Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.5% → 81.2%

Time: 34.6s

Alternatives: 27

Speedup: 0.5×

• 57.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

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) - (i * a)))) + (j * ((c * t) - (i * y)));
}

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) - (i * a)))) + (j * ((c * t) - (i * y)))
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) - (i * a)))) + (j * ((c * t) - (i * y)));
}

Python

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

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(i * a)))) + Float64(j * Float64(Float64(c * t) - Float64(i * y))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
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[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 73.5% accurate, 1.0× speedup

Math

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

FPCore

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

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) - (i * a)))) + (j * ((c * t) - (i * y)));
}

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) - (i * a)))) + (j * ((c * t) - (i * y)))
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) - (i * a)))) + (j * ((c * t) - (i * y)));
}

Python

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

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(i * a)))) + Float64(j * Float64(Float64(c * t) - Float64(i * y))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
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[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 81.2% accurate, 0.1× speedup

Math

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

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* t c) (* y i)))
        (t_2 (* b (- (* a i) (* z c))))
        (t_3 (* j t_1)))
   (if (<= (+ (- t_2 (* x (- (* t a) (* y z)))) t_3) INFINITY)
     (fma j t_1 (+ (* x (fma y z (* t (- a)))) t_2))
     t_3)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (t * c) - (y * i);
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = j * t_1;
	double tmp;
	if (((t_2 - (x * ((t * a) - (y * z)))) + t_3) <= ((double) INFINITY)) {
		tmp = fma(j, t_1, ((x * fma(y, z, (t * -a))) + t_2));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(t * c) - Float64(y * i))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_3 = Float64(j * t_1)
	tmp = 0.0
	if (Float64(Float64(t_2 - Float64(x * Float64(Float64(t * a) - Float64(y * z)))) + t_3) <= Inf)
		tmp = fma(j, t_1, Float64(Float64(x * fma(y, z, Float64(t * Float64(-a)))) + t_2));
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 89.1%

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

      1. +-commutative 89.1%

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

      2. fma-define 89.1%

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

      3. *-commutative 89.1%

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

      4. *-commutative 89.1%

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

      5. cancel-sign-sub-inv 89.1%

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

      6. cancel-sign-sub 89.1%

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

      7. *-commutative 89.1%

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

      8. fma-neg 89.1%

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

      9. *-commutative 89.1%

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

      10. distribute-rgt-neg-out 89.1%

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

      11. remove-double-neg 89.1%

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

      12. *-commutative 89.1%

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

      13. *-commutative 89.1%

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

   3. Simplified 89.1%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in j around inf 47.9%

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

4. Final simplification 80.2%

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

Alternative 2: 81.2% accurate, 0.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

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

   1. Initial program 89.1%

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

   3. Taylor expanded in c around 0 88.4%

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

      1. +-commutative 88.4%

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

      2. *-commutative 88.4%

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

      3. associate-*r* 89.0%

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

      4. associate-*r* 89.0%

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

      5. *-commutative 89.0%

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

      6. associate-*r* 88.6%

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

      7. neg-mul-1 88.6%

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

      8. distribute-lft-neg-in 88.6%

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

      9. distribute-rgt-in 89.1%

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

      10. sub-neg 89.1%

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

      11. fma-neg 89.1%

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

      12. *-commutative 89.1%

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

      13. distribute-rgt-neg-in 89.1%

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

   5. Simplified 89.1%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in j around inf 47.9%

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

4. Final simplification 80.2%

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

Alternative 3: 81.2% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 89.1%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in j around inf 47.9%

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

4. Final simplification 80.2%

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

Alternative 4: 51.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -1.55 \cdot 10^{+50}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -4.5 \cdot 10^{-63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -2.8 \cdot 10^{-98}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 6.5 \cdot 10^{-291}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 2.4 \cdot 10^{-215}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 3.45 \cdot 10^{-130}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 4.5 \cdot 10^{+25}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* a b) (* y j)))) (t_2 (* c (- (* t j) (* z b)))))
   (if (<= c -1.55e+50)
     t_2
     (if (<= c -4.5e-63)
       t_1
       (if (<= c -2.8e-98)
         t_2
         (if (<= c 6.5e-291)
           t_1
           (if (<= c 2.4e-215)
             (* x (- (* y z) (* t a)))
             (if (<= c 3.45e-130)
               t_1
               (if (<= c 4.5e+25) (* y (- (* x z) (* i j))) t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -1.55e+50) {
		tmp = t_2;
	} else if (c <= -4.5e-63) {
		tmp = t_1;
	} else if (c <= -2.8e-98) {
		tmp = t_2;
	} else if (c <= 6.5e-291) {
		tmp = t_1;
	} else if (c <= 2.4e-215) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= 3.45e-130) {
		tmp = t_1;
	} else if (c <= 4.5e+25) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i * ((a * b) - (y * j))
    t_2 = c * ((t * j) - (z * b))
    if (c <= (-1.55d+50)) then
        tmp = t_2
    else if (c <= (-4.5d-63)) then
        tmp = t_1
    else if (c <= (-2.8d-98)) then
        tmp = t_2
    else if (c <= 6.5d-291) then
        tmp = t_1
    else if (c <= 2.4d-215) then
        tmp = x * ((y * z) - (t * a))
    else if (c <= 3.45d-130) then
        tmp = t_1
    else if (c <= 4.5d+25) then
        tmp = y * ((x * z) - (i * j))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -1.55e+50) {
		tmp = t_2;
	} else if (c <= -4.5e-63) {
		tmp = t_1;
	} else if (c <= -2.8e-98) {
		tmp = t_2;
	} else if (c <= 6.5e-291) {
		tmp = t_1;
	} else if (c <= 2.4e-215) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= 3.45e-130) {
		tmp = t_1;
	} else if (c <= 4.5e+25) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((a * b) - (y * j))
	t_2 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -1.55e+50:
		tmp = t_2
	elif c <= -4.5e-63:
		tmp = t_1
	elif c <= -2.8e-98:
		tmp = t_2
	elif c <= 6.5e-291:
		tmp = t_1
	elif c <= 2.4e-215:
		tmp = x * ((y * z) - (t * a))
	elif c <= 3.45e-130:
		tmp = t_1
	elif c <= 4.5e+25:
		tmp = y * ((x * z) - (i * j))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -1.55e+50)
		tmp = t_2;
	elseif (c <= -4.5e-63)
		tmp = t_1;
	elseif (c <= -2.8e-98)
		tmp = t_2;
	elseif (c <= 6.5e-291)
		tmp = t_1;
	elseif (c <= 2.4e-215)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (c <= 3.45e-130)
		tmp = t_1;
	elseif (c <= 4.5e+25)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((a * b) - (y * j));
	t_2 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -1.55e+50)
		tmp = t_2;
	elseif (c <= -4.5e-63)
		tmp = t_1;
	elseif (c <= -2.8e-98)
		tmp = t_2;
	elseif (c <= 6.5e-291)
		tmp = t_1;
	elseif (c <= 2.4e-215)
		tmp = x * ((y * z) - (t * a));
	elseif (c <= 3.45e-130)
		tmp = t_1;
	elseif (c <= 4.5e+25)
		tmp = y * ((x * z) - (i * j));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.55e+50], t$95$2, If[LessEqual[c, -4.5e-63], t$95$1, If[LessEqual[c, -2.8e-98], t$95$2, If[LessEqual[c, 6.5e-291], t$95$1, If[LessEqual[c, 2.4e-215], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.45e-130], t$95$1, If[LessEqual[c, 4.5e+25], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.55000000000000001e50 or -4.5e-63 < c < -2.7999999999999999e-98 or 4.5000000000000003e25 < c

   1. Initial program 61.0%

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

   3. Taylor expanded in c around inf 67.7%

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

   if -1.55000000000000001e50 < c < -4.5e-63 or -2.7999999999999999e-98 < c < 6.50000000000000002e-291 or 2.4000000000000001e-215 < c < 3.45000000000000018e-130

   1. Initial program 73.6%

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

   3. Taylor expanded in i around inf 59.4%

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

      1. distribute-lft-out-- 59.4%

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

      2. *-commutative 59.4%

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

   5. Simplified 59.4%

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

   6. Taylor expanded in i around 0 59.4%

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

      1. associate-*r* 59.4%

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

      2. *-commutative 59.4%

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

      3. sub-neg 59.4%

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

      4. +-commutative 59.4%

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

      5. *-commutative 59.4%

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

      6. +-commutative 59.4%

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

      7. sub-neg 59.4%

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

      8. associate-*r* 59.4%

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

      9. neg-mul-1 59.4%

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

      10. neg-sub0 59.4%

          \[\leadsto i \cdot \color{blue}{\left(0 - \left(j \cdot y - b \cdot a\right)\right)} \]

      11. sub-neg 59.4%

          \[\leadsto i \cdot \left(0 - \color{blue}{\left(j \cdot y + \left(-b \cdot a\right)\right)}\right) \]

      12. +-commutative 59.4%

          \[\leadsto i \cdot \left(0 - \color{blue}{\left(\left(-b \cdot a\right) + j \cdot y\right)}\right) \]

      13. associate--r+ 59.4%

          \[\leadsto i \cdot \color{blue}{\left(\left(0 - \left(-b \cdot a\right)\right) - j \cdot y\right)} \]

      14. neg-sub0 59.4%

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

      15. remove-double-neg 59.4%

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

      16. *-commutative 59.4%

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

      17. *-commutative 59.4%

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

   8. Simplified 59.4%

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

   if 6.50000000000000002e-291 < c < 2.4000000000000001e-215

   1. Initial program 93.5%

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

   3. Taylor expanded in x around inf 58.0%

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

      1. *-commutative 58.0%

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

   5. Simplified 58.0%

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

   if 3.45000000000000018e-130 < c < 4.5000000000000003e25

   1. Initial program 81.7%

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

   3. Taylor expanded in y around inf 62.3%

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

      1. +-commutative 62.3%

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

      2. mul-1-neg 62.3%

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

      3. unsub-neg 62.3%

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

      4. *-commutative 62.3%

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

   5. Simplified 62.3%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.55 \cdot 10^{+50}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -4.5 \cdot 10^{-63}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq -2.8 \cdot 10^{-98}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq 6.5 \cdot 10^{-291}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 2.4 \cdot 10^{-215}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 3.45 \cdot 10^{-130}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 4.5 \cdot 10^{+25}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 30.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(j \cdot \left(-i\right)\right)\\ \mathbf{if}\;i \leq -3.7 \cdot 10^{-5}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -9.5 \cdot 10^{-298}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;i \leq 1.65 \cdot 10^{-214}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 7.5 \cdot 10^{-168}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;i \leq 5.8 \cdot 10^{-113}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 1.5 \cdot 10^{+14}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;i \leq 10^{+165}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* j (- i)))))
   (if (<= i -3.7e-5)
     t_1
     (if (<= i -9.5e-298)
       (* x (* t (- a)))
       (if (<= i 1.65e-214)
         (* y (* x z))
         (if (<= i 7.5e-168)
           (* t (* x (- a)))
           (if (<= i 5.8e-113)
             (* x (* y z))
             (if (<= i 1.5e+14)
               (* c (* t j))
               (if (<= i 1e+165) (* b (* a i)) t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (j * -i);
	double tmp;
	if (i <= -3.7e-5) {
		tmp = t_1;
	} else if (i <= -9.5e-298) {
		tmp = x * (t * -a);
	} else if (i <= 1.65e-214) {
		tmp = y * (x * z);
	} else if (i <= 7.5e-168) {
		tmp = t * (x * -a);
	} else if (i <= 5.8e-113) {
		tmp = x * (y * z);
	} else if (i <= 1.5e+14) {
		tmp = c * (t * j);
	} else if (i <= 1e+165) {
		tmp = b * (a * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (j * -i)
    if (i <= (-3.7d-5)) then
        tmp = t_1
    else if (i <= (-9.5d-298)) then
        tmp = x * (t * -a)
    else if (i <= 1.65d-214) then
        tmp = y * (x * z)
    else if (i <= 7.5d-168) then
        tmp = t * (x * -a)
    else if (i <= 5.8d-113) then
        tmp = x * (y * z)
    else if (i <= 1.5d+14) then
        tmp = c * (t * j)
    else if (i <= 1d+165) then
        tmp = b * (a * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (j * -i);
	double tmp;
	if (i <= -3.7e-5) {
		tmp = t_1;
	} else if (i <= -9.5e-298) {
		tmp = x * (t * -a);
	} else if (i <= 1.65e-214) {
		tmp = y * (x * z);
	} else if (i <= 7.5e-168) {
		tmp = t * (x * -a);
	} else if (i <= 5.8e-113) {
		tmp = x * (y * z);
	} else if (i <= 1.5e+14) {
		tmp = c * (t * j);
	} else if (i <= 1e+165) {
		tmp = b * (a * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (j * -i)
	tmp = 0
	if i <= -3.7e-5:
		tmp = t_1
	elif i <= -9.5e-298:
		tmp = x * (t * -a)
	elif i <= 1.65e-214:
		tmp = y * (x * z)
	elif i <= 7.5e-168:
		tmp = t * (x * -a)
	elif i <= 5.8e-113:
		tmp = x * (y * z)
	elif i <= 1.5e+14:
		tmp = c * (t * j)
	elif i <= 1e+165:
		tmp = b * (a * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(j * Float64(-i)))
	tmp = 0.0
	if (i <= -3.7e-5)
		tmp = t_1;
	elseif (i <= -9.5e-298)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (i <= 1.65e-214)
		tmp = Float64(y * Float64(x * z));
	elseif (i <= 7.5e-168)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (i <= 5.8e-113)
		tmp = Float64(x * Float64(y * z));
	elseif (i <= 1.5e+14)
		tmp = Float64(c * Float64(t * j));
	elseif (i <= 1e+165)
		tmp = Float64(b * Float64(a * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * (j * -i);
	tmp = 0.0;
	if (i <= -3.7e-5)
		tmp = t_1;
	elseif (i <= -9.5e-298)
		tmp = x * (t * -a);
	elseif (i <= 1.65e-214)
		tmp = y * (x * z);
	elseif (i <= 7.5e-168)
		tmp = t * (x * -a);
	elseif (i <= 5.8e-113)
		tmp = x * (y * z);
	elseif (i <= 1.5e+14)
		tmp = c * (t * j);
	elseif (i <= 1e+165)
		tmp = b * (a * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(j * (-i)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -3.7e-5], t$95$1, If[LessEqual[i, -9.5e-298], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.65e-214], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 7.5e-168], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5.8e-113], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.5e+14], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1e+165], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if i < -3.69999999999999981e-5 or 9.99999999999999899e164 < i

   1. Initial program 57.5%

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

   3. Taylor expanded in i around inf 66.4%

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

      1. distribute-lft-out-- 66.4%

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

      2. *-commutative 66.4%

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

   5. Simplified 66.4%

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

   6. Taylor expanded in j around inf 47.0%

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

      1. neg-mul-1 47.0%

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

      2. *-commutative 47.0%

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

      3. *-commutative 47.0%

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

      4. associate-*r* 50.2%

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

      5. *-commutative 50.2%

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

      6. distribute-rgt-neg-out 50.2%

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

      7. *-commutative 50.2%

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

      8. distribute-rgt-neg-in 50.2%

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

   8. Simplified 50.2%

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

   if -3.69999999999999981e-5 < i < -9.50000000000000012e-298

   1. Initial program 82.8%

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

   3. Taylor expanded in x around inf 56.4%

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

      1. *-commutative 56.4%

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

   5. Simplified 56.4%

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

   6. Taylor expanded in y around 0 44.1%

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

      1. mul-1-neg 44.1%

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

      2. distribute-lft-neg-out 44.1%

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

      3. *-commutative 44.1%

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

   8. Simplified 44.1%

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

   if -9.50000000000000012e-298 < i < 1.6499999999999999e-214

   1. Initial program 86.7%

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

   3. Taylor expanded in x around inf 45.6%

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

      1. *-commutative 45.6%

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

   5. Simplified 45.6%

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

   6. Taylor expanded in y around inf 36.9%

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

      1. *-commutative 36.9%

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

      2. associate-*r* 45.0%

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

   8. Simplified 45.0%

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

   if 1.6499999999999999e-214 < i < 7.4999999999999995e-168

   1. Initial program 68.0%

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

   3. Taylor expanded in x around inf 30.1%

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

      1. *-commutative 30.1%

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

   5. Simplified 30.1%

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

   6. Taylor expanded in y around 0 35.4%

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

      1. mul-1-neg 35.4%

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

      2. associate-*r* 27.4%

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

      3. *-commutative 27.4%

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

      4. associate-*r* 43.0%

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

      5. distribute-rgt-neg-out 43.0%

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

      6. *-commutative 43.0%

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

      7. distribute-rgt-neg-in 43.0%

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

   8. Simplified 43.0%

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

   if 7.4999999999999995e-168 < i < 5.80000000000000008e-113

   1. Initial program 79.8%

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

   3. Taylor expanded in x around inf 47.7%

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

      1. *-commutative 47.7%

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

   5. Simplified 47.7%

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

   6. Taylor expanded in y around inf 47.1%

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

   if 5.80000000000000008e-113 < i < 1.5e14

   1. Initial program 63.2%

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

   3. Taylor expanded in b around 0 59.6%

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

   4. Taylor expanded in c around inf 38.4%

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

   if 1.5e14 < i < 9.99999999999999899e164

   1. Initial program 68.2%

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

   3. Taylor expanded in b around inf 68.3%

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

      1. *-commutative 68.3%

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

   5. Simplified 68.3%

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

   6. Taylor expanded in i around inf 47.3%

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

      1. *-commutative 47.3%

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

      2. associate-*r* 54.1%

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

   8. Simplified 54.1%

      \[\leadsto \color{blue}{\left(a \cdot i\right) \cdot b} \]
3. Recombined 7 regimes into one program.

4. Final simplification 46.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.7 \cdot 10^{-5}:\\ \;\;\;\;y \cdot \left(j \cdot \left(-i\right)\right)\\ \mathbf{elif}\;i \leq -9.5 \cdot 10^{-298}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;i \leq 1.65 \cdot 10^{-214}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 7.5 \cdot 10^{-168}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;i \leq 5.8 \cdot 10^{-113}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 1.5 \cdot 10^{+14}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;i \leq 10^{+165}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(j \cdot \left(-i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_4 := i \cdot \left(y \cdot j\right)\\ \mathbf{if}\;b \leq -2.8 \cdot 10^{+138}:\\ \;\;\;\;t\_2 - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;b \leq -1.25 \cdot 10^{-108}:\\ \;\;\;\;\left(t\_3 + t\_1\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + \left(c \cdot \left(t \cdot j\right) - t\_4\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+130}:\\ \;\;\;\;\left(t\_1 - t\_4\right) + t\_2\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{+141}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z)))
        (t_2 (* b (- (* a i) (* z c))))
        (t_3 (* j (- (* t c) (* y i))))
        (t_4 (* i (* y j))))
   (if (<= b -2.8e+138)
     (- t_2 (* x (- (* t a) (* y z))))
     (if (<= b -1.25e-108)
       (- (+ t_3 t_1) (* b (* z c)))
       (if (<= b 5.2e+18)
         (+ (* x (- (* y z) (* t a))) (- (* c (* t j)) t_4))
         (if (<= b 4e+130)
           (+ (- t_1 t_4) t_2)
           (if (<= b 1.8e+141) t_3 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 = b * ((a * i) - (z * c));
	double t_3 = j * ((t * c) - (y * i));
	double t_4 = i * (y * j);
	double tmp;
	if (b <= -2.8e+138) {
		tmp = t_2 - (x * ((t * a) - (y * z)));
	} else if (b <= -1.25e-108) {
		tmp = (t_3 + t_1) - (b * (z * c));
	} else if (b <= 5.2e+18) {
		tmp = (x * ((y * z) - (t * a))) + ((c * (t * j)) - t_4);
	} else if (b <= 4e+130) {
		tmp = (t_1 - t_4) + t_2;
	} else if (b <= 1.8e+141) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = x * (y * z)
    t_2 = b * ((a * i) - (z * c))
    t_3 = j * ((t * c) - (y * i))
    t_4 = i * (y * j)
    if (b <= (-2.8d+138)) then
        tmp = t_2 - (x * ((t * a) - (y * z)))
    else if (b <= (-1.25d-108)) then
        tmp = (t_3 + t_1) - (b * (z * c))
    else if (b <= 5.2d+18) then
        tmp = (x * ((y * z) - (t * a))) + ((c * (t * j)) - t_4)
    else if (b <= 4d+130) then
        tmp = (t_1 - t_4) + t_2
    else if (b <= 1.8d+141) then
        tmp = t_3
    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 = b * ((a * i) - (z * c));
	double t_3 = j * ((t * c) - (y * i));
	double t_4 = i * (y * j);
	double tmp;
	if (b <= -2.8e+138) {
		tmp = t_2 - (x * ((t * a) - (y * z)));
	} else if (b <= -1.25e-108) {
		tmp = (t_3 + t_1) - (b * (z * c));
	} else if (b <= 5.2e+18) {
		tmp = (x * ((y * z) - (t * a))) + ((c * (t * j)) - t_4);
	} else if (b <= 4e+130) {
		tmp = (t_1 - t_4) + t_2;
	} else if (b <= 1.8e+141) {
		tmp = t_3;
	} 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 = b * ((a * i) - (z * c))
	t_3 = j * ((t * c) - (y * i))
	t_4 = i * (y * j)
	tmp = 0
	if b <= -2.8e+138:
		tmp = t_2 - (x * ((t * a) - (y * z)))
	elif b <= -1.25e-108:
		tmp = (t_3 + t_1) - (b * (z * c))
	elif b <= 5.2e+18:
		tmp = (x * ((y * z) - (t * a))) + ((c * (t * j)) - t_4)
	elif b <= 4e+130:
		tmp = (t_1 - t_4) + t_2
	elif b <= 1.8e+141:
		tmp = t_3
	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(b * Float64(Float64(a * i) - Float64(z * c)))
	t_3 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_4 = Float64(i * Float64(y * j))
	tmp = 0.0
	if (b <= -2.8e+138)
		tmp = Float64(t_2 - Float64(x * Float64(Float64(t * a) - Float64(y * z))));
	elseif (b <= -1.25e-108)
		tmp = Float64(Float64(t_3 + t_1) - Float64(b * Float64(z * c)));
	elseif (b <= 5.2e+18)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(Float64(c * Float64(t * j)) - t_4));
	elseif (b <= 4e+130)
		tmp = Float64(Float64(t_1 - t_4) + t_2);
	elseif (b <= 1.8e+141)
		tmp = t_3;
	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 = b * ((a * i) - (z * c));
	t_3 = j * ((t * c) - (y * i));
	t_4 = i * (y * j);
	tmp = 0.0;
	if (b <= -2.8e+138)
		tmp = t_2 - (x * ((t * a) - (y * z)));
	elseif (b <= -1.25e-108)
		tmp = (t_3 + t_1) - (b * (z * c));
	elseif (b <= 5.2e+18)
		tmp = (x * ((y * z) - (t * a))) + ((c * (t * j)) - t_4);
	elseif (b <= 4e+130)
		tmp = (t_1 - t_4) + t_2;
	elseif (b <= 1.8e+141)
		tmp = t_3;
	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[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.8e+138], N[(t$95$2 - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.25e-108], N[(N[(t$95$3 + t$95$1), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.2e+18], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision] - t$95$4), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4e+130], N[(N[(t$95$1 - t$95$4), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[b, 1.8e+141], t$95$3, t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -2.8000000000000001e138

   1. Initial program 71.8%

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

   3. Taylor expanded in j around 0 82.6%

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

      1. *-commutative 82.6%

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

      2. *-commutative 82.6%

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

   5. Simplified 82.6%

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

   if -2.8000000000000001e138 < b < -1.25e-108

   1. Initial program 69.6%

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

   3. Taylor expanded in a around 0 67.7%

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

   if -1.25e-108 < b < 5.2e18

   1. Initial program 67.7%

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

   3. Taylor expanded in b around 0 72.5%

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

   4. Taylor expanded in c around 0 76.8%

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

   if 5.2e18 < b < 4.0000000000000002e130

   1. Initial program 80.8%

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

   3. Taylor expanded in t around 0 81.1%

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

   if 4.0000000000000002e130 < b < 1.8000000000000001e141

   1. Initial program 0.0%

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

   3. Taylor expanded in j around inf 100.0%

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

   if 1.8000000000000001e141 < b

   1. Initial program 72.4%

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

   3. Taylor expanded in b around inf 86.4%

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

      1. *-commutative 86.4%

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

   5. Simplified 86.4%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.8 \cdot 10^{+138}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;b \leq -1.25 \cdot 10^{-108}:\\ \;\;\;\;\left(j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + \left(c \cdot \left(t \cdot j\right) - i \cdot \left(y \cdot j\right)\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+130}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z\right) - i \cdot \left(y \cdot j\right)\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{+141}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -4.7 \cdot 10^{+172}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -3.2 \cdot 10^{+152}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq -7.2 \cdot 10^{+96}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.85 \cdot 10^{-247}:\\ \;\;\;\;t\_1 + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{+141}:\\ \;\;\;\;t\_1 - t \cdot \left(x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))) (t_2 (* b (- (* a i) (* z c)))))
   (if (<= b -4.7e+172)
     t_2
     (if (<= b -3.2e+152)
       (* x (- (* y z) (* t a)))
       (if (<= b -7.2e+96)
         t_2
         (if (<= b -1.85e-247)
           (+ t_1 (* x (* y z)))
           (if (<= b 1.1e+141) (- t_1 (* t (* 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 = j * ((t * c) - (y * i));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -4.7e+172) {
		tmp = t_2;
	} else if (b <= -3.2e+152) {
		tmp = x * ((y * z) - (t * a));
	} else if (b <= -7.2e+96) {
		tmp = t_2;
	} else if (b <= -1.85e-247) {
		tmp = t_1 + (x * (y * z));
	} else if (b <= 1.1e+141) {
		tmp = t_1 - (t * (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 = j * ((t * c) - (y * i))
    t_2 = b * ((a * i) - (z * c))
    if (b <= (-4.7d+172)) then
        tmp = t_2
    else if (b <= (-3.2d+152)) then
        tmp = x * ((y * z) - (t * a))
    else if (b <= (-7.2d+96)) then
        tmp = t_2
    else if (b <= (-1.85d-247)) then
        tmp = t_1 + (x * (y * z))
    else if (b <= 1.1d+141) then
        tmp = t_1 - (t * (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 = j * ((t * c) - (y * i));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -4.7e+172) {
		tmp = t_2;
	} else if (b <= -3.2e+152) {
		tmp = x * ((y * z) - (t * a));
	} else if (b <= -7.2e+96) {
		tmp = t_2;
	} else if (b <= -1.85e-247) {
		tmp = t_1 + (x * (y * z));
	} else if (b <= 1.1e+141) {
		tmp = t_1 - (t * (x * a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -4.7e+172:
		tmp = t_2
	elif b <= -3.2e+152:
		tmp = x * ((y * z) - (t * a))
	elif b <= -7.2e+96:
		tmp = t_2
	elif b <= -1.85e-247:
		tmp = t_1 + (x * (y * z))
	elif b <= 1.1e+141:
		tmp = t_1 - (t * (x * a))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -4.7e+172)
		tmp = t_2;
	elseif (b <= -3.2e+152)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (b <= -7.2e+96)
		tmp = t_2;
	elseif (b <= -1.85e-247)
		tmp = Float64(t_1 + Float64(x * Float64(y * z)));
	elseif (b <= 1.1e+141)
		tmp = Float64(t_1 - Float64(t * 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 = j * ((t * c) - (y * i));
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -4.7e+172)
		tmp = t_2;
	elseif (b <= -3.2e+152)
		tmp = x * ((y * z) - (t * a));
	elseif (b <= -7.2e+96)
		tmp = t_2;
	elseif (b <= -1.85e-247)
		tmp = t_1 + (x * (y * z));
	elseif (b <= 1.1e+141)
		tmp = t_1 - (t * (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[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.7e+172], t$95$2, If[LessEqual[b, -3.2e+152], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -7.2e+96], t$95$2, If[LessEqual[b, -1.85e-247], N[(t$95$1 + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.1e+141], N[(t$95$1 - N[(t * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -4.7000000000000001e172 or -3.20000000000000005e152 < b < -7.20000000000000026e96 or 1.1e141 < b

   1. Initial program 71.2%

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

   3. Taylor expanded in b around inf 79.9%

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

      1. *-commutative 79.9%

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

   5. Simplified 79.9%

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

   if -4.7000000000000001e172 < b < -3.20000000000000005e152

   1. Initial program 51.0%

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

   3. Taylor expanded in x around inf 99.5%

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

      1. *-commutative 99.5%

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

   5. Simplified 99.5%

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

   if -7.20000000000000026e96 < b < -1.85000000000000005e-247

   1. Initial program 71.1%

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

   3. Taylor expanded in b around 0 65.3%

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

   4. Taylor expanded in a around 0 61.3%

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

   if -1.85000000000000005e-247 < b < 1.1e141

   1. Initial program 69.2%

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

   3. Taylor expanded in b around 0 70.4%

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

   4. Taylor expanded in z around 0 64.8%

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

      1. +-commutative 64.8%

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

      2. *-commutative 64.8%

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

      3. mul-1-neg 64.8%

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

      4. associate-*r* 64.6%

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

      5. unsub-neg 64.6%

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

      6. *-commutative 64.6%

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

      7. associate-*r* 64.7%

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

   6. Simplified 64.7%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.7 \cdot 10^{+172}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -3.2 \cdot 10^{+152}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq -7.2 \cdot 10^{+96}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.85 \cdot 10^{-247}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{+141}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - t \cdot \left(x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 42.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;i \leq -4.5 \cdot 10^{+219}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;i \leq -1.42 \cdot 10^{-11}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -5.5 \cdot 10^{-144}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -2.95 \cdot 10^{-297}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;i \leq 1500000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 6.8 \cdot 10^{+165}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(j \cdot \left(-i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))) (t_2 (* b (- (* a i) (* z c)))))
   (if (<= i -4.5e+219)
     (* i (* j (- y)))
     (if (<= i -1.42e-11)
       t_2
       (if (<= i -5.5e-144)
         t_1
         (if (<= i -2.95e-297)
           (* x (* t (- a)))
           (if (<= i 1500000000000.0)
             t_1
             (if (<= i 6.8e+165) t_2 (* y (* j (- 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 = c * ((t * j) - (z * b));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (i <= -4.5e+219) {
		tmp = i * (j * -y);
	} else if (i <= -1.42e-11) {
		tmp = t_2;
	} else if (i <= -5.5e-144) {
		tmp = t_1;
	} else if (i <= -2.95e-297) {
		tmp = x * (t * -a);
	} else if (i <= 1500000000000.0) {
		tmp = t_1;
	} else if (i <= 6.8e+165) {
		tmp = t_2;
	} else {
		tmp = y * (j * -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 = c * ((t * j) - (z * b))
    t_2 = b * ((a * i) - (z * c))
    if (i <= (-4.5d+219)) then
        tmp = i * (j * -y)
    else if (i <= (-1.42d-11)) then
        tmp = t_2
    else if (i <= (-5.5d-144)) then
        tmp = t_1
    else if (i <= (-2.95d-297)) then
        tmp = x * (t * -a)
    else if (i <= 1500000000000.0d0) then
        tmp = t_1
    else if (i <= 6.8d+165) then
        tmp = t_2
    else
        tmp = y * (j * -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 = c * ((t * j) - (z * b));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (i <= -4.5e+219) {
		tmp = i * (j * -y);
	} else if (i <= -1.42e-11) {
		tmp = t_2;
	} else if (i <= -5.5e-144) {
		tmp = t_1;
	} else if (i <= -2.95e-297) {
		tmp = x * (t * -a);
	} else if (i <= 1500000000000.0) {
		tmp = t_1;
	} else if (i <= 6.8e+165) {
		tmp = t_2;
	} else {
		tmp = y * (j * -i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if i <= -4.5e+219:
		tmp = i * (j * -y)
	elif i <= -1.42e-11:
		tmp = t_2
	elif i <= -5.5e-144:
		tmp = t_1
	elif i <= -2.95e-297:
		tmp = x * (t * -a)
	elif i <= 1500000000000.0:
		tmp = t_1
	elif i <= 6.8e+165:
		tmp = t_2
	else:
		tmp = y * (j * -i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (i <= -4.5e+219)
		tmp = Float64(i * Float64(j * Float64(-y)));
	elseif (i <= -1.42e-11)
		tmp = t_2;
	elseif (i <= -5.5e-144)
		tmp = t_1;
	elseif (i <= -2.95e-297)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (i <= 1500000000000.0)
		tmp = t_1;
	elseif (i <= 6.8e+165)
		tmp = t_2;
	else
		tmp = Float64(y * Float64(j * Float64(-i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((t * j) - (z * b));
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (i <= -4.5e+219)
		tmp = i * (j * -y);
	elseif (i <= -1.42e-11)
		tmp = t_2;
	elseif (i <= -5.5e-144)
		tmp = t_1;
	elseif (i <= -2.95e-297)
		tmp = x * (t * -a);
	elseif (i <= 1500000000000.0)
		tmp = t_1;
	elseif (i <= 6.8e+165)
		tmp = t_2;
	else
		tmp = y * (j * -i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -4.5e+219], N[(i * N[(j * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.42e-11], t$95$2, If[LessEqual[i, -5.5e-144], t$95$1, If[LessEqual[i, -2.95e-297], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1500000000000.0], t$95$1, If[LessEqual[i, 6.8e+165], t$95$2, N[(y * N[(j * (-i)), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -4.50000000000000023e219

   1. Initial program 47.1%

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

   3. Taylor expanded in c around 0 53.8%

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

      1. +-commutative 53.8%

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

      2. *-commutative 53.8%

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

      3. associate-*r* 61.5%

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

      4. associate-*r* 61.5%

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

      5. *-commutative 61.5%

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

      6. associate-*r* 47.1%

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

      7. neg-mul-1 47.1%

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

      8. distribute-lft-neg-in 47.1%

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

      9. distribute-rgt-in 47.1%

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

      10. sub-neg 47.1%

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

      11. fma-neg 47.1%

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

      12. *-commutative 47.1%

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

      13. distribute-rgt-neg-in 47.1%

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

   5. Simplified 47.1%

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

   6. Taylor expanded in y around inf 77.0%

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

      1. +-commutative 77.0%

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

      2. mul-1-neg 77.0%

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

      3. *-commutative 77.0%

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

      4. unsub-neg 77.0%

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

      5. *-commutative 77.0%

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

   8. Simplified 77.0%

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

   9. Taylor expanded in z around 0 77.0%

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

       1. associate-*r* 77.0%

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

       2. neg-mul-1 77.0%

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

   11. Simplified 77.0%

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

   if -4.50000000000000023e219 < i < -1.42e-11 or 1.5e12 < i < 6.80000000000000022e165

   1. Initial program 66.3%

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

   3. Taylor expanded in b around inf 56.6%

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

      1. *-commutative 56.6%

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

   5. Simplified 56.6%

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

   if -1.42e-11 < i < -5.49999999999999973e-144 or -2.9499999999999999e-297 < i < 1.5e12

   1. Initial program 74.9%

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

   3. Taylor expanded in c around inf 56.0%

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

   if -5.49999999999999973e-144 < i < -2.9499999999999999e-297

   1. Initial program 84.7%

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

   3. Taylor expanded in x around inf 70.6%

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

      1. *-commutative 70.6%

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

   5. Simplified 70.6%

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

   6. Taylor expanded in y around 0 56.1%

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

      1. mul-1-neg 56.1%

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

      2. distribute-lft-neg-out 56.1%

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

      3. *-commutative 56.1%

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

   8. Simplified 56.1%

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

   if 6.80000000000000022e165 < i

   1. Initial program 54.9%

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

   3. Taylor expanded in i around inf 64.0%

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

      1. distribute-lft-out-- 64.0%

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

      2. *-commutative 64.0%

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

   5. Simplified 64.0%

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

   6. Taylor expanded in j around inf 52.2%

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

      1. neg-mul-1 52.2%

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

      2. *-commutative 52.2%

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

      3. *-commutative 52.2%

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

      4. associate-*r* 57.5%

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

      5. *-commutative 57.5%

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

      6. distribute-rgt-neg-out 57.5%

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

      7. *-commutative 57.5%

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

      8. distribute-rgt-neg-in 57.5%

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

   8. Simplified 57.5%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4.5 \cdot 10^{+219}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;i \leq -1.42 \cdot 10^{-11}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq -5.5 \cdot 10^{-144}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq -2.95 \cdot 10^{-297}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;i \leq 1500000000000:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 6.8 \cdot 10^{+165}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(j \cdot \left(-i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 48.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_2 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -1.25 \cdot 10^{-11}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -1.3 \cdot 10^{-146}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -4.9 \cdot 10^{-297}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;i \leq 4 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 1.35 \cdot 10^{+165}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq 1.16 \cdot 10^{+232}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))) (t_2 (* i (- (* a b) (* y j)))))
   (if (<= i -1.25e-11)
     t_2
     (if (<= i -1.3e-146)
       t_1
       (if (<= i -4.9e-297)
         (* x (* t (- a)))
         (if (<= i 4e+14)
           t_1
           (if (<= i 1.35e+165)
             (* b (- (* a i) (* z c)))
             (if (<= i 1.16e+232) (* j (- (* t c) (* y i))) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double t_2 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -1.25e-11) {
		tmp = t_2;
	} else if (i <= -1.3e-146) {
		tmp = t_1;
	} else if (i <= -4.9e-297) {
		tmp = x * (t * -a);
	} else if (i <= 4e+14) {
		tmp = t_1;
	} else if (i <= 1.35e+165) {
		tmp = b * ((a * i) - (z * c));
	} else if (i <= 1.16e+232) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * ((t * j) - (z * b))
    t_2 = i * ((a * b) - (y * j))
    if (i <= (-1.25d-11)) then
        tmp = t_2
    else if (i <= (-1.3d-146)) then
        tmp = t_1
    else if (i <= (-4.9d-297)) then
        tmp = x * (t * -a)
    else if (i <= 4d+14) then
        tmp = t_1
    else if (i <= 1.35d+165) then
        tmp = b * ((a * i) - (z * c))
    else if (i <= 1.16d+232) then
        tmp = j * ((t * c) - (y * i))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double t_2 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -1.25e-11) {
		tmp = t_2;
	} else if (i <= -1.3e-146) {
		tmp = t_1;
	} else if (i <= -4.9e-297) {
		tmp = x * (t * -a);
	} else if (i <= 4e+14) {
		tmp = t_1;
	} else if (i <= 1.35e+165) {
		tmp = b * ((a * i) - (z * c));
	} else if (i <= 1.16e+232) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	t_2 = i * ((a * b) - (y * j))
	tmp = 0
	if i <= -1.25e-11:
		tmp = t_2
	elif i <= -1.3e-146:
		tmp = t_1
	elif i <= -4.9e-297:
		tmp = x * (t * -a)
	elif i <= 4e+14:
		tmp = t_1
	elif i <= 1.35e+165:
		tmp = b * ((a * i) - (z * c))
	elif i <= 1.16e+232:
		tmp = j * ((t * c) - (y * i))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	t_2 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -1.25e-11)
		tmp = t_2;
	elseif (i <= -1.3e-146)
		tmp = t_1;
	elseif (i <= -4.9e-297)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (i <= 4e+14)
		tmp = t_1;
	elseif (i <= 1.35e+165)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (i <= 1.16e+232)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((t * j) - (z * b));
	t_2 = i * ((a * b) - (y * j));
	tmp = 0.0;
	if (i <= -1.25e-11)
		tmp = t_2;
	elseif (i <= -1.3e-146)
		tmp = t_1;
	elseif (i <= -4.9e-297)
		tmp = x * (t * -a);
	elseif (i <= 4e+14)
		tmp = t_1;
	elseif (i <= 1.35e+165)
		tmp = b * ((a * i) - (z * c));
	elseif (i <= 1.16e+232)
		tmp = j * ((t * c) - (y * i));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.25e-11], t$95$2, If[LessEqual[i, -1.3e-146], t$95$1, If[LessEqual[i, -4.9e-297], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4e+14], t$95$1, If[LessEqual[i, 1.35e+165], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.16e+232], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -1.25000000000000005e-11 or 1.16e232 < i

   1. Initial program 60.6%

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

   3. Taylor expanded in i around inf 71.2%

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

      1. distribute-lft-out-- 71.2%

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

      2. *-commutative 71.2%

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

   5. Simplified 71.2%

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

   6. Taylor expanded in i around 0 71.2%

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

      1. associate-*r* 71.2%

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

      2. *-commutative 71.2%

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

      3. sub-neg 71.2%

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

      4. +-commutative 71.2%

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

      5. *-commutative 71.2%

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

      6. +-commutative 71.2%

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

      7. sub-neg 71.2%

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

      8. associate-*r* 71.2%

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

      9. neg-mul-1 71.2%

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

      10. neg-sub0 71.2%

          \[\leadsto i \cdot \color{blue}{\left(0 - \left(j \cdot y - b \cdot a\right)\right)} \]

      11. sub-neg 71.2%

          \[\leadsto i \cdot \left(0 - \color{blue}{\left(j \cdot y + \left(-b \cdot a\right)\right)}\right) \]

      12. +-commutative 71.2%

          \[\leadsto i \cdot \left(0 - \color{blue}{\left(\left(-b \cdot a\right) + j \cdot y\right)}\right) \]

      13. associate--r+ 71.2%

          \[\leadsto i \cdot \color{blue}{\left(\left(0 - \left(-b \cdot a\right)\right) - j \cdot y\right)} \]

      14. neg-sub0 71.2%

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

      15. remove-double-neg 71.2%

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

      16. *-commutative 71.2%

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

      17. *-commutative 71.2%

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

   8. Simplified 71.2%

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

   if -1.25000000000000005e-11 < i < -1.29999999999999993e-146 or -4.89999999999999997e-297 < i < 4e14

   1. Initial program 74.9%

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

   3. Taylor expanded in c around inf 56.0%

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

   if -1.29999999999999993e-146 < i < -4.89999999999999997e-297

   1. Initial program 84.7%

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

   3. Taylor expanded in x around inf 70.6%

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

      1. *-commutative 70.6%

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

   5. Simplified 70.6%

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

   6. Taylor expanded in y around 0 56.1%

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

      1. mul-1-neg 56.1%

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

      2. distribute-lft-neg-out 56.1%

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

      3. *-commutative 56.1%

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

   8. Simplified 56.1%

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

   if 4e14 < i < 1.35e165

   1. Initial program 68.2%

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

   3. Taylor expanded in b around inf 68.3%

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

      1. *-commutative 68.3%

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

   5. Simplified 68.3%

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

   if 1.35e165 < i < 1.16e232

   1. Initial program 50.2%

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

   3. Taylor expanded in j around inf 62.0%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.25 \cdot 10^{-11}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -1.3 \cdot 10^{-146}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq -4.9 \cdot 10^{-297}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;i \leq 4 \cdot 10^{+14}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 1.35 \cdot 10^{+165}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq 1.16 \cdot 10^{+232}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_2 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -4.6 \cdot 10^{-9}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -1.8 \cdot 10^{-111}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -8 \cdot 10^{-298}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;i \leq 80000000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 6.2 \cdot 10^{+165}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq 1.16 \cdot 10^{+232}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))) (t_2 (* i (- (* a b) (* y j)))))
   (if (<= i -4.6e-9)
     t_2
     (if (<= i -1.8e-111)
       t_1
       (if (<= i -8e-298)
         (* t (- (* c j) (* x a)))
         (if (<= i 80000000000000.0)
           t_1
           (if (<= i 6.2e+165)
             (* b (- (* a i) (* z c)))
             (if (<= i 1.16e+232) (* j (- (* t c) (* y i))) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double t_2 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -4.6e-9) {
		tmp = t_2;
	} else if (i <= -1.8e-111) {
		tmp = t_1;
	} else if (i <= -8e-298) {
		tmp = t * ((c * j) - (x * a));
	} else if (i <= 80000000000000.0) {
		tmp = t_1;
	} else if (i <= 6.2e+165) {
		tmp = b * ((a * i) - (z * c));
	} else if (i <= 1.16e+232) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * ((t * j) - (z * b))
    t_2 = i * ((a * b) - (y * j))
    if (i <= (-4.6d-9)) then
        tmp = t_2
    else if (i <= (-1.8d-111)) then
        tmp = t_1
    else if (i <= (-8d-298)) then
        tmp = t * ((c * j) - (x * a))
    else if (i <= 80000000000000.0d0) then
        tmp = t_1
    else if (i <= 6.2d+165) then
        tmp = b * ((a * i) - (z * c))
    else if (i <= 1.16d+232) then
        tmp = j * ((t * c) - (y * i))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double t_2 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -4.6e-9) {
		tmp = t_2;
	} else if (i <= -1.8e-111) {
		tmp = t_1;
	} else if (i <= -8e-298) {
		tmp = t * ((c * j) - (x * a));
	} else if (i <= 80000000000000.0) {
		tmp = t_1;
	} else if (i <= 6.2e+165) {
		tmp = b * ((a * i) - (z * c));
	} else if (i <= 1.16e+232) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	t_2 = i * ((a * b) - (y * j))
	tmp = 0
	if i <= -4.6e-9:
		tmp = t_2
	elif i <= -1.8e-111:
		tmp = t_1
	elif i <= -8e-298:
		tmp = t * ((c * j) - (x * a))
	elif i <= 80000000000000.0:
		tmp = t_1
	elif i <= 6.2e+165:
		tmp = b * ((a * i) - (z * c))
	elif i <= 1.16e+232:
		tmp = j * ((t * c) - (y * i))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	t_2 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -4.6e-9)
		tmp = t_2;
	elseif (i <= -1.8e-111)
		tmp = t_1;
	elseif (i <= -8e-298)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (i <= 80000000000000.0)
		tmp = t_1;
	elseif (i <= 6.2e+165)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (i <= 1.16e+232)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((t * j) - (z * b));
	t_2 = i * ((a * b) - (y * j));
	tmp = 0.0;
	if (i <= -4.6e-9)
		tmp = t_2;
	elseif (i <= -1.8e-111)
		tmp = t_1;
	elseif (i <= -8e-298)
		tmp = t * ((c * j) - (x * a));
	elseif (i <= 80000000000000.0)
		tmp = t_1;
	elseif (i <= 6.2e+165)
		tmp = b * ((a * i) - (z * c));
	elseif (i <= 1.16e+232)
		tmp = j * ((t * c) - (y * i));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -4.6e-9], t$95$2, If[LessEqual[i, -1.8e-111], t$95$1, If[LessEqual[i, -8e-298], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 80000000000000.0], t$95$1, If[LessEqual[i, 6.2e+165], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.16e+232], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -4.5999999999999998e-9 or 1.16e232 < i

   1. Initial program 60.6%

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

   3. Taylor expanded in i around inf 71.2%

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

      1. distribute-lft-out-- 71.2%

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

      2. *-commutative 71.2%

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

   5. Simplified 71.2%

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

   6. Taylor expanded in i around 0 71.2%

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

      1. associate-*r* 71.2%

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

      2. *-commutative 71.2%

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

      3. sub-neg 71.2%

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

      4. +-commutative 71.2%

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

      5. *-commutative 71.2%

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

      6. +-commutative 71.2%

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

      7. sub-neg 71.2%

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

      8. associate-*r* 71.2%

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

      9. neg-mul-1 71.2%

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

      10. neg-sub0 71.2%

          \[\leadsto i \cdot \color{blue}{\left(0 - \left(j \cdot y - b \cdot a\right)\right)} \]

      11. sub-neg 71.2%

          \[\leadsto i \cdot \left(0 - \color{blue}{\left(j \cdot y + \left(-b \cdot a\right)\right)}\right) \]

      12. +-commutative 71.2%

          \[\leadsto i \cdot \left(0 - \color{blue}{\left(\left(-b \cdot a\right) + j \cdot y\right)}\right) \]

      13. associate--r+ 71.2%

          \[\leadsto i \cdot \color{blue}{\left(\left(0 - \left(-b \cdot a\right)\right) - j \cdot y\right)} \]

      14. neg-sub0 71.2%

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

      15. remove-double-neg 71.2%

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

      16. *-commutative 71.2%

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

      17. *-commutative 71.2%

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

   8. Simplified 71.2%

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

   if -4.5999999999999998e-9 < i < -1.80000000000000005e-111 or -7.9999999999999993e-298 < i < 8e13

   1. Initial program 75.7%

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

   3. Taylor expanded in c around inf 56.8%

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

   if -1.80000000000000005e-111 < i < -7.9999999999999993e-298

   1. Initial program 82.0%

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

   3. Taylor expanded in t around inf 63.1%

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

      1. +-commutative 63.1%

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

      2. mul-1-neg 63.1%

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

      3. unsub-neg 63.1%

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

      4. *-commutative 63.1%

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

   5. Simplified 63.1%

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

   if 8e13 < i < 6.2000000000000003e165

   1. Initial program 68.2%

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

   3. Taylor expanded in b around inf 68.3%

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

      1. *-commutative 68.3%

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

   5. Simplified 68.3%

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

   if 6.2000000000000003e165 < i < 1.16e232

   1. Initial program 50.2%

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

   3. Taylor expanded in j around inf 62.0%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4.6 \cdot 10^{-9}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -1.8 \cdot 10^{-111}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq -8 \cdot 10^{-298}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;i \leq 80000000000000:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 6.2 \cdot 10^{+165}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq 1.16 \cdot 10^{+232}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -3.4 \cdot 10^{+23}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-226}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-294}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{-240}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-133}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+142}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* a b) (* y j)))) (t_2 (* x (- (* y z) (* t a)))))
   (if (<= x -3.4e+23)
     t_2
     (if (<= x -5.5e-226)
       (* b (- (* a i) (* z c)))
       (if (<= x 8.5e-294)
         t_1
         (if (<= x 6.6e-240)
           (* c (- (* t j) (* z b)))
           (if (<= x 1.9e-133)
             t_1
             (if (<= x 4.6e+142) (* j (- (* t c) (* y i))) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -3.4e+23) {
		tmp = t_2;
	} else if (x <= -5.5e-226) {
		tmp = b * ((a * i) - (z * c));
	} else if (x <= 8.5e-294) {
		tmp = t_1;
	} else if (x <= 6.6e-240) {
		tmp = c * ((t * j) - (z * b));
	} else if (x <= 1.9e-133) {
		tmp = t_1;
	} else if (x <= 4.6e+142) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i * ((a * b) - (y * j))
    t_2 = x * ((y * z) - (t * a))
    if (x <= (-3.4d+23)) then
        tmp = t_2
    else if (x <= (-5.5d-226)) then
        tmp = b * ((a * i) - (z * c))
    else if (x <= 8.5d-294) then
        tmp = t_1
    else if (x <= 6.6d-240) then
        tmp = c * ((t * j) - (z * b))
    else if (x <= 1.9d-133) then
        tmp = t_1
    else if (x <= 4.6d+142) then
        tmp = j * ((t * c) - (y * i))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -3.4e+23) {
		tmp = t_2;
	} else if (x <= -5.5e-226) {
		tmp = b * ((a * i) - (z * c));
	} else if (x <= 8.5e-294) {
		tmp = t_1;
	} else if (x <= 6.6e-240) {
		tmp = c * ((t * j) - (z * b));
	} else if (x <= 1.9e-133) {
		tmp = t_1;
	} else if (x <= 4.6e+142) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((a * b) - (y * j))
	t_2 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -3.4e+23:
		tmp = t_2
	elif x <= -5.5e-226:
		tmp = b * ((a * i) - (z * c))
	elif x <= 8.5e-294:
		tmp = t_1
	elif x <= 6.6e-240:
		tmp = c * ((t * j) - (z * b))
	elif x <= 1.9e-133:
		tmp = t_1
	elif x <= 4.6e+142:
		tmp = j * ((t * c) - (y * i))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -3.4e+23)
		tmp = t_2;
	elseif (x <= -5.5e-226)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (x <= 8.5e-294)
		tmp = t_1;
	elseif (x <= 6.6e-240)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (x <= 1.9e-133)
		tmp = t_1;
	elseif (x <= 4.6e+142)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((a * b) - (y * j));
	t_2 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -3.4e+23)
		tmp = t_2;
	elseif (x <= -5.5e-226)
		tmp = b * ((a * i) - (z * c));
	elseif (x <= 8.5e-294)
		tmp = t_1;
	elseif (x <= 6.6e-240)
		tmp = c * ((t * j) - (z * b));
	elseif (x <= 1.9e-133)
		tmp = t_1;
	elseif (x <= 4.6e+142)
		tmp = j * ((t * c) - (y * i));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(a * 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]}, If[LessEqual[x, -3.4e+23], t$95$2, If[LessEqual[x, -5.5e-226], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.5e-294], t$95$1, If[LessEqual[x, 6.6e-240], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.9e-133], t$95$1, If[LessEqual[x, 4.6e+142], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -3.39999999999999992e23 or 4.60000000000000004e142 < x

   1. Initial program 73.2%

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

   3. Taylor expanded in x around inf 64.2%

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

      1. *-commutative 64.2%

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

   5. Simplified 64.2%

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

   if -3.39999999999999992e23 < x < -5.5e-226

   1. Initial program 68.9%

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

   3. Taylor expanded in b around inf 58.2%

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

      1. *-commutative 58.2%

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

   5. Simplified 58.2%

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

   if -5.5e-226 < x < 8.4999999999999999e-294 or 6.6000000000000003e-240 < x < 1.9000000000000002e-133

   1. Initial program 57.9%

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

   3. Taylor expanded in i around inf 73.8%

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

      1. distribute-lft-out-- 73.8%

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

      2. *-commutative 73.8%

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

   5. Simplified 73.8%

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

   6. Taylor expanded in i around 0 73.8%

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

      1. associate-*r* 73.8%

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

      2. *-commutative 73.8%

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

      3. sub-neg 73.8%

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

      4. +-commutative 73.8%

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

      5. *-commutative 73.8%

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

      6. +-commutative 73.8%

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

      7. sub-neg 73.8%

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

      8. associate-*r* 73.8%

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

      9. neg-mul-1 73.8%

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

      10. neg-sub0 73.8%

          \[\leadsto i \cdot \color{blue}{\left(0 - \left(j \cdot y - b \cdot a\right)\right)} \]

      11. sub-neg 73.8%

          \[\leadsto i \cdot \left(0 - \color{blue}{\left(j \cdot y + \left(-b \cdot a\right)\right)}\right) \]

      12. +-commutative 73.8%

          \[\leadsto i \cdot \left(0 - \color{blue}{\left(\left(-b \cdot a\right) + j \cdot y\right)}\right) \]

      13. associate--r+ 73.8%

          \[\leadsto i \cdot \color{blue}{\left(\left(0 - \left(-b \cdot a\right)\right) - j \cdot y\right)} \]

      14. neg-sub0 73.8%

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

      15. remove-double-neg 73.8%

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

      16. *-commutative 73.8%

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

      17. *-commutative 73.8%

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

   8. Simplified 73.8%

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

   if 8.4999999999999999e-294 < x < 6.6000000000000003e-240

   1. Initial program 61.0%

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

   3. Taylor expanded in c around inf 90.4%

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

   if 1.9000000000000002e-133 < x < 4.60000000000000004e142

   1. Initial program 77.6%

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

   3. Taylor expanded in j around inf 46.9%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+23}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-226}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-294}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{-240}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-133}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+142}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 67.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -4.7 \cdot 10^{+172}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3.2 \cdot 10^{+152}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq -1.8 \cdot 10^{+92} \lor \neg \left(b \leq 8.2 \cdot 10^{+141}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= b -4.7e+172)
     t_1
     (if (<= b -3.2e+152)
       (* x (- (* y z) (* t a)))
       (if (or (<= b -1.8e+92) (not (<= b 8.2e+141)))
         t_1
         (- (* j (- (* t c) (* y i))) (* x (- (* t a) (* y z)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -4.7e+172) {
		tmp = t_1;
	} else if (b <= -3.2e+152) {
		tmp = x * ((y * z) - (t * a));
	} else if ((b <= -1.8e+92) || !(b <= 8.2e+141)) {
		tmp = t_1;
	} else {
		tmp = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    if (b <= (-4.7d+172)) then
        tmp = t_1
    else if (b <= (-3.2d+152)) then
        tmp = x * ((y * z) - (t * a))
    else if ((b <= (-1.8d+92)) .or. (.not. (b <= 8.2d+141))) then
        tmp = t_1
    else
        tmp = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -4.7e+172) {
		tmp = t_1;
	} else if (b <= -3.2e+152) {
		tmp = x * ((y * z) - (t * a));
	} else if ((b <= -1.8e+92) || !(b <= 8.2e+141)) {
		tmp = t_1;
	} else {
		tmp = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -4.7e+172:
		tmp = t_1
	elif b <= -3.2e+152:
		tmp = x * ((y * z) - (t * a))
	elif (b <= -1.8e+92) or not (b <= 8.2e+141):
		tmp = t_1
	else:
		tmp = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -4.7e+172)
		tmp = t_1;
	elseif (b <= -3.2e+152)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif ((b <= -1.8e+92) || !(b <= 8.2e+141))
		tmp = t_1;
	else
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) - Float64(x * Float64(Float64(t * a) - Float64(y * z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -4.7e+172)
		tmp = t_1;
	elseif (b <= -3.2e+152)
		tmp = x * ((y * z) - (t * a));
	elseif ((b <= -1.8e+92) || ~((b <= 8.2e+141)))
		tmp = t_1;
	else
		tmp = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.7e+172], t$95$1, If[LessEqual[b, -3.2e+152], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, -1.8e+92], N[Not[LessEqual[b, 8.2e+141]], $MachinePrecision]], t$95$1, N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.7000000000000001e172 or -3.20000000000000005e152 < b < -1.8e92 or 8.20000000000000044e141 < b

   1. Initial program 71.2%

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

   3. Taylor expanded in b around inf 79.9%

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

      1. *-commutative 79.9%

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

   5. Simplified 79.9%

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

   if -4.7000000000000001e172 < b < -3.20000000000000005e152

   1. Initial program 51.0%

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

   3. Taylor expanded in x around inf 99.5%

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

      1. *-commutative 99.5%

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

   5. Simplified 99.5%

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

   if -1.8e92 < b < 8.20000000000000044e141

   1. Initial program 70.0%

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

   3. Taylor expanded in b around 0 68.3%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.7 \cdot 10^{+172}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -3.2 \cdot 10^{+152}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq -1.8 \cdot 10^{+92} \lor \neg \left(b \leq 8.2 \cdot 10^{+141}\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 31.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(z \cdot \left(-c\right)\right)\\ t_2 := y \cdot \left(j \cdot \left(-i\right)\right)\\ \mathbf{if}\;i \leq -3.9 \cdot 10^{+32}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -2.3 \cdot 10^{-105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -1.9 \cdot 10^{-162}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq -2.45 \cdot 10^{-297}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;i \leq 2 \cdot 10^{-32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 1.02 \cdot 10^{+166}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* z (- c)))) (t_2 (* y (* j (- i)))))
   (if (<= i -3.9e+32)
     t_2
     (if (<= i -2.3e-105)
       t_1
       (if (<= i -1.9e-162)
         (* x (* y z))
         (if (<= i -2.45e-297)
           (* x (* t (- a)))
           (if (<= i 2e-32) t_1 (if (<= i 1.02e+166) (* b (* a 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 * (z * -c);
	double t_2 = y * (j * -i);
	double tmp;
	if (i <= -3.9e+32) {
		tmp = t_2;
	} else if (i <= -2.3e-105) {
		tmp = t_1;
	} else if (i <= -1.9e-162) {
		tmp = x * (y * z);
	} else if (i <= -2.45e-297) {
		tmp = x * (t * -a);
	} else if (i <= 2e-32) {
		tmp = t_1;
	} else if (i <= 1.02e+166) {
		tmp = b * (a * 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 * (z * -c)
    t_2 = y * (j * -i)
    if (i <= (-3.9d+32)) then
        tmp = t_2
    else if (i <= (-2.3d-105)) then
        tmp = t_1
    else if (i <= (-1.9d-162)) then
        tmp = x * (y * z)
    else if (i <= (-2.45d-297)) then
        tmp = x * (t * -a)
    else if (i <= 2d-32) then
        tmp = t_1
    else if (i <= 1.02d+166) then
        tmp = b * (a * 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 * (z * -c);
	double t_2 = y * (j * -i);
	double tmp;
	if (i <= -3.9e+32) {
		tmp = t_2;
	} else if (i <= -2.3e-105) {
		tmp = t_1;
	} else if (i <= -1.9e-162) {
		tmp = x * (y * z);
	} else if (i <= -2.45e-297) {
		tmp = x * (t * -a);
	} else if (i <= 2e-32) {
		tmp = t_1;
	} else if (i <= 1.02e+166) {
		tmp = b * (a * i);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (z * -c)
	t_2 = y * (j * -i)
	tmp = 0
	if i <= -3.9e+32:
		tmp = t_2
	elif i <= -2.3e-105:
		tmp = t_1
	elif i <= -1.9e-162:
		tmp = x * (y * z)
	elif i <= -2.45e-297:
		tmp = x * (t * -a)
	elif i <= 2e-32:
		tmp = t_1
	elif i <= 1.02e+166:
		tmp = b * (a * i)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(z * Float64(-c)))
	t_2 = Float64(y * Float64(j * Float64(-i)))
	tmp = 0.0
	if (i <= -3.9e+32)
		tmp = t_2;
	elseif (i <= -2.3e-105)
		tmp = t_1;
	elseif (i <= -1.9e-162)
		tmp = Float64(x * Float64(y * z));
	elseif (i <= -2.45e-297)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (i <= 2e-32)
		tmp = t_1;
	elseif (i <= 1.02e+166)
		tmp = Float64(b * Float64(a * 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 * (z * -c);
	t_2 = y * (j * -i);
	tmp = 0.0;
	if (i <= -3.9e+32)
		tmp = t_2;
	elseif (i <= -2.3e-105)
		tmp = t_1;
	elseif (i <= -1.9e-162)
		tmp = x * (y * z);
	elseif (i <= -2.45e-297)
		tmp = x * (t * -a);
	elseif (i <= 2e-32)
		tmp = t_1;
	elseif (i <= 1.02e+166)
		tmp = b * (a * 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[(z * (-c)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(j * (-i)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -3.9e+32], t$95$2, If[LessEqual[i, -2.3e-105], t$95$1, If[LessEqual[i, -1.9e-162], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -2.45e-297], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2e-32], t$95$1, If[LessEqual[i, 1.02e+166], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -3.8999999999999999e32 or 1.0200000000000001e166 < i

   1. Initial program 55.8%

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

   3. Taylor expanded in i around inf 68.6%

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

      1. distribute-lft-out-- 68.6%

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

      2. *-commutative 68.6%

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

   5. Simplified 68.6%

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

   6. Taylor expanded in j around inf 50.3%

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

      1. neg-mul-1 50.3%

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

      2. *-commutative 50.3%

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

      3. *-commutative 50.3%

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

      4. associate-*r* 53.9%

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

      5. *-commutative 53.9%

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

      6. distribute-rgt-neg-out 53.9%

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

      7. *-commutative 53.9%

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

      8. distribute-rgt-neg-in 53.9%

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

   8. Simplified 53.9%

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

   if -3.8999999999999999e32 < i < -2.3000000000000001e-105 or -2.44999999999999999e-297 < i < 2.00000000000000011e-32

   1. Initial program 76.7%

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

   3. Taylor expanded in b around inf 44.9%

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

      1. *-commutative 44.9%

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

   5. Simplified 44.9%

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

   6. Taylor expanded in i around 0 39.1%

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

      1. associate-*r* 39.1%

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

      2. neg-mul-1 39.1%

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

      3. *-commutative 39.1%

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

   8. Simplified 39.1%

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

   if -2.3000000000000001e-105 < i < -1.90000000000000002e-162

   1. Initial program 77.8%

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

   3. Taylor expanded in x around inf 56.6%

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

      1. *-commutative 56.6%

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

   5. Simplified 56.6%

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

   6. Taylor expanded in y around inf 46.0%

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

   if -1.90000000000000002e-162 < i < -2.44999999999999999e-297

   1. Initial program 83.5%

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

   3. Taylor expanded in x around inf 68.2%

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

      1. *-commutative 68.2%

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

   5. Simplified 68.2%

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

   6. Taylor expanded in y around 0 57.8%

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

      1. mul-1-neg 57.8%

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

      2. distribute-lft-neg-out 57.8%

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

      3. *-commutative 57.8%

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

   8. Simplified 57.8%

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

   if 2.00000000000000011e-32 < i < 1.0200000000000001e166

   1. Initial program 68.0%

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

   3. Taylor expanded in b around inf 57.6%

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

      1. *-commutative 57.6%

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

   5. Simplified 57.6%

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

   6. Taylor expanded in i around inf 41.7%

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

      1. *-commutative 41.7%

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

      2. associate-*r* 46.9%

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

   8. Simplified 46.9%

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

4. Final simplification 47.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.9 \cdot 10^{+32}:\\ \;\;\;\;y \cdot \left(j \cdot \left(-i\right)\right)\\ \mathbf{elif}\;i \leq -2.3 \cdot 10^{-105}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;i \leq -1.9 \cdot 10^{-162}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq -2.45 \cdot 10^{-297}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;i \leq 2 \cdot 10^{-32}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;i \leq 1.02 \cdot 10^{+166}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(j \cdot \left(-i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 66.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -4 \cdot 10^{+138}:\\ \;\;\;\;t\_1 - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;b \leq -1.8 \cdot 10^{-108}:\\ \;\;\;\;\left(j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+141}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + \left(c \cdot \left(t \cdot j\right) - i \cdot \left(y \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= b -4e+138)
     (- t_1 (* x (- (* t a) (* y z))))
     (if (<= b -1.8e-108)
       (- (+ (* j (- (* t c) (* y i))) (* x (* y z))) (* b (* z c)))
       (if (<= b 7e+141)
         (+ (* x (- (* y z) (* t a))) (- (* c (* t j)) (* i (* y j))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -4e+138) {
		tmp = t_1 - (x * ((t * a) - (y * z)));
	} else if (b <= -1.8e-108) {
		tmp = ((j * ((t * c) - (y * i))) + (x * (y * z))) - (b * (z * c));
	} else if (b <= 7e+141) {
		tmp = (x * ((y * z) - (t * a))) + ((c * (t * j)) - (i * (y * j)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    if (b <= (-4d+138)) then
        tmp = t_1 - (x * ((t * a) - (y * z)))
    else if (b <= (-1.8d-108)) then
        tmp = ((j * ((t * c) - (y * i))) + (x * (y * z))) - (b * (z * c))
    else if (b <= 7d+141) then
        tmp = (x * ((y * z) - (t * a))) + ((c * (t * j)) - (i * (y * j)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -4e+138) {
		tmp = t_1 - (x * ((t * a) - (y * z)));
	} else if (b <= -1.8e-108) {
		tmp = ((j * ((t * c) - (y * i))) + (x * (y * z))) - (b * (z * c));
	} else if (b <= 7e+141) {
		tmp = (x * ((y * z) - (t * a))) + ((c * (t * j)) - (i * (y * j)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -4e+138:
		tmp = t_1 - (x * ((t * a) - (y * z)))
	elif b <= -1.8e-108:
		tmp = ((j * ((t * c) - (y * i))) + (x * (y * z))) - (b * (z * c))
	elif b <= 7e+141:
		tmp = (x * ((y * z) - (t * a))) + ((c * (t * j)) - (i * (y * j)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -4e+138)
		tmp = Float64(t_1 - Float64(x * Float64(Float64(t * a) - Float64(y * z))));
	elseif (b <= -1.8e-108)
		tmp = Float64(Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(x * Float64(y * z))) - Float64(b * Float64(z * c)));
	elseif (b <= 7e+141)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(Float64(c * Float64(t * j)) - Float64(i * Float64(y * j))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -4e+138)
		tmp = t_1 - (x * ((t * a) - (y * z)));
	elseif (b <= -1.8e-108)
		tmp = ((j * ((t * c) - (y * i))) + (x * (y * z))) - (b * (z * c));
	elseif (b <= 7e+141)
		tmp = (x * ((y * z) - (t * a))) + ((c * (t * j)) - (i * (y * j)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4e+138], N[(t$95$1 - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.8e-108], N[(N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7e+141], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 4 regimes

2. if b < -4.0000000000000001e138

   1. Initial program 71.8%

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

   3. Taylor expanded in j around 0 82.6%

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

      1. *-commutative 82.6%

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

      2. *-commutative 82.6%

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

   5. Simplified 82.6%

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

   if -4.0000000000000001e138 < b < -1.8e-108

   1. Initial program 69.6%

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

   3. Taylor expanded in a around 0 67.7%

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

   if -1.8e-108 < b < 6.9999999999999999e141

   1. Initial program 68.8%

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

   3. Taylor expanded in b around 0 70.5%

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

   4. Taylor expanded in c around 0 74.0%

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

   if 6.9999999999999999e141 < b

   1. Initial program 72.4%

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

   3. Taylor expanded in b around inf 86.4%

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

      1. *-commutative 86.4%

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

   5. Simplified 86.4%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{+138}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;b \leq -1.8 \cdot 10^{-108}:\\ \;\;\;\;\left(j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+141}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + \left(c \cdot \left(t \cdot j\right) - i \cdot \left(y \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 58.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.05 \cdot 10^{+173}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3.2 \cdot 10^{+152}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{+91} \lor \neg \left(b \leq 1.1 \cdot 10^{+141}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= b -1.05e+173)
     t_1
     (if (<= b -3.2e+152)
       (* x (- (* y z) (* t a)))
       (if (or (<= b -6.5e+91) (not (<= b 1.1e+141)))
         t_1
         (+ (* j (- (* t c) (* y i))) (* x (* y z))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.05e+173) {
		tmp = t_1;
	} else if (b <= -3.2e+152) {
		tmp = x * ((y * z) - (t * a));
	} else if ((b <= -6.5e+91) || !(b <= 1.1e+141)) {
		tmp = t_1;
	} else {
		tmp = (j * ((t * c) - (y * i))) + (x * (y * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    if (b <= (-1.05d+173)) then
        tmp = t_1
    else if (b <= (-3.2d+152)) then
        tmp = x * ((y * z) - (t * a))
    else if ((b <= (-6.5d+91)) .or. (.not. (b <= 1.1d+141))) then
        tmp = t_1
    else
        tmp = (j * ((t * c) - (y * i))) + (x * (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.05e+173) {
		tmp = t_1;
	} else if (b <= -3.2e+152) {
		tmp = x * ((y * z) - (t * a));
	} else if ((b <= -6.5e+91) || !(b <= 1.1e+141)) {
		tmp = t_1;
	} else {
		tmp = (j * ((t * c) - (y * i))) + (x * (y * z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -1.05e+173:
		tmp = t_1
	elif b <= -3.2e+152:
		tmp = x * ((y * z) - (t * a))
	elif (b <= -6.5e+91) or not (b <= 1.1e+141):
		tmp = t_1
	else:
		tmp = (j * ((t * c) - (y * i))) + (x * (y * z))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -1.05e+173)
		tmp = t_1;
	elseif (b <= -3.2e+152)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif ((b <= -6.5e+91) || !(b <= 1.1e+141))
		tmp = t_1;
	else
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(x * Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -1.05e+173)
		tmp = t_1;
	elseif (b <= -3.2e+152)
		tmp = x * ((y * z) - (t * a));
	elseif ((b <= -6.5e+91) || ~((b <= 1.1e+141)))
		tmp = t_1;
	else
		tmp = (j * ((t * c) - (y * i))) + (x * (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.05e+173], t$95$1, If[LessEqual[b, -3.2e+152], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, -6.5e+91], N[Not[LessEqual[b, 1.1e+141]], $MachinePrecision]], t$95$1, N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.05e173 or -3.20000000000000005e152 < b < -6.4999999999999997e91 or 1.1e141 < b

   1. Initial program 71.2%

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

   3. Taylor expanded in b around inf 79.9%

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

      1. *-commutative 79.9%

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

   5. Simplified 79.9%

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

   if -1.05e173 < b < -3.20000000000000005e152

   1. Initial program 51.0%

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

   3. Taylor expanded in x around inf 99.5%

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

      1. *-commutative 99.5%

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

   5. Simplified 99.5%

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

   if -6.4999999999999997e91 < b < 1.1e141

   1. Initial program 70.0%

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

   3. Taylor expanded in b around 0 68.3%

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

   4. Taylor expanded in a around 0 59.7%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.05 \cdot 10^{+173}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -3.2 \cdot 10^{+152}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{+91} \lor \neg \left(b \leq 1.1 \cdot 10^{+141}\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 68.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := x \cdot \left(t \cdot a - y \cdot z\right)\\ t_3 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_4 := t\_3 - t\_2\\ \mathbf{if}\;b \leq -1.3 \cdot 10^{+66}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{-29}:\\ \;\;\;\;t\_1 - t\_2\\ \mathbf{elif}\;b \leq 1.12 \cdot 10^{+116}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{+141}:\\ \;\;\;\;t\_1 + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i))))
        (t_2 (* x (- (* t a) (* y z))))
        (t_3 (* b (- (* a i) (* z c))))
        (t_4 (- t_3 t_2)))
   (if (<= b -1.3e+66)
     t_4
     (if (<= b 4.1e-29)
       (- t_1 t_2)
       (if (<= b 1.12e+116)
         t_4
         (if (<= b 2.3e+141) (+ t_1 (* 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 = j * ((t * c) - (y * i));
	double t_2 = x * ((t * a) - (y * z));
	double t_3 = b * ((a * i) - (z * c));
	double t_4 = t_3 - t_2;
	double tmp;
	if (b <= -1.3e+66) {
		tmp = t_4;
	} else if (b <= 4.1e-29) {
		tmp = t_1 - t_2;
	} else if (b <= 1.12e+116) {
		tmp = t_4;
	} else if (b <= 2.3e+141) {
		tmp = t_1 + (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) :: t_4
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = x * ((t * a) - (y * z))
    t_3 = b * ((a * i) - (z * c))
    t_4 = t_3 - t_2
    if (b <= (-1.3d+66)) then
        tmp = t_4
    else if (b <= 4.1d-29) then
        tmp = t_1 - t_2
    else if (b <= 1.12d+116) then
        tmp = t_4
    else if (b <= 2.3d+141) then
        tmp = t_1 + (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 = j * ((t * c) - (y * i));
	double t_2 = x * ((t * a) - (y * z));
	double t_3 = b * ((a * i) - (z * c));
	double t_4 = t_3 - t_2;
	double tmp;
	if (b <= -1.3e+66) {
		tmp = t_4;
	} else if (b <= 4.1e-29) {
		tmp = t_1 - t_2;
	} else if (b <= 1.12e+116) {
		tmp = t_4;
	} else if (b <= 2.3e+141) {
		tmp = t_1 + (x * (y * z));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = x * ((t * a) - (y * z))
	t_3 = b * ((a * i) - (z * c))
	t_4 = t_3 - t_2
	tmp = 0
	if b <= -1.3e+66:
		tmp = t_4
	elif b <= 4.1e-29:
		tmp = t_1 - t_2
	elif b <= 1.12e+116:
		tmp = t_4
	elif b <= 2.3e+141:
		tmp = t_1 + (x * (y * z))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(x * Float64(Float64(t * a) - Float64(y * z)))
	t_3 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_4 = Float64(t_3 - t_2)
	tmp = 0.0
	if (b <= -1.3e+66)
		tmp = t_4;
	elseif (b <= 4.1e-29)
		tmp = Float64(t_1 - t_2);
	elseif (b <= 1.12e+116)
		tmp = t_4;
	elseif (b <= 2.3e+141)
		tmp = Float64(t_1 + 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 = j * ((t * c) - (y * i));
	t_2 = x * ((t * a) - (y * z));
	t_3 = b * ((a * i) - (z * c));
	t_4 = t_3 - t_2;
	tmp = 0.0;
	if (b <= -1.3e+66)
		tmp = t_4;
	elseif (b <= 4.1e-29)
		tmp = t_1 - t_2;
	elseif (b <= 1.12e+116)
		tmp = t_4;
	elseif (b <= 2.3e+141)
		tmp = t_1 + (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[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 - t$95$2), $MachinePrecision]}, If[LessEqual[b, -1.3e+66], t$95$4, If[LessEqual[b, 4.1e-29], N[(t$95$1 - t$95$2), $MachinePrecision], If[LessEqual[b, 1.12e+116], t$95$4, If[LessEqual[b, 2.3e+141], N[(t$95$1 + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.30000000000000006e66 or 4.0999999999999998e-29 < b < 1.12e116

   1. Initial program 70.6%

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

   3. Taylor expanded in j around 0 73.8%

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

      1. *-commutative 73.8%

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

      2. *-commutative 73.8%

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

   5. Simplified 73.8%

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

   if -1.30000000000000006e66 < b < 4.0999999999999998e-29

   1. Initial program 70.4%

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

   3. Taylor expanded in b around 0 71.8%

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

   if 1.12e116 < b < 2.3000000000000002e141

   1. Initial program 42.6%

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

   3. Taylor expanded in b around 0 71.3%

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

   4. Taylor expanded in a around 0 71.8%

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

   if 2.3000000000000002e141 < b

   1. Initial program 72.4%

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

   3. Taylor expanded in b around inf 86.4%

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

      1. *-commutative 86.4%

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

   5. Simplified 86.4%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{+66}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{-29}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;b \leq 1.12 \cdot 10^{+116}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{+141}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 51.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -4.5 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -5.8 \cdot 10^{-42}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;c \leq -2.45 \cdot 10^{-147}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq 3.8 \cdot 10^{-131}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 3.9 \cdot 10^{+26}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))))
   (if (<= c -4.5e+98)
     t_1
     (if (<= c -5.8e-42)
       (* z (- (* x y) (* b c)))
       (if (<= c -2.45e-147)
         (* b (- (* a i) (* z c)))
         (if (<= c 3.8e-131)
           (* i (- (* a b) (* y j)))
           (if (<= c 3.9e+26) (* 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 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -4.5e+98) {
		tmp = t_1;
	} else if (c <= -5.8e-42) {
		tmp = z * ((x * y) - (b * c));
	} else if (c <= -2.45e-147) {
		tmp = b * ((a * i) - (z * c));
	} else if (c <= 3.8e-131) {
		tmp = i * ((a * b) - (y * j));
	} else if (c <= 3.9e+26) {
		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 = c * ((t * j) - (z * b))
    if (c <= (-4.5d+98)) then
        tmp = t_1
    else if (c <= (-5.8d-42)) then
        tmp = z * ((x * y) - (b * c))
    else if (c <= (-2.45d-147)) then
        tmp = b * ((a * i) - (z * c))
    else if (c <= 3.8d-131) then
        tmp = i * ((a * b) - (y * j))
    else if (c <= 3.9d+26) 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 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -4.5e+98) {
		tmp = t_1;
	} else if (c <= -5.8e-42) {
		tmp = z * ((x * y) - (b * c));
	} else if (c <= -2.45e-147) {
		tmp = b * ((a * i) - (z * c));
	} else if (c <= 3.8e-131) {
		tmp = i * ((a * b) - (y * j));
	} else if (c <= 3.9e+26) {
		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 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -4.5e+98:
		tmp = t_1
	elif c <= -5.8e-42:
		tmp = z * ((x * y) - (b * c))
	elif c <= -2.45e-147:
		tmp = b * ((a * i) - (z * c))
	elif c <= 3.8e-131:
		tmp = i * ((a * b) - (y * j))
	elif c <= 3.9e+26:
		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(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -4.5e+98)
		tmp = t_1;
	elseif (c <= -5.8e-42)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (c <= -2.45e-147)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (c <= 3.8e-131)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (c <= 3.9e+26)
		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 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -4.5e+98)
		tmp = t_1;
	elseif (c <= -5.8e-42)
		tmp = z * ((x * y) - (b * c));
	elseif (c <= -2.45e-147)
		tmp = b * ((a * i) - (z * c));
	elseif (c <= 3.8e-131)
		tmp = i * ((a * b) - (y * j));
	elseif (c <= 3.9e+26)
		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[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4.5e+98], t$95$1, If[LessEqual[c, -5.8e-42], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.45e-147], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.8e-131], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.9e+26], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -4.5000000000000002e98 or 3.9e26 < c

   1. Initial program 57.3%

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

   3. Taylor expanded in c around inf 67.5%

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

   if -4.5000000000000002e98 < c < -5.8000000000000006e-42

   1. Initial program 67.1%

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

   3. Taylor expanded in z around inf 61.4%

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

      1. *-commutative 61.4%

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

      2. *-commutative 61.4%

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

   5. Simplified 61.4%

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

   if -5.8000000000000006e-42 < c < -2.45000000000000002e-147

   1. Initial program 76.2%

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

   3. Taylor expanded in b around inf 56.8%

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

      1. *-commutative 56.8%

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

   5. Simplified 56.8%

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

   if -2.45000000000000002e-147 < c < 3.79999999999999995e-131

   1. Initial program 84.2%

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

   3. Taylor expanded in i around inf 56.9%

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

      1. distribute-lft-out-- 56.9%

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

      2. *-commutative 56.9%

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

   5. Simplified 56.9%

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

   6. Taylor expanded in i around 0 56.9%

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

      1. associate-*r* 56.9%

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

      2. *-commutative 56.9%

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

      3. sub-neg 56.9%

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

      4. +-commutative 56.9%

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

      5. *-commutative 56.9%

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

      6. +-commutative 56.9%

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

      7. sub-neg 56.9%

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

      8. associate-*r* 56.9%

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

      9. neg-mul-1 56.9%

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

      10. neg-sub0 56.9%

          \[\leadsto i \cdot \color{blue}{\left(0 - \left(j \cdot y - b \cdot a\right)\right)} \]

      11. sub-neg 56.9%

          \[\leadsto i \cdot \left(0 - \color{blue}{\left(j \cdot y + \left(-b \cdot a\right)\right)}\right) \]

      12. +-commutative 56.9%

          \[\leadsto i \cdot \left(0 - \color{blue}{\left(\left(-b \cdot a\right) + j \cdot y\right)}\right) \]

      13. associate--r+ 56.9%

          \[\leadsto i \cdot \color{blue}{\left(\left(0 - \left(-b \cdot a\right)\right) - j \cdot y\right)} \]

      14. neg-sub0 56.9%

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

      15. remove-double-neg 56.9%

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

      16. *-commutative 56.9%

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

      17. *-commutative 56.9%

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

   8. Simplified 56.9%

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

   if 3.79999999999999995e-131 < c < 3.9e26

   1. Initial program 81.7%

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

   3. Taylor expanded in y around inf 62.3%

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

      1. +-commutative 62.3%

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

      2. mul-1-neg 62.3%

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

      3. unsub-neg 62.3%

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

      4. *-commutative 62.3%

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

   5. Simplified 62.3%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.5 \cdot 10^{+98}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -5.8 \cdot 10^{-42}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;c \leq -2.45 \cdot 10^{-147}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq 3.8 \cdot 10^{-131}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 3.9 \cdot 10^{+26}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 52.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -3.05 \cdot 10^{+54}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -1.2 \cdot 10^{-63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -2 \cdot 10^{-97}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -3.1 \cdot 10^{-257}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 1.16 \cdot 10^{+28}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))) (t_2 (* c (- (* t j) (* z b)))))
   (if (<= c -3.05e+54)
     t_2
     (if (<= c -1.2e-63)
       t_1
       (if (<= c -2e-97)
         t_2
         (if (<= c -3.1e-257)
           t_1
           (if (<= c 1.16e+28) (* y (- (* x z) (* i j))) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -3.05e+54) {
		tmp = t_2;
	} else if (c <= -1.2e-63) {
		tmp = t_1;
	} else if (c <= -2e-97) {
		tmp = t_2;
	} else if (c <= -3.1e-257) {
		tmp = t_1;
	} else if (c <= 1.16e+28) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((b * i) - (x * t))
    t_2 = c * ((t * j) - (z * b))
    if (c <= (-3.05d+54)) then
        tmp = t_2
    else if (c <= (-1.2d-63)) then
        tmp = t_1
    else if (c <= (-2d-97)) then
        tmp = t_2
    else if (c <= (-3.1d-257)) then
        tmp = t_1
    else if (c <= 1.16d+28) then
        tmp = y * ((x * z) - (i * j))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -3.05e+54) {
		tmp = t_2;
	} else if (c <= -1.2e-63) {
		tmp = t_1;
	} else if (c <= -2e-97) {
		tmp = t_2;
	} else if (c <= -3.1e-257) {
		tmp = t_1;
	} else if (c <= 1.16e+28) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	t_2 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -3.05e+54:
		tmp = t_2
	elif c <= -1.2e-63:
		tmp = t_1
	elif c <= -2e-97:
		tmp = t_2
	elif c <= -3.1e-257:
		tmp = t_1
	elif c <= 1.16e+28:
		tmp = y * ((x * z) - (i * j))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -3.05e+54)
		tmp = t_2;
	elseif (c <= -1.2e-63)
		tmp = t_1;
	elseif (c <= -2e-97)
		tmp = t_2;
	elseif (c <= -3.1e-257)
		tmp = t_1;
	elseif (c <= 1.16e+28)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((b * i) - (x * t));
	t_2 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -3.05e+54)
		tmp = t_2;
	elseif (c <= -1.2e-63)
		tmp = t_1;
	elseif (c <= -2e-97)
		tmp = t_2;
	elseif (c <= -3.1e-257)
		tmp = t_1;
	elseif (c <= 1.16e+28)
		tmp = y * ((x * z) - (i * j));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.05e+54], t$95$2, If[LessEqual[c, -1.2e-63], t$95$1, If[LessEqual[c, -2e-97], t$95$2, If[LessEqual[c, -3.1e-257], t$95$1, If[LessEqual[c, 1.16e+28], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -3.0499999999999999e54 or -1.2e-63 < c < -2.00000000000000007e-97 or 1.16e28 < c

   1. Initial program 60.7%

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

   3. Taylor expanded in c around inf 68.2%

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

   if -3.0499999999999999e54 < c < -1.2e-63 or -2.00000000000000007e-97 < c < -3.10000000000000008e-257

   1. Initial program 70.0%

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

   3. Taylor expanded in a around inf 62.7%

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

      1. distribute-lft-out-- 62.7%

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

      2. *-commutative 62.7%

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

   5. Simplified 62.7%

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

   if -3.10000000000000008e-257 < c < 1.16e28

   1. Initial program 83.0%

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

   3. Taylor expanded in y around inf 56.6%

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

      1. +-commutative 56.6%

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

      2. mul-1-neg 56.6%

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

      3. unsub-neg 56.6%

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

      4. *-commutative 56.6%

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

   5. Simplified 56.6%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.05 \cdot 10^{+54}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -1.2 \cdot 10^{-63}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq -2 \cdot 10^{-97}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -3.1 \cdot 10^{-257}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 1.16 \cdot 10^{+28}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 28.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ \mathbf{if}\;b \leq -4.2 \cdot 10^{+187}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{-265}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{+112}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{+145}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j))))
   (if (<= b -4.2e+187)
     (* a (* b i))
     (if (<= b -3.6e-265)
       (* x (* y z))
       (if (<= b 6e-31)
         t_1
         (if (<= b 2.2e+112)
           (* a (* t (- x)))
           (if (<= b 8.2e+145) t_1 (* i (* a b)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double tmp;
	if (b <= -4.2e+187) {
		tmp = a * (b * i);
	} else if (b <= -3.6e-265) {
		tmp = x * (y * z);
	} else if (b <= 6e-31) {
		tmp = t_1;
	} else if (b <= 2.2e+112) {
		tmp = a * (t * -x);
	} else if (b <= 8.2e+145) {
		tmp = t_1;
	} else {
		tmp = i * (a * 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) :: t_1
    real(8) :: tmp
    t_1 = c * (t * j)
    if (b <= (-4.2d+187)) then
        tmp = a * (b * i)
    else if (b <= (-3.6d-265)) then
        tmp = x * (y * z)
    else if (b <= 6d-31) then
        tmp = t_1
    else if (b <= 2.2d+112) then
        tmp = a * (t * -x)
    else if (b <= 8.2d+145) then
        tmp = t_1
    else
        tmp = i * (a * 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 t_1 = c * (t * j);
	double tmp;
	if (b <= -4.2e+187) {
		tmp = a * (b * i);
	} else if (b <= -3.6e-265) {
		tmp = x * (y * z);
	} else if (b <= 6e-31) {
		tmp = t_1;
	} else if (b <= 2.2e+112) {
		tmp = a * (t * -x);
	} else if (b <= 8.2e+145) {
		tmp = t_1;
	} else {
		tmp = i * (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (t * j)
	tmp = 0
	if b <= -4.2e+187:
		tmp = a * (b * i)
	elif b <= -3.6e-265:
		tmp = x * (y * z)
	elif b <= 6e-31:
		tmp = t_1
	elif b <= 2.2e+112:
		tmp = a * (t * -x)
	elif b <= 8.2e+145:
		tmp = t_1
	else:
		tmp = i * (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(t * j))
	tmp = 0.0
	if (b <= -4.2e+187)
		tmp = Float64(a * Float64(b * i));
	elseif (b <= -3.6e-265)
		tmp = Float64(x * Float64(y * z));
	elseif (b <= 6e-31)
		tmp = t_1;
	elseif (b <= 2.2e+112)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (b <= 8.2e+145)
		tmp = t_1;
	else
		tmp = Float64(i * Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (t * j);
	tmp = 0.0;
	if (b <= -4.2e+187)
		tmp = a * (b * i);
	elseif (b <= -3.6e-265)
		tmp = x * (y * z);
	elseif (b <= 6e-31)
		tmp = t_1;
	elseif (b <= 2.2e+112)
		tmp = a * (t * -x);
	elseif (b <= 8.2e+145)
		tmp = t_1;
	else
		tmp = i * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.2e+187], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.6e-265], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6e-31], t$95$1, If[LessEqual[b, 2.2e+112], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.2e+145], t$95$1, N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -4.2e187

   1. Initial program 72.1%

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

   3. Taylor expanded in b around inf 78.3%

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

      1. *-commutative 78.3%

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

   5. Simplified 78.3%

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

   6. Taylor expanded in i around inf 43.5%

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

   if -4.2e187 < b < -3.6000000000000002e-265

   1. Initial program 69.3%

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

   3. Taylor expanded in x around inf 41.1%

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

      1. *-commutative 41.1%

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

   5. Simplified 41.1%

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

   6. Taylor expanded in y around inf 31.2%

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

   if -3.6000000000000002e-265 < b < 5.99999999999999962e-31 or 2.1999999999999999e112 < b < 8.2000000000000003e145

   1. Initial program 66.0%

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

   3. Taylor expanded in b around 0 71.5%

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

   4. Taylor expanded in c around inf 42.5%

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

   if 5.99999999999999962e-31 < b < 2.1999999999999999e112

   1. Initial program 76.2%

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

   3. Taylor expanded in x around inf 48.9%

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

      1. *-commutative 48.9%

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

   5. Simplified 48.9%

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

   6. Taylor expanded in y around 0 33.8%

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

      1. mul-1-neg 33.8%

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

   8. Simplified 33.8%

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

   if 8.2000000000000003e145 < b

   1. Initial program 74.0%

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

   3. Taylor expanded in j around 0 77.8%

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

      1. *-commutative 77.8%

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

      2. *-commutative 77.8%

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

   5. Simplified 77.8%

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

   6. Taylor expanded in i around inf 45.9%

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

      1. *-commutative 45.9%

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

      2. *-commutative 45.9%

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

      3. associate-*l* 56.7%

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

   8. Simplified 56.7%

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

4. Final simplification 39.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{+187}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{-265}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-31}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{+112}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{+145}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 37.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;i \leq -1.05 \cdot 10^{+220}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;i \leq -3.8 \cdot 10^{-112}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -2.3 \cdot 10^{-297}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;i \leq 1.42 \cdot 10^{+165}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(j \cdot \left(-i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= i -1.05e+220)
     (* i (* j (- y)))
     (if (<= i -3.8e-112)
       t_1
       (if (<= i -2.3e-297)
         (* x (* t (- a)))
         (if (<= i 1.42e+165) t_1 (* y (* j (- 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 = b * ((a * i) - (z * c));
	double tmp;
	if (i <= -1.05e+220) {
		tmp = i * (j * -y);
	} else if (i <= -3.8e-112) {
		tmp = t_1;
	} else if (i <= -2.3e-297) {
		tmp = x * (t * -a);
	} else if (i <= 1.42e+165) {
		tmp = t_1;
	} else {
		tmp = y * (j * -i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    if (i <= (-1.05d+220)) then
        tmp = i * (j * -y)
    else if (i <= (-3.8d-112)) then
        tmp = t_1
    else if (i <= (-2.3d-297)) then
        tmp = x * (t * -a)
    else if (i <= 1.42d+165) then
        tmp = t_1
    else
        tmp = y * (j * -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 = b * ((a * i) - (z * c));
	double tmp;
	if (i <= -1.05e+220) {
		tmp = i * (j * -y);
	} else if (i <= -3.8e-112) {
		tmp = t_1;
	} else if (i <= -2.3e-297) {
		tmp = x * (t * -a);
	} else if (i <= 1.42e+165) {
		tmp = t_1;
	} else {
		tmp = y * (j * -i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	tmp = 0
	if i <= -1.05e+220:
		tmp = i * (j * -y)
	elif i <= -3.8e-112:
		tmp = t_1
	elif i <= -2.3e-297:
		tmp = x * (t * -a)
	elif i <= 1.42e+165:
		tmp = t_1
	else:
		tmp = y * (j * -i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (i <= -1.05e+220)
		tmp = Float64(i * Float64(j * Float64(-y)));
	elseif (i <= -3.8e-112)
		tmp = t_1;
	elseif (i <= -2.3e-297)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (i <= 1.42e+165)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(j * Float64(-i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (i <= -1.05e+220)
		tmp = i * (j * -y);
	elseif (i <= -3.8e-112)
		tmp = t_1;
	elseif (i <= -2.3e-297)
		tmp = x * (t * -a);
	elseif (i <= 1.42e+165)
		tmp = t_1;
	else
		tmp = y * (j * -i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.05e+220], N[(i * N[(j * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -3.8e-112], t$95$1, If[LessEqual[i, -2.3e-297], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.42e+165], t$95$1, N[(y * N[(j * (-i)), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -1.05000000000000003e220

   1. Initial program 47.1%

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

   3. Taylor expanded in c around 0 53.8%

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

      1. +-commutative 53.8%

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

      2. *-commutative 53.8%

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

      3. associate-*r* 61.5%

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

      4. associate-*r* 61.5%

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

      5. *-commutative 61.5%

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

      6. associate-*r* 47.1%

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

      7. neg-mul-1 47.1%

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

      8. distribute-lft-neg-in 47.1%

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

      9. distribute-rgt-in 47.1%

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

      10. sub-neg 47.1%

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

      11. fma-neg 47.1%

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

      12. *-commutative 47.1%

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

      13. distribute-rgt-neg-in 47.1%

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

   5. Simplified 47.1%

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

   6. Taylor expanded in y around inf 77.0%

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

      1. +-commutative 77.0%

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

      2. mul-1-neg 77.0%

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

      3. *-commutative 77.0%

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

      4. unsub-neg 77.0%

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

      5. *-commutative 77.0%

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

   8. Simplified 77.0%

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

   9. Taylor expanded in z around 0 77.0%

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

       1. associate-*r* 77.0%

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

       2. neg-mul-1 77.0%

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

   11. Simplified 77.0%

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

   if -1.05000000000000003e220 < i < -3.79999999999999995e-112 or -2.2999999999999999e-297 < i < 1.42e165

   1. Initial program 71.7%

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

   3. Taylor expanded in b around inf 47.9%

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

      1. *-commutative 47.9%

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

   5. Simplified 47.9%

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

   if -3.79999999999999995e-112 < i < -2.2999999999999999e-297

   1. Initial program 82.0%

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

   3. Taylor expanded in x around inf 65.2%

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

      1. *-commutative 65.2%

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

   5. Simplified 65.2%

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

   6. Taylor expanded in y around 0 50.1%

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

      1. mul-1-neg 50.1%

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

      2. distribute-lft-neg-out 50.1%

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

      3. *-commutative 50.1%

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

   8. Simplified 50.1%

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

   if 1.42e165 < i

   1. Initial program 54.9%

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

   3. Taylor expanded in i around inf 64.0%

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

      1. distribute-lft-out-- 64.0%

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

      2. *-commutative 64.0%

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

   5. Simplified 64.0%

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

   6. Taylor expanded in j around inf 52.2%

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

      1. neg-mul-1 52.2%

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

      2. *-commutative 52.2%

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

      3. *-commutative 52.2%

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

      4. associate-*r* 57.5%

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

      5. *-commutative 57.5%

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

      6. distribute-rgt-neg-out 57.5%

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

      7. *-commutative 57.5%

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

      8. distribute-rgt-neg-in 57.5%

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

   8. Simplified 57.5%

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

4. Final simplification 51.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.05 \cdot 10^{+220}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;i \leq -3.8 \cdot 10^{-112}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq -2.3 \cdot 10^{-297}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;i \leq 1.42 \cdot 10^{+165}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(j \cdot \left(-i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 50.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_2 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -1.32 \cdot 10^{-11}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -1.3 \cdot 10^{-146}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -4.9 \cdot 10^{-297}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;i \leq 1.4 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))) (t_2 (* i (- (* a b) (* y j)))))
   (if (<= i -1.32e-11)
     t_2
     (if (<= i -1.3e-146)
       t_1
       (if (<= i -4.9e-297) (* x (* t (- a))) (if (<= i 1.4e+14) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double t_2 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -1.32e-11) {
		tmp = t_2;
	} else if (i <= -1.3e-146) {
		tmp = t_1;
	} else if (i <= -4.9e-297) {
		tmp = x * (t * -a);
	} else if (i <= 1.4e+14) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * ((t * j) - (z * b))
    t_2 = i * ((a * b) - (y * j))
    if (i <= (-1.32d-11)) then
        tmp = t_2
    else if (i <= (-1.3d-146)) then
        tmp = t_1
    else if (i <= (-4.9d-297)) then
        tmp = x * (t * -a)
    else if (i <= 1.4d+14) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double t_2 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -1.32e-11) {
		tmp = t_2;
	} else if (i <= -1.3e-146) {
		tmp = t_1;
	} else if (i <= -4.9e-297) {
		tmp = x * (t * -a);
	} else if (i <= 1.4e+14) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	t_2 = i * ((a * b) - (y * j))
	tmp = 0
	if i <= -1.32e-11:
		tmp = t_2
	elif i <= -1.3e-146:
		tmp = t_1
	elif i <= -4.9e-297:
		tmp = x * (t * -a)
	elif i <= 1.4e+14:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	t_2 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -1.32e-11)
		tmp = t_2;
	elseif (i <= -1.3e-146)
		tmp = t_1;
	elseif (i <= -4.9e-297)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (i <= 1.4e+14)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((t * j) - (z * b));
	t_2 = i * ((a * b) - (y * j));
	tmp = 0.0;
	if (i <= -1.32e-11)
		tmp = t_2;
	elseif (i <= -1.3e-146)
		tmp = t_1;
	elseif (i <= -4.9e-297)
		tmp = x * (t * -a);
	elseif (i <= 1.4e+14)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.32e-11], t$95$2, If[LessEqual[i, -1.3e-146], t$95$1, If[LessEqual[i, -4.9e-297], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.4e+14], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -1.32e-11 or 1.4e14 < i

   1. Initial program 60.8%

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

   3. Taylor expanded in i around inf 64.3%

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

      1. distribute-lft-out-- 64.3%

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

      2. *-commutative 64.3%

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

   5. Simplified 64.3%

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

   6. Taylor expanded in i around 0 64.3%

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

      1. associate-*r* 64.3%

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

      2. *-commutative 64.3%

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

      3. sub-neg 64.3%

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

      4. +-commutative 64.3%

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

      5. *-commutative 64.3%

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

      6. +-commutative 64.3%

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

      7. sub-neg 64.3%

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

      8. associate-*r* 64.3%

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

      9. neg-mul-1 64.3%

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

      10. neg-sub0 64.3%

          \[\leadsto i \cdot \color{blue}{\left(0 - \left(j \cdot y - b \cdot a\right)\right)} \]

      11. sub-neg 64.3%

          \[\leadsto i \cdot \left(0 - \color{blue}{\left(j \cdot y + \left(-b \cdot a\right)\right)}\right) \]

      12. +-commutative 64.3%

          \[\leadsto i \cdot \left(0 - \color{blue}{\left(\left(-b \cdot a\right) + j \cdot y\right)}\right) \]

      13. associate--r+ 64.3%

          \[\leadsto i \cdot \color{blue}{\left(\left(0 - \left(-b \cdot a\right)\right) - j \cdot y\right)} \]

      14. neg-sub0 64.3%

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

      15. remove-double-neg 64.3%

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

      16. *-commutative 64.3%

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

      17. *-commutative 64.3%

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

   8. Simplified 64.3%

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

   if -1.32e-11 < i < -1.29999999999999993e-146 or -4.89999999999999997e-297 < i < 1.4e14

   1. Initial program 74.9%

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

   3. Taylor expanded in c around inf 56.0%

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

   if -1.29999999999999993e-146 < i < -4.89999999999999997e-297

   1. Initial program 84.7%

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

   3. Taylor expanded in x around inf 70.6%

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

      1. *-commutative 70.6%

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

   5. Simplified 70.6%

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

   6. Taylor expanded in y around 0 56.1%

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

      1. mul-1-neg 56.1%

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

      2. distribute-lft-neg-out 56.1%

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

      3. *-commutative 56.1%

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

   8. Simplified 56.1%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.32 \cdot 10^{-11}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -1.3 \cdot 10^{-146}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq -4.9 \cdot 10^{-297}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;i \leq 1.4 \cdot 10^{+14}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 28.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.95 \cdot 10^{+187}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq -8.8 \cdot 10^{-265}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-25}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+116}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -2.95e+187)
   (* a (* b i))
   (if (<= b -8.8e-265)
     (* x (* y z))
     (if (<= b 2e-25)
       (* c (* t j))
       (if (<= b 8.5e+116) (* t (* x (- a))) (* i (* a b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -2.95e+187) {
		tmp = a * (b * i);
	} else if (b <= -8.8e-265) {
		tmp = x * (y * z);
	} else if (b <= 2e-25) {
		tmp = c * (t * j);
	} else if (b <= 8.5e+116) {
		tmp = t * (x * -a);
	} else {
		tmp = i * (a * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-2.95d+187)) then
        tmp = a * (b * i)
    else if (b <= (-8.8d-265)) then
        tmp = x * (y * z)
    else if (b <= 2d-25) then
        tmp = c * (t * j)
    else if (b <= 8.5d+116) then
        tmp = t * (x * -a)
    else
        tmp = i * (a * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -2.95e+187) {
		tmp = a * (b * i);
	} else if (b <= -8.8e-265) {
		tmp = x * (y * z);
	} else if (b <= 2e-25) {
		tmp = c * (t * j);
	} else if (b <= 8.5e+116) {
		tmp = t * (x * -a);
	} else {
		tmp = i * (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -2.95e+187:
		tmp = a * (b * i)
	elif b <= -8.8e-265:
		tmp = x * (y * z)
	elif b <= 2e-25:
		tmp = c * (t * j)
	elif b <= 8.5e+116:
		tmp = t * (x * -a)
	else:
		tmp = i * (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -2.95e+187)
		tmp = Float64(a * Float64(b * i));
	elseif (b <= -8.8e-265)
		tmp = Float64(x * Float64(y * z));
	elseif (b <= 2e-25)
		tmp = Float64(c * Float64(t * j));
	elseif (b <= 8.5e+116)
		tmp = Float64(t * Float64(x * Float64(-a)));
	else
		tmp = Float64(i * Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -2.95e+187)
		tmp = a * (b * i);
	elseif (b <= -8.8e-265)
		tmp = x * (y * z);
	elseif (b <= 2e-25)
		tmp = c * (t * j);
	elseif (b <= 8.5e+116)
		tmp = t * (x * -a);
	else
		tmp = i * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -2.95e+187], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -8.8e-265], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2e-25], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.5e+116], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -2.95e187

   1. Initial program 72.1%

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

   3. Taylor expanded in b around inf 78.3%

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

      1. *-commutative 78.3%

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

   5. Simplified 78.3%

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

   6. Taylor expanded in i around inf 43.5%

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

   if -2.95e187 < b < -8.80000000000000042e-265

   1. Initial program 69.3%

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

   3. Taylor expanded in x around inf 41.1%

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

      1. *-commutative 41.1%

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

   5. Simplified 41.1%

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

   6. Taylor expanded in y around inf 31.2%

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

   if -8.80000000000000042e-265 < b < 2.00000000000000008e-25

   1. Initial program 68.6%

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

   3. Taylor expanded in b around 0 74.9%

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

   4. Taylor expanded in c around inf 42.7%

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

   if 2.00000000000000008e-25 < b < 8.5000000000000002e116

   1. Initial program 74.2%

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

   3. Taylor expanded in x around inf 49.0%

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

      1. *-commutative 49.0%

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

   5. Simplified 49.0%

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

   6. Taylor expanded in y around 0 35.0%

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

      1. mul-1-neg 35.0%

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

      2. associate-*r* 38.1%

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

      3. *-commutative 38.1%

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

      4. associate-*r* 41.7%

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

      5. distribute-rgt-neg-out 41.7%

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

      6. *-commutative 41.7%

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

      7. distribute-rgt-neg-in 41.7%

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

   8. Simplified 41.7%

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

   if 8.5000000000000002e116 < b

   1. Initial program 68.5%

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

   3. Taylor expanded in j around 0 65.8%

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

      1. *-commutative 65.8%

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

      2. *-commutative 65.8%

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

   5. Simplified 65.8%

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

   6. Taylor expanded in i around inf 38.4%

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

      1. *-commutative 38.4%

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

      2. *-commutative 38.4%

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

      3. associate-*l* 46.7%

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

   8. Simplified 46.7%

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

4. Final simplification 38.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.95 \cdot 10^{+187}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq -8.8 \cdot 10^{-265}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-25}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+116}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 28.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{+187}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq -4.8 \cdot 10^{-265}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{+146}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -3e+187)
   (* a (* b i))
   (if (<= b -4.8e-265)
     (* x (* y z))
     (if (<= b 2.2e+146) (* c (* t j)) (* i (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -3e+187) {
		tmp = a * (b * i);
	} else if (b <= -4.8e-265) {
		tmp = x * (y * z);
	} else if (b <= 2.2e+146) {
		tmp = c * (t * j);
	} else {
		tmp = i * (a * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-3d+187)) then
        tmp = a * (b * i)
    else if (b <= (-4.8d-265)) then
        tmp = x * (y * z)
    else if (b <= 2.2d+146) then
        tmp = c * (t * j)
    else
        tmp = i * (a * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -3e+187) {
		tmp = a * (b * i);
	} else if (b <= -4.8e-265) {
		tmp = x * (y * z);
	} else if (b <= 2.2e+146) {
		tmp = c * (t * j);
	} else {
		tmp = i * (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -3e+187:
		tmp = a * (b * i)
	elif b <= -4.8e-265:
		tmp = x * (y * z)
	elif b <= 2.2e+146:
		tmp = c * (t * j)
	else:
		tmp = i * (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -3e+187)
		tmp = Float64(a * Float64(b * i));
	elseif (b <= -4.8e-265)
		tmp = Float64(x * Float64(y * z));
	elseif (b <= 2.2e+146)
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(i * Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -3e+187)
		tmp = a * (b * i);
	elseif (b <= -4.8e-265)
		tmp = x * (y * z);
	elseif (b <= 2.2e+146)
		tmp = c * (t * j);
	else
		tmp = i * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -3e+187], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.8e-265], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.2e+146], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.9999999999999999e187

   1. Initial program 72.1%

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

   3. Taylor expanded in b around inf 78.3%

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

      1. *-commutative 78.3%

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

   5. Simplified 78.3%

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

   6. Taylor expanded in i around inf 43.5%

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

   if -2.9999999999999999e187 < b < -4.7999999999999999e-265

   1. Initial program 69.3%

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

   3. Taylor expanded in x around inf 41.1%

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

      1. *-commutative 41.1%

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

   5. Simplified 41.1%

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

   6. Taylor expanded in y around inf 31.2%

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

   if -4.7999999999999999e-265 < b < 2.1999999999999998e146

   1. Initial program 68.6%

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

   3. Taylor expanded in b around 0 67.8%

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

   4. Taylor expanded in c around inf 35.2%

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

   if 2.1999999999999998e146 < b

   1. Initial program 74.0%

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

   3. Taylor expanded in j around 0 77.8%

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

      1. *-commutative 77.8%

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

      2. *-commutative 77.8%

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

   5. Simplified 77.8%

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

   6. Taylor expanded in i around inf 45.9%

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

      1. *-commutative 45.9%

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

      2. *-commutative 45.9%

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

      3. associate-*l* 56.7%

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

   8. Simplified 56.7%

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

4. Final simplification 37.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{+187}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq -4.8 \cdot 10^{-265}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{+146}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 28.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -5.5 \cdot 10^{+98} \lor \neg \left(c \leq 650000000000\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -5.5e+98) (not (<= c 650000000000.0)))
   (* c (* t j))
   (* a (* b i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -5.5e+98) || !(c <= 650000000000.0)) {
		tmp = c * (t * j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((c <= (-5.5d+98)) .or. (.not. (c <= 650000000000.0d0))) then
        tmp = c * (t * j)
    else
        tmp = a * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -5.5e+98) || !(c <= 650000000000.0)) {
		tmp = c * (t * j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -5.5e+98) or not (c <= 650000000000.0):
		tmp = c * (t * j)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -5.5e+98) || !(c <= 650000000000.0))
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -5.5e+98) || ~((c <= 650000000000.0)))
		tmp = c * (t * j);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -5.5e+98], N[Not[LessEqual[c, 650000000000.0]], $MachinePrecision]], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -5.49999999999999946e98 or 6.5e11 < c

   1. Initial program 58.1%

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

   3. Taylor expanded in b around 0 52.7%

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

   4. Taylor expanded in c around inf 38.1%

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

   if -5.49999999999999946e98 < c < 6.5e11

   1. Initial program 78.3%

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

   3. Taylor expanded in b around inf 40.0%

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

      1. *-commutative 40.0%

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

   5. Simplified 40.0%

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

   6. Taylor expanded in i around inf 26.6%

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

4. Final simplification 31.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.5 \cdot 10^{+98} \lor \neg \left(c \leq 650000000000\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 28.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.16 \cdot 10^{+100} \lor \neg \left(c \leq 12200000000000\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -1.16e+100) (not (<= c 12200000000000.0)))
   (* c (* t j))
   (* i (* a 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 ((c <= -1.16e+100) || !(c <= 12200000000000.0)) {
		tmp = c * (t * j);
	} else {
		tmp = i * (a * 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 ((c <= (-1.16d+100)) .or. (.not. (c <= 12200000000000.0d0))) then
        tmp = c * (t * j)
    else
        tmp = i * (a * 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 ((c <= -1.16e+100) || !(c <= 12200000000000.0)) {
		tmp = c * (t * j);
	} else {
		tmp = i * (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -1.16e+100) or not (c <= 12200000000000.0):
		tmp = c * (t * j)
	else:
		tmp = i * (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -1.16e+100) || !(c <= 12200000000000.0))
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(i * Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -1.16e+100) || ~((c <= 12200000000000.0)))
		tmp = c * (t * j);
	else
		tmp = i * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -1.16e+100], N[Not[LessEqual[c, 12200000000000.0]], $MachinePrecision]], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.1600000000000001e100 or 1.22e13 < c

   1. Initial program 58.1%

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

   3. Taylor expanded in b around 0 52.7%

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

   4. Taylor expanded in c around inf 38.1%

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

   if -1.1600000000000001e100 < c < 1.22e13

   1. Initial program 78.3%

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

   3. Taylor expanded in j around 0 61.4%

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

      1. *-commutative 61.4%

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

      2. *-commutative 61.4%

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

   5. Simplified 61.4%

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

   6. Taylor expanded in i around inf 26.6%

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

      1. *-commutative 26.6%

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

      2. *-commutative 26.6%

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

      3. associate-*l* 27.3%

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

   8. Simplified 27.3%

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

4. Final simplification 31.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.16 \cdot 10^{+100} \lor \neg \left(c \leq 12200000000000\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 29.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -9.6 \cdot 10^{+98}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq 26500000000000:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -9.6e+98)
   (* t (* c j))
   (if (<= c 26500000000000.0) (* i (* a b)) (* c (* t j)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -9.6e+98) {
		tmp = t * (c * j);
	} else if (c <= 26500000000000.0) {
		tmp = i * (a * b);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (c <= (-9.6d+98)) then
        tmp = t * (c * j)
    else if (c <= 26500000000000.0d0) then
        tmp = i * (a * b)
    else
        tmp = c * (t * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -9.6e+98) {
		tmp = t * (c * j);
	} else if (c <= 26500000000000.0) {
		tmp = i * (a * b);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -9.6e+98:
		tmp = t * (c * j)
	elif c <= 26500000000000.0:
		tmp = i * (a * b)
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -9.6e+98)
		tmp = Float64(t * Float64(c * j));
	elseif (c <= 26500000000000.0)
		tmp = Float64(i * Float64(a * b));
	else
		tmp = Float64(c * Float64(t * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -9.6e+98)
		tmp = t * (c * j);
	elseif (c <= 26500000000000.0)
		tmp = i * (a * b);
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -9.6e+98], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 26500000000000.0], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -9.5999999999999995e98

   1. Initial program 51.8%

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

   3. Taylor expanded in t around inf 61.0%

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

      1. +-commutative 61.0%

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

      2. mul-1-neg 61.0%

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

      3. unsub-neg 61.0%

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

      4. *-commutative 61.0%

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

   5. Simplified 61.0%

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

   6. Taylor expanded in j around inf 46.5%

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

      1. *-commutative 46.5%

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

   8. Simplified 46.5%

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

   if -9.5999999999999995e98 < c < 2.65e13

   1. Initial program 78.3%

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

   3. Taylor expanded in j around 0 61.4%

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

      1. *-commutative 61.4%

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

      2. *-commutative 61.4%

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

   5. Simplified 61.4%

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

   6. Taylor expanded in i around inf 26.6%

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

      1. *-commutative 26.6%

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

      2. *-commutative 26.6%

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

      3. associate-*l* 27.3%

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

   8. Simplified 27.3%

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

   if 2.65e13 < c

   1. Initial program 64.5%

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

   3. Taylor expanded in b around 0 53.5%

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

   4. Taylor expanded in c around inf 31.5%

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

4. Final simplification 32.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -9.6 \cdot 10^{+98}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq 26500000000000:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 21.9% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(b \cdot i\right) \end{array} \]

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 69.9%

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

3. Taylor expanded in b around inf 39.7%

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

   1. *-commutative 39.7%

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

5. Simplified 39.7%

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

6. Taylor expanded in i around inf 19.5%

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

7. Final simplification 19.5%

   \[\leadsto a \cdot \left(b \cdot i\right) \]
8. Add Preprocessing

Developer target: 68.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ t_2 := x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{if}\;t < -8.120978919195912 \cdot 10^{-33}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < -4.712553818218485 \cdot 10^{-169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t < -7.633533346031584 \cdot 10^{-308}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 1.0535888557455487 \cdot 10^{-139}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
          (/
           (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0)))
           (+ (* c t) (* i y)))))
        (t_2
         (-
          (* x (- (* z y) (* a t)))
          (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))
   (if (< t -8.120978919195912e-33)
     t_2
     (if (< t -4.712553818218485e-169)
       t_1
       (if (< t -7.633533346031584e-308)
         t_2
         (if (< t 1.0535888557455487e-139) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (pow((c * t), 2.0) - pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ** 2.0d0) - ((i * y) ** 2.0d0))) / ((c * t) + (i * y)))
    t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
    if (t < (-8.120978919195912d-33)) then
        tmp = t_2
    else if (t < (-4.712553818218485d-169)) then
        tmp = t_1
    else if (t < (-7.633533346031584d-308)) then
        tmp = t_2
    else if (t < 1.0535888557455487d-139) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (Math.pow((c * t), 2.0) - Math.pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (math.pow((c * t), 2.0) - math.pow((i * y), 2.0))) / ((c * t) + (i * y)))
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
	tmp = 0
	if t < -8.120978919195912e-33:
		tmp = t_2
	elif t < -4.712553818218485e-169:
		tmp = t_1
	elif t < -7.633533346031584e-308:
		tmp = t_2
	elif t < 1.0535888557455487e-139:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(Float64(j * Float64((Float64(c * t) ^ 2.0) - (Float64(i * y) ^ 2.0))) / Float64(Float64(c * t) + Float64(i * y))))
	t_2 = Float64(Float64(x * Float64(Float64(z * y) - Float64(a * t))) - Float64(Float64(b * Float64(Float64(z * c) - Float64(a * i))) - Float64(Float64(Float64(c * t) - Float64(y * i)) * j)))
	tmp = 0.0
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ^ 2.0) - ((i * y) ^ 2.0))) / ((c * t) + (i * y)));
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	tmp = 0.0;
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[Power[N[(c * t), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(i * y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * t), $MachinePrecision] + N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(c * t), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -8.120978919195912e-33], t$95$2, If[Less[t, -4.712553818218485e-169], t$95$1, If[Less[t, -7.633533346031584e-308], t$95$2, If[Less[t, 1.0535888557455487e-139], t$95$1, t$95$2]]]]]]

Reproduce

herbie shell --seed 2024034 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< t -8.120978919195912e-33) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -4.712553818218485e-169) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (if (< t -7.633533346031584e-308) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 1.0535888557455487e-139) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))