <= 1.4e-103:
		tmp = t_1
	elif a <= 5.6e-25:
		tmp = t_2
	elif a <= 8.2e+58:
		tmp = t_1
	elif a <= 8.4e+58:
		tmp = x * (y * z)
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_3 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -7.2e+88)
		tmp = t_3;
	elseif (a <= -1.4e-8)
		tmp = t_2;
	elseif (a <= -9.4e-222)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (a <= 9e-142)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (a <= 1.4e-103)
		tmp = t_1;
	elseif (a <= 5.6e-25)
		tmp = t_2;
	elseif (a <= 8.2e+58)
		tmp = t_1;
	elseif (a <= 8.4e+58)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((t * b) - (y * j));
	t_2 = x * ((y * z) - (t * a));
	t_3 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -7.2e+88)
		tmp = t_3;
	elseif (a <= -1.4e-8)
		tmp = t_2;
	elseif (a <= -9.4e-222)
		tmp = b * ((t * i) - (z * c));
	elseif (a <= 9e-142)
		tmp = y * ((x * z) - (i * j));
	elseif (a <= 1.4e-103)
		tmp = t_1;
	elseif (a <= 5.6e-25)
		tmp = t_2;
	elseif (a <= 8.2e+58)
		tmp = t_1;
	elseif (a <= 8.4e+58)
		tmp = x * (y * z);
	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[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.2e+88], t$95$3, If[LessEqual[a, -1.4e-8], t$95$2, If[LessEqual[a, -9.4e-222], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9e-142], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.4e-103], t$95$1, If[LessEqual[a, 5.6e-25], t$95$2, If[LessEqual[a, 8.2e+58], t$95$1, If[LessEqual[a, 8.4e+58], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -7.2000000000000004e88 or 8.40000000000000048e58 < a

   1. Initial program 58.5%

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

   3. Taylor expanded in a around inf 69.2%

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

      1. +-commutative 69.2%

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

      2. mul-1-neg 69.2%

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

      3. unsub-neg 69.2%

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

      4. *-commutative 69.2%

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

   5. Simplified 69.2%

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

   if -7.2000000000000004e88 < a < -1.4e-8 or 1.40000000000000011e-103 < a < 5.59999999999999976e-25

   1. Initial program 69.8%

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

   3. Taylor expanded in x around inf 66.2%

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

   if -1.4e-8 < a < -9.3999999999999995e-222

   1. Initial program 73.7%

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

   3. Taylor expanded in b around inf 62.1%

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

   if -9.3999999999999995e-222 < a < 9.00000000000000037e-142

   1. Initial program 76.2%

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

   3. Taylor expanded in y around inf 63.1%

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

      1. +-commutative 63.1%

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

      2. mul-1-neg 63.1%

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

      3. unsub-neg 63.1%

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

      4. *-commutative 63.1%

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

      5. *-commutative 63.1%

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

   5. Simplified 63.1%

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

   if 9.00000000000000037e-142 < a < 1.40000000000000011e-103 or 5.59999999999999976e-25 < a < 8.2e58

   1. Initial program 71.8%

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

   3. Taylor expanded in y around 0 71.3%

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

   4. Taylor expanded in i around -inf 79.2%

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

      1. associate-*r* 79.2%

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

      2. neg-mul-1 79.2%

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

      3. *-commutative 79.2%

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

   6. Simplified 79.2%

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

   if 8.2e58 < a < 8.40000000000000048e58

   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 0.0%

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

   5. Simplified 0.0%

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

   6. Taylor expanded in x around inf 100.0%

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

      1. associate-*r* 100.0%

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

      2. *-commutative 100.0%

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

      3. mul-1-neg 100.0%

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

      4. unsub-neg 100.0%

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

      5. associate-/l* 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in y around inf 100.0%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{+88}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq -9.4 \cdot 10^{-222}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-142}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-103}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-25}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+58}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 8.4 \cdot 10^{+58}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 58.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := a \cdot \left(c \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;x \leq -6.2 \cdot 10^{+25}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(z - a \cdot \frac{t}{y}\right)\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-92}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-161}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-203}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 3700:\\ \;\;\;\;t\_1 - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+140}:\\ \;\;\;\;y \cdot \left(x \cdot z + \frac{t \cdot \left(b \cdot i - x \cdot a\right)}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i))))
        (t_2 (+ (* a (* c j)) (* b (- (* t i) (* z c))))))
   (if (<= x -6.2e+25)
     (* (* x y) (- z (* a (/ t y))))
     (if (<= x -7.5e-92)
       t_2
       (if (<= x -1.5e-161)
         t_1
         (if (<= x 1.2e-203)
           t_2
           (if (<= x 3700.0)
             (- t_1 (* b (* z c)))
             (if (<= x 6.5e+140)
               (* y (+ (* x z) (/ (* t (- (* b i) (* x a))) y)))
               (* x (- (* y z) (* t a)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = (a * (c * j)) + (b * ((t * i) - (z * c)));
	double tmp;
	if (x <= -6.2e+25) {
		tmp = (x * y) * (z - (a * (t / y)));
	} else if (x <= -7.5e-92) {
		tmp = t_2;
	} else if (x <= -1.5e-161) {
		tmp = t_1;
	} else if (x <= 1.2e-203) {
		tmp = t_2;
	} else if (x <= 3700.0) {
		tmp = t_1 - (b * (z * c));
	} else if (x <= 6.5e+140) {
		tmp = y * ((x * z) + ((t * ((b * i) - (x * a))) / y));
	} else {
		tmp = x * ((y * z) - (t * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = (a * (c * j)) + (b * ((t * i) - (z * c)))
    if (x <= (-6.2d+25)) then
        tmp = (x * y) * (z - (a * (t / y)))
    else if (x <= (-7.5d-92)) then
        tmp = t_2
    else if (x <= (-1.5d-161)) then
        tmp = t_1
    else if (x <= 1.2d-203) then
        tmp = t_2
    else if (x <= 3700.0d0) then
        tmp = t_1 - (b * (z * c))
    else if (x <= 6.5d+140) then
        tmp = y * ((x * z) + ((t * ((b * i) - (x * a))) / y))
    else
        tmp = x * ((y * z) - (t * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = (a * (c * j)) + (b * ((t * i) - (z * c)));
	double tmp;
	if (x <= -6.2e+25) {
		tmp = (x * y) * (z - (a * (t / y)));
	} else if (x <= -7.5e-92) {
		tmp = t_2;
	} else if (x <= -1.5e-161) {
		tmp = t_1;
	} else if (x <= 1.2e-203) {
		tmp = t_2;
	} else if (x <= 3700.0) {
		tmp = t_1 - (b * (z * c));
	} else if (x <= 6.5e+140) {
		tmp = y * ((x * z) + ((t * ((b * i) - (x * a))) / y));
	} else {
		tmp = x * ((y * z) - (t * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = (a * (c * j)) + (b * ((t * i) - (z * c)))
	tmp = 0
	if x <= -6.2e+25:
		tmp = (x * y) * (z - (a * (t / y)))
	elif x <= -7.5e-92:
		tmp = t_2
	elif x <= -1.5e-161:
		tmp = t_1
	elif x <= 1.2e-203:
		tmp = t_2
	elif x <= 3700.0:
		tmp = t_1 - (b * (z * c))
	elif x <= 6.5e+140:
		tmp = y * ((x * z) + ((t * ((b * i) - (x * a))) / y))
	else:
		tmp = x * ((y * z) - (t * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(Float64(a * Float64(c * j)) + Float64(b * Float64(Float64(t * i) - Float64(z * c))))
	tmp = 0.0
	if (x <= -6.2e+25)
		tmp = Float64(Float64(x * y) * Float64(z - Float64(a * Float64(t / y))));
	elseif (x <= -7.5e-92)
		tmp = t_2;
	elseif (x <= -1.5e-161)
		tmp = t_1;
	elseif (x <= 1.2e-203)
		tmp = t_2;
	elseif (x <= 3700.0)
		tmp = Float64(t_1 - Float64(b * Float64(z * c)));
	elseif (x <= 6.5e+140)
		tmp = Float64(y * Float64(Float64(x * z) + Float64(Float64(t * Float64(Float64(b * i) - Float64(x * a))) / y)));
	else
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = (a * (c * j)) + (b * ((t * i) - (z * c)));
	tmp = 0.0;
	if (x <= -6.2e+25)
		tmp = (x * y) * (z - (a * (t / y)));
	elseif (x <= -7.5e-92)
		tmp = t_2;
	elseif (x <= -1.5e-161)
		tmp = t_1;
	elseif (x <= 1.2e-203)
		tmp = t_2;
	elseif (x <= 3700.0)
		tmp = t_1 - (b * (z * c));
	elseif (x <= 6.5e+140)
		tmp = y * ((x * z) + ((t * ((b * i) - (x * a))) / y));
	else
		tmp = x * ((y * z) - (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.2e+25], N[(N[(x * y), $MachinePrecision] * N[(z - N[(a * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7.5e-92], t$95$2, If[LessEqual[x, -1.5e-161], t$95$1, If[LessEqual[x, 1.2e-203], t$95$2, If[LessEqual[x, 3700.0], N[(t$95$1 - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.5e+140], N[(y * N[(N[(x * z), $MachinePrecision] + N[(N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -6.1999999999999996e25

   1. Initial program 58.0%

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

   3. Taylor expanded in y around -inf 52.9%

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

   5. Simplified 56.6%

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

   6. Taylor expanded in x around inf 59.2%

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

      1. associate-*r* 59.3%

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

      2. *-commutative 59.3%

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

      3. mul-1-neg 59.3%

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

      4. unsub-neg 59.3%

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

      5. associate-/l* 60.3%

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

   8. Simplified 60.3%

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

   if -6.1999999999999996e25 < x < -7.5000000000000005e-92 or -1.49999999999999994e-161 < x < 1.1999999999999999e-203

   1. Initial program 69.0%

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

   3. Taylor expanded in x around 0 72.6%

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

   4. Taylor expanded in y around 0 65.7%

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

   if -7.5000000000000005e-92 < x < -1.49999999999999994e-161

   1. Initial program 78.0%

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

   3. Taylor expanded in j around inf 85.1%

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

   if 1.1999999999999999e-203 < x < 3700

   1. Initial program 67.2%

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

   3. Taylor expanded in x around 0 70.2%

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

   4. Taylor expanded in c around inf 68.3%

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

   if 3700 < x < 6.4999999999999999e140

   1. Initial program 74.2%

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

   3. Taylor expanded in y around -inf 67.9%

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

   5. Simplified 74.3%

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

   6. Taylor expanded in t around inf 75.8%

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

      1. associate-/l* 71.8%

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

      2. +-commutative 71.8%

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

      3. mul-1-neg 71.8%

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

      4. unsub-neg 71.8%

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

      5. *-commutative 71.8%

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

   8. Simplified 71.8%

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

   9. Taylor expanded in j around 0 69.4%

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

   if 6.4999999999999999e140 < x

   1. Initial program 65.8%

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

   3. Taylor expanded in x around inf 76.7%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+25}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(z - a \cdot \frac{t}{y}\right)\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-92}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-161}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-203}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 3700:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+140}:\\ \;\;\;\;y \cdot \left(x \cdot z + \frac{t \cdot \left(b \cdot i - x \cdot a\right)}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 58.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_3 := y \cdot \left(x \cdot z + \left(\frac{t\_1}{y} - i \cdot j\right)\right)\\ t_4 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;y \leq -3 \cdot 10^{-60}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-306}:\\ \;\;\;\;t\_1 + t\_4\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-155}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-94}:\\ \;\;\;\;t\_4 - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-63}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+80}:\\ \;\;\;\;y \cdot \left(x \cdot z + \frac{t \cdot \left(b \cdot i - x \cdot a\right)}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j)))
        (t_2 (* a (- (* c j) (* x t))))
        (t_3 (* y (+ (* x z) (- (/ t_1 y) (* i j)))))
        (t_4 (* b (- (* t i) (* z c)))))
   (if (<= y -3e-60)
     t_3
     (if (<= y 2.8e-306)
       (+ t_1 t_4)
       (if (<= y 8e-155)
         t_2
         (if (<= y 4.4e-94)
           (- t_4 (* i (* y j)))
           (if (<= y 3.5e-63)
             t_2
             (if (<= y 7e+80)
               (* y (+ (* x z) (/ (* t (- (* b i) (* x a))) y)))
               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 = a * (c * j);
	double t_2 = a * ((c * j) - (x * t));
	double t_3 = y * ((x * z) + ((t_1 / y) - (i * j)));
	double t_4 = b * ((t * i) - (z * c));
	double tmp;
	if (y <= -3e-60) {
		tmp = t_3;
	} else if (y <= 2.8e-306) {
		tmp = t_1 + t_4;
	} else if (y <= 8e-155) {
		tmp = t_2;
	} else if (y <= 4.4e-94) {
		tmp = t_4 - (i * (y * j));
	} else if (y <= 3.5e-63) {
		tmp = t_2;
	} else if (y <= 7e+80) {
		tmp = y * ((x * z) + ((t * ((b * i) - (x * a))) / y));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = a * (c * j)
    t_2 = a * ((c * j) - (x * t))
    t_3 = y * ((x * z) + ((t_1 / y) - (i * j)))
    t_4 = b * ((t * i) - (z * c))
    if (y <= (-3d-60)) then
        tmp = t_3
    else if (y <= 2.8d-306) then
        tmp = t_1 + t_4
    else if (y <= 8d-155) then
        tmp = t_2
    else if (y <= 4.4d-94) then
        tmp = t_4 - (i * (y * j))
    else if (y <= 3.5d-63) then
        tmp = t_2
    else if (y <= 7d+80) then
        tmp = y * ((x * z) + ((t * ((b * i) - (x * a))) / y))
    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 = a * (c * j);
	double t_2 = a * ((c * j) - (x * t));
	double t_3 = y * ((x * z) + ((t_1 / y) - (i * j)));
	double t_4 = b * ((t * i) - (z * c));
	double tmp;
	if (y <= -3e-60) {
		tmp = t_3;
	} else if (y <= 2.8e-306) {
		tmp = t_1 + t_4;
	} else if (y <= 8e-155) {
		tmp = t_2;
	} else if (y <= 4.4e-94) {
		tmp = t_4 - (i * (y * j));
	} else if (y <= 3.5e-63) {
		tmp = t_2;
	} else if (y <= 7e+80) {
		tmp = y * ((x * z) + ((t * ((b * i) - (x * a))) / y));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	t_2 = a * ((c * j) - (x * t))
	t_3 = y * ((x * z) + ((t_1 / y) - (i * j)))
	t_4 = b * ((t * i) - (z * c))
	tmp = 0
	if y <= -3e-60:
		tmp = t_3
	elif y <= 2.8e-306:
		tmp = t_1 + t_4
	elif y <= 8e-155:
		tmp = t_2
	elif y <= 4.4e-94:
		tmp = t_4 - (i * (y * j))
	elif y <= 3.5e-63:
		tmp = t_2
	elif y <= 7e+80:
		tmp = y * ((x * z) + ((t * ((b * i) - (x * a))) / y))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_3 = Float64(y * Float64(Float64(x * z) + Float64(Float64(t_1 / y) - Float64(i * j))))
	t_4 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (y <= -3e-60)
		tmp = t_3;
	elseif (y <= 2.8e-306)
		tmp = Float64(t_1 + t_4);
	elseif (y <= 8e-155)
		tmp = t_2;
	elseif (y <= 4.4e-94)
		tmp = Float64(t_4 - Float64(i * Float64(y * j)));
	elseif (y <= 3.5e-63)
		tmp = t_2;
	elseif (y <= 7e+80)
		tmp = Float64(y * Float64(Float64(x * z) + Float64(Float64(t * Float64(Float64(b * i) - Float64(x * a))) / y)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (c * j);
	t_2 = a * ((c * j) - (x * t));
	t_3 = y * ((x * z) + ((t_1 / y) - (i * j)));
	t_4 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (y <= -3e-60)
		tmp = t_3;
	elseif (y <= 2.8e-306)
		tmp = t_1 + t_4;
	elseif (y <= 8e-155)
		tmp = t_2;
	elseif (y <= 4.4e-94)
		tmp = t_4 - (i * (y * j));
	elseif (y <= 3.5e-63)
		tmp = t_2;
	elseif (y <= 7e+80)
		tmp = y * ((x * z) + ((t * ((b * i) - (x * a))) / y));
	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[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(N[(x * z), $MachinePrecision] + N[(N[(t$95$1 / y), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3e-60], t$95$3, If[LessEqual[y, 2.8e-306], N[(t$95$1 + t$95$4), $MachinePrecision], If[LessEqual[y, 8e-155], t$95$2, If[LessEqual[y, 4.4e-94], N[(t$95$4 - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e-63], t$95$2, If[LessEqual[y, 7e+80], N[(y * N[(N[(x * z), $MachinePrecision] + N[(N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.00000000000000019e-60 or 6.99999999999999987e80 < y

   1. Initial program 61.7%

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

   3. Taylor expanded in y around -inf 76.7%

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

   5. Simplified 77.5%

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

   6. Taylor expanded in j around inf 72.4%

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

   if -3.00000000000000019e-60 < y < 2.8000000000000001e-306

   1. Initial program 70.9%

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

   3. Taylor expanded in x around 0 68.0%

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

   4. Taylor expanded in y around 0 60.4%

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

   if 2.8000000000000001e-306 < y < 8.00000000000000011e-155 or 4.40000000000000002e-94 < y < 3.50000000000000003e-63

   1. Initial program 78.7%

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

   3. Taylor expanded in a around inf 71.2%

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

      1. +-commutative 71.2%

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

      2. mul-1-neg 71.2%

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

      3. unsub-neg 71.2%

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

      4. *-commutative 71.2%

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

   5. Simplified 71.2%

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

   if 8.00000000000000011e-155 < y < 4.40000000000000002e-94

   1. Initial program 71.0%

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

   3. Taylor expanded in x around 0 65.1%

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

   4. Taylor expanded in a around 0 65.5%

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

   if 3.50000000000000003e-63 < y < 6.99999999999999987e80

   1. Initial program 65.5%

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

   3. Taylor expanded in y around -inf 60.1%

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

   5. Simplified 62.9%

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

   6. Taylor expanded in t around inf 78.0%

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

      1. associate-/l* 78.0%

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

      2. +-commutative 78.0%

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

      3. mul-1-neg 78.0%

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

      4. unsub-neg 78.0%

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

      5. *-commutative 78.0%

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

   8. Simplified 78.0%

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

   9. Taylor expanded in j around 0 74.5%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-60}:\\ \;\;\;\;y \cdot \left(x \cdot z + \left(\frac{a \cdot \left(c \cdot j\right)}{y} - i \cdot j\right)\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-306}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-155}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-94}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-63}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+80}:\\ \;\;\;\;y \cdot \left(x \cdot z + \frac{t \cdot \left(b \cdot i - x \cdot a\right)}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z + \left(\frac{a \cdot \left(c \cdot j\right)}{y} - i \cdot j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;a \leq -0.00044:\\ \;\;\;\;t\_3 + t\_2\\ \mathbf{elif}\;a \leq -1.12 \cdot 10^{-110}:\\ \;\;\;\;t\_3 + t\_1\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-195}:\\ \;\;\;\;t\_3 + \left(t\_2 + i \cdot \left(t \cdot b\right)\right)\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-99}:\\ \;\;\;\;t\_3 + \left(y \cdot \left(x \cdot z\right) + t\_1\right)\\ \mathbf{elif}\;a \leq 9.1 \cdot 10^{+58}:\\ \;\;\;\;y \cdot \left(x \cdot z + \left(t \cdot \frac{b \cdot i - x \cdot a}{y} - i \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c))))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (* j (- (* a c) (* y i)))))
   (if (<= a -0.00044)
     (+ t_3 t_2)
     (if (<= a -1.12e-110)
       (+ t_3 t_1)
       (if (<= a -3.6e-195)
         (+ t_3 (+ t_2 (* i (* t b))))
         (if (<= a 3.3e-99)
           (+ t_3 (+ (* y (* x z)) t_1))
           (if (<= a 9.1e+58)
             (* y (+ (* x z) (- (* t (/ (- (* b i) (* x a)) y)) (* i j))))
             (* a (- (* c j) (* x t))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (a <= -0.00044) {
		tmp = t_3 + t_2;
	} else if (a <= -1.12e-110) {
		tmp = t_3 + t_1;
	} else if (a <= -3.6e-195) {
		tmp = t_3 + (t_2 + (i * (t * b)));
	} else if (a <= 3.3e-99) {
		tmp = t_3 + ((y * (x * z)) + t_1);
	} else if (a <= 9.1e+58) {
		tmp = y * ((x * z) + ((t * (((b * i) - (x * a)) / y)) - (i * j)));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = x * ((y * z) - (t * a))
    t_3 = j * ((a * c) - (y * i))
    if (a <= (-0.00044d0)) then
        tmp = t_3 + t_2
    else if (a <= (-1.12d-110)) then
        tmp = t_3 + t_1
    else if (a <= (-3.6d-195)) then
        tmp = t_3 + (t_2 + (i * (t * b)))
    else if (a <= 3.3d-99) then
        tmp = t_3 + ((y * (x * z)) + t_1)
    else if (a <= 9.1d+58) then
        tmp = y * ((x * z) + ((t * (((b * i) - (x * a)) / y)) - (i * j)))
    else
        tmp = a * ((c * j) - (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (a <= -0.00044) {
		tmp = t_3 + t_2;
	} else if (a <= -1.12e-110) {
		tmp = t_3 + t_1;
	} else if (a <= -3.6e-195) {
		tmp = t_3 + (t_2 + (i * (t * b)));
	} else if (a <= 3.3e-99) {
		tmp = t_3 + ((y * (x * z)) + t_1);
	} else if (a <= 9.1e+58) {
		tmp = y * ((x * z) + ((t * (((b * i) - (x * a)) / y)) - (i * j)));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = x * ((y * z) - (t * a))
	t_3 = j * ((a * c) - (y * i))
	tmp = 0
	if a <= -0.00044:
		tmp = t_3 + t_2
	elif a <= -1.12e-110:
		tmp = t_3 + t_1
	elif a <= -3.6e-195:
		tmp = t_3 + (t_2 + (i * (t * b)))
	elif a <= 3.3e-99:
		tmp = t_3 + ((y * (x * z)) + t_1)
	elif a <= 9.1e+58:
		tmp = y * ((x * z) + ((t * (((b * i) - (x * a)) / y)) - (i * j)))
	else:
		tmp = a * ((c * j) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_3 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (a <= -0.00044)
		tmp = Float64(t_3 + t_2);
	elseif (a <= -1.12e-110)
		tmp = Float64(t_3 + t_1);
	elseif (a <= -3.6e-195)
		tmp = Float64(t_3 + Float64(t_2 + Float64(i * Float64(t * b))));
	elseif (a <= 3.3e-99)
		tmp = Float64(t_3 + Float64(Float64(y * Float64(x * z)) + t_1));
	elseif (a <= 9.1e+58)
		tmp = Float64(y * Float64(Float64(x * z) + Float64(Float64(t * Float64(Float64(Float64(b * i) - Float64(x * a)) / y)) - Float64(i * j))));
	else
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = x * ((y * z) - (t * a));
	t_3 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (a <= -0.00044)
		tmp = t_3 + t_2;
	elseif (a <= -1.12e-110)
		tmp = t_3 + t_1;
	elseif (a <= -3.6e-195)
		tmp = t_3 + (t_2 + (i * (t * b)));
	elseif (a <= 3.3e-99)
		tmp = t_3 + ((y * (x * z)) + t_1);
	elseif (a <= 9.1e+58)
		tmp = y * ((x * z) + ((t * (((b * i) - (x * a)) / y)) - (i * j)));
	else
		tmp = a * ((c * j) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -0.00044], N[(t$95$3 + t$95$2), $MachinePrecision], If[LessEqual[a, -1.12e-110], N[(t$95$3 + t$95$1), $MachinePrecision], If[LessEqual[a, -3.6e-195], N[(t$95$3 + N[(t$95$2 + N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.3e-99], N[(t$95$3 + N[(N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.1e+58], 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], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -4.40000000000000016e-4

   1. Initial program 65.5%

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

   3. Taylor expanded in b around 0 72.0%

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

   if -4.40000000000000016e-4 < a < -1.11999999999999998e-110

   1. Initial program 71.4%

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

   3. Taylor expanded in x around 0 85.6%

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

   if -1.11999999999999998e-110 < a < -3.6e-195

   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 c around 0 77.6%

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

      1. mul-1-neg 77.6%

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

      2. associate-*r* 90.0%

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

      3. *-commutative 90.0%

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

      4. associate-*r* 90.1%

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

      5. distribute-rgt-neg-out 90.1%

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

      6. *-commutative 90.1%

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

      7. distribute-rgt-neg-in 90.1%

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

   5. Simplified 90.1%

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

   if -3.6e-195 < a < 3.29999999999999986e-99

   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 y around inf 77.2%

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

      1. *-commutative 77.2%

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

      2. associate-*l* 81.0%

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

   5. Simplified 81.0%

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

   if 3.29999999999999986e-99 < a < 9.10000000000000042e58

   1. Initial program 66.0%

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

   3. Taylor expanded in y around -inf 59.9%

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

   5. Simplified 59.9%

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

   6. Taylor expanded in t around inf 81.9%

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

      1. associate-/l* 85.0%

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

      2. +-commutative 85.0%

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

      3. mul-1-neg 85.0%

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

      4. unsub-neg 85.0%

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

      5. *-commutative 85.0%

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

   8. Simplified 85.0%

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

   if 9.10000000000000042e58 < a

   1. Initial program 52.2%

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

   3. Taylor expanded in a around inf 72.7%

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

      1. +-commutative 72.7%

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

      2. mul-1-neg 72.7%

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

      3. unsub-neg 72.7%

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

      4. *-commutative 72.7%

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

   5. Simplified 72.7%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.00044:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq -1.12 \cdot 10^{-110}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-195}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + i \cdot \left(t \cdot b\right)\right)\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-99}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + \left(y \cdot \left(x \cdot z\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right)\\ \mathbf{elif}\;a \leq 9.1 \cdot 10^{+58}:\\ \;\;\;\;y \cdot \left(x \cdot z + \left(t \cdot \frac{b \cdot i - x \cdot a}{y} - i \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_2 := \left(x \cdot y\right) \cdot \left(z - a \cdot \frac{t}{y}\right)\\ t_3 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.55 \cdot 10^{+89}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-10}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{-222}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{-140}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-25}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 8.4 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j))))
        (t_2 (* (* x y) (- z (* a (/ t y)))))
        (t_3 (* a (- (* c j) (* x t)))))
   (if (<= a -1.55e+89)
     t_3
     (if (<= a -2e-10)
       t_2
       (if (<= a -9.2e-222)
         (* b (- (* t i) (* z c)))
         (if (<= a 4.9e-140)
           (* y (- (* x z) (* i j)))
           (if (<= a 1.1e-98)
             t_1
             (if (<= a 7.5e-25) t_2 (if (<= a 8.4e+58) t_1 t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double t_2 = (x * y) * (z - (a * (t / y)));
	double t_3 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.55e+89) {
		tmp = t_3;
	} else if (a <= -2e-10) {
		tmp = t_2;
	} else if (a <= -9.2e-222) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 4.9e-140) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= 1.1e-98) {
		tmp = t_1;
	} else if (a <= 7.5e-25) {
		tmp = t_2;
	} else if (a <= 8.4e+58) {
		tmp = t_1;
	} 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 = i * ((t * b) - (y * j))
    t_2 = (x * y) * (z - (a * (t / y)))
    t_3 = a * ((c * j) - (x * t))
    if (a <= (-1.55d+89)) then
        tmp = t_3
    else if (a <= (-2d-10)) then
        tmp = t_2
    else if (a <= (-9.2d-222)) then
        tmp = b * ((t * i) - (z * c))
    else if (a <= 4.9d-140) then
        tmp = y * ((x * z) - (i * j))
    else if (a <= 1.1d-98) then
        tmp = t_1
    else if (a <= 7.5d-25) then
        tmp = t_2
    else if (a <= 8.4d+58) then
        tmp = t_1
    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 = i * ((t * b) - (y * j));
	double t_2 = (x * y) * (z - (a * (t / y)));
	double t_3 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.55e+89) {
		tmp = t_3;
	} else if (a <= -2e-10) {
		tmp = t_2;
	} else if (a <= -9.2e-222) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 4.9e-140) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= 1.1e-98) {
		tmp = t_1;
	} else if (a <= 7.5e-25) {
		tmp = t_2;
	} else if (a <= 8.4e+58) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	t_2 = (x * y) * (z - (a * (t / y)))
	t_3 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -1.55e+89:
		tmp = t_3
	elif a <= -2e-10:
		tmp = t_2
	elif a <= -9.2e-222:
		tmp = b * ((t * i) - (z * c))
	elif a <= 4.9e-140:
		tmp = y * ((x * z) - (i * j))
	elif a <= 1.1e-98:
		tmp = t_1
	elif a <= 7.5e-25:
		tmp = t_2
	elif a <= 8.4e+58:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	t_2 = Float64(Float64(x * y) * Float64(z - Float64(a * Float64(t / y))))
	t_3 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -1.55e+89)
		tmp = t_3;
	elseif (a <= -2e-10)
		tmp = t_2;
	elseif (a <= -9.2e-222)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (a <= 4.9e-140)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (a <= 1.1e-98)
		tmp = t_1;
	elseif (a <= 7.5e-25)
		tmp = t_2;
	elseif (a <= 8.4e+58)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((t * b) - (y * j));
	t_2 = (x * y) * (z - (a * (t / y)));
	t_3 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -1.55e+89)
		tmp = t_3;
	elseif (a <= -2e-10)
		tmp = t_2;
	elseif (a <= -9.2e-222)
		tmp = b * ((t * i) - (z * c));
	elseif (a <= 4.9e-140)
		tmp = y * ((x * z) - (i * j));
	elseif (a <= 1.1e-98)
		tmp = t_1;
	elseif (a <= 7.5e-25)
		tmp = t_2;
	elseif (a <= 8.4e+58)
		tmp = t_1;
	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[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] * N[(z - N[(a * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.55e+89], t$95$3, If[LessEqual[a, -2e-10], t$95$2, If[LessEqual[a, -9.2e-222], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.9e-140], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.1e-98], t$95$1, If[LessEqual[a, 7.5e-25], t$95$2, If[LessEqual[a, 8.4e+58], t$95$1, t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.55e89 or 8.40000000000000048e58 < a

   1. Initial program 58.5%

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

   3. Taylor expanded in a around inf 69.2%

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

      1. +-commutative 69.2%

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

      2. mul-1-neg 69.2%

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

      3. unsub-neg 69.2%

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

      4. *-commutative 69.2%

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

   5. Simplified 69.2%

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

   if -1.55e89 < a < -2.00000000000000007e-10 or 1.09999999999999998e-98 < a < 7.49999999999999989e-25

   1. Initial program 69.8%

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

   3. Taylor expanded in y around -inf 60.6%

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

   5. Simplified 60.6%

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

   6. Taylor expanded in x around inf 70.7%

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

      1. associate-*r* 70.0%

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

      2. *-commutative 70.0%

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

      3. mul-1-neg 70.0%

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

      4. unsub-neg 70.0%

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

      5. associate-/l* 70.0%

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

   8. Simplified 70.0%

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

   if -2.00000000000000007e-10 < a < -9.2000000000000005e-222

   1. Initial program 73.7%

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

   3. Taylor expanded in b around inf 62.1%

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

   if -9.2000000000000005e-222 < a < 4.8999999999999999e-140

   1. Initial program 76.2%

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

   3. Taylor expanded in y around inf 63.1%

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

      1. +-commutative 63.1%

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

      2. mul-1-neg 63.1%

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

      3. unsub-neg 63.1%

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

      4. *-commutative 63.1%

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

      5. *-commutative 63.1%

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

   5. Simplified 63.1%

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

   if 4.8999999999999999e-140 < a < 1.09999999999999998e-98 or 7.49999999999999989e-25 < a < 8.40000000000000048e58

   1. Initial program 68.9%

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

   3. Taylor expanded in y around 0 68.5%

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

   4. Taylor expanded in i around -inf 76.0%

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

      1. associate-*r* 76.0%

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

      2. neg-mul-1 76.0%

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

      3. *-commutative 76.0%

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

   6. Simplified 76.0%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{+89}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-10}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(z - a \cdot \frac{t}{y}\right)\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{-222}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{-140}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-98}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-25}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(z - a \cdot \frac{t}{y}\right)\\ \mathbf{elif}\;a \leq 8.4 \cdot 10^{+58}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 52.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_2 := \left(x \cdot y\right) \cdot \left(z - a \cdot \frac{t}{y}\right)\\ t_3 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -4.2 \cdot 10^{+88}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-8}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-249}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-141}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{-98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-25}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j))))
        (t_2 (* (* x y) (- z (* a (/ t y)))))
        (t_3 (* a (- (* c j) (* x t)))))
   (if (<= a -4.2e+88)
     t_3
     (if (<= a -2.6e-8)
       t_2
       (if (<= a -8.5e-249)
         (+ (* a (* c j)) (* b (- (* t i) (* z c))))
         (if (<= a 2.8e-141)
           (* y (- (* x z) (* i j)))
           (if (<= a 9.8e-98)
             t_1
             (if (<= a 3.2e-25) t_2 (if (<= a 9.5e+58) t_1 t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double t_2 = (x * y) * (z - (a * (t / y)));
	double t_3 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -4.2e+88) {
		tmp = t_3;
	} else if (a <= -2.6e-8) {
		tmp = t_2;
	} else if (a <= -8.5e-249) {
		tmp = (a * (c * j)) + (b * ((t * i) - (z * c)));
	} else if (a <= 2.8e-141) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= 9.8e-98) {
		tmp = t_1;
	} else if (a <= 3.2e-25) {
		tmp = t_2;
	} else if (a <= 9.5e+58) {
		tmp = t_1;
	} 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 = i * ((t * b) - (y * j))
    t_2 = (x * y) * (z - (a * (t / y)))
    t_3 = a * ((c * j) - (x * t))
    if (a <= (-4.2d+88)) then
        tmp = t_3
    else if (a <= (-2.6d-8)) then
        tmp = t_2
    else if (a <= (-8.5d-249)) then
        tmp = (a * (c * j)) + (b * ((t * i) - (z * c)))
    else if (a <= 2.8d-141) then
        tmp = y * ((x * z) - (i * j))
    else if (a <= 9.8d-98) then
        tmp = t_1
    else if (a <= 3.2d-25) then
        tmp = t_2
    else if (a <= 9.5d+58) then
        tmp = t_1
    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 = i * ((t * b) - (y * j));
	double t_2 = (x * y) * (z - (a * (t / y)));
	double t_3 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -4.2e+88) {
		tmp = t_3;
	} else if (a <= -2.6e-8) {
		tmp = t_2;
	} else if (a <= -8.5e-249) {
		tmp = (a * (c * j)) + (b * ((t * i) - (z * c)));
	} else if (a <= 2.8e-141) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= 9.8e-98) {
		tmp = t_1;
	} else if (a <= 3.2e-25) {
		tmp = t_2;
	} else if (a <= 9.5e+58) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	t_2 = (x * y) * (z - (a * (t / y)))
	t_3 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -4.2e+88:
		tmp = t_3
	elif a <= -2.6e-8:
		tmp = t_2
	elif a <= -8.5e-249:
		tmp = (a * (c * j)) + (b * ((t * i) - (z * c)))
	elif a <= 2.8e-141:
		tmp = y * ((x * z) - (i * j))
	elif a <= 9.8e-98:
		tmp = t_1
	elif a <= 3.2e-25:
		tmp = t_2
	elif a <= 9.5e+58:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	t_2 = Float64(Float64(x * y) * Float64(z - Float64(a * Float64(t / y))))
	t_3 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -4.2e+88)
		tmp = t_3;
	elseif (a <= -2.6e-8)
		tmp = t_2;
	elseif (a <= -8.5e-249)
		tmp = Float64(Float64(a * Float64(c * j)) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	elseif (a <= 2.8e-141)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (a <= 9.8e-98)
		tmp = t_1;
	elseif (a <= 3.2e-25)
		tmp = t_2;
	elseif (a <= 9.5e+58)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((t * b) - (y * j));
	t_2 = (x * y) * (z - (a * (t / y)));
	t_3 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -4.2e+88)
		tmp = t_3;
	elseif (a <= -2.6e-8)
		tmp = t_2;
	elseif (a <= -8.5e-249)
		tmp = (a * (c * j)) + (b * ((t * i) - (z * c)));
	elseif (a <= 2.8e-141)
		tmp = y * ((x * z) - (i * j));
	elseif (a <= 9.8e-98)
		tmp = t_1;
	elseif (a <= 3.2e-25)
		tmp = t_2;
	elseif (a <= 9.5e+58)
		tmp = t_1;
	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[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] * N[(z - N[(a * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.2e+88], t$95$3, If[LessEqual[a, -2.6e-8], t$95$2, If[LessEqual[a, -8.5e-249], N[(N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.8e-141], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.8e-98], t$95$1, If[LessEqual[a, 3.2e-25], t$95$2, If[LessEqual[a, 9.5e+58], t$95$1, t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -4.2e88 or 9.5000000000000002e58 < a

   1. Initial program 58.5%

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

   3. Taylor expanded in a around inf 69.2%

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

      1. +-commutative 69.2%

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

      2. mul-1-neg 69.2%

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

      3. unsub-neg 69.2%

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

      4. *-commutative 69.2%

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

   5. Simplified 69.2%

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

   if -4.2e88 < a < -2.6000000000000001e-8 or 9.80000000000000028e-98 < a < 3.2000000000000001e-25

   1. Initial program 69.8%

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

   3. Taylor expanded in y around -inf 60.6%

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

   5. Simplified 60.6%

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

   6. Taylor expanded in x around inf 70.7%

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

      1. associate-*r* 70.0%

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

      2. *-commutative 70.0%

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

      3. mul-1-neg 70.0%

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

      4. unsub-neg 70.0%

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

      5. associate-/l* 70.0%

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

   8. Simplified 70.0%

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

   if -2.6000000000000001e-8 < a < -8.4999999999999995e-249

   1. Initial program 74.0%

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

   3. Taylor expanded in x around 0 69.4%

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

   4. Taylor expanded in y around 0 63.3%

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

   if -8.4999999999999995e-249 < a < 2.80000000000000012e-141

   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 y around inf 67.5%

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

      1. +-commutative 67.5%

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

      2. mul-1-neg 67.5%

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

      3. unsub-neg 67.5%

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

      4. *-commutative 67.5%

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

      5. *-commutative 67.5%

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

   5. Simplified 67.5%

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

   if 2.80000000000000012e-141 < a < 9.80000000000000028e-98 or 3.2000000000000001e-25 < a < 9.5000000000000002e58

   1. Initial program 68.9%

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

   3. Taylor expanded in y around 0 68.5%

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

   4. Taylor expanded in i around -inf 76.0%

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

      1. associate-*r* 76.0%

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

      2. neg-mul-1 76.0%

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

      3. *-commutative 76.0%

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

   6. Simplified 76.0%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{+88}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-8}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(z - a \cdot \frac{t}{y}\right)\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-249}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-141}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{-98}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-25}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(z - a \cdot \frac{t}{y}\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+58}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 57.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;a \leq -8.8 \cdot 10^{-11}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.25 \cdot 10^{-104}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq -2.45 \cdot 10^{-181}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-229}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{+58}:\\ \;\;\;\;y \cdot \left(x \cdot z + \left(\frac{b \cdot \left(t \cdot i\right)}{y} - i \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* j (- (* a c) (* y i))) (* x (- (* y z) (* t a))))))
   (if (<= a -8.8e-11)
     t_1
     (if (<= a -2.25e-104)
       (* b (- (* t i) (* z c)))
       (if (<= a -2.45e-181)
         t_1
         (if (<= a -8.5e-229)
           (* i (- (* t b) (* y j)))
           (if (<= a 9.6e+58)
             (* y (+ (* x z) (- (/ (* b (* t i)) y) (* i j))))
             (* a (- (* c j) (* x t))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	double tmp;
	if (a <= -8.8e-11) {
		tmp = t_1;
	} else if (a <= -2.25e-104) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= -2.45e-181) {
		tmp = t_1;
	} else if (a <= -8.5e-229) {
		tmp = i * ((t * b) - (y * j));
	} else if (a <= 9.6e+58) {
		tmp = y * ((x * z) + (((b * (t * i)) / y) - (i * j)));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
    if (a <= (-8.8d-11)) then
        tmp = t_1
    else if (a <= (-2.25d-104)) then
        tmp = b * ((t * i) - (z * c))
    else if (a <= (-2.45d-181)) then
        tmp = t_1
    else if (a <= (-8.5d-229)) then
        tmp = i * ((t * b) - (y * j))
    else if (a <= 9.6d+58) then
        tmp = y * ((x * z) + (((b * (t * i)) / y) - (i * j)))
    else
        tmp = a * ((c * j) - (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	double tmp;
	if (a <= -8.8e-11) {
		tmp = t_1;
	} else if (a <= -2.25e-104) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= -2.45e-181) {
		tmp = t_1;
	} else if (a <= -8.5e-229) {
		tmp = i * ((t * b) - (y * j));
	} else if (a <= 9.6e+58) {
		tmp = y * ((x * z) + (((b * (t * i)) / y) - (i * j)));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
	tmp = 0
	if a <= -8.8e-11:
		tmp = t_1
	elif a <= -2.25e-104:
		tmp = b * ((t * i) - (z * c))
	elif a <= -2.45e-181:
		tmp = t_1
	elif a <= -8.5e-229:
		tmp = i * ((t * b) - (y * j))
	elif a <= 9.6e+58:
		tmp = y * ((x * z) + (((b * (t * i)) / y) - (i * j)))
	else:
		tmp = a * ((c * j) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))))
	tmp = 0.0
	if (a <= -8.8e-11)
		tmp = t_1;
	elseif (a <= -2.25e-104)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (a <= -2.45e-181)
		tmp = t_1;
	elseif (a <= -8.5e-229)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (a <= 9.6e+58)
		tmp = Float64(y * Float64(Float64(x * z) + Float64(Float64(Float64(b * Float64(t * i)) / y) - Float64(i * j))));
	else
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	tmp = 0.0;
	if (a <= -8.8e-11)
		tmp = t_1;
	elseif (a <= -2.25e-104)
		tmp = b * ((t * i) - (z * c));
	elseif (a <= -2.45e-181)
		tmp = t_1;
	elseif (a <= -8.5e-229)
		tmp = i * ((t * b) - (y * j));
	elseif (a <= 9.6e+58)
		tmp = y * ((x * z) + (((b * (t * i)) / y) - (i * j)));
	else
		tmp = a * ((c * j) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.8e-11], t$95$1, If[LessEqual[a, -2.25e-104], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.45e-181], t$95$1, If[LessEqual[a, -8.5e-229], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.6e+58], N[(y * N[(N[(x * z), $MachinePrecision] + N[(N[(N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -8.8000000000000006e-11 or -2.2499999999999999e-104 < a < -2.44999999999999981e-181

   1. Initial program 70.9%

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

   3. Taylor expanded in b around 0 74.2%

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

   if -8.8000000000000006e-11 < a < -2.2499999999999999e-104

   1. Initial program 62.4%

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

   3. Taylor expanded in b around inf 81.3%

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

   if -2.44999999999999981e-181 < a < -8.49999999999999977e-229

   1. Initial program 55.2%

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

   3. Taylor expanded in y around 0 55.2%

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

   4. Taylor expanded in i around -inf 78.4%

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

      1. associate-*r* 78.4%

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

      2. neg-mul-1 78.4%

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

      3. *-commutative 78.4%

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

   6. Simplified 78.4%

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

   if -8.49999999999999977e-229 < a < 9.5999999999999999e58

   1. Initial program 73.6%

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

   3. Taylor expanded in y around -inf 69.6%

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

   5. Simplified 69.6%

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

   6. Taylor expanded in i around inf 68.4%

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

   if 9.5999999999999999e58 < a

   1. Initial program 52.2%

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

   3. Taylor expanded in a around inf 72.7%

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

      1. +-commutative 72.7%

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

      2. mul-1-neg 72.7%

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

      3. unsub-neg 72.7%

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

      4. *-commutative 72.7%

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

   5. Simplified 72.7%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.8 \cdot 10^{-11}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq -2.25 \cdot 10^{-104}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq -2.45 \cdot 10^{-181}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-229}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{+58}:\\ \;\;\;\;y \cdot \left(x \cdot z + \left(\frac{b \cdot \left(t \cdot i\right)}{y} - i \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 48.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.65 \cdot 10^{+41}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{-273}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-237}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 10^{-97}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-24}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+58}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* a (- (* c j) (* x t)))))
   (if (<= a -1.65e+41)
     t_2
     (if (<= a -1.45e-273)
       t_1
       (if (<= a 7.5e-237)
         (* y (* x z))
         (if (<= a 1e-97)
           t_1
           (if (<= a 5.8e-24)
             (* x (* y z))
             (if (<= a 8.5e+58) (* t (* b i)) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.65e+41) {
		tmp = t_2;
	} else if (a <= -1.45e-273) {
		tmp = t_1;
	} else if (a <= 7.5e-237) {
		tmp = y * (x * z);
	} else if (a <= 1e-97) {
		tmp = t_1;
	} else if (a <= 5.8e-24) {
		tmp = x * (y * z);
	} else if (a <= 8.5e+58) {
		tmp = t * (b * i);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = a * ((c * j) - (x * t))
    if (a <= (-1.65d+41)) then
        tmp = t_2
    else if (a <= (-1.45d-273)) then
        tmp = t_1
    else if (a <= 7.5d-237) then
        tmp = y * (x * z)
    else if (a <= 1d-97) then
        tmp = t_1
    else if (a <= 5.8d-24) then
        tmp = x * (y * z)
    else if (a <= 8.5d+58) then
        tmp = t * (b * i)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.65e+41) {
		tmp = t_2;
	} else if (a <= -1.45e-273) {
		tmp = t_1;
	} else if (a <= 7.5e-237) {
		tmp = y * (x * z);
	} else if (a <= 1e-97) {
		tmp = t_1;
	} else if (a <= 5.8e-24) {
		tmp = x * (y * z);
	} else if (a <= 8.5e+58) {
		tmp = t * (b * i);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -1.65e+41:
		tmp = t_2
	elif a <= -1.45e-273:
		tmp = t_1
	elif a <= 7.5e-237:
		tmp = y * (x * z)
	elif a <= 1e-97:
		tmp = t_1
	elif a <= 5.8e-24:
		tmp = x * (y * z)
	elif a <= 8.5e+58:
		tmp = t * (b * i)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -1.65e+41)
		tmp = t_2;
	elseif (a <= -1.45e-273)
		tmp = t_1;
	elseif (a <= 7.5e-237)
		tmp = Float64(y * Float64(x * z));
	elseif (a <= 1e-97)
		tmp = t_1;
	elseif (a <= 5.8e-24)
		tmp = Float64(x * Float64(y * z));
	elseif (a <= 8.5e+58)
		tmp = Float64(t * Float64(b * i));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -1.65e+41)
		tmp = t_2;
	elseif (a <= -1.45e-273)
		tmp = t_1;
	elseif (a <= 7.5e-237)
		tmp = y * (x * z);
	elseif (a <= 1e-97)
		tmp = t_1;
	elseif (a <= 5.8e-24)
		tmp = x * (y * z);
	elseif (a <= 8.5e+58)
		tmp = t * (b * i);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.65e+41], t$95$2, If[LessEqual[a, -1.45e-273], t$95$1, If[LessEqual[a, 7.5e-237], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1e-97], t$95$1, If[LessEqual[a, 5.8e-24], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.5e+58], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.65e41 or 8.50000000000000015e58 < a

   1. Initial program 58.1%

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

   3. Taylor expanded in a around inf 66.3%

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

      1. +-commutative 66.3%

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

      2. mul-1-neg 66.3%

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

      3. unsub-neg 66.3%

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

      4. *-commutative 66.3%

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

   5. Simplified 66.3%

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

   if -1.65e41 < a < -1.44999999999999993e-273 or 7.50000000000000034e-237 < a < 1.00000000000000004e-97

   1. Initial program 77.3%

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

   3. Taylor expanded in b around inf 51.5%

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

   if -1.44999999999999993e-273 < a < 7.50000000000000034e-237

   1. Initial program 72.2%

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

   3. Taylor expanded in y around inf 75.8%

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

      1. +-commutative 75.8%

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

      2. mul-1-neg 75.8%

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

      3. unsub-neg 75.8%

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

      4. *-commutative 75.8%

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

      5. *-commutative 75.8%

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

   5. Simplified 75.8%

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

   6. Taylor expanded in z around inf 42.9%

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

      1. *-commutative 42.9%

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

   8. Simplified 42.9%

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

   if 1.00000000000000004e-97 < a < 5.7999999999999997e-24

   1. Initial program 68.3%

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

   3. Taylor expanded in y around -inf 58.8%

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

   5. Simplified 58.8%

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

   6. Taylor expanded in x around inf 69.4%

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

      1. associate-*r* 67.8%

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

      2. *-commutative 67.8%

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

      3. mul-1-neg 67.8%

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

      4. unsub-neg 67.8%

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

      5. associate-/l* 67.9%

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

   8. Simplified 67.9%

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

   9. Taylor expanded in y around inf 54.1%

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

   if 5.7999999999999997e-24 < a < 8.50000000000000015e58

   1. Initial program 62.6%

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

   3. Taylor expanded in x around 0 70.3%

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

   4. Taylor expanded in t around inf 54.4%

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

      1. associate-*r* 60.6%

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

   6. Simplified 60.6%

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

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{+41}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{-273}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-237}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 10^{-97}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-24}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+58}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 49.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -6.5 \cdot 10^{+41}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{-222}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-247}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-60}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{+58}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* a (- (* c j) (* x t)))))
   (if (<= a -6.5e+41)
     t_2
     (if (<= a -9.2e-222)
       t_1
       (if (<= a 8e-247)
         (* j (- (* a c) (* y i)))
         (if (<= a 2.3e-98)
           t_1
           (if (<= a 2.6e-60)
             (* x (* y z))
             (if (<= a 8.8e+58) (* t (- (* b i) (* x a))) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -6.5e+41) {
		tmp = t_2;
	} else if (a <= -9.2e-222) {
		tmp = t_1;
	} else if (a <= 8e-247) {
		tmp = j * ((a * c) - (y * i));
	} else if (a <= 2.3e-98) {
		tmp = t_1;
	} else if (a <= 2.6e-60) {
		tmp = x * (y * z);
	} else if (a <= 8.8e+58) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = a * ((c * j) - (x * t))
    if (a <= (-6.5d+41)) then
        tmp = t_2
    else if (a <= (-9.2d-222)) then
        tmp = t_1
    else if (a <= 8d-247) then
        tmp = j * ((a * c) - (y * i))
    else if (a <= 2.3d-98) then
        tmp = t_1
    else if (a <= 2.6d-60) then
        tmp = x * (y * z)
    else if (a <= 8.8d+58) then
        tmp = t * ((b * i) - (x * a))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -6.5e+41) {
		tmp = t_2;
	} else if (a <= -9.2e-222) {
		tmp = t_1;
	} else if (a <= 8e-247) {
		tmp = j * ((a * c) - (y * i));
	} else if (a <= 2.3e-98) {
		tmp = t_1;
	} else if (a <= 2.6e-60) {
		tmp = x * (y * z);
	} else if (a <= 8.8e+58) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -6.5e+41:
		tmp = t_2
	elif a <= -9.2e-222:
		tmp = t_1
	elif a <= 8e-247:
		tmp = j * ((a * c) - (y * i))
	elif a <= 2.3e-98:
		tmp = t_1
	elif a <= 2.6e-60:
		tmp = x * (y * z)
	elif a <= 8.8e+58:
		tmp = t * ((b * i) - (x * a))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -6.5e+41)
		tmp = t_2;
	elseif (a <= -9.2e-222)
		tmp = t_1;
	elseif (a <= 8e-247)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (a <= 2.3e-98)
		tmp = t_1;
	elseif (a <= 2.6e-60)
		tmp = Float64(x * Float64(y * z));
	elseif (a <= 8.8e+58)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -6.5e+41)
		tmp = t_2;
	elseif (a <= -9.2e-222)
		tmp = t_1;
	elseif (a <= 8e-247)
		tmp = j * ((a * c) - (y * i));
	elseif (a <= 2.3e-98)
		tmp = t_1;
	elseif (a <= 2.6e-60)
		tmp = x * (y * z);
	elseif (a <= 8.8e+58)
		tmp = t * ((b * i) - (x * a));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.5e+41], t$95$2, If[LessEqual[a, -9.2e-222], t$95$1, If[LessEqual[a, 8e-247], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.3e-98], t$95$1, If[LessEqual[a, 2.6e-60], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.8e+58], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -6.49999999999999975e41 or 8.8000000000000003e58 < a

   1. Initial program 58.1%

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

   3. Taylor expanded in a around inf 66.3%

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

      1. +-commutative 66.3%

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

      2. mul-1-neg 66.3%

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

      3. unsub-neg 66.3%

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

      4. *-commutative 66.3%

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

   5. Simplified 66.3%

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

   if -6.49999999999999975e41 < a < -9.2000000000000005e-222 or 8.0000000000000002e-247 < a < 2.30000000000000001e-98

   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 51.5%

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

   if -9.2000000000000005e-222 < a < 8.0000000000000002e-247

   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 53.6%

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

   if 2.30000000000000001e-98 < a < 2.5999999999999998e-60

   1. Initial program 63.5%

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

   3. Taylor expanded in y around -inf 47.0%

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

   5. Simplified 47.0%

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

   6. Taylor expanded in x around inf 73.7%

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

      1. associate-*r* 65.2%

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

      2. *-commutative 65.2%

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

      3. mul-1-neg 65.2%

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

      4. unsub-neg 65.2%

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

      5. associate-/l* 65.2%

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

   8. Simplified 65.2%

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

   9. Taylor expanded in y around inf 73.4%

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

   if 2.5999999999999998e-60 < a < 8.8000000000000003e58

   1. Initial program 67.3%

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

   3. Taylor expanded in y around 0 66.7%

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

   4. Taylor expanded in t around inf 57.2%

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

      1. associate-*r* 57.2%

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

      2. neg-mul-1 57.2%

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

      3. cancel-sign-sub 57.2%

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

      4. +-commutative 57.2%

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

      5. mul-1-neg 57.2%

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

      6. unsub-neg 57.2%

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

      7. *-commutative 57.2%

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

   6. Simplified 57.2%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{+41}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{-222}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-247}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-98}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-60}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{+58}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 62.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;a \leq -0.007:\\ \;\;\;\;t\_1 + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-273}:\\ \;\;\;\;t\_1 + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+58}:\\ \;\;\;\;y \cdot \left(x \cdot z + \left(t \cdot \frac{b \cdot i - x \cdot a}{y} - i \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (<= a -0.007)
     (+ t_1 (* x (- (* y z) (* t a))))
     (if (<= a -2.1e-273)
       (+ t_1 (* b (- (* t i) (* z c))))
       (if (<= a 9e+58)
         (* y (+ (* x z) (- (* t (/ (- (* b i) (* x a)) y)) (* i j))))
         (* a (- (* c j) (* x t))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (a <= -0.007) {
		tmp = t_1 + (x * ((y * z) - (t * a)));
	} else if (a <= -2.1e-273) {
		tmp = t_1 + (b * ((t * i) - (z * c)));
	} else if (a <= 9e+58) {
		tmp = y * ((x * z) + ((t * (((b * i) - (x * a)) / y)) - (i * j)));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    if (a <= (-0.007d0)) then
        tmp = t_1 + (x * ((y * z) - (t * a)))
    else if (a <= (-2.1d-273)) then
        tmp = t_1 + (b * ((t * i) - (z * c)))
    else if (a <= 9d+58) then
        tmp = y * ((x * z) + ((t * (((b * i) - (x * a)) / y)) - (i * j)))
    else
        tmp = a * ((c * j) - (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (a <= -0.007) {
		tmp = t_1 + (x * ((y * z) - (t * a)));
	} else if (a <= -2.1e-273) {
		tmp = t_1 + (b * ((t * i) - (z * c)));
	} else if (a <= 9e+58) {
		tmp = y * ((x * z) + ((t * (((b * i) - (x * a)) / y)) - (i * j)));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	tmp = 0
	if a <= -0.007:
		tmp = t_1 + (x * ((y * z) - (t * a)))
	elif a <= -2.1e-273:
		tmp = t_1 + (b * ((t * i) - (z * c)))
	elif a <= 9e+58:
		tmp = y * ((x * z) + ((t * (((b * i) - (x * a)) / y)) - (i * j)))
	else:
		tmp = a * ((c * j) - (x * t))
	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 (a <= -0.007)
		tmp = Float64(t_1 + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	elseif (a <= -2.1e-273)
		tmp = Float64(t_1 + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	elseif (a <= 9e+58)
		tmp = Float64(y * Float64(Float64(x * z) + Float64(Float64(t * Float64(Float64(Float64(b * i) - Float64(x * a)) / y)) - Float64(i * j))));
	else
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (a <= -0.007)
		tmp = t_1 + (x * ((y * z) - (t * a)));
	elseif (a <= -2.1e-273)
		tmp = t_1 + (b * ((t * i) - (z * c)));
	elseif (a <= 9e+58)
		tmp = y * ((x * z) + ((t * (((b * i) - (x * a)) / y)) - (i * j)));
	else
		tmp = a * ((c * j) - (x * t));
	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[LessEqual[a, -0.007], N[(t$95$1 + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.1e-273], N[(t$95$1 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9e+58], 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], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -0.00700000000000000015

   1. Initial program 65.5%

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

   3. Taylor expanded in b around 0 72.0%

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

   if -0.00700000000000000015 < a < -2.1000000000000002e-273

   1. Initial program 75.6%

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

   3. Taylor expanded in x around 0 71.2%

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

   if -2.1000000000000002e-273 < a < 8.9999999999999996e58

   1. Initial program 72.3%

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

   3. Taylor expanded in y around -inf 67.9%

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

   5. Simplified 67.9%

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

   6. Taylor expanded in t around inf 77.8%

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

      1. associate-/l* 77.8%

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

      2. +-commutative 77.8%

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

      3. mul-1-neg 77.8%

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

      4. unsub-neg 77.8%

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

      5. *-commutative 77.8%

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

   8. Simplified 77.8%

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

   if 8.9999999999999996e58 < a

   1. Initial program 52.2%

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

   3. Taylor expanded in a around inf 72.7%

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

      1. +-commutative 72.7%

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

      2. mul-1-neg 72.7%

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

      3. unsub-neg 72.7%

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

      4. *-commutative 72.7%

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

   5. Simplified 72.7%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.007:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-273}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+58}:\\ \;\;\;\;y \cdot \left(x \cdot z + \left(t \cdot \frac{b \cdot i - x \cdot a}{y} - i \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 67.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;a \leq -0.00011:\\ \;\;\;\;t\_1 + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{-98}:\\ \;\;\;\;t\_1 + \left(y \cdot \left(x \cdot z\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+58}:\\ \;\;\;\;y \cdot \left(x \cdot z + \left(t \cdot \frac{b \cdot i - x \cdot a}{y} - i \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (<= a -0.00011)
     (+ t_1 (* x (- (* y z) (* t a))))
     (if (<= a 7.8e-98)
       (+ t_1 (+ (* y (* x z)) (* b (- (* t i) (* z c)))))
       (if (<= a 9.5e+58)
         (* y (+ (* x z) (- (* t (/ (- (* b i) (* x a)) y)) (* i j))))
         (* a (- (* c j) (* x t))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (a <= -0.00011) {
		tmp = t_1 + (x * ((y * z) - (t * a)));
	} else if (a <= 7.8e-98) {
		tmp = t_1 + ((y * (x * z)) + (b * ((t * i) - (z * c))));
	} else if (a <= 9.5e+58) {
		tmp = y * ((x * z) + ((t * (((b * i) - (x * a)) / y)) - (i * j)));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    if (a <= (-0.00011d0)) then
        tmp = t_1 + (x * ((y * z) - (t * a)))
    else if (a <= 7.8d-98) then
        tmp = t_1 + ((y * (x * z)) + (b * ((t * i) - (z * c))))
    else if (a <= 9.5d+58) then
        tmp = y * ((x * z) + ((t * (((b * i) - (x * a)) / y)) - (i * j)))
    else
        tmp = a * ((c * j) - (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (a <= -0.00011) {
		tmp = t_1 + (x * ((y * z) - (t * a)));
	} else if (a <= 7.8e-98) {
		tmp = t_1 + ((y * (x * z)) + (b * ((t * i) - (z * c))));
	} else if (a <= 9.5e+58) {
		tmp = y * ((x * z) + ((t * (((b * i) - (x * a)) / y)) - (i * j)));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	tmp = 0
	if a <= -0.00011:
		tmp = t_1 + (x * ((y * z) - (t * a)))
	elif a <= 7.8e-98:
		tmp = t_1 + ((y * (x * z)) + (b * ((t * i) - (z * c))))
	elif a <= 9.5e+58:
		tmp = y * ((x * z) + ((t * (((b * i) - (x * a)) / y)) - (i * j)))
	else:
		tmp = a * ((c * j) - (x * t))
	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 (a <= -0.00011)
		tmp = Float64(t_1 + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	elseif (a <= 7.8e-98)
		tmp = Float64(t_1 + Float64(Float64(y * Float64(x * z)) + Float64(b * Float64(Float64(t * i) - Float64(z * c)))));
	elseif (a <= 9.5e+58)
		tmp = Float64(y * Float64(Float64(x * z) + Float64(Float64(t * Float64(Float64(Float64(b * i) - Float64(x * a)) / y)) - Float64(i * j))));
	else
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (a <= -0.00011)
		tmp = t_1 + (x * ((y * z) - (t * a)));
	elseif (a <= 7.8e-98)
		tmp = t_1 + ((y * (x * z)) + (b * ((t * i) - (z * c))));
	elseif (a <= 9.5e+58)
		tmp = y * ((x * z) + ((t * (((b * i) - (x * a)) / y)) - (i * j)));
	else
		tmp = a * ((c * j) - (x * t));
	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[LessEqual[a, -0.00011], N[(t$95$1 + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.8e-98], N[(t$95$1 + N[(N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.5e+58], 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], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.10000000000000004e-4

   1. Initial program 65.5%

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

   3. Taylor expanded in b around 0 72.0%

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

   if -1.10000000000000004e-4 < a < 7.79999999999999943e-98

   1. Initial program 76.0%

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

   3. Taylor expanded in y around inf 74.6%

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

      1. *-commutative 74.6%

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

      2. associate-*l* 76.3%

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

   5. Simplified 76.3%

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

   if 7.79999999999999943e-98 < a < 9.5000000000000002e58

   1. Initial program 66.0%

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

   3. Taylor expanded in y around -inf 59.9%

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

   5. Simplified 59.9%

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

   6. Taylor expanded in t around inf 81.9%

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

      1. associate-/l* 85.0%

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

      2. +-commutative 85.0%

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

      3. mul-1-neg 85.0%

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

      4. unsub-neg 85.0%

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

      5. *-commutative 85.0%

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

   8. Simplified 85.0%

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

   if 9.5000000000000002e58 < a

   1. Initial program 52.2%

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

   3. Taylor expanded in a around inf 72.7%

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

      1. +-commutative 72.7%

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

      2. mul-1-neg 72.7%

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

      3. unsub-neg 72.7%

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

      4. *-commutative 72.7%

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

   5. Simplified 72.7%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.00011:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{-98}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + \left(y \cdot \left(x \cdot z\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+58}:\\ \;\;\;\;y \cdot \left(x \cdot z + \left(t \cdot \frac{b \cdot i - x \cdot a}{y} - i \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 29.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := b \cdot \left(t \cdot i\right)\\ t_3 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;a \leq -1.9 \cdot 10^{+44}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.75 \cdot 10^{-283}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+58}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+72}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))) (t_2 (* b (* t i))) (t_3 (* a (* c j))))
   (if (<= a -1.9e+44)
     t_3
     (if (<= a -1.1e-45)
       t_1
       (if (<= a 2.75e-283)
         t_2
         (if (<= a 9.5e-22)
           t_1
           (if (<= a 6.8e+58) t_2 (if (<= a 2.5e+72) t_1 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double t_2 = b * (t * i);
	double t_3 = a * (c * j);
	double tmp;
	if (a <= -1.9e+44) {
		tmp = t_3;
	} else if (a <= -1.1e-45) {
		tmp = t_1;
	} else if (a <= 2.75e-283) {
		tmp = t_2;
	} else if (a <= 9.5e-22) {
		tmp = t_1;
	} else if (a <= 6.8e+58) {
		tmp = t_2;
	} else if (a <= 2.5e+72) {
		tmp = t_1;
	} 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_2 = b * (t * i)
    t_3 = a * (c * j)
    if (a <= (-1.9d+44)) then
        tmp = t_3
    else if (a <= (-1.1d-45)) then
        tmp = t_1
    else if (a <= 2.75d-283) then
        tmp = t_2
    else if (a <= 9.5d-22) then
        tmp = t_1
    else if (a <= 6.8d+58) then
        tmp = t_2
    else if (a <= 2.5d+72) then
        tmp = t_1
    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);
	double t_2 = b * (t * i);
	double t_3 = a * (c * j);
	double tmp;
	if (a <= -1.9e+44) {
		tmp = t_3;
	} else if (a <= -1.1e-45) {
		tmp = t_1;
	} else if (a <= 2.75e-283) {
		tmp = t_2;
	} else if (a <= 9.5e-22) {
		tmp = t_1;
	} else if (a <= 6.8e+58) {
		tmp = t_2;
	} else if (a <= 2.5e+72) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	t_2 = b * (t * i)
	t_3 = a * (c * j)
	tmp = 0
	if a <= -1.9e+44:
		tmp = t_3
	elif a <= -1.1e-45:
		tmp = t_1
	elif a <= 2.75e-283:
		tmp = t_2
	elif a <= 9.5e-22:
		tmp = t_1
	elif a <= 6.8e+58:
		tmp = t_2
	elif a <= 2.5e+72:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(y * z))
	t_2 = Float64(b * Float64(t * i))
	t_3 = Float64(a * Float64(c * j))
	tmp = 0.0
	if (a <= -1.9e+44)
		tmp = t_3;
	elseif (a <= -1.1e-45)
		tmp = t_1;
	elseif (a <= 2.75e-283)
		tmp = t_2;
	elseif (a <= 9.5e-22)
		tmp = t_1;
	elseif (a <= 6.8e+58)
		tmp = t_2;
	elseif (a <= 2.5e+72)
		tmp = t_1;
	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_2 = b * (t * i);
	t_3 = a * (c * j);
	tmp = 0.0;
	if (a <= -1.9e+44)
		tmp = t_3;
	elseif (a <= -1.1e-45)
		tmp = t_1;
	elseif (a <= 2.75e-283)
		tmp = t_2;
	elseif (a <= 9.5e-22)
		tmp = t_1;
	elseif (a <= 6.8e+58)
		tmp = t_2;
	elseif (a <= 2.5e+72)
		tmp = t_1;
	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[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.9e+44], t$95$3, If[LessEqual[a, -1.1e-45], t$95$1, If[LessEqual[a, 2.75e-283], t$95$2, If[LessEqual[a, 9.5e-22], t$95$1, If[LessEqual[a, 6.8e+58], t$95$2, If[LessEqual[a, 2.5e+72], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.9000000000000001e44 or 2.49999999999999996e72 < a

   1. Initial program 57.5%

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

   3. Taylor expanded in a around inf 65.9%

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

      1. +-commutative 65.9%

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

      2. mul-1-neg 65.9%

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

      3. unsub-neg 65.9%

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

      4. *-commutative 65.9%

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

   5. Simplified 65.9%

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

   6. Taylor expanded in j around inf 44.5%

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

   if -1.9000000000000001e44 < a < -1.09999999999999997e-45 or 2.74999999999999976e-283 < a < 9.4999999999999994e-22 or 6.8000000000000001e58 < a < 2.49999999999999996e72

   1. Initial program 74.8%

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

   3. Taylor expanded in y around -inf 67.5%

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

   5. Simplified 67.5%

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

   6. Taylor expanded in x around inf 54.6%

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

      1. associate-*r* 52.1%

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

      2. *-commutative 52.1%

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

      3. mul-1-neg 52.1%

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

      4. unsub-neg 52.1%

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

      5. associate-/l* 52.7%

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

   8. Simplified 52.7%

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

   9. Taylor expanded in y around inf 47.8%

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

   if -1.09999999999999997e-45 < a < 2.74999999999999976e-283 or 9.4999999999999994e-22 < a < 6.8000000000000001e58

   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 x around 0 71.3%

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

   4. Taylor expanded in t around inf 34.0%

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

4. Final simplification 43.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+44}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-45}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 2.75 \cdot 10^{-283}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-22}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+58}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+72}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 29.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;a \leq -1.9 \cdot 10^{+44}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.46 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.35 \cdot 10^{-101}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-283}:\\ \;\;\;\;y \cdot \left(-i \cdot j\right)\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+58}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))) (t_2 (* a (* c j))))
   (if (<= a -1.9e+44)
     t_2
     (if (<= a -1.46e-9)
       t_1
       (if (<= a -2.35e-101)
         (* (* z c) (- b))
         (if (<= a 4e-283)
           (* y (- (* i j)))
           (if (<= a 2.1e-21) t_1 (if (<= a 9.5e+58) (* t (* b i)) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double t_2 = a * (c * j);
	double tmp;
	if (a <= -1.9e+44) {
		tmp = t_2;
	} else if (a <= -1.46e-9) {
		tmp = t_1;
	} else if (a <= -2.35e-101) {
		tmp = (z * c) * -b;
	} else if (a <= 4e-283) {
		tmp = y * -(i * j);
	} else if (a <= 2.1e-21) {
		tmp = t_1;
	} else if (a <= 9.5e+58) {
		tmp = t * (b * i);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (y * z)
    t_2 = a * (c * j)
    if (a <= (-1.9d+44)) then
        tmp = t_2
    else if (a <= (-1.46d-9)) then
        tmp = t_1
    else if (a <= (-2.35d-101)) then
        tmp = (z * c) * -b
    else if (a <= 4d-283) then
        tmp = y * -(i * j)
    else if (a <= 2.1d-21) then
        tmp = t_1
    else if (a <= 9.5d+58) then
        tmp = t * (b * i)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double t_2 = a * (c * j);
	double tmp;
	if (a <= -1.9e+44) {
		tmp = t_2;
	} else if (a <= -1.46e-9) {
		tmp = t_1;
	} else if (a <= -2.35e-101) {
		tmp = (z * c) * -b;
	} else if (a <= 4e-283) {
		tmp = y * -(i * j);
	} else if (a <= 2.1e-21) {
		tmp = t_1;
	} else if (a <= 9.5e+58) {
		tmp = t * (b * i);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	t_2 = a * (c * j)
	tmp = 0
	if a <= -1.9e+44:
		tmp = t_2
	elif a <= -1.46e-9:
		tmp = t_1
	elif a <= -2.35e-101:
		tmp = (z * c) * -b
	elif a <= 4e-283:
		tmp = y * -(i * j)
	elif a <= 2.1e-21:
		tmp = t_1
	elif a <= 9.5e+58:
		tmp = t * (b * i)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(y * z))
	t_2 = Float64(a * Float64(c * j))
	tmp = 0.0
	if (a <= -1.9e+44)
		tmp = t_2;
	elseif (a <= -1.46e-9)
		tmp = t_1;
	elseif (a <= -2.35e-101)
		tmp = Float64(Float64(z * c) * Float64(-b));
	elseif (a <= 4e-283)
		tmp = Float64(y * Float64(-Float64(i * j)));
	elseif (a <= 2.1e-21)
		tmp = t_1;
	elseif (a <= 9.5e+58)
		tmp = Float64(t * Float64(b * i));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (y * z);
	t_2 = a * (c * j);
	tmp = 0.0;
	if (a <= -1.9e+44)
		tmp = t_2;
	elseif (a <= -1.46e-9)
		tmp = t_1;
	elseif (a <= -2.35e-101)
		tmp = (z * c) * -b;
	elseif (a <= 4e-283)
		tmp = y * -(i * j);
	elseif (a <= 2.1e-21)
		tmp = t_1;
	elseif (a <= 9.5e+58)
		tmp = t * (b * i);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.9e+44], t$95$2, If[LessEqual[a, -1.46e-9], t$95$1, If[LessEqual[a, -2.35e-101], N[(N[(z * c), $MachinePrecision] * (-b)), $MachinePrecision], If[LessEqual[a, 4e-283], N[(y * (-N[(i * j), $MachinePrecision])), $MachinePrecision], If[LessEqual[a, 2.1e-21], t$95$1, If[LessEqual[a, 9.5e+58], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.9000000000000001e44 or 9.5000000000000002e58 < a

   1. Initial program 58.6%

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

   3. Taylor expanded in a around inf 66.0%

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

      1. +-commutative 66.0%

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

      2. mul-1-neg 66.0%

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

      3. unsub-neg 66.0%

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

      4. *-commutative 66.0%

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

   5. Simplified 66.0%

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

   6. Taylor expanded in j around inf 44.2%

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

   if -1.9000000000000001e44 < a < -1.4599999999999999e-9 or 3.99999999999999979e-283 < a < 2.10000000000000013e-21

   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 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%

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

   6. Taylor expanded in x around inf 53.9%

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

      1. associate-*r* 52.4%

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

      2. *-commutative 52.4%

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

      3. mul-1-neg 52.4%

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

      4. unsub-neg 52.4%

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

      5. associate-/l* 53.0%

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

   8. Simplified 53.0%

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

   9. Taylor expanded in y around inf 47.4%

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

   if -1.4599999999999999e-9 < a < -2.35e-101

   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 x around 0 81.2%

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

   4. Taylor expanded in z around inf 63.3%

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

      1. associate-*r* 63.3%

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

      2. neg-mul-1 63.3%

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

   6. Simplified 63.3%

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

   if -2.35e-101 < a < 3.99999999999999979e-283

   1. Initial program 74.5%

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

   3. Taylor expanded in y around inf 50.6%

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

      1. +-commutative 50.6%

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

      2. mul-1-neg 50.6%

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

      3. unsub-neg 50.6%

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

      4. *-commutative 50.6%

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

      5. *-commutative 50.6%

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

   5. Simplified 50.6%

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

   6. Taylor expanded in z around 0 37.9%

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

      1. neg-mul-1 37.9%

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

      2. distribute-rgt-neg-in 37.9%

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

   8. Simplified 37.9%

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

   if 2.10000000000000013e-21 < a < 9.5000000000000002e58

   1. Initial program 62.6%

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

   3. Taylor expanded in x around 0 70.3%

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

   4. Taylor expanded in t around inf 54.4%

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

      1. associate-*r* 60.6%

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

   6. Simplified 60.6%

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

4. Final simplification 46.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+44}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq -1.46 \cdot 10^{-9}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq -2.35 \cdot 10^{-101}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-283}:\\ \;\;\;\;y \cdot \left(-i \cdot j\right)\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-21}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+58}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 49.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -4.5 \cdot 10^{+35}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -1.45 \cdot 10^{-228}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 1.85 \cdot 10^{-296}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 1.55 \cdot 10^{-155}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 7 \cdot 10^{+75}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* j (- (* a c) (* y i)))))
   (if (<= j -4.5e+35)
     t_2
     (if (<= j -1.45e-228)
       t_1
       (if (<= j 1.85e-296)
         (* y (* x z))
         (if (<= j 1.55e-155)
           t_1
           (if (<= j 7e+75) (* a (- (* c j) (* x t))) 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 <= -4.5e+35) {
		tmp = t_2;
	} else if (j <= -1.45e-228) {
		tmp = t_1;
	} else if (j <= 1.85e-296) {
		tmp = y * (x * z);
	} else if (j <= 1.55e-155) {
		tmp = t_1;
	} else if (j <= 7e+75) {
		tmp = a * ((c * j) - (x * t));
	} 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 <= (-4.5d+35)) then
        tmp = t_2
    else if (j <= (-1.45d-228)) then
        tmp = t_1
    else if (j <= 1.85d-296) then
        tmp = y * (x * z)
    else if (j <= 1.55d-155) then
        tmp = t_1
    else if (j <= 7d+75) then
        tmp = a * ((c * j) - (x * t))
    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 <= -4.5e+35) {
		tmp = t_2;
	} else if (j <= -1.45e-228) {
		tmp = t_1;
	} else if (j <= 1.85e-296) {
		tmp = y * (x * z);
	} else if (j <= 1.55e-155) {
		tmp = t_1;
	} else if (j <= 7e+75) {
		tmp = a * ((c * j) - (x * t));
	} 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 <= -4.5e+35:
		tmp = t_2
	elif j <= -1.45e-228:
		tmp = t_1
	elif j <= 1.85e-296:
		tmp = y * (x * z)
	elif j <= 1.55e-155:
		tmp = t_1
	elif j <= 7e+75:
		tmp = a * ((c * j) - (x * t))
	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 <= -4.5e+35)
		tmp = t_2;
	elseif (j <= -1.45e-228)
		tmp = t_1;
	elseif (j <= 1.85e-296)
		tmp = Float64(y * Float64(x * z));
	elseif (j <= 1.55e-155)
		tmp = t_1;
	elseif (j <= 7e+75)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	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 <= -4.5e+35)
		tmp = t_2;
	elseif (j <= -1.45e-228)
		tmp = t_1;
	elseif (j <= 1.85e-296)
		tmp = y * (x * z);
	elseif (j <= 1.55e-155)
		tmp = t_1;
	elseif (j <= 7e+75)
		tmp = a * ((c * j) - (x * t));
	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, -4.5e+35], t$95$2, If[LessEqual[j, -1.45e-228], t$95$1, If[LessEqual[j, 1.85e-296], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.55e-155], t$95$1, If[LessEqual[j, 7e+75], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -4.4999999999999997e35 or 6.9999999999999997e75 < j

   1. Initial program 67.7%

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

   3. Taylor expanded in j around inf 66.9%

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

   if -4.4999999999999997e35 < j < -1.4500000000000001e-228 or 1.85000000000000013e-296 < j < 1.55e-155

   1. Initial program 68.8%

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

   3. Taylor expanded in b around inf 47.5%

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

   if -1.4500000000000001e-228 < j < 1.85000000000000013e-296

   1. Initial program 62.6%

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

   3. Taylor expanded in y around inf 56.7%

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

      1. +-commutative 56.7%

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

      2. mul-1-neg 56.7%

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

      3. unsub-neg 56.7%

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

      4. *-commutative 56.7%

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

      5. *-commutative 56.7%

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

   5. Simplified 56.7%

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

   6. Taylor expanded in z around inf 56.7%

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

      1. *-commutative 56.7%

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

   8. Simplified 56.7%

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

   if 1.55e-155 < j < 6.9999999999999997e75

   1. Initial program 64.5%

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

   3. Taylor expanded in a around inf 54.2%

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

      1. +-commutative 54.2%

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

      2. mul-1-neg 54.2%

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

      3. unsub-neg 54.2%

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

      4. *-commutative 54.2%

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

   5. Simplified 54.2%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4.5 \cdot 10^{+35}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -1.45 \cdot 10^{-228}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.85 \cdot 10^{-296}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 1.55 \cdot 10^{-155}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 7 \cdot 10^{+75}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 61.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;a \leq -3.1 \cdot 10^{-5}:\\ \;\;\;\;t\_1 + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-269}:\\ \;\;\;\;t\_1 + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+58}:\\ \;\;\;\;y \cdot \left(x \cdot z + \left(\frac{b \cdot \left(t \cdot i\right)}{y} - i \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (<= a -3.1e-5)
     (+ t_1 (* x (- (* y z) (* t a))))
     (if (<= a -3e-269)
       (+ t_1 (* b (- (* t i) (* z c))))
       (if (<= a 9.5e+58)
         (* y (+ (* x z) (- (/ (* b (* t i)) y) (* i j))))
         (* a (- (* c j) (* x t))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (a <= -3.1e-5) {
		tmp = t_1 + (x * ((y * z) - (t * a)));
	} else if (a <= -3e-269) {
		tmp = t_1 + (b * ((t * i) - (z * c)));
	} else if (a <= 9.5e+58) {
		tmp = y * ((x * z) + (((b * (t * i)) / y) - (i * j)));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    if (a <= (-3.1d-5)) then
        tmp = t_1 + (x * ((y * z) - (t * a)))
    else if (a <= (-3d-269)) then
        tmp = t_1 + (b * ((t * i) - (z * c)))
    else if (a <= 9.5d+58) then
        tmp = y * ((x * z) + (((b * (t * i)) / y) - (i * j)))
    else
        tmp = a * ((c * j) - (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (a <= -3.1e-5) {
		tmp = t_1 + (x * ((y * z) - (t * a)));
	} else if (a <= -3e-269) {
		tmp = t_1 + (b * ((t * i) - (z * c)));
	} else if (a <= 9.5e+58) {
		tmp = y * ((x * z) + (((b * (t * i)) / y) - (i * j)));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	tmp = 0
	if a <= -3.1e-5:
		tmp = t_1 + (x * ((y * z) - (t * a)))
	elif a <= -3e-269:
		tmp = t_1 + (b * ((t * i) - (z * c)))
	elif a <= 9.5e+58:
		tmp = y * ((x * z) + (((b * (t * i)) / y) - (i * j)))
	else:
		tmp = a * ((c * j) - (x * t))
	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 (a <= -3.1e-5)
		tmp = Float64(t_1 + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	elseif (a <= -3e-269)
		tmp = Float64(t_1 + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	elseif (a <= 9.5e+58)
		tmp = Float64(y * Float64(Float64(x * z) + Float64(Float64(Float64(b * Float64(t * i)) / y) - Float64(i * j))));
	else
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (a <= -3.1e-5)
		tmp = t_1 + (x * ((y * z) - (t * a)));
	elseif (a <= -3e-269)
		tmp = t_1 + (b * ((t * i) - (z * c)));
	elseif (a <= 9.5e+58)
		tmp = y * ((x * z) + (((b * (t * i)) / y) - (i * j)));
	else
		tmp = a * ((c * j) - (x * t));
	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[LessEqual[a, -3.1e-5], N[(t$95$1 + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3e-269], N[(t$95$1 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.5e+58], N[(y * N[(N[(x * z), $MachinePrecision] + N[(N[(N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.10000000000000014e-5

   1. Initial program 65.5%

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

   3. Taylor expanded in b around 0 72.0%

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

   if -3.10000000000000014e-5 < a < -2.9999999999999999e-269

   1. Initial program 75.6%

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

   3. Taylor expanded in x around 0 71.2%

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

   if -2.9999999999999999e-269 < a < 9.5000000000000002e58

   1. Initial program 72.3%

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

   3. Taylor expanded in y around -inf 67.9%

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

   5. Simplified 67.9%

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

   6. Taylor expanded in i around inf 71.2%

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

   if 9.5000000000000002e58 < a

   1. Initial program 52.2%

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

   3. Taylor expanded in a around inf 72.7%

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

      1. +-commutative 72.7%

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

      2. mul-1-neg 72.7%

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

      3. unsub-neg 72.7%

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

      4. *-commutative 72.7%

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

   5. Simplified 72.7%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{-5}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-269}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+58}:\\ \;\;\;\;y \cdot \left(x \cdot z + \left(\frac{b \cdot \left(t \cdot i\right)}{y} - i \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 28.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ t_2 := t \cdot \left(b \cdot i\right)\\ \mathbf{if}\;b \leq -9.5 \cdot 10^{+184}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -7.2 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{-51}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{-292}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+89}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))) (t_2 (* t (* b i))))
   (if (<= b -9.5e+184)
     t_2
     (if (<= b -7.2e+22)
       t_1
       (if (<= b -1.05e-51)
         t_2
         (if (<= b 7.2e-292)
           (* x (* y z))
           (if (<= b 4e+89) t_1 (* b (* t i)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double t_2 = t * (b * i);
	double tmp;
	if (b <= -9.5e+184) {
		tmp = t_2;
	} else if (b <= -7.2e+22) {
		tmp = t_1;
	} else if (b <= -1.05e-51) {
		tmp = t_2;
	} else if (b <= 7.2e-292) {
		tmp = x * (y * z);
	} else if (b <= 4e+89) {
		tmp = t_1;
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (c * j)
    t_2 = t * (b * i)
    if (b <= (-9.5d+184)) then
        tmp = t_2
    else if (b <= (-7.2d+22)) then
        tmp = t_1
    else if (b <= (-1.05d-51)) then
        tmp = t_2
    else if (b <= 7.2d-292) then
        tmp = x * (y * z)
    else if (b <= 4d+89) then
        tmp = t_1
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double t_2 = t * (b * i);
	double tmp;
	if (b <= -9.5e+184) {
		tmp = t_2;
	} else if (b <= -7.2e+22) {
		tmp = t_1;
	} else if (b <= -1.05e-51) {
		tmp = t_2;
	} else if (b <= 7.2e-292) {
		tmp = x * (y * z);
	} else if (b <= 4e+89) {
		tmp = t_1;
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	t_2 = t * (b * i)
	tmp = 0
	if b <= -9.5e+184:
		tmp = t_2
	elif b <= -7.2e+22:
		tmp = t_1
	elif b <= -1.05e-51:
		tmp = t_2
	elif b <= 7.2e-292:
		tmp = x * (y * z)
	elif b <= 4e+89:
		tmp = t_1
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	t_2 = Float64(t * Float64(b * i))
	tmp = 0.0
	if (b <= -9.5e+184)
		tmp = t_2;
	elseif (b <= -7.2e+22)
		tmp = t_1;
	elseif (b <= -1.05e-51)
		tmp = t_2;
	elseif (b <= 7.2e-292)
		tmp = Float64(x * Float64(y * z));
	elseif (b <= 4e+89)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (c * j);
	t_2 = t * (b * i);
	tmp = 0.0;
	if (b <= -9.5e+184)
		tmp = t_2;
	elseif (b <= -7.2e+22)
		tmp = t_1;
	elseif (b <= -1.05e-51)
		tmp = t_2;
	elseif (b <= 7.2e-292)
		tmp = x * (y * z);
	elseif (b <= 4e+89)
		tmp = t_1;
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9.5e+184], t$95$2, If[LessEqual[b, -7.2e+22], t$95$1, If[LessEqual[b, -1.05e-51], t$95$2, If[LessEqual[b, 7.2e-292], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4e+89], t$95$1, N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -9.4999999999999995e184 or -7.2e22 < b < -1.05000000000000001e-51

   1. Initial program 66.3%

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

   3. Taylor expanded in x around 0 59.4%

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

   4. Taylor expanded in t around inf 36.0%

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

      1. associate-*r* 43.1%

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

   6. Simplified 43.1%

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

   if -9.4999999999999995e184 < b < -7.2e22 or 7.2000000000000004e-292 < b < 3.99999999999999998e89

   1. Initial program 70.1%

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

   3. Taylor expanded in a around inf 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%

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

      4. *-commutative 50.3%

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

   5. Simplified 50.3%

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

   6. Taylor expanded in j around inf 37.0%

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

   if -1.05000000000000001e-51 < b < 7.2000000000000004e-292

   1. Initial program 66.6%

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

   3. Taylor expanded in y around -inf 63.9%

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

   5. Simplified 63.9%

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

   6. Taylor expanded in x around inf 55.5%

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

      1. associate-*r* 50.6%

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

      2. *-commutative 50.6%

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

      3. mul-1-neg 50.6%

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

      4. unsub-neg 50.6%

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

      5. associate-/l* 51.2%

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

   8. Simplified 51.2%

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

   9. Taylor expanded in y around inf 41.8%

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

   if 3.99999999999999998e89 < b

   1. Initial program 61.6%

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

   3. Taylor expanded in x around 0 64.2%

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

   4. Taylor expanded in t around inf 52.3%

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

4. Final simplification 42.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{+184}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq -7.2 \cdot 10^{+22}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{-51}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{-292}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+89}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 51.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -5.8 \cdot 10^{+25}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-171}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-198}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))) (t_2 (* x (- (* y z) (* t a)))))
   (if (<= x -5.8e+25)
     t_2
     (if (<= x -3e-171)
       t_1
       (if (<= x 1.65e-198)
         (* b (- (* t i) (* z c)))
         (if (<= x 8.6e+16) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -5.8e+25) {
		tmp = t_2;
	} else if (x <= -3e-171) {
		tmp = t_1;
	} else if (x <= 1.65e-198) {
		tmp = b * ((t * i) - (z * c));
	} else if (x <= 8.6e+16) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = x * ((y * z) - (t * a))
    if (x <= (-5.8d+25)) then
        tmp = t_2
    else if (x <= (-3d-171)) then
        tmp = t_1
    else if (x <= 1.65d-198) then
        tmp = b * ((t * i) - (z * c))
    else if (x <= 8.6d+16) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -5.8e+25) {
		tmp = t_2;
	} else if (x <= -3e-171) {
		tmp = t_1;
	} else if (x <= 1.65e-198) {
		tmp = b * ((t * i) - (z * c));
	} else if (x <= 8.6e+16) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -5.8e+25:
		tmp = t_2
	elif x <= -3e-171:
		tmp = t_1
	elif x <= 1.65e-198:
		tmp = b * ((t * i) - (z * c))
	elif x <= 8.6e+16:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -5.8e+25)
		tmp = t_2;
	elseif (x <= -3e-171)
		tmp = t_1;
	elseif (x <= 1.65e-198)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (x <= 8.6e+16)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -5.8e+25)
		tmp = t_2;
	elseif (x <= -3e-171)
		tmp = t_1;
	elseif (x <= 1.65e-198)
		tmp = b * ((t * i) - (z * c));
	elseif (x <= 8.6e+16)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.8e+25], t$95$2, If[LessEqual[x, -3e-171], t$95$1, If[LessEqual[x, 1.65e-198], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.6e+16], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.7999999999999998e25 or 8.6e16 < x

   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 62.5%

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

   if -5.7999999999999998e25 < x < -3e-171 or 1.65e-198 < x < 8.6e16

   1. Initial program 73.0%

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

   3. Taylor expanded in j around inf 58.8%

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

   if -3e-171 < x < 1.65e-198

   1. Initial program 62.5%

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

   3. Taylor expanded in b around inf 60.7%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+25}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-171}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-198}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{+16}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 51.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -2 \cdot 10^{+90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq -9.4 \cdot 10^{-222}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+58}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -2e+90)
     t_1
     (if (<= a -3.8e-10)
       (* x (- (* y z) (* t a)))
       (if (<= a -9.4e-222)
         (* b (- (* t i) (* z c)))
         (if (<= a 9e+58) (* y (- (* x z) (* i j))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -2e+90) {
		tmp = t_1;
	} else if (a <= -3.8e-10) {
		tmp = x * ((y * z) - (t * a));
	} else if (a <= -9.4e-222) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 9e+58) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (a <= (-2d+90)) then
        tmp = t_1
    else if (a <= (-3.8d-10)) then
        tmp = x * ((y * z) - (t * a))
    else if (a <= (-9.4d-222)) then
        tmp = b * ((t * i) - (z * c))
    else if (a <= 9d+58) then
        tmp = y * ((x * z) - (i * j))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -2e+90) {
		tmp = t_1;
	} else if (a <= -3.8e-10) {
		tmp = x * ((y * z) - (t * a));
	} else if (a <= -9.4e-222) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 9e+58) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -2e+90:
		tmp = t_1
	elif a <= -3.8e-10:
		tmp = x * ((y * z) - (t * a))
	elif a <= -9.4e-222:
		tmp = b * ((t * i) - (z * c))
	elif a <= 9e+58:
		tmp = y * ((x * z) - (i * j))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -2e+90)
		tmp = t_1;
	elseif (a <= -3.8e-10)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (a <= -9.4e-222)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (a <= 9e+58)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -2e+90)
		tmp = t_1;
	elseif (a <= -3.8e-10)
		tmp = x * ((y * z) - (t * a));
	elseif (a <= -9.4e-222)
		tmp = b * ((t * i) - (z * c));
	elseif (a <= 9e+58)
		tmp = y * ((x * z) - (i * j));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2e+90], t$95$1, If[LessEqual[a, -3.8e-10], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -9.4e-222], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9e+58], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.99999999999999993e90 or 8.9999999999999996e58 < a

   1. Initial program 58.5%

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

   3. Taylor expanded in a around inf 69.2%

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

      1. +-commutative 69.2%

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

      2. mul-1-neg 69.2%

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

      3. unsub-neg 69.2%

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

      4. *-commutative 69.2%

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

   5. Simplified 69.2%

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

   if -1.99999999999999993e90 < a < -3.7999999999999998e-10

   1. Initial program 69.3%

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

   3. Taylor expanded in x around inf 61.7%

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

   if -3.7999999999999998e-10 < a < -9.3999999999999995e-222

   1. Initial program 73.7%

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

   3. Taylor expanded in b around inf 62.1%

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

   if -9.3999999999999995e-222 < a < 8.9999999999999996e58

   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 y around inf 58.8%

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

      1. +-commutative 58.8%

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

      2. mul-1-neg 58.8%

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

      3. unsub-neg 58.8%

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

      4. *-commutative 58.8%

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

      5. *-commutative 58.8%

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

   5. Simplified 58.8%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{+90}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq -9.4 \cdot 10^{-222}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+58}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 28.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -15:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-193}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-23}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+208}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -15.0)
   (* x (* y z))
   (if (<= z 2.8e-193)
     (* t (* b i))
     (if (<= z 1.45e-23)
       (* a (* x (- t)))
       (if (<= z 1.3e+208) (* i (* y (- j))) (* (* z c) (- b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -15.0) {
		tmp = x * (y * z);
	} else if (z <= 2.8e-193) {
		tmp = t * (b * i);
	} else if (z <= 1.45e-23) {
		tmp = a * (x * -t);
	} else if (z <= 1.3e+208) {
		tmp = i * (y * -j);
	} else {
		tmp = (z * c) * -b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-15.0d0)) then
        tmp = x * (y * z)
    else if (z <= 2.8d-193) then
        tmp = t * (b * i)
    else if (z <= 1.45d-23) then
        tmp = a * (x * -t)
    else if (z <= 1.3d+208) then
        tmp = i * (y * -j)
    else
        tmp = (z * c) * -b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -15.0) {
		tmp = x * (y * z);
	} else if (z <= 2.8e-193) {
		tmp = t * (b * i);
	} else if (z <= 1.45e-23) {
		tmp = a * (x * -t);
	} else if (z <= 1.3e+208) {
		tmp = i * (y * -j);
	} else {
		tmp = (z * c) * -b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -15.0:
		tmp = x * (y * z)
	elif z <= 2.8e-193:
		tmp = t * (b * i)
	elif z <= 1.45e-23:
		tmp = a * (x * -t)
	elif z <= 1.3e+208:
		tmp = i * (y * -j)
	else:
		tmp = (z * c) * -b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -15.0)
		tmp = Float64(x * Float64(y * z));
	elseif (z <= 2.8e-193)
		tmp = Float64(t * Float64(b * i));
	elseif (z <= 1.45e-23)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (z <= 1.3e+208)
		tmp = Float64(i * Float64(y * Float64(-j)));
	else
		tmp = Float64(Float64(z * c) * Float64(-b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -15.0)
		tmp = x * (y * z);
	elseif (z <= 2.8e-193)
		tmp = t * (b * i);
	elseif (z <= 1.45e-23)
		tmp = a * (x * -t);
	elseif (z <= 1.3e+208)
		tmp = i * (y * -j);
	else
		tmp = (z * c) * -b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -15.0], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e-193], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e-23], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e+208], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], N[(N[(z * c), $MachinePrecision] * (-b)), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -15

   1. Initial program 65.8%

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

   3. Taylor expanded in y around -inf 60.6%

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

   5. Simplified 60.6%

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

   6. Taylor expanded in x around inf 55.1%

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

      1. associate-*r* 52.3%

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

      2. *-commutative 52.3%

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

      3. mul-1-neg 52.3%

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

      4. unsub-neg 52.3%

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

      5. associate-/l* 52.3%

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

   8. Simplified 52.3%

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

   9. Taylor expanded in y around inf 50.8%

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

   if -15 < z < 2.8000000000000002e-193

   1. Initial program 71.1%

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

   3. Taylor expanded in x around 0 67.0%

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

   4. Taylor expanded in t around inf 30.3%

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

      1. associate-*r* 34.7%

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

   6. Simplified 34.7%

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

   if 2.8000000000000002e-193 < z < 1.4500000000000001e-23

   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 58.6%

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

      1. +-commutative 58.6%

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

      2. mul-1-neg 58.6%

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

      3. unsub-neg 58.6%

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

      4. *-commutative 58.6%

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

   5. Simplified 58.6%

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

   6. Taylor expanded in j around 0 39.2%

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

      1. neg-mul-1 39.2%

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

      2. distribute-rgt-neg-in 39.2%

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

   8. Simplified 39.2%

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

   if 1.4500000000000001e-23 < z < 1.3e208

   1. Initial program 68.6%

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

   3. Taylor expanded in x around 0 56.2%

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

   4. Taylor expanded in c around inf 46.1%

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

   5. Taylor expanded in c around 0 36.1%

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

      1. associate-*r* 36.1%

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

      2. neg-mul-1 36.1%

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

      3. *-commutative 36.1%

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

   7. Simplified 36.1%

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

   if 1.3e208 < z

   1. Initial program 47.9%

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

   3. Taylor expanded in x around 0 64.4%

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

   4. Taylor expanded in z around inf 68.6%

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

      1. associate-*r* 68.6%

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

      2. neg-mul-1 68.6%

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

   6. Simplified 68.6%

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

4. Final simplification 43.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -15:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-193}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-23}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+208}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 29.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.05 \cdot 10^{-45}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-292}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+89}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -1.05e-45)
   (* c (* z (- b)))
   (if (<= b 5.2e-292)
     (* x (* y z))
     (if (<= b 1.5e+89) (* 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 (b <= -1.05e-45) {
		tmp = c * (z * -b);
	} else if (b <= 5.2e-292) {
		tmp = x * (y * z);
	} else if (b <= 1.5e+89) {
		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 (b <= (-1.05d-45)) then
        tmp = c * (z * -b)
    else if (b <= 5.2d-292) then
        tmp = x * (y * z)
    else if (b <= 1.5d+89) 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 (b <= -1.05e-45) {
		tmp = c * (z * -b);
	} else if (b <= 5.2e-292) {
		tmp = x * (y * z);
	} else if (b <= 1.5e+89) {
		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 b <= -1.05e-45:
		tmp = c * (z * -b)
	elif b <= 5.2e-292:
		tmp = x * (y * z)
	elif b <= 1.5e+89:
		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 (b <= -1.05e-45)
		tmp = Float64(c * Float64(z * Float64(-b)));
	elseif (b <= 5.2e-292)
		tmp = Float64(x * Float64(y * z));
	elseif (b <= 1.5e+89)
		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 (b <= -1.05e-45)
		tmp = c * (z * -b);
	elseif (b <= 5.2e-292)
		tmp = x * (y * z);
	elseif (b <= 1.5e+89)
		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[LessEqual[b, -1.05e-45], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.2e-292], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.5e+89], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.04999999999999998e-45

   1. Initial program 66.9%

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

   3. Taylor expanded in x around 0 62.6%

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

   4. Taylor expanded in c around inf 50.7%

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

   5. Taylor expanded in a around 0 42.7%

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

      1. associate-*r* 42.7%

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

      2. neg-mul-1 42.7%

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

      3. *-commutative 42.7%

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

      4. *-commutative 42.7%

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

   7. Simplified 42.7%

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

   8. Taylor expanded in i around 0 36.0%

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

      1. associate-*r* 34.6%

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

      2. associate-*r* 34.6%

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

      3. mul-1-neg 34.6%

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

      4. *-commutative 34.6%

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

      5. distribute-rgt-neg-in 34.6%

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

      6. associate-*r* 37.5%

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

   10. Simplified 37.5%

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

   if -1.04999999999999998e-45 < b < 5.20000000000000027e-292

   1. Initial program 65.8%

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

   3. Taylor expanded in y around -inf 63.2%

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

   5. Simplified 63.2%

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

   6. Taylor expanded in x around inf 54.7%

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

      1. associate-*r* 49.9%

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

      2. *-commutative 49.9%

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

      3. mul-1-neg 49.9%

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

      4. unsub-neg 49.9%

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

      5. associate-/l* 50.5%

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

   8. Simplified 50.5%

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

   9. Taylor expanded in y around inf 41.2%

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

   if 5.20000000000000027e-292 < b < 1.50000000000000006e89

   1. Initial program 71.5%

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

   3. Taylor expanded in a around inf 50.6%

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

      1. +-commutative 50.6%

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

      2. mul-1-neg 50.6%

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

      3. unsub-neg 50.6%

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

      4. *-commutative 50.6%

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

   5. Simplified 50.6%

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

   6. Taylor expanded in j around inf 36.4%

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

   if 1.50000000000000006e89 < b

   1. Initial program 61.6%

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

   3. Taylor expanded in x around 0 64.2%

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

   4. Taylor expanded in t around inf 52.3%

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

4. Final simplification 40.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.05 \cdot 10^{-45}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-292}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+89}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 40.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+203}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -2.2e+33)
   (* x (* y z))
   (if (<= z 5e+203) (* a (- (* c j) (* x t))) (* (* z c) (- b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -2.2e+33) {
		tmp = x * (y * z);
	} else if (z <= 5e+203) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = (z * c) * -b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-2.2d+33)) then
        tmp = x * (y * z)
    else if (z <= 5d+203) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = (z * c) * -b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -2.2e+33) {
		tmp = x * (y * z);
	} else if (z <= 5e+203) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = (z * c) * -b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -2.2e+33:
		tmp = x * (y * z)
	elif z <= 5e+203:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = (z * c) * -b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -2.2e+33)
		tmp = Float64(x * Float64(y * z));
	elseif (z <= 5e+203)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = Float64(Float64(z * c) * Float64(-b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -2.2e+33)
		tmp = x * (y * z);
	elseif (z <= 5e+203)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = (z * c) * -b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -2.2e+33], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e+203], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * c), $MachinePrecision] * (-b)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.19999999999999994e33

   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 y around -inf 59.1%

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

   5. Simplified 59.1%

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

   6. Taylor expanded in x around inf 54.6%

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

      1. associate-*r* 51.7%

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

      2. *-commutative 51.7%

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

      3. mul-1-neg 51.7%

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

      4. unsub-neg 51.7%

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

      5. associate-/l* 51.7%

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

   8. Simplified 51.7%

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

   9. Taylor expanded in y around inf 51.5%

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

   if -2.19999999999999994e33 < z < 4.99999999999999994e203

   1. Initial program 70.6%

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

   3. Taylor expanded in a around inf 48.0%

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

      1. +-commutative 48.0%

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

      2. mul-1-neg 48.0%

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

      3. unsub-neg 48.0%

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

      4. *-commutative 48.0%

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

   5. Simplified 48.0%

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

   if 4.99999999999999994e203 < z

   1. Initial program 49.8%

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

   3. Taylor expanded in x around 0 65.7%

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

   4. Taylor expanded in z around inf 66.1%

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

      1. associate-*r* 66.1%

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

      2. neg-mul-1 66.1%

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

   6. Simplified 66.1%

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

4. Final simplification 50.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+203}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 29.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+87} \lor \neg \left(a \leq 9.5 \cdot 10^{+58}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -6.2e+87) (not (<= a 9.5e+58))) (* a (* c j)) (* b (* t i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -6.2e+87) || !(a <= 9.5e+58)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((a <= (-6.2d+87)) .or. (.not. (a <= 9.5d+58))) then
        tmp = a * (c * j)
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -6.2e+87) || !(a <= 9.5e+58)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (a <= -6.2e+87) or not (a <= 9.5e+58):
		tmp = a * (c * j)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -6.2e+87) || !(a <= 9.5e+58))
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((a <= -6.2e+87) || ~((a <= 9.5e+58)))
		tmp = a * (c * j);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -6.2e+87], N[Not[LessEqual[a, 9.5e+58]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -6.1999999999999999e87 or 9.5000000000000002e58 < a

   1. Initial program 58.0%

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

   3. Taylor expanded in a around inf 68.6%

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

      1. +-commutative 68.6%

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

      2. mul-1-neg 68.6%

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

      3. unsub-neg 68.6%

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

      4. *-commutative 68.6%

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

   5. Simplified 68.6%

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

   6. Taylor expanded in j around inf 45.9%

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

   if -6.1999999999999999e87 < a < 9.5000000000000002e58

   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 x around 0 60.0%

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

   4. Taylor expanded in t around inf 27.1%

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

4. Final simplification 34.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+87} \lor \neg \left(a \leq 9.5 \cdot 10^{+58}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 22.1% 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 67.0%

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

3. Taylor expanded in a around inf 40.1%

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

   1. +-commutative 40.1%

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

   2. mul-1-neg 40.1%

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

   3. unsub-neg 40.1%

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

   4. *-commutative 40.1%

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

5. Simplified 40.1%

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

6. Taylor expanded in j around inf 25.0%

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

7. Final simplification 25.0%

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

Developer target: 58.4% 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 2024059 
(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)))))