Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 74.4% → 82.4%

Time: 27.0s

Alternatives: 24

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: 74.4% 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: 82.4% accurate, 0.1× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (((t_1 - (x * ((t * a) - (y * z)))) - (j * ((y * i) - (t * c)))) <= ((double) INFINITY)) {
		tmp = fma(j, ((t * c) - (y * i)), ((x * fma(y, z, (t * -a))) + t_1));
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	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 (Float64(Float64(t_1 - Float64(x * Float64(Float64(t * a) - Float64(y * z)))) - Float64(j * Float64(Float64(y * i) - Float64(t * c)))) <= Inf)
		tmp = fma(j, Float64(Float64(t * c) - Float64(y * i)), Float64(Float64(x * fma(y, z, Float64(t * Float64(-a)))) + t_1));
	else
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	end
	return 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[N[(N[(t$95$1 - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(y * i), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[(y * z + N[(t * (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 93.3%

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

      1. +-commutative 93.3%

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

      2. fma-define 93.3%

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

      3. *-commutative 93.3%

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

      4. *-commutative 93.3%

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

      5. cancel-sign-sub-inv 93.3%

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

      6. cancel-sign-sub 93.3%

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

      7. sub-neg 93.3%

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

      8. sub-neg 93.3%

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

      9. *-commutative 93.3%

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

      10. fma-neg 93.3%

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

      11. *-commutative 93.3%

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

      12. distribute-rgt-neg-out 93.3%

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

      13. remove-double-neg 93.3%

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

      14. *-commutative 93.3%

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

      15. *-commutative 93.3%

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

   3. Simplified 93.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   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 z around inf 60.7%

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

      1. *-commutative 60.7%

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

   5. Simplified 60.7%

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

4. Final simplification 86.5%

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

Alternative 2: 82.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 93.3%

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

   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 z around inf 60.7%

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

      1. *-commutative 60.7%

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

   5. Simplified 60.7%

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

4. Final simplification 86.5%

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

Alternative 3: 69.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(y \cdot i - t \cdot c\right)\\ t_3 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_4 := t\_3 - t\_2\\ \mathbf{if}\;b \leq -3 \cdot 10^{+187}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -9.2 \cdot 10^{-37}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{-72}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + t\_1\\ \mathbf{elif}\;b \leq 245000:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - t\_2\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{+48}:\\ \;\;\;\;j \cdot \left(t \cdot \left(c - i \cdot \frac{y}{t}\right)\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (* j (- (* y i) (* t c))))
        (t_3 (* b (- (* a i) (* z c))))
        (t_4 (- t_3 t_2)))
   (if (<= b -3e+187)
     t_3
     (if (<= b -9.2e-37)
       t_4
       (if (<= b 1.02e-72)
         (+ (* j (- (* t c) (* y i))) t_1)
         (if (<= b 245000.0)
           (- (* z (- (* x y) (* b c))) t_2)
           (if (<= b 9.2e+48)
             (+ (* j (* t (- c (* i (/ y t))))) t_1)
             t_4)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = j * ((y * i) - (t * c));
	double t_3 = b * ((a * i) - (z * c));
	double t_4 = t_3 - t_2;
	double tmp;
	if (b <= -3e+187) {
		tmp = t_3;
	} else if (b <= -9.2e-37) {
		tmp = t_4;
	} else if (b <= 1.02e-72) {
		tmp = (j * ((t * c) - (y * i))) + t_1;
	} else if (b <= 245000.0) {
		tmp = (z * ((x * y) - (b * c))) - t_2;
	} else if (b <= 9.2e+48) {
		tmp = (j * (t * (c - (i * (y / t))))) + t_1;
	} else {
		tmp = t_4;
	}
	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 * a))
    t_2 = j * ((y * i) - (t * c))
    t_3 = b * ((a * i) - (z * c))
    t_4 = t_3 - t_2
    if (b <= (-3d+187)) then
        tmp = t_3
    else if (b <= (-9.2d-37)) then
        tmp = t_4
    else if (b <= 1.02d-72) then
        tmp = (j * ((t * c) - (y * i))) + t_1
    else if (b <= 245000.0d0) then
        tmp = (z * ((x * y) - (b * c))) - t_2
    else if (b <= 9.2d+48) then
        tmp = (j * (t * (c - (i * (y / t))))) + t_1
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = j * ((y * i) - (t * c));
	double t_3 = b * ((a * i) - (z * c));
	double t_4 = t_3 - t_2;
	double tmp;
	if (b <= -3e+187) {
		tmp = t_3;
	} else if (b <= -9.2e-37) {
		tmp = t_4;
	} else if (b <= 1.02e-72) {
		tmp = (j * ((t * c) - (y * i))) + t_1;
	} else if (b <= 245000.0) {
		tmp = (z * ((x * y) - (b * c))) - t_2;
	} else if (b <= 9.2e+48) {
		tmp = (j * (t * (c - (i * (y / t))))) + t_1;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = j * ((y * i) - (t * c))
	t_3 = b * ((a * i) - (z * c))
	t_4 = t_3 - t_2
	tmp = 0
	if b <= -3e+187:
		tmp = t_3
	elif b <= -9.2e-37:
		tmp = t_4
	elif b <= 1.02e-72:
		tmp = (j * ((t * c) - (y * i))) + t_1
	elif b <= 245000.0:
		tmp = (z * ((x * y) - (b * c))) - t_2
	elif b <= 9.2e+48:
		tmp = (j * (t * (c - (i * (y / t))))) + t_1
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(j * Float64(Float64(y * i) - Float64(t * c)))
	t_3 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_4 = Float64(t_3 - t_2)
	tmp = 0.0
	if (b <= -3e+187)
		tmp = t_3;
	elseif (b <= -9.2e-37)
		tmp = t_4;
	elseif (b <= 1.02e-72)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + t_1);
	elseif (b <= 245000.0)
		tmp = Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) - t_2);
	elseif (b <= 9.2e+48)
		tmp = Float64(Float64(j * Float64(t * Float64(c - Float64(i * Float64(y / t))))) + t_1);
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = j * ((y * i) - (t * c));
	t_3 = b * ((a * i) - (z * c));
	t_4 = t_3 - t_2;
	tmp = 0.0;
	if (b <= -3e+187)
		tmp = t_3;
	elseif (b <= -9.2e-37)
		tmp = t_4;
	elseif (b <= 1.02e-72)
		tmp = (j * ((t * c) - (y * i))) + t_1;
	elseif (b <= 245000.0)
		tmp = (z * ((x * y) - (b * c))) - t_2;
	elseif (b <= 9.2e+48)
		tmp = (j * (t * (c - (i * (y / t))))) + t_1;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(y * i), $MachinePrecision] - N[(t * c), $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, -3e+187], t$95$3, If[LessEqual[b, -9.2e-37], t$95$4, If[LessEqual[b, 1.02e-72], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[b, 245000.0], N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[b, 9.2e+48], N[(N[(j * N[(t * N[(c - N[(i * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], t$95$4]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -2.9999999999999999e187

   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 83.1%

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

   if -2.9999999999999999e187 < b < -9.1999999999999999e-37 or 9.2000000000000001e48 < b

   1. Initial program 77.7%

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

   3. Taylor expanded in x around 0 78.4%

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

   if -9.1999999999999999e-37 < b < 1.02e-72

   1. Initial program 72.6%

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

   3. Taylor expanded in b around 0 79.0%

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

   if 1.02e-72 < b < 245000

   1. Initial program 72.8%

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

   3. Taylor expanded in z around 0 79.8%

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

   4. Taylor expanded in a around 0 93.1%

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

   5. Taylor expanded in a around 0 80.6%

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

   if 245000 < b < 9.2000000000000001e48

   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 70.8%

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

   4. Taylor expanded in t around inf 80.0%

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

      1. mul-1-neg 80.0%

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

      2. unsub-neg 80.0%

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

      3. associate-/l* 80.0%

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

   6. Simplified 80.0%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{+187}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -9.2 \cdot 10^{-37}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{-72}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 245000:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{+48}:\\ \;\;\;\;j \cdot \left(t \cdot \left(c - i \cdot \frac{y}{t}\right)\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(y \cdot i - t \cdot c\right)\\ t_2 := \left(z \cdot \left(x \cdot y - b \cdot c\right) - t\_1\right) + a \cdot \left(b \cdot i\right)\\ t_3 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -4.8 \cdot 10^{+185}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-86}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-74}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+113}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3 - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* y i) (* t c))))
        (t_2 (+ (- (* z (- (* x y) (* b c))) t_1) (* a (* b i))))
        (t_3 (* b (- (* a i) (* z c)))))
   (if (<= b -4.8e+185)
     t_3
     (if (<= b -2e-86)
       t_2
       (if (<= b 3.2e-74)
         (+ (* j (- (* t c) (* y i))) (* x (- (* y z) (* t a))))
         (if (<= b 1.5e+113) t_2 (- t_3 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 * ((y * i) - (t * c));
	double t_2 = ((z * ((x * y) - (b * c))) - t_1) + (a * (b * i));
	double t_3 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -4.8e+185) {
		tmp = t_3;
	} else if (b <= -2e-86) {
		tmp = t_2;
	} else if (b <= 3.2e-74) {
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else if (b <= 1.5e+113) {
		tmp = t_2;
	} else {
		tmp = t_3 - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * ((y * i) - (t * c))
    t_2 = ((z * ((x * y) - (b * c))) - t_1) + (a * (b * i))
    t_3 = b * ((a * i) - (z * c))
    if (b <= (-4.8d+185)) then
        tmp = t_3
    else if (b <= (-2d-86)) then
        tmp = t_2
    else if (b <= 3.2d-74) then
        tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)))
    else if (b <= 1.5d+113) then
        tmp = t_2
    else
        tmp = t_3 - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((y * i) - (t * c));
	double t_2 = ((z * ((x * y) - (b * c))) - t_1) + (a * (b * i));
	double t_3 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -4.8e+185) {
		tmp = t_3;
	} else if (b <= -2e-86) {
		tmp = t_2;
	} else if (b <= 3.2e-74) {
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else if (b <= 1.5e+113) {
		tmp = t_2;
	} else {
		tmp = t_3 - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((y * i) - (t * c))
	t_2 = ((z * ((x * y) - (b * c))) - t_1) + (a * (b * i))
	t_3 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -4.8e+185:
		tmp = t_3
	elif b <= -2e-86:
		tmp = t_2
	elif b <= 3.2e-74:
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)))
	elif b <= 1.5e+113:
		tmp = t_2
	else:
		tmp = t_3 - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(y * i) - Float64(t * c)))
	t_2 = Float64(Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) - t_1) + Float64(a * Float64(b * i)))
	t_3 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -4.8e+185)
		tmp = t_3;
	elseif (b <= -2e-86)
		tmp = t_2;
	elseif (b <= 3.2e-74)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	elseif (b <= 1.5e+113)
		tmp = t_2;
	else
		tmp = Float64(t_3 - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((y * i) - (t * c));
	t_2 = ((z * ((x * y) - (b * c))) - t_1) + (a * (b * i));
	t_3 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -4.8e+185)
		tmp = t_3;
	elseif (b <= -2e-86)
		tmp = t_2;
	elseif (b <= 3.2e-74)
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	elseif (b <= 1.5e+113)
		tmp = t_2;
	else
		tmp = t_3 - 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[(y * i), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] + N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.8e+185], t$95$3, If[LessEqual[b, -2e-86], t$95$2, If[LessEqual[b, 3.2e-74], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.5e+113], t$95$2, N[(t$95$3 - t$95$1), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -4.79999999999999978e185

   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 83.6%

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

   if -4.79999999999999978e185 < b < -2.00000000000000017e-86 or 3.1999999999999999e-74 < b < 1.5e113

   1. Initial program 77.2%

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

   3. Taylor expanded in z around 0 78.5%

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

   4. Taylor expanded in a around 0 75.7%

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

   if -2.00000000000000017e-86 < b < 3.1999999999999999e-74

   1. Initial program 75.1%

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

   3. Taylor expanded in b around 0 82.0%

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

   if 1.5e113 < b

   1. Initial program 65.7%

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

   3. Taylor expanded in x around 0 80.5%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.8 \cdot 10^{+185}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-86}:\\ \;\;\;\;\left(z \cdot \left(x \cdot y - b \cdot c\right) - j \cdot \left(y \cdot i - t \cdot c\right)\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-74}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+113}:\\ \;\;\;\;\left(z \cdot \left(x \cdot y - b \cdot c\right) - j \cdot \left(y \cdot i - t \cdot c\right)\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ t_3 := j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;b \leq -7.8 \cdot 10^{+64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{-81}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-74}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 0.066:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+58}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c))))
        (t_2 (- (* z (- (* x y) (* b c))) (* j (- (* y i) (* t c)))))
        (t_3 (+ (* j (- (* t c) (* y i))) (* x (- (* y z) (* t a))))))
   (if (<= b -7.8e+64)
     t_1
     (if (<= b -8.5e-81)
       t_2
       (if (<= b 9.5e-74)
         t_3
         (if (<= b 0.066) t_2 (if (<= b 9.5e+58) t_3 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 t_2 = (z * ((x * y) - (b * c))) - (j * ((y * i) - (t * c)));
	double t_3 = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	double tmp;
	if (b <= -7.8e+64) {
		tmp = t_1;
	} else if (b <= -8.5e-81) {
		tmp = t_2;
	} else if (b <= 9.5e-74) {
		tmp = t_3;
	} else if (b <= 0.066) {
		tmp = t_2;
	} else if (b <= 9.5e+58) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = (z * ((x * y) - (b * c))) - (j * ((y * i) - (t * c)))
    t_3 = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)))
    if (b <= (-7.8d+64)) then
        tmp = t_1
    else if (b <= (-8.5d-81)) then
        tmp = t_2
    else if (b <= 9.5d-74) then
        tmp = t_3
    else if (b <= 0.066d0) then
        tmp = t_2
    else if (b <= 9.5d+58) then
        tmp = t_3
    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 t_2 = (z * ((x * y) - (b * c))) - (j * ((y * i) - (t * c)));
	double t_3 = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	double tmp;
	if (b <= -7.8e+64) {
		tmp = t_1;
	} else if (b <= -8.5e-81) {
		tmp = t_2;
	} else if (b <= 9.5e-74) {
		tmp = t_3;
	} else if (b <= 0.066) {
		tmp = t_2;
	} else if (b <= 9.5e+58) {
		tmp = t_3;
	} 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))
	t_2 = (z * ((x * y) - (b * c))) - (j * ((y * i) - (t * c)))
	t_3 = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)))
	tmp = 0
	if b <= -7.8e+64:
		tmp = t_1
	elif b <= -8.5e-81:
		tmp = t_2
	elif b <= 9.5e-74:
		tmp = t_3
	elif b <= 0.066:
		tmp = t_2
	elif b <= 9.5e+58:
		tmp = t_3
	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)))
	t_2 = Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) - Float64(j * Float64(Float64(y * i) - Float64(t * c))))
	t_3 = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))))
	tmp = 0.0
	if (b <= -7.8e+64)
		tmp = t_1;
	elseif (b <= -8.5e-81)
		tmp = t_2;
	elseif (b <= 9.5e-74)
		tmp = t_3;
	elseif (b <= 0.066)
		tmp = t_2;
	elseif (b <= 9.5e+58)
		tmp = t_3;
	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));
	t_2 = (z * ((x * y) - (b * c))) - (j * ((y * i) - (t * c)));
	t_3 = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	tmp = 0.0;
	if (b <= -7.8e+64)
		tmp = t_1;
	elseif (b <= -8.5e-81)
		tmp = t_2;
	elseif (b <= 9.5e-74)
		tmp = t_3;
	elseif (b <= 0.066)
		tmp = t_2;
	elseif (b <= 9.5e+58)
		tmp = t_3;
	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]}, Block[{t$95$2 = N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(y * i), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.8e+64], t$95$1, If[LessEqual[b, -8.5e-81], t$95$2, If[LessEqual[b, 9.5e-74], t$95$3, If[LessEqual[b, 0.066], t$95$2, If[LessEqual[b, 9.5e+58], t$95$3, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.7999999999999996e64 or 9.5000000000000002e58 < b

   1. Initial program 71.9%

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

   3. Taylor expanded in b around inf 73.6%

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

   if -7.7999999999999996e64 < b < -8.5000000000000001e-81 or 9.5000000000000007e-74 < b < 0.066000000000000003

   1. Initial program 75.4%

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

   3. Taylor expanded in z around 0 79.4%

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

   4. Taylor expanded in a around 0 81.8%

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

   5. Taylor expanded in a around 0 72.0%

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

   if -8.5000000000000001e-81 < b < 9.5000000000000007e-74 or 0.066000000000000003 < b < 9.5000000000000002e58

   1. Initial program 75.1%

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

   3. Taylor expanded in b around 0 81.3%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.8 \cdot 10^{+64}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{-81}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-74}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 0.066:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+58}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 69.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(y \cdot i - t \cdot c\right)\\ t_3 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_4 := t\_3 - t\_2\\ \mathbf{if}\;b \leq -8 \cdot 10^{+188}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -1.25 \cdot 10^{-36}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 50000:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - t\_2\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{+55}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* j (- (* t c) (* y i))) (* x (- (* y z) (* t a)))))
        (t_2 (* j (- (* y i) (* t c))))
        (t_3 (* b (- (* a i) (* z c))))
        (t_4 (- t_3 t_2)))
   (if (<= b -8e+188)
     t_3
     (if (<= b -1.25e-36)
       t_4
       (if (<= b 1.2e-72)
         t_1
         (if (<= b 50000.0)
           (- (* z (- (* x y) (* b c))) t_2)
           (if (<= b 6.2e+55) t_1 t_4)))))))

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))) + (x * ((y * z) - (t * a)));
	double t_2 = j * ((y * i) - (t * c));
	double t_3 = b * ((a * i) - (z * c));
	double t_4 = t_3 - t_2;
	double tmp;
	if (b <= -8e+188) {
		tmp = t_3;
	} else if (b <= -1.25e-36) {
		tmp = t_4;
	} else if (b <= 1.2e-72) {
		tmp = t_1;
	} else if (b <= 50000.0) {
		tmp = (z * ((x * y) - (b * c))) - t_2;
	} else if (b <= 6.2e+55) {
		tmp = t_1;
	} else {
		tmp = t_4;
	}
	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))) + (x * ((y * z) - (t * a)))
    t_2 = j * ((y * i) - (t * c))
    t_3 = b * ((a * i) - (z * c))
    t_4 = t_3 - t_2
    if (b <= (-8d+188)) then
        tmp = t_3
    else if (b <= (-1.25d-36)) then
        tmp = t_4
    else if (b <= 1.2d-72) then
        tmp = t_1
    else if (b <= 50000.0d0) then
        tmp = (z * ((x * y) - (b * c))) - t_2
    else if (b <= 6.2d+55) then
        tmp = t_1
    else
        tmp = t_4
    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))) + (x * ((y * z) - (t * a)));
	double t_2 = j * ((y * i) - (t * c));
	double t_3 = b * ((a * i) - (z * c));
	double t_4 = t_3 - t_2;
	double tmp;
	if (b <= -8e+188) {
		tmp = t_3;
	} else if (b <= -1.25e-36) {
		tmp = t_4;
	} else if (b <= 1.2e-72) {
		tmp = t_1;
	} else if (b <= 50000.0) {
		tmp = (z * ((x * y) - (b * c))) - t_2;
	} else if (b <= 6.2e+55) {
		tmp = t_1;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)))
	t_2 = j * ((y * i) - (t * c))
	t_3 = b * ((a * i) - (z * c))
	t_4 = t_3 - t_2
	tmp = 0
	if b <= -8e+188:
		tmp = t_3
	elif b <= -1.25e-36:
		tmp = t_4
	elif b <= 1.2e-72:
		tmp = t_1
	elif b <= 50000.0:
		tmp = (z * ((x * y) - (b * c))) - t_2
	elif b <= 6.2e+55:
		tmp = t_1
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))))
	t_2 = Float64(j * Float64(Float64(y * i) - Float64(t * c)))
	t_3 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_4 = Float64(t_3 - t_2)
	tmp = 0.0
	if (b <= -8e+188)
		tmp = t_3;
	elseif (b <= -1.25e-36)
		tmp = t_4;
	elseif (b <= 1.2e-72)
		tmp = t_1;
	elseif (b <= 50000.0)
		tmp = Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) - t_2);
	elseif (b <= 6.2e+55)
		tmp = t_1;
	else
		tmp = t_4;
	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))) + (x * ((y * z) - (t * a)));
	t_2 = j * ((y * i) - (t * c));
	t_3 = b * ((a * i) - (z * c));
	t_4 = t_3 - t_2;
	tmp = 0.0;
	if (b <= -8e+188)
		tmp = t_3;
	elseif (b <= -1.25e-36)
		tmp = t_4;
	elseif (b <= 1.2e-72)
		tmp = t_1;
	elseif (b <= 50000.0)
		tmp = (z * ((x * y) - (b * c))) - t_2;
	elseif (b <= 6.2e+55)
		tmp = t_1;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(y * i), $MachinePrecision] - N[(t * c), $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, -8e+188], t$95$3, If[LessEqual[b, -1.25e-36], t$95$4, If[LessEqual[b, 1.2e-72], t$95$1, If[LessEqual[b, 50000.0], N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[b, 6.2e+55], t$95$1, t$95$4]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -8.0000000000000002e188

   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 83.1%

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

   if -8.0000000000000002e188 < b < -1.25000000000000001e-36 or 6.19999999999999987e55 < b

   1. Initial program 77.5%

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

   3. Taylor expanded in x around 0 78.9%

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

   if -1.25000000000000001e-36 < b < 1.2e-72 or 5e4 < b < 6.19999999999999987e55

   1. Initial program 72.6%

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

   3. Taylor expanded in b around 0 78.5%

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

   if 1.2e-72 < b < 5e4

   1. Initial program 72.8%

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

   3. Taylor expanded in z around 0 79.8%

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

   4. Taylor expanded in a around 0 93.1%

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

   5. Taylor expanded in a around 0 80.6%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8 \cdot 10^{+188}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.25 \cdot 10^{-36}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-72}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 50000:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{+55}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 69.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := t\_2 - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{if}\;b \leq -3.3 \cdot 10^{+189}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -5.6 \cdot 10^{-38}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{-73}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 780000:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - j \cdot \left(t \cdot \left(i \cdot \frac{y}{t} - c\right)\right)\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{+55}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* j (- (* t c) (* y i))) (* x (- (* y z) (* t a)))))
        (t_2 (* b (- (* a i) (* z c))))
        (t_3 (- t_2 (* j (- (* y i) (* t c))))))
   (if (<= b -3.3e+189)
     t_2
     (if (<= b -5.6e-38)
       t_3
       (if (<= b 1.75e-73)
         t_1
         (if (<= b 780000.0)
           (- (* z (- (* x y) (* b c))) (* j (* t (- (* i (/ y t)) c))))
           (if (<= b 6.8e+55) t_1 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = t_2 - (j * ((y * i) - (t * c)));
	double tmp;
	if (b <= -3.3e+189) {
		tmp = t_2;
	} else if (b <= -5.6e-38) {
		tmp = t_3;
	} else if (b <= 1.75e-73) {
		tmp = t_1;
	} else if (b <= 780000.0) {
		tmp = (z * ((x * y) - (b * c))) - (j * (t * ((i * (y / t)) - c)));
	} else if (b <= 6.8e+55) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)))
    t_2 = b * ((a * i) - (z * c))
    t_3 = t_2 - (j * ((y * i) - (t * c)))
    if (b <= (-3.3d+189)) then
        tmp = t_2
    else if (b <= (-5.6d-38)) then
        tmp = t_3
    else if (b <= 1.75d-73) then
        tmp = t_1
    else if (b <= 780000.0d0) then
        tmp = (z * ((x * y) - (b * c))) - (j * (t * ((i * (y / t)) - c)))
    else if (b <= 6.8d+55) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = t_2 - (j * ((y * i) - (t * c)));
	double tmp;
	if (b <= -3.3e+189) {
		tmp = t_2;
	} else if (b <= -5.6e-38) {
		tmp = t_3;
	} else if (b <= 1.75e-73) {
		tmp = t_1;
	} else if (b <= 780000.0) {
		tmp = (z * ((x * y) - (b * c))) - (j * (t * ((i * (y / t)) - c)));
	} else if (b <= 6.8e+55) {
		tmp = t_1;
	} 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))) + (x * ((y * z) - (t * a)))
	t_2 = b * ((a * i) - (z * c))
	t_3 = t_2 - (j * ((y * i) - (t * c)))
	tmp = 0
	if b <= -3.3e+189:
		tmp = t_2
	elif b <= -5.6e-38:
		tmp = t_3
	elif b <= 1.75e-73:
		tmp = t_1
	elif b <= 780000.0:
		tmp = (z * ((x * y) - (b * c))) - (j * (t * ((i * (y / t)) - c)))
	elif b <= 6.8e+55:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_3 = Float64(t_2 - Float64(j * Float64(Float64(y * i) - Float64(t * c))))
	tmp = 0.0
	if (b <= -3.3e+189)
		tmp = t_2;
	elseif (b <= -5.6e-38)
		tmp = t_3;
	elseif (b <= 1.75e-73)
		tmp = t_1;
	elseif (b <= 780000.0)
		tmp = Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) - Float64(j * Float64(t * Float64(Float64(i * Float64(y / t)) - c))));
	elseif (b <= 6.8e+55)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	t_2 = b * ((a * i) - (z * c));
	t_3 = t_2 - (j * ((y * i) - (t * c)));
	tmp = 0.0;
	if (b <= -3.3e+189)
		tmp = t_2;
	elseif (b <= -5.6e-38)
		tmp = t_3;
	elseif (b <= 1.75e-73)
		tmp = t_1;
	elseif (b <= 780000.0)
		tmp = (z * ((x * y) - (b * c))) - (j * (t * ((i * (y / t)) - c)));
	elseif (b <= 6.8e+55)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 - N[(j * N[(N[(y * i), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.3e+189], t$95$2, If[LessEqual[b, -5.6e-38], t$95$3, If[LessEqual[b, 1.75e-73], t$95$1, If[LessEqual[b, 780000.0], N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(t * N[(N[(i * N[(y / t), $MachinePrecision]), $MachinePrecision] - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.8e+55], t$95$1, t$95$3]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.3000000000000002e189

   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 83.1%

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

   if -3.3000000000000002e189 < b < -5.6e-38 or 6.7999999999999996e55 < b

   1. Initial program 77.5%

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

   3. Taylor expanded in x around 0 78.9%

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

   if -5.6e-38 < b < 1.7499999999999999e-73 or 7.8e5 < b < 6.7999999999999996e55

   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 0 79.1%

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

   if 1.7499999999999999e-73 < b < 7.8e5

   1. Initial program 74.5%

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

   3. Taylor expanded in z around 0 81.1%

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

   4. Taylor expanded in a around 0 93.6%

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

   5. Taylor expanded in a around 0 76.1%

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

   6. Taylor expanded in t around inf 81.8%

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

      1. mul-1-neg 45.0%

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

      2. unsub-neg 45.0%

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

      3. associate-/l* 44.9%

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

   8. Simplified 81.7%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.3 \cdot 10^{+189}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -5.6 \cdot 10^{-38}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{-73}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 780000:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - j \cdot \left(t \cdot \left(i \cdot \frac{y}{t} - c\right)\right)\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{+55}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := t\_1 + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;c \leq -2.8 \cdot 10^{-126}:\\ \;\;\;\;t\_1 - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;c \leq 6 \cdot 10^{-174}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 3.55 \cdot 10^{-130}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{+157}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i))))
        (t_2 (+ t_1 (* x (- (* y z) (* t a))))))
   (if (<= c -2.8e-126)
     (- t_1 (* z (* b c)))
     (if (<= c 6e-174)
       t_2
       (if (<= c 3.55e-130)
         (* i (- (* a b) (* y j)))
         (if (<= c 1.55e+157) t_2 (* c (- (* t j) (* z 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 = j * ((t * c) - (y * i));
	double t_2 = t_1 + (x * ((y * z) - (t * a)));
	double tmp;
	if (c <= -2.8e-126) {
		tmp = t_1 - (z * (b * c));
	} else if (c <= 6e-174) {
		tmp = t_2;
	} else if (c <= 3.55e-130) {
		tmp = i * ((a * b) - (y * j));
	} else if (c <= 1.55e+157) {
		tmp = t_2;
	} else {
		tmp = c * ((t * j) - (z * 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) :: t_2
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = t_1 + (x * ((y * z) - (t * a)))
    if (c <= (-2.8d-126)) then
        tmp = t_1 - (z * (b * c))
    else if (c <= 6d-174) then
        tmp = t_2
    else if (c <= 3.55d-130) then
        tmp = i * ((a * b) - (y * j))
    else if (c <= 1.55d+157) then
        tmp = t_2
    else
        tmp = c * ((t * j) - (z * 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 = j * ((t * c) - (y * i));
	double t_2 = t_1 + (x * ((y * z) - (t * a)));
	double tmp;
	if (c <= -2.8e-126) {
		tmp = t_1 - (z * (b * c));
	} else if (c <= 6e-174) {
		tmp = t_2;
	} else if (c <= 3.55e-130) {
		tmp = i * ((a * b) - (y * j));
	} else if (c <= 1.55e+157) {
		tmp = t_2;
	} else {
		tmp = c * ((t * j) - (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = t_1 + (x * ((y * z) - (t * a)))
	tmp = 0
	if c <= -2.8e-126:
		tmp = t_1 - (z * (b * c))
	elif c <= 6e-174:
		tmp = t_2
	elif c <= 3.55e-130:
		tmp = i * ((a * b) - (y * j))
	elif c <= 1.55e+157:
		tmp = t_2
	else:
		tmp = c * ((t * j) - (z * b))
	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(t_1 + Float64(x * Float64(Float64(y * z) - Float64(t * a))))
	tmp = 0.0
	if (c <= -2.8e-126)
		tmp = Float64(t_1 - Float64(z * Float64(b * c)));
	elseif (c <= 6e-174)
		tmp = t_2;
	elseif (c <= 3.55e-130)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (c <= 1.55e+157)
		tmp = t_2;
	else
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	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 = t_1 + (x * ((y * z) - (t * a)));
	tmp = 0.0;
	if (c <= -2.8e-126)
		tmp = t_1 - (z * (b * c));
	elseif (c <= 6e-174)
		tmp = t_2;
	elseif (c <= 3.55e-130)
		tmp = i * ((a * b) - (y * j));
	elseif (c <= 1.55e+157)
		tmp = t_2;
	else
		tmp = c * ((t * j) - (z * b));
	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[(t$95$1 + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.8e-126], N[(t$95$1 - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6e-174], t$95$2, If[LessEqual[c, 3.55e-130], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.55e+157], t$95$2, N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -2.79999999999999992e-126

   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 z around 0 76.8%

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

   4. Taylor expanded in a around 0 77.0%

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

   5. Taylor expanded in a around 0 71.0%

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

   6. Taylor expanded in x around 0 68.4%

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

      1. +-commutative 68.4%

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

      2. mul-1-neg 68.4%

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

      3. unsub-neg 68.4%

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

      4. *-commutative 68.4%

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

      5. associate-*r* 73.3%

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

      6. *-commutative 73.3%

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

   8. Simplified 73.3%

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

   if -2.79999999999999992e-126 < c < 6.00000000000000042e-174 or 3.55e-130 < c < 1.5499999999999999e157

   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 b around 0 71.2%

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

   if 6.00000000000000042e-174 < c < 3.55e-130

   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 i around inf 92.2%

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

      1. distribute-lft-out-- 92.2%

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

      2. *-commutative 92.2%

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

   5. Simplified 92.2%

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

   if 1.5499999999999999e157 < c

   1. Initial program 55.7%

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

   3. Taylor expanded in c around inf 80.7%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.8 \cdot 10^{-126}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;c \leq 6 \cdot 10^{-174}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 3.55 \cdot 10^{-130}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{+157}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 51.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -4.4 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -3.5 \cdot 10^{-251}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 2.05 \cdot 10^{-260}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{-129}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{+106}:\\ \;\;\;\;x \cdot \left(a \cdot \left(\frac{y \cdot z}{a} - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))))
   (if (<= c -4.4e-10)
     t_1
     (if (<= c -3.5e-251)
       (* y (- (* x z) (* i j)))
       (if (<= c 2.05e-260)
         (* x (- (* y z) (* t a)))
         (if (<= c 1.3e-129)
           (* i (- (* a b) (* y j)))
           (if (<= c 1.7e+106) (* x (* a (- (/ (* y z) a) t))) 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 <= -4.4e-10) {
		tmp = t_1;
	} else if (c <= -3.5e-251) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 2.05e-260) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= 1.3e-129) {
		tmp = i * ((a * b) - (y * j));
	} else if (c <= 1.7e+106) {
		tmp = x * (a * (((y * z) / a) - t));
	} 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 <= (-4.4d-10)) then
        tmp = t_1
    else if (c <= (-3.5d-251)) then
        tmp = y * ((x * z) - (i * j))
    else if (c <= 2.05d-260) then
        tmp = x * ((y * z) - (t * a))
    else if (c <= 1.3d-129) then
        tmp = i * ((a * b) - (y * j))
    else if (c <= 1.7d+106) then
        tmp = x * (a * (((y * z) / a) - t))
    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 <= -4.4e-10) {
		tmp = t_1;
	} else if (c <= -3.5e-251) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 2.05e-260) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= 1.3e-129) {
		tmp = i * ((a * b) - (y * j));
	} else if (c <= 1.7e+106) {
		tmp = x * (a * (((y * z) / a) - t));
	} 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 <= -4.4e-10:
		tmp = t_1
	elif c <= -3.5e-251:
		tmp = y * ((x * z) - (i * j))
	elif c <= 2.05e-260:
		tmp = x * ((y * z) - (t * a))
	elif c <= 1.3e-129:
		tmp = i * ((a * b) - (y * j))
	elif c <= 1.7e+106:
		tmp = x * (a * (((y * z) / a) - t))
	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 <= -4.4e-10)
		tmp = t_1;
	elseif (c <= -3.5e-251)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (c <= 2.05e-260)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (c <= 1.3e-129)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (c <= 1.7e+106)
		tmp = Float64(x * Float64(a * Float64(Float64(Float64(y * z) / a) - t)));
	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 <= -4.4e-10)
		tmp = t_1;
	elseif (c <= -3.5e-251)
		tmp = y * ((x * z) - (i * j));
	elseif (c <= 2.05e-260)
		tmp = x * ((y * z) - (t * a));
	elseif (c <= 1.3e-129)
		tmp = i * ((a * b) - (y * j));
	elseif (c <= 1.7e+106)
		tmp = x * (a * (((y * z) / a) - t));
	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, -4.4e-10], t$95$1, If[LessEqual[c, -3.5e-251], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.05e-260], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.3e-129], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.7e+106], N[(x * N[(a * N[(N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -4.3999999999999998e-10 or 1.69999999999999997e106 < c

   1. Initial program 63.6%

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

   3. Taylor expanded in c around inf 69.7%

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

   if -4.3999999999999998e-10 < c < -3.50000000000000034e-251

   1. Initial program 77.2%

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

   3. Taylor expanded in y around inf 63.1%

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

      1. +-commutative 63.1%

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

      2. mul-1-neg 63.1%

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

      3. unsub-neg 63.1%

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

      4. *-commutative 63.1%

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

   5. Simplified 63.1%

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

   if -3.50000000000000034e-251 < c < 2.04999999999999998e-260

   1. Initial program 90.0%

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

   3. Taylor expanded in x around inf 63.4%

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

      1. *-commutative 63.4%

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

   5. Simplified 63.4%

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

   if 2.04999999999999998e-260 < c < 1.3e-129

   1. Initial program 84.6%

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

   3. Taylor expanded in i around inf 73.6%

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

      1. distribute-lft-out-- 73.6%

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

      2. *-commutative 73.6%

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

   5. Simplified 73.6%

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

   if 1.3e-129 < c < 1.69999999999999997e106

   1. Initial program 77.3%

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

   3. Taylor expanded in x around inf 59.3%

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

      1. *-commutative 59.3%

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

   5. Simplified 59.3%

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

   6. Taylor expanded in a around inf 63.4%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.4 \cdot 10^{-10}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -3.5 \cdot 10^{-251}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 2.05 \cdot 10^{-260}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{-129}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{+106}:\\ \;\;\;\;x \cdot \left(a \cdot \left(\frac{y \cdot z}{a} - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.15 \cdot 10^{-123}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;c \leq -5.3 \cdot 10^{-251}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 4.2 \cdot 10^{-258}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{-128}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{+106}:\\ \;\;\;\;x \cdot \left(a \cdot \left(\frac{y \cdot z}{a} - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -1.15e-123)
   (- (* j (- (* t c) (* y i))) (* z (* b c)))
   (if (<= c -5.3e-251)
     (* y (- (* x z) (* i j)))
     (if (<= c 4.2e-258)
       (* x (- (* y z) (* t a)))
       (if (<= c 1.6e-128)
         (* i (- (* a b) (* y j)))
         (if (<= c 5.8e+106)
           (* x (* a (- (/ (* y z) a) t)))
           (* c (- (* t j) (* z 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 <= -1.15e-123) {
		tmp = (j * ((t * c) - (y * i))) - (z * (b * c));
	} else if (c <= -5.3e-251) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 4.2e-258) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= 1.6e-128) {
		tmp = i * ((a * b) - (y * j));
	} else if (c <= 5.8e+106) {
		tmp = x * (a * (((y * z) / a) - t));
	} else {
		tmp = c * ((t * j) - (z * 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 <= (-1.15d-123)) then
        tmp = (j * ((t * c) - (y * i))) - (z * (b * c))
    else if (c <= (-5.3d-251)) then
        tmp = y * ((x * z) - (i * j))
    else if (c <= 4.2d-258) then
        tmp = x * ((y * z) - (t * a))
    else if (c <= 1.6d-128) then
        tmp = i * ((a * b) - (y * j))
    else if (c <= 5.8d+106) then
        tmp = x * (a * (((y * z) / a) - t))
    else
        tmp = c * ((t * j) - (z * 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 <= -1.15e-123) {
		tmp = (j * ((t * c) - (y * i))) - (z * (b * c));
	} else if (c <= -5.3e-251) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 4.2e-258) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= 1.6e-128) {
		tmp = i * ((a * b) - (y * j));
	} else if (c <= 5.8e+106) {
		tmp = x * (a * (((y * z) / a) - t));
	} else {
		tmp = c * ((t * j) - (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -1.15e-123:
		tmp = (j * ((t * c) - (y * i))) - (z * (b * c))
	elif c <= -5.3e-251:
		tmp = y * ((x * z) - (i * j))
	elif c <= 4.2e-258:
		tmp = x * ((y * z) - (t * a))
	elif c <= 1.6e-128:
		tmp = i * ((a * b) - (y * j))
	elif c <= 5.8e+106:
		tmp = x * (a * (((y * z) / a) - t))
	else:
		tmp = c * ((t * j) - (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -1.15e-123)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) - Float64(z * Float64(b * c)));
	elseif (c <= -5.3e-251)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (c <= 4.2e-258)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (c <= 1.6e-128)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (c <= 5.8e+106)
		tmp = Float64(x * Float64(a * Float64(Float64(Float64(y * z) / a) - t)));
	else
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -1.15e-123)
		tmp = (j * ((t * c) - (y * i))) - (z * (b * c));
	elseif (c <= -5.3e-251)
		tmp = y * ((x * z) - (i * j));
	elseif (c <= 4.2e-258)
		tmp = x * ((y * z) - (t * a));
	elseif (c <= 1.6e-128)
		tmp = i * ((a * b) - (y * j));
	elseif (c <= 5.8e+106)
		tmp = x * (a * (((y * z) / a) - t));
	else
		tmp = c * ((t * j) - (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -1.15e-123], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -5.3e-251], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.2e-258], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.6e-128], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.8e+106], N[(x * N[(a * N[(N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -1.14999999999999993e-123

   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 z around 0 76.8%

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

   4. Taylor expanded in a around 0 77.0%

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

   5. Taylor expanded in a around 0 71.0%

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

   6. Taylor expanded in x around 0 68.4%

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

      1. +-commutative 68.4%

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

      2. mul-1-neg 68.4%

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

      3. unsub-neg 68.4%

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

      4. *-commutative 68.4%

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

      5. associate-*r* 73.3%

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

      6. *-commutative 73.3%

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

   8. Simplified 73.3%

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

   if -1.14999999999999993e-123 < c < -5.29999999999999963e-251

   1. Initial program 78.9%

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

   3. Taylor expanded in y around inf 71.9%

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

      1. +-commutative 71.9%

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

      2. mul-1-neg 71.9%

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

      3. unsub-neg 71.9%

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

      4. *-commutative 71.9%

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

   5. Simplified 71.9%

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

   if -5.29999999999999963e-251 < c < 4.1999999999999998e-258

   1. Initial program 90.0%

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

   3. Taylor expanded in x around inf 63.4%

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

      1. *-commutative 63.4%

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

   5. Simplified 63.4%

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

   if 4.1999999999999998e-258 < c < 1.5999999999999999e-128

   1. Initial program 84.6%

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

   3. Taylor expanded in i around inf 73.6%

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

      1. distribute-lft-out-- 73.6%

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

      2. *-commutative 73.6%

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

   5. Simplified 73.6%

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

   if 1.5999999999999999e-128 < c < 5.8000000000000004e106

   1. Initial program 77.3%

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

   3. Taylor expanded in x around inf 59.3%

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

      1. *-commutative 59.3%

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

   5. Simplified 59.3%

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

   6. Taylor expanded in a around inf 63.4%

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

   if 5.8000000000000004e106 < c

   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 c around inf 74.8%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.15 \cdot 10^{-123}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;c \leq -5.3 \cdot 10^{-251}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 4.2 \cdot 10^{-258}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{-128}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{+106}:\\ \;\;\;\;x \cdot \left(a \cdot \left(\frac{y \cdot z}{a} - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 47.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_3 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -5.6 \cdot 10^{-11}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq -1.35 \cdot 10^{-228}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 2.3 \cdot 10^{-257}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 2.8 \cdot 10^{-129}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 1.45 \cdot 10^{+106}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (* j (- (* t c) (* y i))))
        (t_3 (* c (- (* t j) (* z b)))))
   (if (<= c -5.6e-11)
     t_3
     (if (<= c -1.35e-228)
       t_2
       (if (<= c 2.3e-257)
         t_1
         (if (<= c 2.8e-129) t_2 (if (<= c 1.45e+106) t_1 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = j * ((t * c) - (y * i));
	double t_3 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -5.6e-11) {
		tmp = t_3;
	} else if (c <= -1.35e-228) {
		tmp = t_2;
	} else if (c <= 2.3e-257) {
		tmp = t_1;
	} else if (c <= 2.8e-129) {
		tmp = t_2;
	} else if (c <= 1.45e+106) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = j * ((t * c) - (y * i))
    t_3 = c * ((t * j) - (z * b))
    if (c <= (-5.6d-11)) then
        tmp = t_3
    else if (c <= (-1.35d-228)) then
        tmp = t_2
    else if (c <= 2.3d-257) then
        tmp = t_1
    else if (c <= 2.8d-129) then
        tmp = t_2
    else if (c <= 1.45d+106) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = j * ((t * c) - (y * i));
	double t_3 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -5.6e-11) {
		tmp = t_3;
	} else if (c <= -1.35e-228) {
		tmp = t_2;
	} else if (c <= 2.3e-257) {
		tmp = t_1;
	} else if (c <= 2.8e-129) {
		tmp = t_2;
	} else if (c <= 1.45e+106) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = j * ((t * c) - (y * i))
	t_3 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -5.6e-11:
		tmp = t_3
	elif c <= -1.35e-228:
		tmp = t_2
	elif c <= 2.3e-257:
		tmp = t_1
	elif c <= 2.8e-129:
		tmp = t_2
	elif c <= 1.45e+106:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_3 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -5.6e-11)
		tmp = t_3;
	elseif (c <= -1.35e-228)
		tmp = t_2;
	elseif (c <= 2.3e-257)
		tmp = t_1;
	elseif (c <= 2.8e-129)
		tmp = t_2;
	elseif (c <= 1.45e+106)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = j * ((t * c) - (y * i));
	t_3 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -5.6e-11)
		tmp = t_3;
	elseif (c <= -1.35e-228)
		tmp = t_2;
	elseif (c <= 2.3e-257)
		tmp = t_1;
	elseif (c <= 2.8e-129)
		tmp = t_2;
	elseif (c <= 1.45e+106)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -5.6e-11], t$95$3, If[LessEqual[c, -1.35e-228], t$95$2, If[LessEqual[c, 2.3e-257], t$95$1, If[LessEqual[c, 2.8e-129], t$95$2, If[LessEqual[c, 1.45e+106], t$95$1, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -5.6e-11 or 1.4500000000000001e106 < c

   1. Initial program 63.6%

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

   3. Taylor expanded in c around inf 69.7%

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

   if -5.6e-11 < c < -1.34999999999999992e-228 or 2.3e-257 < c < 2.7999999999999999e-129

   1. Initial program 81.3%

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

   3. Taylor expanded in j around inf 53.9%

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

   if -1.34999999999999992e-228 < c < 2.3e-257 or 2.7999999999999999e-129 < c < 1.4500000000000001e106

   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 x around inf 60.0%

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

      1. *-commutative 60.0%

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

   5. Simplified 60.0%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.6 \cdot 10^{-11}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -1.35 \cdot 10^{-228}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;c \leq 2.3 \cdot 10^{-257}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 2.8 \cdot 10^{-129}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;c \leq 1.45 \cdot 10^{+106}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 49.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -2.7 \cdot 10^{-11}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -8.6 \cdot 10^{-251}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 2.8 \cdot 10^{-257}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 6 \cdot 10^{-130}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{+106}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (* c (- (* t j) (* z b)))))
   (if (<= c -2.7e-11)
     t_2
     (if (<= c -8.6e-251)
       (* y (- (* x z) (* i j)))
       (if (<= c 2.8e-257)
         t_1
         (if (<= c 6e-130)
           (* j (- (* t c) (* y i)))
           (if (<= c 5.8e+106) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -2.7e-11) {
		tmp = t_2;
	} else if (c <= -8.6e-251) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 2.8e-257) {
		tmp = t_1;
	} else if (c <= 6e-130) {
		tmp = j * ((t * c) - (y * i));
	} else if (c <= 5.8e+106) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = c * ((t * j) - (z * b))
    if (c <= (-2.7d-11)) then
        tmp = t_2
    else if (c <= (-8.6d-251)) then
        tmp = y * ((x * z) - (i * j))
    else if (c <= 2.8d-257) then
        tmp = t_1
    else if (c <= 6d-130) then
        tmp = j * ((t * c) - (y * i))
    else if (c <= 5.8d+106) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -2.7e-11) {
		tmp = t_2;
	} else if (c <= -8.6e-251) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 2.8e-257) {
		tmp = t_1;
	} else if (c <= 6e-130) {
		tmp = j * ((t * c) - (y * i));
	} else if (c <= 5.8e+106) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -2.7e-11:
		tmp = t_2
	elif c <= -8.6e-251:
		tmp = y * ((x * z) - (i * j))
	elif c <= 2.8e-257:
		tmp = t_1
	elif c <= 6e-130:
		tmp = j * ((t * c) - (y * i))
	elif c <= 5.8e+106:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -2.7e-11)
		tmp = t_2;
	elseif (c <= -8.6e-251)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (c <= 2.8e-257)
		tmp = t_1;
	elseif (c <= 6e-130)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (c <= 5.8e+106)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -2.7e-11)
		tmp = t_2;
	elseif (c <= -8.6e-251)
		tmp = y * ((x * z) - (i * j));
	elseif (c <= 2.8e-257)
		tmp = t_1;
	elseif (c <= 6e-130)
		tmp = j * ((t * c) - (y * i));
	elseif (c <= 5.8e+106)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.7e-11], t$95$2, If[LessEqual[c, -8.6e-251], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.8e-257], t$95$1, If[LessEqual[c, 6e-130], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.8e+106], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -2.70000000000000005e-11 or 5.8000000000000004e106 < c

   1. Initial program 63.6%

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

   3. Taylor expanded in c around inf 69.7%

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

   if -2.70000000000000005e-11 < c < -8.6000000000000004e-251

   1. Initial program 77.2%

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

   3. Taylor expanded in y around inf 63.1%

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

      1. +-commutative 63.1%

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

      2. mul-1-neg 63.1%

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

      3. unsub-neg 63.1%

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

      4. *-commutative 63.1%

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

   5. Simplified 63.1%

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

   if -8.6000000000000004e-251 < c < 2.80000000000000001e-257 or 5.99999999999999972e-130 < c < 5.8000000000000004e106

   1. Initial program 82.2%

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

   3. Taylor expanded in x around inf 60.9%

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

      1. *-commutative 60.9%

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

   5. Simplified 60.9%

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

   if 2.80000000000000001e-257 < c < 5.99999999999999972e-130

   1. Initial program 84.6%

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

   3. Taylor expanded in j around inf 59.1%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.7 \cdot 10^{-11}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -8.6 \cdot 10^{-251}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 2.8 \cdot 10^{-257}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 6 \cdot 10^{-130}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{+106}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -1.8 \cdot 10^{-10}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -5.3 \cdot 10^{-251}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 1.4 \cdot 10^{-260}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 3.7 \cdot 10^{-129}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 1.45 \cdot 10^{+106}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (* c (- (* t j) (* z b)))))
   (if (<= c -1.8e-10)
     t_2
     (if (<= c -5.3e-251)
       (* y (- (* x z) (* i j)))
       (if (<= c 1.4e-260)
         t_1
         (if (<= c 3.7e-129)
           (* i (- (* a b) (* y j)))
           (if (<= c 1.45e+106) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -1.8e-10) {
		tmp = t_2;
	} else if (c <= -5.3e-251) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 1.4e-260) {
		tmp = t_1;
	} else if (c <= 3.7e-129) {
		tmp = i * ((a * b) - (y * j));
	} else if (c <= 1.45e+106) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = c * ((t * j) - (z * b))
    if (c <= (-1.8d-10)) then
        tmp = t_2
    else if (c <= (-5.3d-251)) then
        tmp = y * ((x * z) - (i * j))
    else if (c <= 1.4d-260) then
        tmp = t_1
    else if (c <= 3.7d-129) then
        tmp = i * ((a * b) - (y * j))
    else if (c <= 1.45d+106) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -1.8e-10) {
		tmp = t_2;
	} else if (c <= -5.3e-251) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 1.4e-260) {
		tmp = t_1;
	} else if (c <= 3.7e-129) {
		tmp = i * ((a * b) - (y * j));
	} else if (c <= 1.45e+106) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -1.8e-10:
		tmp = t_2
	elif c <= -5.3e-251:
		tmp = y * ((x * z) - (i * j))
	elif c <= 1.4e-260:
		tmp = t_1
	elif c <= 3.7e-129:
		tmp = i * ((a * b) - (y * j))
	elif c <= 1.45e+106:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -1.8e-10)
		tmp = t_2;
	elseif (c <= -5.3e-251)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (c <= 1.4e-260)
		tmp = t_1;
	elseif (c <= 3.7e-129)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (c <= 1.45e+106)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -1.8e-10)
		tmp = t_2;
	elseif (c <= -5.3e-251)
		tmp = y * ((x * z) - (i * j));
	elseif (c <= 1.4e-260)
		tmp = t_1;
	elseif (c <= 3.7e-129)
		tmp = i * ((a * b) - (y * j));
	elseif (c <= 1.45e+106)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.8e-10], t$95$2, If[LessEqual[c, -5.3e-251], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.4e-260], t$95$1, If[LessEqual[c, 3.7e-129], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.45e+106], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.8e-10 or 1.4500000000000001e106 < c

   1. Initial program 63.6%

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

   3. Taylor expanded in c around inf 69.7%

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

   if -1.8e-10 < c < -5.29999999999999963e-251

   1. Initial program 77.2%

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

   3. Taylor expanded in y around inf 63.1%

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

      1. +-commutative 63.1%

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

      2. mul-1-neg 63.1%

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

      3. unsub-neg 63.1%

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

      4. *-commutative 63.1%

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

   5. Simplified 63.1%

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

   if -5.29999999999999963e-251 < c < 1.3999999999999999e-260 or 3.7000000000000002e-129 < c < 1.4500000000000001e106

   1. Initial program 82.2%

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

   3. Taylor expanded in x around inf 60.9%

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

      1. *-commutative 60.9%

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

   5. Simplified 60.9%

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

   if 1.3999999999999999e-260 < c < 3.7000000000000002e-129

   1. Initial program 84.6%

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

   3. Taylor expanded in i around inf 73.6%

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

      1. distribute-lft-out-- 73.6%

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

      2. *-commutative 73.6%

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

   5. Simplified 73.6%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - b \cdot a\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.8 \cdot 10^{-10}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -5.3 \cdot 10^{-251}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 1.4 \cdot 10^{-260}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 3.7 \cdot 10^{-129}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 1.45 \cdot 10^{+106}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 28.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(i \cdot \left(-j\right)\right)\\ t_2 := \left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{if}\;c \leq -5 \cdot 10^{-11}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -3.7 \cdot 10^{-249}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{-272}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{-128}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 7.5 \cdot 10^{+40}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* i (- j)))) (t_2 (* (* z b) (- c))))
   (if (<= c -5e-11)
     t_2
     (if (<= c -3.7e-249)
       t_1
       (if (<= c 5.8e-272)
         (* z (* x y))
         (if (<= c 1.6e-128)
           t_1
           (if (<= c 7.5e+40) (* (* t a) (- x)) 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 = y * (i * -j);
	double t_2 = (z * b) * -c;
	double tmp;
	if (c <= -5e-11) {
		tmp = t_2;
	} else if (c <= -3.7e-249) {
		tmp = t_1;
	} else if (c <= 5.8e-272) {
		tmp = z * (x * y);
	} else if (c <= 1.6e-128) {
		tmp = t_1;
	} else if (c <= 7.5e+40) {
		tmp = (t * a) * -x;
	} 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 = y * (i * -j)
    t_2 = (z * b) * -c
    if (c <= (-5d-11)) then
        tmp = t_2
    else if (c <= (-3.7d-249)) then
        tmp = t_1
    else if (c <= 5.8d-272) then
        tmp = z * (x * y)
    else if (c <= 1.6d-128) then
        tmp = t_1
    else if (c <= 7.5d+40) then
        tmp = (t * a) * -x
    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 = y * (i * -j);
	double t_2 = (z * b) * -c;
	double tmp;
	if (c <= -5e-11) {
		tmp = t_2;
	} else if (c <= -3.7e-249) {
		tmp = t_1;
	} else if (c <= 5.8e-272) {
		tmp = z * (x * y);
	} else if (c <= 1.6e-128) {
		tmp = t_1;
	} else if (c <= 7.5e+40) {
		tmp = (t * a) * -x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (i * -j)
	t_2 = (z * b) * -c
	tmp = 0
	if c <= -5e-11:
		tmp = t_2
	elif c <= -3.7e-249:
		tmp = t_1
	elif c <= 5.8e-272:
		tmp = z * (x * y)
	elif c <= 1.6e-128:
		tmp = t_1
	elif c <= 7.5e+40:
		tmp = (t * a) * -x
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(i * Float64(-j)))
	t_2 = Float64(Float64(z * b) * Float64(-c))
	tmp = 0.0
	if (c <= -5e-11)
		tmp = t_2;
	elseif (c <= -3.7e-249)
		tmp = t_1;
	elseif (c <= 5.8e-272)
		tmp = Float64(z * Float64(x * y));
	elseif (c <= 1.6e-128)
		tmp = t_1;
	elseif (c <= 7.5e+40)
		tmp = Float64(Float64(t * a) * Float64(-x));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * (i * -j);
	t_2 = (z * b) * -c;
	tmp = 0.0;
	if (c <= -5e-11)
		tmp = t_2;
	elseif (c <= -3.7e-249)
		tmp = t_1;
	elseif (c <= 5.8e-272)
		tmp = z * (x * y);
	elseif (c <= 1.6e-128)
		tmp = t_1;
	elseif (c <= 7.5e+40)
		tmp = (t * a) * -x;
	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[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * b), $MachinePrecision] * (-c)), $MachinePrecision]}, If[LessEqual[c, -5e-11], t$95$2, If[LessEqual[c, -3.7e-249], t$95$1, If[LessEqual[c, 5.8e-272], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.6e-128], t$95$1, If[LessEqual[c, 7.5e+40], N[(N[(t * a), $MachinePrecision] * (-x)), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -5.00000000000000018e-11 or 7.4999999999999996e40 < c

   1. Initial program 64.4%

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

   3. Taylor expanded in z around 0 66.1%

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

   4. Taylor expanded in a around 0 66.3%

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

   5. Taylor expanded in a around 0 68.0%

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

   6. Taylor expanded in b around inf 46.4%

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

      1. mul-1-neg 46.4%

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

      2. *-commutative 46.4%

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

      3. associate-*r* 48.4%

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

      4. *-commutative 48.4%

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

      5. distribute-rgt-neg-out 48.4%

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

      6. *-commutative 48.4%

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

      7. distribute-rgt-neg-in 48.4%

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

   8. Simplified 48.4%

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

   if -5.00000000000000018e-11 < c < -3.69999999999999977e-249 or 5.79999999999999989e-272 < c < 1.5999999999999999e-128

   1. Initial program 80.3%

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

   3. Taylor expanded in i around inf 62.5%

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

      1. distribute-lft-out-- 62.5%

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

      2. *-commutative 62.5%

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

   5. Simplified 62.5%

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

   6. Taylor expanded in j around inf 45.8%

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

   7. Taylor expanded in i around 0 45.8%

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

      1. mul-1-neg 45.8%

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

      2. *-commutative 45.8%

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

      3. *-commutative 45.8%

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

      4. associate-*r* 43.7%

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

      5. *-commutative 43.7%

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

      6. distribute-rgt-neg-out 43.7%

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

      7. distribute-rgt-neg-in 43.7%

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

   9. Simplified 43.7%

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

   if -3.69999999999999977e-249 < c < 5.79999999999999989e-272

   1. Initial program 89.3%

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

   3. Taylor expanded in z around 0 93.0%

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

   4. Taylor expanded in a around 0 76.1%

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

   5. Taylor expanded in x around inf 39.4%

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

      1. *-commutative 39.4%

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

      2. *-commutative 39.4%

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

      3. associate-*r* 42.7%

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

      4. *-commutative 42.7%

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

   7. Simplified 42.7%

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

   if 1.5999999999999999e-128 < c < 7.4999999999999996e40

   1. Initial program 81.4%

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

   3. Taylor expanded in x around inf 58.5%

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

      1. *-commutative 58.5%

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

   5. Simplified 58.5%

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

   6. Taylor expanded in z around 0 41.9%

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

      1. neg-mul-1 41.9%

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

      2. *-commutative 41.9%

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

      3. distribute-rgt-neg-in 41.9%

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

   8. Simplified 41.9%

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

4. Final simplification 45.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5 \cdot 10^{-11}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{elif}\;c \leq -3.7 \cdot 10^{-249}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{-272}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{-128}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 7.5 \cdot 10^{+40}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 28.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{if}\;c \leq -1.75 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -3.7 \cdot 10^{-250}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 5.9 \cdot 10^{-269}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 4.6 \cdot 10^{-129}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 5.3 \cdot 10^{+40}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* z b) (- c))))
   (if (<= c -1.75e-10)
     t_1
     (if (<= c -3.7e-250)
       (* y (* i (- j)))
       (if (<= c 5.9e-269)
         (* z (* x y))
         (if (<= c 4.6e-129)
           (* i (* y (- j)))
           (if (<= c 5.3e+40) (* (* t a) (- x)) 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 = (z * b) * -c;
	double tmp;
	if (c <= -1.75e-10) {
		tmp = t_1;
	} else if (c <= -3.7e-250) {
		tmp = y * (i * -j);
	} else if (c <= 5.9e-269) {
		tmp = z * (x * y);
	} else if (c <= 4.6e-129) {
		tmp = i * (y * -j);
	} else if (c <= 5.3e+40) {
		tmp = (t * a) * -x;
	} 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 = (z * b) * -c
    if (c <= (-1.75d-10)) then
        tmp = t_1
    else if (c <= (-3.7d-250)) then
        tmp = y * (i * -j)
    else if (c <= 5.9d-269) then
        tmp = z * (x * y)
    else if (c <= 4.6d-129) then
        tmp = i * (y * -j)
    else if (c <= 5.3d+40) then
        tmp = (t * a) * -x
    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 = (z * b) * -c;
	double tmp;
	if (c <= -1.75e-10) {
		tmp = t_1;
	} else if (c <= -3.7e-250) {
		tmp = y * (i * -j);
	} else if (c <= 5.9e-269) {
		tmp = z * (x * y);
	} else if (c <= 4.6e-129) {
		tmp = i * (y * -j);
	} else if (c <= 5.3e+40) {
		tmp = (t * a) * -x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (z * b) * -c
	tmp = 0
	if c <= -1.75e-10:
		tmp = t_1
	elif c <= -3.7e-250:
		tmp = y * (i * -j)
	elif c <= 5.9e-269:
		tmp = z * (x * y)
	elif c <= 4.6e-129:
		tmp = i * (y * -j)
	elif c <= 5.3e+40:
		tmp = (t * a) * -x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(z * b) * Float64(-c))
	tmp = 0.0
	if (c <= -1.75e-10)
		tmp = t_1;
	elseif (c <= -3.7e-250)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (c <= 5.9e-269)
		tmp = Float64(z * Float64(x * y));
	elseif (c <= 4.6e-129)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (c <= 5.3e+40)
		tmp = Float64(Float64(t * a) * Float64(-x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (z * b) * -c;
	tmp = 0.0;
	if (c <= -1.75e-10)
		tmp = t_1;
	elseif (c <= -3.7e-250)
		tmp = y * (i * -j);
	elseif (c <= 5.9e-269)
		tmp = z * (x * y);
	elseif (c <= 4.6e-129)
		tmp = i * (y * -j);
	elseif (c <= 5.3e+40)
		tmp = (t * a) * -x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(z * b), $MachinePrecision] * (-c)), $MachinePrecision]}, If[LessEqual[c, -1.75e-10], t$95$1, If[LessEqual[c, -3.7e-250], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.9e-269], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.6e-129], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.3e+40], N[(N[(t * a), $MachinePrecision] * (-x)), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -1.7499999999999999e-10 or 5.3e40 < c

   1. Initial program 64.4%

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

   3. Taylor expanded in z around 0 66.1%

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

   4. Taylor expanded in a around 0 66.3%

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

   5. Taylor expanded in a around 0 68.0%

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

   6. Taylor expanded in b around inf 46.4%

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

      1. mul-1-neg 46.4%

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

      2. *-commutative 46.4%

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

      3. associate-*r* 48.4%

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

      4. *-commutative 48.4%

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

      5. distribute-rgt-neg-out 48.4%

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

      6. *-commutative 48.4%

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

      7. distribute-rgt-neg-in 48.4%

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

   8. Simplified 48.4%

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

   if -1.7499999999999999e-10 < c < -3.6999999999999998e-250

   1. Initial program 76.8%

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

   3. Taylor expanded in i around inf 58.0%

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

      1. distribute-lft-out-- 58.0%

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

      2. *-commutative 58.0%

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

   5. Simplified 58.0%

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

   6. Taylor expanded in j around inf 41.8%

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

   7. Taylor expanded in i around 0 41.8%

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

      1. mul-1-neg 41.8%

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

      2. *-commutative 41.8%

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

      3. *-commutative 41.8%

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

      4. associate-*r* 42.1%

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

      5. *-commutative 42.1%

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

      6. distribute-rgt-neg-out 42.1%

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

      7. distribute-rgt-neg-in 42.1%

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

   9. Simplified 42.1%

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

   if -3.6999999999999998e-250 < c < 5.9e-269

   1. Initial program 89.3%

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

   3. Taylor expanded in z around 0 93.0%

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

   4. Taylor expanded in a around 0 76.1%

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

   5. Taylor expanded in x around inf 39.4%

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

      1. *-commutative 39.4%

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

      2. *-commutative 39.4%

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

      3. associate-*r* 42.7%

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

      4. *-commutative 42.7%

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

   7. Simplified 42.7%

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

   if 5.9e-269 < c < 4.5999999999999999e-129

   1. Initial program 86.2%

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

   3. Taylor expanded in i around inf 69.7%

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

      1. distribute-lft-out-- 69.7%

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

      2. *-commutative 69.7%

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

   5. Simplified 69.7%

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

   6. Taylor expanded in j around inf 52.5%

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

   7. Taylor expanded in i around 0 52.5%

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

      1. associate-*r* 52.5%

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

      2. neg-mul-1 52.5%

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

      3. *-commutative 52.5%

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

   9. Simplified 52.5%

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

   if 4.5999999999999999e-129 < c < 5.3e40

   1. Initial program 81.4%

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

   3. Taylor expanded in x around inf 58.5%

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

      1. *-commutative 58.5%

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

   5. Simplified 58.5%

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

   6. Taylor expanded in z around 0 41.9%

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

      1. neg-mul-1 41.9%

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

      2. *-commutative 41.9%

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

      3. distribute-rgt-neg-in 41.9%

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

   8. Simplified 41.9%

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

4. Final simplification 46.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.75 \cdot 10^{-10}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{elif}\;c \leq -3.7 \cdot 10^{-250}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 5.9 \cdot 10^{-269}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 4.6 \cdot 10^{-129}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 5.3 \cdot 10^{+40}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 52.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.45 \cdot 10^{-34}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 1.72 \cdot 10^{-177}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-154}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))) (t_2 (* b (- (* a i) (* z c)))))
   (if (<= b -1.45e-34)
     t_2
     (if (<= b 1.72e-177)
       t_1
       (if (<= b 1.05e-154)
         (* t (- (* c j) (* x a)))
         (if (<= b 2.7e-31) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.45e-34) {
		tmp = t_2;
	} else if (b <= 1.72e-177) {
		tmp = t_1;
	} else if (b <= 1.05e-154) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= 2.7e-31) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = b * ((a * i) - (z * c))
    if (b <= (-1.45d-34)) then
        tmp = t_2
    else if (b <= 1.72d-177) then
        tmp = t_1
    else if (b <= 1.05d-154) then
        tmp = t * ((c * j) - (x * a))
    else if (b <= 2.7d-31) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.45e-34) {
		tmp = t_2;
	} else if (b <= 1.72e-177) {
		tmp = t_1;
	} else if (b <= 1.05e-154) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= 2.7e-31) {
		tmp = t_1;
	} 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 <= -1.45e-34:
		tmp = t_2
	elif b <= 1.72e-177:
		tmp = t_1
	elif b <= 1.05e-154:
		tmp = t * ((c * j) - (x * a))
	elif b <= 2.7e-31:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -1.45e-34)
		tmp = t_2;
	elseif (b <= 1.72e-177)
		tmp = t_1;
	elseif (b <= 1.05e-154)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (b <= 2.7e-31)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -1.45e-34)
		tmp = t_2;
	elseif (b <= 1.72e-177)
		tmp = t_1;
	elseif (b <= 1.05e-154)
		tmp = t * ((c * j) - (x * a));
	elseif (b <= 2.7e-31)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(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, -1.45e-34], t$95$2, If[LessEqual[b, 1.72e-177], t$95$1, If[LessEqual[b, 1.05e-154], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.7e-31], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.4500000000000001e-34 or 2.70000000000000014e-31 < b

   1. Initial program 75.3%

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

   3. Taylor expanded in b around inf 65.5%

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

   if -1.4500000000000001e-34 < b < 1.72e-177 or 1.04999999999999992e-154 < b < 2.70000000000000014e-31

   1. Initial program 72.6%

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

   3. Taylor expanded in j around inf 52.8%

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

   if 1.72e-177 < b < 1.04999999999999992e-154

   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 t around inf 99.7%

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

      1. +-commutative 99.7%

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

      2. mul-1-neg 99.7%

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

      3. unsub-neg 99.7%

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

   5. Simplified 99.7%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.45 \cdot 10^{-34}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 1.72 \cdot 10^{-177}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-154}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-31}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 29.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{if}\;b \leq -2.4 \cdot 10^{+232}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -5.6 \cdot 10^{+97}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-81} \lor \neg \left(b \leq 6.5 \cdot 10^{+55}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* z c) (- b))))
   (if (<= b -2.4e+232)
     t_1
     (if (<= b -5.6e+97)
       (* a (* b i))
       (if (or (<= b -1e-81) (not (<= b 6.5e+55))) t_1 (* x (* y z)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (z * c) * -b;
	double tmp;
	if (b <= -2.4e+232) {
		tmp = t_1;
	} else if (b <= -5.6e+97) {
		tmp = a * (b * i);
	} else if ((b <= -1e-81) || !(b <= 6.5e+55)) {
		tmp = t_1;
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * c) * -b
    if (b <= (-2.4d+232)) then
        tmp = t_1
    else if (b <= (-5.6d+97)) then
        tmp = a * (b * i)
    else if ((b <= (-1d-81)) .or. (.not. (b <= 6.5d+55))) then
        tmp = t_1
    else
        tmp = x * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (z * c) * -b;
	double tmp;
	if (b <= -2.4e+232) {
		tmp = t_1;
	} else if (b <= -5.6e+97) {
		tmp = a * (b * i);
	} else if ((b <= -1e-81) || !(b <= 6.5e+55)) {
		tmp = t_1;
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (z * c) * -b
	tmp = 0
	if b <= -2.4e+232:
		tmp = t_1
	elif b <= -5.6e+97:
		tmp = a * (b * i)
	elif (b <= -1e-81) or not (b <= 6.5e+55):
		tmp = t_1
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(z * c) * Float64(-b))
	tmp = 0.0
	if (b <= -2.4e+232)
		tmp = t_1;
	elseif (b <= -5.6e+97)
		tmp = Float64(a * Float64(b * i));
	elseif ((b <= -1e-81) || !(b <= 6.5e+55))
		tmp = t_1;
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (z * c) * -b;
	tmp = 0.0;
	if (b <= -2.4e+232)
		tmp = t_1;
	elseif (b <= -5.6e+97)
		tmp = a * (b * i);
	elseif ((b <= -1e-81) || ~((b <= 6.5e+55)))
		tmp = t_1;
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(z * c), $MachinePrecision] * (-b)), $MachinePrecision]}, If[LessEqual[b, -2.4e+232], t$95$1, If[LessEqual[b, -5.6e+97], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, -1e-81], N[Not[LessEqual[b, 6.5e+55]], $MachinePrecision]], t$95$1, N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.4000000000000001e232 or -5.5999999999999998e97 < b < -9.9999999999999996e-82 or 6.50000000000000027e55 < b

   1. Initial program 71.4%

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

   3. Taylor expanded in b around inf 68.2%

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

   4. Taylor expanded in a around 0 48.5%

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

      1. neg-mul-1 48.5%

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

      2. distribute-rgt-neg-in 48.5%

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

   6. Simplified 48.5%

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

   if -2.4000000000000001e232 < b < -5.5999999999999998e97

   1. Initial program 79.1%

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

   3. Taylor expanded in b around inf 64.3%

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

   4. Taylor expanded in a around inf 46.8%

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

      1. *-commutative 46.8%

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

   6. Simplified 46.8%

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

   if -9.9999999999999996e-82 < b < 6.50000000000000027e55

   1. Initial program 74.6%

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

   3. Taylor expanded in 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%

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

   5. Simplified 48.9%

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

   6. Taylor expanded in z around inf 28.5%

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

4. Final simplification 38.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.4 \cdot 10^{+232}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;b \leq -5.6 \cdot 10^{+97}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-81} \lor \neg \left(b \leq 6.5 \cdot 10^{+55}\right):\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 28.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{if}\;i \leq -2.4 \cdot 10^{+77}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;i \leq -2 \cdot 10^{-161}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -5.5 \cdot 10^{-251}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 6.5 \cdot 10^{+193}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* z b) (- c))))
   (if (<= i -2.4e+77)
     (* b (* a i))
     (if (<= i -2e-161)
       t_1
       (if (<= i -5.5e-251)
         (* x (* y z))
         (if (<= i 6.5e+193) t_1 (* 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 t_1 = (z * b) * -c;
	double tmp;
	if (i <= -2.4e+77) {
		tmp = b * (a * i);
	} else if (i <= -2e-161) {
		tmp = t_1;
	} else if (i <= -5.5e-251) {
		tmp = x * (y * z);
	} else if (i <= 6.5e+193) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (z * b) * -c
    if (i <= (-2.4d+77)) then
        tmp = b * (a * i)
    else if (i <= (-2d-161)) then
        tmp = t_1
    else if (i <= (-5.5d-251)) then
        tmp = x * (y * z)
    else if (i <= 6.5d+193) then
        tmp = t_1
    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 t_1 = (z * b) * -c;
	double tmp;
	if (i <= -2.4e+77) {
		tmp = b * (a * i);
	} else if (i <= -2e-161) {
		tmp = t_1;
	} else if (i <= -5.5e-251) {
		tmp = x * (y * z);
	} else if (i <= 6.5e+193) {
		tmp = t_1;
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (z * b) * -c
	tmp = 0
	if i <= -2.4e+77:
		tmp = b * (a * i)
	elif i <= -2e-161:
		tmp = t_1
	elif i <= -5.5e-251:
		tmp = x * (y * z)
	elif i <= 6.5e+193:
		tmp = t_1
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(z * b) * Float64(-c))
	tmp = 0.0
	if (i <= -2.4e+77)
		tmp = Float64(b * Float64(a * i));
	elseif (i <= -2e-161)
		tmp = t_1;
	elseif (i <= -5.5e-251)
		tmp = Float64(x * Float64(y * z));
	elseif (i <= 6.5e+193)
		tmp = t_1;
	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)
	t_1 = (z * b) * -c;
	tmp = 0.0;
	if (i <= -2.4e+77)
		tmp = b * (a * i);
	elseif (i <= -2e-161)
		tmp = t_1;
	elseif (i <= -5.5e-251)
		tmp = x * (y * z);
	elseif (i <= 6.5e+193)
		tmp = t_1;
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(z * b), $MachinePrecision] * (-c)), $MachinePrecision]}, If[LessEqual[i, -2.4e+77], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -2e-161], t$95$1, If[LessEqual[i, -5.5e-251], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 6.5e+193], t$95$1, N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -2.3999999999999999e77

   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 inf 45.0%

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

   4. Taylor expanded in a around inf 39.0%

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

      1. *-commutative 39.0%

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

   6. Simplified 39.0%

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

   if -2.3999999999999999e77 < i < -2.00000000000000006e-161 or -5.5e-251 < i < 6.4999999999999997e193

   1. Initial program 77.1%

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

   3. Taylor expanded in z around 0 80.9%

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

   4. Taylor expanded in a around 0 73.5%

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

   5. Taylor expanded in a around 0 69.7%

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

   6. Taylor expanded in b around inf 34.1%

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

      1. mul-1-neg 34.1%

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

      2. *-commutative 34.1%

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

      3. associate-*r* 37.1%

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

      4. *-commutative 37.1%

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

      5. distribute-rgt-neg-out 37.1%

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

      6. *-commutative 37.1%

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

      7. distribute-rgt-neg-in 37.1%

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

   8. Simplified 37.1%

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

   if -2.00000000000000006e-161 < i < -5.5e-251

   1. Initial program 81.8%

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

   3. Taylor expanded in x around inf 69.0%

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

      1. *-commutative 69.0%

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

   5. Simplified 69.0%

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

   6. Taylor expanded in z around inf 51.2%

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

   if 6.4999999999999997e193 < i

   1. Initial program 59.0%

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

   3. Taylor expanded in b around inf 42.3%

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

   4. Taylor expanded in a around inf 42.3%

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

      1. *-commutative 42.3%

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

   6. Simplified 42.3%

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

4. Final simplification 39.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.4 \cdot 10^{+77}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;i \leq -2 \cdot 10^{-161}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{elif}\;i \leq -5.5 \cdot 10^{-251}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 6.5 \cdot 10^{+193}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 40.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+253}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-70} \lor \neg \left(y \leq 1.02 \cdot 10^{+100}\right):\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -7.8e+253)
   (* x (* y z))
   (if (or (<= y -7.5e-70) (not (<= y 1.02e+100)))
     (* i (* y (- j)))
     (* b (- (* a i) (* z c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -7.8e+253) {
		tmp = x * (y * z);
	} else if ((y <= -7.5e-70) || !(y <= 1.02e+100)) {
		tmp = i * (y * -j);
	} else {
		tmp = b * ((a * i) - (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-7.8d+253)) then
        tmp = x * (y * z)
    else if ((y <= (-7.5d-70)) .or. (.not. (y <= 1.02d+100))) then
        tmp = i * (y * -j)
    else
        tmp = b * ((a * i) - (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -7.8e+253) {
		tmp = x * (y * z);
	} else if ((y <= -7.5e-70) || !(y <= 1.02e+100)) {
		tmp = i * (y * -j);
	} else {
		tmp = b * ((a * i) - (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -7.8e+253:
		tmp = x * (y * z)
	elif (y <= -7.5e-70) or not (y <= 1.02e+100):
		tmp = i * (y * -j)
	else:
		tmp = b * ((a * i) - (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -7.8e+253)
		tmp = Float64(x * Float64(y * z));
	elseif ((y <= -7.5e-70) || !(y <= 1.02e+100))
		tmp = Float64(i * Float64(y * Float64(-j)));
	else
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -7.8e+253)
		tmp = x * (y * z);
	elseif ((y <= -7.5e-70) || ~((y <= 1.02e+100)))
		tmp = i * (y * -j);
	else
		tmp = b * ((a * i) - (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -7.8e+253], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -7.5e-70], N[Not[LessEqual[y, 1.02e+100]], $MachinePrecision]], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.8000000000000003e253

   1. Initial program 54.5%

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

   3. Taylor expanded in x around inf 62.6%

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

      1. *-commutative 62.6%

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

   5. Simplified 62.6%

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

   6. Taylor expanded in z around inf 62.6%

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

   if -7.8000000000000003e253 < y < -7.49999999999999973e-70 or 1.0199999999999999e100 < y

   1. Initial program 69.8%

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

   3. Taylor expanded in i around inf 50.9%

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

      1. distribute-lft-out-- 50.9%

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

      2. *-commutative 50.9%

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

   5. Simplified 50.9%

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

   6. Taylor expanded in j around inf 46.3%

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

   7. Taylor expanded in i around 0 46.3%

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

      1. associate-*r* 46.3%

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

      2. neg-mul-1 46.3%

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

      3. *-commutative 46.3%

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

   9. Simplified 46.3%

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

   if -7.49999999999999973e-70 < y < 1.0199999999999999e100

   1. Initial program 78.0%

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

   3. Taylor expanded in b around inf 49.5%

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

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+253}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-70} \lor \neg \left(y \leq 1.02 \cdot 10^{+100}\right):\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 44.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{+206}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-50} \lor \neg \left(a \leq 4 \cdot 10^{+74}\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -1.1e+206)
   (* (* t a) (- x))
   (if (or (<= a -1.9e-50) (not (<= a 4e+74)))
     (* b (- (* a i) (* z c)))
     (* c (- (* t j) (* z b))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -1.1e+206) {
		tmp = (t * a) * -x;
	} else if ((a <= -1.9e-50) || !(a <= 4e+74)) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = c * ((t * j) - (z * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (a <= (-1.1d+206)) then
        tmp = (t * a) * -x
    else if ((a <= (-1.9d-50)) .or. (.not. (a <= 4d+74))) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = c * ((t * j) - (z * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -1.1e+206) {
		tmp = (t * a) * -x;
	} else if ((a <= -1.9e-50) || !(a <= 4e+74)) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = c * ((t * j) - (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -1.1e+206:
		tmp = (t * a) * -x
	elif (a <= -1.9e-50) or not (a <= 4e+74):
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = c * ((t * j) - (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -1.1e+206)
		tmp = Float64(Float64(t * a) * Float64(-x));
	elseif ((a <= -1.9e-50) || !(a <= 4e+74))
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -1.1e+206)
		tmp = (t * a) * -x;
	elseif ((a <= -1.9e-50) || ~((a <= 4e+74)))
		tmp = b * ((a * i) - (z * c));
	else
		tmp = c * ((t * j) - (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -1.1e+206], N[(N[(t * a), $MachinePrecision] * (-x)), $MachinePrecision], If[Or[LessEqual[a, -1.9e-50], N[Not[LessEqual[a, 4e+74]], $MachinePrecision]], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.10000000000000001e206

   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 x around inf 69.4%

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

      1. *-commutative 69.4%

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

   5. Simplified 69.4%

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

   6. Taylor expanded in z around 0 69.6%

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

      1. neg-mul-1 69.6%

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

      2. *-commutative 69.6%

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

      3. distribute-rgt-neg-in 69.6%

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

   8. Simplified 69.6%

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

   if -1.10000000000000001e206 < a < -1.9e-50 or 3.99999999999999981e74 < a

   1. Initial program 68.7%

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

   3. Taylor expanded in b around inf 50.8%

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

   if -1.9e-50 < a < 3.99999999999999981e74

   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 c around inf 51.8%

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

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{+206}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-50} \lor \neg \left(a \leq 4 \cdot 10^{+74}\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 27.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ \mathbf{if}\;j \leq -1.6 \cdot 10^{+247}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 3.6 \cdot 10^{-270}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 3.8 \cdot 10^{-9}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j))))
   (if (<= j -1.6e+247)
     t_1
     (if (<= j 3.6e-270) (* x (* y z)) (if (<= j 3.8e-9) (* 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 = c * (t * j);
	double tmp;
	if (j <= -1.6e+247) {
		tmp = t_1;
	} else if (j <= 3.6e-270) {
		tmp = x * (y * z);
	} else if (j <= 3.8e-9) {
		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 = c * (t * j)
    if (j <= (-1.6d+247)) then
        tmp = t_1
    else if (j <= 3.6d-270) then
        tmp = x * (y * z)
    else if (j <= 3.8d-9) 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 = c * (t * j);
	double tmp;
	if (j <= -1.6e+247) {
		tmp = t_1;
	} else if (j <= 3.6e-270) {
		tmp = x * (y * z);
	} else if (j <= 3.8e-9) {
		tmp = b * (a * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (t * j)
	tmp = 0
	if j <= -1.6e+247:
		tmp = t_1
	elif j <= 3.6e-270:
		tmp = x * (y * z)
	elif j <= 3.8e-9:
		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(c * Float64(t * j))
	tmp = 0.0
	if (j <= -1.6e+247)
		tmp = t_1;
	elseif (j <= 3.6e-270)
		tmp = Float64(x * Float64(y * z));
	elseif (j <= 3.8e-9)
		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 = c * (t * j);
	tmp = 0.0;
	if (j <= -1.6e+247)
		tmp = t_1;
	elseif (j <= 3.6e-270)
		tmp = x * (y * z);
	elseif (j <= 3.8e-9)
		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[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.6e+247], t$95$1, If[LessEqual[j, 3.6e-270], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.8e-9], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.60000000000000011e247 or 3.80000000000000011e-9 < j

   1. Initial program 67.2%

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

   3. Taylor expanded in y around 0 53.5%

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

   4. Taylor expanded in j around inf 45.7%

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

   if -1.60000000000000011e247 < j < 3.5999999999999998e-270

   1. Initial program 76.5%

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

   3. Taylor expanded in x around inf 46.3%

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

      1. *-commutative 46.3%

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

   5. Simplified 46.3%

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

   6. Taylor expanded in z around inf 29.6%

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

   if 3.5999999999999998e-270 < j < 3.80000000000000011e-9

   1. Initial program 76.6%

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

   3. Taylor expanded in b around inf 53.9%

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

   4. Taylor expanded in a around inf 28.8%

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

      1. *-commutative 28.8%

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

   6. Simplified 28.8%

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

4. Final simplification 33.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.6 \cdot 10^{+247}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;j \leq 3.6 \cdot 10^{-270}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 3.8 \cdot 10^{-9}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 52.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.1 \cdot 10^{-35} \lor \neg \left(b \leq 3.2 \cdot 10^{-31}\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -2.1e-35) (not (<= b 3.2e-31)))
   (* b (- (* a i) (* z c)))
   (* j (- (* t c) (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -2.1e-35) || !(b <= 3.2e-31)) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = j * ((t * c) - (y * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-2.1d-35)) .or. (.not. (b <= 3.2d-31))) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = j * ((t * c) - (y * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -2.1e-35) || !(b <= 3.2e-31)) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = j * ((t * c) - (y * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -2.1e-35) or not (b <= 3.2e-31):
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = j * ((t * c) - (y * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -2.1e-35) || !(b <= 3.2e-31))
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -2.1e-35) || ~((b <= 3.2e-31)))
		tmp = b * ((a * i) - (z * c));
	else
		tmp = j * ((t * c) - (y * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -2.1e-35], N[Not[LessEqual[b, 3.2e-31]], $MachinePrecision]], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.1e-35 or 3.20000000000000018e-31 < b

   1. Initial program 75.3%

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

   3. Taylor expanded in b around inf 65.5%

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

   if -2.1e-35 < b < 3.20000000000000018e-31

   1. Initial program 72.3%

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

   3. Taylor expanded in j around inf 51.1%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.1 \cdot 10^{-35} \lor \neg \left(b \leq 3.2 \cdot 10^{-31}\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 30.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{-63} \lor \neg \left(a \leq 9.4 \cdot 10^{+73}\right):\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -7.2e-63) (not (<= a 9.4e+73))) (* b (* a i)) (* 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 ((a <= -7.2e-63) || !(a <= 9.4e+73)) {
		tmp = b * (a * i);
	} 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 ((a <= (-7.2d-63)) .or. (.not. (a <= 9.4d+73))) then
        tmp = b * (a * i)
    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 ((a <= -7.2e-63) || !(a <= 9.4e+73)) {
		tmp = b * (a * i);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (a <= -7.2e-63) or not (a <= 9.4e+73):
		tmp = b * (a * i)
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -7.2e-63) || !(a <= 9.4e+73))
		tmp = Float64(b * Float64(a * i));
	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 ((a <= -7.2e-63) || ~((a <= 9.4e+73)))
		tmp = b * (a * i);
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -7.2e-63], N[Not[LessEqual[a, 9.4e+73]], $MachinePrecision]], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -7.20000000000000016e-63 or 9.4000000000000004e73 < a

   1. Initial program 68.7%

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

   3. Taylor expanded in b around inf 48.6%

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

   4. Taylor expanded in a around inf 38.1%

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

      1. *-commutative 38.1%

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

   6. Simplified 38.1%

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

   if -7.20000000000000016e-63 < a < 9.4000000000000004e73

   1. Initial program 78.1%

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

   3. Taylor expanded in y around 0 54.6%

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

   4. Taylor expanded in j around inf 25.6%

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

4. Final simplification 31.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{-63} \lor \neg \left(a \leq 9.4 \cdot 10^{+73}\right):\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 22.7% 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 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 b around inf 41.3%

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

4. Taylor expanded in a around inf 20.9%

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

   1. *-commutative 20.9%

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

6. Simplified 20.9%

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

7. Final simplification 20.9%

   \[\leadsto a \cdot \left(b \cdot i\right) \]
8. Add Preprocessing

Developer target: 69.8% 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 2024066 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :alt
  (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)))))