Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.2% → 80.8%

Time: 20.3s

Alternatives: 23

Speedup: 0.5×

• 57.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.2% 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: 80.8% accurate, 0.2× speedup

Math

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

FPCore

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 90.9%

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

      1. cancel-sign-sub-inv 90.9%

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

      2. cancel-sign-sub 90.9%

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

      3. *-commutative 90.9%

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

      4. fma-neg 90.9%

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

      5. distribute-rgt-neg-in 90.9%

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

      6. remove-double-neg 90.9%

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

      7. *-commutative 90.9%

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

      8. *-commutative 90.9%

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

      9. sub-neg 90.9%

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

      10. sub-neg 90.9%

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

      11. *-commutative 90.9%

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

      12. *-commutative 90.9%

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

   3. Simplified 90.9%

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

   if +inf.0 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 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 b around inf 57.7%

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

      1. *-commutative 57.7%

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

   5. Simplified 57.7%

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

4. Final simplification 84.9%

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

Alternative 2: 80.8% accurate, 0.5× speedup

Math

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

FPCore

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

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((t * c) - (y * i))) - ((b * ((z * c) - (a * i))) + (x * ((t * a) - (y * z))))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = b * ((a * i) - (z * c))
	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(Float64(b * Float64(Float64(z * c) - Float64(a * i))) + Float64(x * Float64(Float64(t * a) - Float64(y * z)))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	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)
	t_1 = (j * ((t * c) - (y * i))) - ((b * ((z * c) - (a * i))) + (x * ((t * a) - (y * z))));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = b * ((a * i) - (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * 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 90.9%

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

   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 b around inf 57.7%

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

      1. *-commutative 57.7%

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

   5. Simplified 57.7%

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

4. Final simplification 84.9%

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

Alternative 3: 63.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_3 := t\_2 - x \cdot \left(t \cdot a - y \cdot z\right)\\ t_4 := t \cdot \left(c \cdot j - x \cdot a\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;j \leq -5.2 \cdot 10^{+51}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq -0.000185:\\ \;\;\;\;t\_1 - \left(x \cdot y\right) \cdot \left(i \cdot \frac{j}{x} - z\right)\\ \mathbf{elif}\;j \leq 4.4 \cdot 10^{-205}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;j \leq 5.6 \cdot 10^{-91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 3 \cdot 10^{+17}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;j \leq 1.72 \cdot 10^{+195}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c))))
        (t_2 (* j (- (* t c) (* y i))))
        (t_3 (- t_2 (* x (- (* t a) (* y z)))))
        (t_4 (+ (* t (- (* c j) (* x a))) (* z (- (* x y) (* b c))))))
   (if (<= j -5.2e+51)
     t_3
     (if (<= j -0.000185)
       (- t_1 (* (* x y) (- (* i (/ j x)) z)))
       (if (<= j 4.4e-205)
         t_4
         (if (<= j 5.6e-91)
           t_1
           (if (<= j 3e+17) t_4 (if (<= j 1.72e+195) t_3 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = j * ((t * c) - (y * i));
	double t_3 = t_2 - (x * ((t * a) - (y * z)));
	double t_4 = (t * ((c * j) - (x * a))) + (z * ((x * y) - (b * c)));
	double tmp;
	if (j <= -5.2e+51) {
		tmp = t_3;
	} else if (j <= -0.000185) {
		tmp = t_1 - ((x * y) * ((i * (j / x)) - z));
	} else if (j <= 4.4e-205) {
		tmp = t_4;
	} else if (j <= 5.6e-91) {
		tmp = t_1;
	} else if (j <= 3e+17) {
		tmp = t_4;
	} else if (j <= 1.72e+195) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = j * ((t * c) - (y * i))
    t_3 = t_2 - (x * ((t * a) - (y * z)))
    t_4 = (t * ((c * j) - (x * a))) + (z * ((x * y) - (b * c)))
    if (j <= (-5.2d+51)) then
        tmp = t_3
    else if (j <= (-0.000185d0)) then
        tmp = t_1 - ((x * y) * ((i * (j / x)) - z))
    else if (j <= 4.4d-205) then
        tmp = t_4
    else if (j <= 5.6d-91) then
        tmp = t_1
    else if (j <= 3d+17) then
        tmp = t_4
    else if (j <= 1.72d+195) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = j * ((t * c) - (y * i));
	double t_3 = t_2 - (x * ((t * a) - (y * z)));
	double t_4 = (t * ((c * j) - (x * a))) + (z * ((x * y) - (b * c)));
	double tmp;
	if (j <= -5.2e+51) {
		tmp = t_3;
	} else if (j <= -0.000185) {
		tmp = t_1 - ((x * y) * ((i * (j / x)) - z));
	} else if (j <= 4.4e-205) {
		tmp = t_4;
	} else if (j <= 5.6e-91) {
		tmp = t_1;
	} else if (j <= 3e+17) {
		tmp = t_4;
	} else if (j <= 1.72e+195) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = j * ((t * c) - (y * i))
	t_3 = t_2 - (x * ((t * a) - (y * z)))
	t_4 = (t * ((c * j) - (x * a))) + (z * ((x * y) - (b * c)))
	tmp = 0
	if j <= -5.2e+51:
		tmp = t_3
	elif j <= -0.000185:
		tmp = t_1 - ((x * y) * ((i * (j / x)) - z))
	elif j <= 4.4e-205:
		tmp = t_4
	elif j <= 5.6e-91:
		tmp = t_1
	elif j <= 3e+17:
		tmp = t_4
	elif j <= 1.72e+195:
		tmp = t_3
	else:
		tmp = t_2
	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(j * Float64(Float64(t * c) - Float64(y * i)))
	t_3 = Float64(t_2 - Float64(x * Float64(Float64(t * a) - Float64(y * z))))
	t_4 = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) + Float64(z * Float64(Float64(x * y) - Float64(b * c))))
	tmp = 0.0
	if (j <= -5.2e+51)
		tmp = t_3;
	elseif (j <= -0.000185)
		tmp = Float64(t_1 - Float64(Float64(x * y) * Float64(Float64(i * Float64(j / x)) - z)));
	elseif (j <= 4.4e-205)
		tmp = t_4;
	elseif (j <= 5.6e-91)
		tmp = t_1;
	elseif (j <= 3e+17)
		tmp = t_4;
	elseif (j <= 1.72e+195)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = j * ((t * c) - (y * i));
	t_3 = t_2 - (x * ((t * a) - (y * z)));
	t_4 = (t * ((c * j) - (x * a))) + (z * ((x * y) - (b * c)));
	tmp = 0.0;
	if (j <= -5.2e+51)
		tmp = t_3;
	elseif (j <= -0.000185)
		tmp = t_1 - ((x * y) * ((i * (j / x)) - z));
	elseif (j <= 4.4e-205)
		tmp = t_4;
	elseif (j <= 5.6e-91)
		tmp = t_1;
	elseif (j <= 3e+17)
		tmp = t_4;
	elseif (j <= 1.72e+195)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $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[(t$95$2 - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -5.2e+51], t$95$3, If[LessEqual[j, -0.000185], N[(t$95$1 - N[(N[(x * y), $MachinePrecision] * N[(N[(i * N[(j / x), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.4e-205], t$95$4, If[LessEqual[j, 5.6e-91], t$95$1, If[LessEqual[j, 3e+17], t$95$4, If[LessEqual[j, 1.72e+195], t$95$3, t$95$2]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -5.2000000000000002e51 or 3e17 < j < 1.71999999999999998e195

   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 b around 0 77.9%

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

   if -5.2000000000000002e51 < j < -1.85e-4

   1. Initial program 78.3%

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

   3. Taylor expanded in y around 0 78.3%

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

   4. Taylor expanded in x around inf 78.5%

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

      1. +-commutative 78.5%

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

      2. mul-1-neg 78.5%

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

      3. unsub-neg 78.5%

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

      4. associate-/l* 78.5%

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

   6. Simplified 78.5%

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

   7. Taylor expanded in y around 0 78.6%

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

   9. Simplified 78.5%

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

   10. Taylor expanded in t around 0 93.1%

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

       1. associate-*r* 93.0%

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

       2. sub-neg 93.0%

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

       3. associate-*r/ 93.0%

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

       4. sub-neg 93.0%

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

       5. sub-neg 93.0%

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

       6. *-commutative 93.0%

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

       7. distribute-rgt-in 93.0%

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

       8. *-commutative 93.0%

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

       9. distribute-lft-neg-in 93.0%

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

       10. distribute-rgt-in 93.0%

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

       11. cancel-sign-sub-inv 93.0%

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

   12. Simplified 93.0%

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

   if -1.85e-4 < j < 4.40000000000000018e-205 or 5.6e-91 < j < 3e17

   1. Initial program 75.9%

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

   3. Taylor expanded in y around 0 83.0%

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

   4. Taylor expanded in x around inf 79.9%

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

      1. +-commutative 79.9%

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

      2. mul-1-neg 79.9%

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

      3. unsub-neg 79.9%

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

      4. associate-/l* 79.9%

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

   6. Simplified 79.9%

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

   7. Taylor expanded in i around 0 67.3%

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

      1. sub-neg 67.3%

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

      2. associate-+r+ 67.3%

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

      3. associate-+l+ 67.3%

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

      4. +-commutative 67.3%

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

      5. mul-1-neg 67.3%

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

      6. associate-*r* 67.0%

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

      7. *-commutative 67.0%

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

      8. associate-*r* 69.1%

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

      9. distribute-lft-neg-in 69.1%

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

      10. mul-1-neg 69.1%

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

      11. distribute-rgt-in 69.1%

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

      12. mul-1-neg 69.1%

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

      13. unsub-neg 69.1%

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

      14. *-commutative 69.1%

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

      15. *-commutative 69.1%

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

   9. Simplified 80.5%

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

   if 4.40000000000000018e-205 < j < 5.6e-91

   1. Initial program 63.8%

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

   3. Taylor expanded in b around inf 69.1%

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

      1. *-commutative 69.1%

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

   5. Simplified 69.1%

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

   if 1.71999999999999998e195 < j

   1. Initial program 69.0%

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

   3. Taylor expanded in j around inf 67.9%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -5.2 \cdot 10^{+51}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;j \leq -0.000185:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - \left(x \cdot y\right) \cdot \left(i \cdot \frac{j}{x} - z\right)\\ \mathbf{elif}\;j \leq 4.4 \cdot 10^{-205}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 5.6 \cdot 10^{-91}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 3 \cdot 10^{+17}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 1.72 \cdot 10^{+195}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 49.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{+137}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-102}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-270}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-296}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-80}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+110}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a)))) (t_2 (* z (- (* x y) (* b c)))))
   (if (<= z -2.1e+137)
     t_2
     (if (<= z -4.1e-102)
       t_1
       (if (<= z -9.5e-270)
         (* i (- (* a b) (* y j)))
         (if (<= z 1.15e-296)
           t_1
           (if (<= z 1.4e-80)
             (* j (- (* t c) (* y i)))
             (if (<= z 6.4e-22)
               t_1
               (if (<= z 1.15e+110) (* b (- (* a i) (* z c))) 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 = t * ((c * j) - (x * a));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -2.1e+137) {
		tmp = t_2;
	} else if (z <= -4.1e-102) {
		tmp = t_1;
	} else if (z <= -9.5e-270) {
		tmp = i * ((a * b) - (y * j));
	} else if (z <= 1.15e-296) {
		tmp = t_1;
	} else if (z <= 1.4e-80) {
		tmp = j * ((t * c) - (y * i));
	} else if (z <= 6.4e-22) {
		tmp = t_1;
	} else if (z <= 1.15e+110) {
		tmp = b * ((a * i) - (z * c));
	} 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 = t * ((c * j) - (x * a))
    t_2 = z * ((x * y) - (b * c))
    if (z <= (-2.1d+137)) then
        tmp = t_2
    else if (z <= (-4.1d-102)) then
        tmp = t_1
    else if (z <= (-9.5d-270)) then
        tmp = i * ((a * b) - (y * j))
    else if (z <= 1.15d-296) then
        tmp = t_1
    else if (z <= 1.4d-80) then
        tmp = j * ((t * c) - (y * i))
    else if (z <= 6.4d-22) then
        tmp = t_1
    else if (z <= 1.15d+110) then
        tmp = b * ((a * i) - (z * c))
    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 = t * ((c * j) - (x * a));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -2.1e+137) {
		tmp = t_2;
	} else if (z <= -4.1e-102) {
		tmp = t_1;
	} else if (z <= -9.5e-270) {
		tmp = i * ((a * b) - (y * j));
	} else if (z <= 1.15e-296) {
		tmp = t_1;
	} else if (z <= 1.4e-80) {
		tmp = j * ((t * c) - (y * i));
	} else if (z <= 6.4e-22) {
		tmp = t_1;
	} else if (z <= 1.15e+110) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	t_2 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -2.1e+137:
		tmp = t_2
	elif z <= -4.1e-102:
		tmp = t_1
	elif z <= -9.5e-270:
		tmp = i * ((a * b) - (y * j))
	elif z <= 1.15e-296:
		tmp = t_1
	elif z <= 1.4e-80:
		tmp = j * ((t * c) - (y * i))
	elif z <= 6.4e-22:
		tmp = t_1
	elif z <= 1.15e+110:
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_2 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (z <= -2.1e+137)
		tmp = t_2;
	elseif (z <= -4.1e-102)
		tmp = t_1;
	elseif (z <= -9.5e-270)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (z <= 1.15e-296)
		tmp = t_1;
	elseif (z <= 1.4e-80)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (z <= 6.4e-22)
		tmp = t_1;
	elseif (z <= 1.15e+110)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((c * j) - (x * a));
	t_2 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -2.1e+137)
		tmp = t_2;
	elseif (z <= -4.1e-102)
		tmp = t_1;
	elseif (z <= -9.5e-270)
		tmp = i * ((a * b) - (y * j));
	elseif (z <= 1.15e-296)
		tmp = t_1;
	elseif (z <= 1.4e-80)
		tmp = j * ((t * c) - (y * i));
	elseif (z <= 6.4e-22)
		tmp = t_1;
	elseif (z <= 1.15e+110)
		tmp = b * ((a * i) - (z * c));
	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[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.1e+137], t$95$2, If[LessEqual[z, -4.1e-102], t$95$1, If[LessEqual[z, -9.5e-270], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e-296], t$95$1, If[LessEqual[z, 1.4e-80], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.4e-22], t$95$1, If[LessEqual[z, 1.15e+110], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.0999999999999999e137 or 1.15e110 < z

   1. Initial program 54.2%

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

   3. Taylor expanded in z around inf 77.2%

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

      1. *-commutative 77.2%

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

   5. Simplified 77.2%

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

   if -2.0999999999999999e137 < z < -4.1000000000000003e-102 or -9.5000000000000006e-270 < z < 1.15000000000000002e-296 or 1.39999999999999995e-80 < z < 6.39999999999999975e-22

   1. Initial program 77.9%

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

   3. Taylor expanded in t around inf 61.4%

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

      1. +-commutative 61.4%

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

      2. mul-1-neg 61.4%

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

      3. unsub-neg 61.4%

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

      4. *-commutative 61.4%

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

      5. *-commutative 61.4%

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

   5. Simplified 61.4%

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

   if -4.1000000000000003e-102 < z < -9.5000000000000006e-270

   1. Initial program 81.0%

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

   3. Taylor expanded in y around 0 85.2%

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

   4. Taylor expanded in x around inf 81.1%

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

      1. +-commutative 81.1%

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

      2. mul-1-neg 81.1%

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

      3. unsub-neg 81.1%

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

      4. associate-/l* 81.1%

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

   6. Simplified 81.1%

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

   7. Taylor expanded in y around 0 79.0%

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

   9. Simplified 74.5%

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

   10. Taylor expanded in i around inf 65.4%

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

       1. sub-neg 65.4%

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

       2. neg-mul-1 65.4%

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

       3. mul-1-neg 65.4%

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

       4. remove-double-neg 65.4%

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

       5. +-commutative 65.4%

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

       6. unsub-neg 65.4%

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

       7. *-commutative 65.4%

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

   12. Simplified 65.4%

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

   if 1.15000000000000002e-296 < z < 1.39999999999999995e-80

   1. Initial program 88.4%

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

   3. Taylor expanded in j around inf 62.8%

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

   if 6.39999999999999975e-22 < z < 1.15e110

   1. Initial program 86.4%

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

   3. Taylor expanded in b around inf 63.1%

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

      1. *-commutative 63.1%

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

   5. Simplified 63.1%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+137}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-102}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-270}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-296}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-80}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-22}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+110}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -3.1 \cdot 10^{+232}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{+132}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq -1.3 \cdot 10^{-52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-160}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{+28}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{+107}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{+132}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= b -3.1e+232)
     t_1
     (if (<= b -1.35e+132)
       (* i (- (* a b) (* y j)))
       (if (<= b -1.3e-52)
         t_1
         (if (<= b 2.5e-160)
           (* x (- (* y z) (* t a)))
           (if (<= b 4.1e+28)
             (* t (- (* c j) (* x a)))
             (if (<= b 3.6e+107)
               (* y (- (* x z) (* i j)))
               (if (<= b 2.8e+132) (* c (- (* t j) (* z b))) t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -3.1e+232) {
		tmp = t_1;
	} else if (b <= -1.35e+132) {
		tmp = i * ((a * b) - (y * j));
	} else if (b <= -1.3e-52) {
		tmp = t_1;
	} else if (b <= 2.5e-160) {
		tmp = x * ((y * z) - (t * a));
	} else if (b <= 4.1e+28) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= 3.6e+107) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 2.8e+132) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    if (b <= (-3.1d+232)) then
        tmp = t_1
    else if (b <= (-1.35d+132)) then
        tmp = i * ((a * b) - (y * j))
    else if (b <= (-1.3d-52)) then
        tmp = t_1
    else if (b <= 2.5d-160) then
        tmp = x * ((y * z) - (t * a))
    else if (b <= 4.1d+28) then
        tmp = t * ((c * j) - (x * a))
    else if (b <= 3.6d+107) then
        tmp = y * ((x * z) - (i * j))
    else if (b <= 2.8d+132) then
        tmp = c * ((t * j) - (z * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -3.1e+232) {
		tmp = t_1;
	} else if (b <= -1.35e+132) {
		tmp = i * ((a * b) - (y * j));
	} else if (b <= -1.3e-52) {
		tmp = t_1;
	} else if (b <= 2.5e-160) {
		tmp = x * ((y * z) - (t * a));
	} else if (b <= 4.1e+28) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= 3.6e+107) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 2.8e+132) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -3.1e+232:
		tmp = t_1
	elif b <= -1.35e+132:
		tmp = i * ((a * b) - (y * j))
	elif b <= -1.3e-52:
		tmp = t_1
	elif b <= 2.5e-160:
		tmp = x * ((y * z) - (t * a))
	elif b <= 4.1e+28:
		tmp = t * ((c * j) - (x * a))
	elif b <= 3.6e+107:
		tmp = y * ((x * z) - (i * j))
	elif b <= 2.8e+132:
		tmp = c * ((t * j) - (z * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -3.1e+232)
		tmp = t_1;
	elseif (b <= -1.35e+132)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (b <= -1.3e-52)
		tmp = t_1;
	elseif (b <= 2.5e-160)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (b <= 4.1e+28)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (b <= 3.6e+107)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (b <= 2.8e+132)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -3.1e+232)
		tmp = t_1;
	elseif (b <= -1.35e+132)
		tmp = i * ((a * b) - (y * j));
	elseif (b <= -1.3e-52)
		tmp = t_1;
	elseif (b <= 2.5e-160)
		tmp = x * ((y * z) - (t * a));
	elseif (b <= 4.1e+28)
		tmp = t * ((c * j) - (x * a));
	elseif (b <= 3.6e+107)
		tmp = y * ((x * z) - (i * j));
	elseif (b <= 2.8e+132)
		tmp = c * ((t * j) - (z * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.1e+232], t$95$1, If[LessEqual[b, -1.35e+132], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.3e-52], t$95$1, If[LessEqual[b, 2.5e-160], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.1e+28], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.6e+107], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.8e+132], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -3.09999999999999983e232 or -1.35e132 < b < -1.2999999999999999e-52 or 2.7999999999999999e132 < b

   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 69.0%

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

      1. *-commutative 69.0%

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

   5. Simplified 69.0%

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

   if -3.09999999999999983e232 < b < -1.35e132

   1. Initial program 72.7%

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

   3. Taylor expanded in y around 0 64.0%

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

   4. Taylor expanded in x around inf 54.9%

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

      1. +-commutative 54.9%

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

      2. mul-1-neg 54.9%

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

      3. unsub-neg 54.9%

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

      4. associate-/l* 54.9%

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

   6. Simplified 54.9%

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

   7. Taylor expanded in y around 0 55.2%

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

   9. Simplified 50.3%

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

   10. Taylor expanded in i around inf 68.6%

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

       1. sub-neg 68.6%

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

       2. neg-mul-1 68.6%

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

       3. mul-1-neg 68.6%

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

       4. remove-double-neg 68.6%

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

       5. +-commutative 68.6%

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

       6. unsub-neg 68.6%

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

       7. *-commutative 68.6%

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

   12. Simplified 68.6%

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

   if -1.2999999999999999e-52 < b < 2.49999999999999997e-160

   1. Initial program 73.6%

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

   3. Taylor expanded in y around 0 76.0%

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

   4. Taylor expanded in x around inf 57.9%

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

      1. mul-1-neg 57.9%

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

      2. *-commutative 57.9%

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

      3. +-commutative 57.9%

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

      4. sub-neg 57.9%

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

   6. Simplified 57.9%

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

   if 2.49999999999999997e-160 < b < 4.09999999999999981e28

   1. Initial program 86.1%

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

   3. Taylor expanded in t around inf 63.6%

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

      1. +-commutative 63.6%

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

      2. mul-1-neg 63.6%

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

      3. unsub-neg 63.6%

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

      4. *-commutative 63.6%

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

      5. *-commutative 63.6%

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

   5. Simplified 63.6%

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

   if 4.09999999999999981e28 < b < 3.5999999999999998e107

   1. Initial program 73.9%

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

   3. Taylor expanded in y around 0 74.0%

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

   4. Taylor expanded in y around inf 66.3%

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

      1. +-commutative 66.3%

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

      2. mul-1-neg 66.3%

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

      3. unsub-neg 66.3%

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

      4. *-commutative 66.3%

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

   6. Simplified 66.3%

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

   if 3.5999999999999998e107 < b < 2.7999999999999999e132

   1. Initial program 83.3%

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

   3. Taylor expanded in c around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. *-commutative 100.0%

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

   5. Simplified 100.0%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.1 \cdot 10^{+232}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{+132}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq -1.3 \cdot 10^{-52}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-160}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{+28}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{+107}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{+132}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 49.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.45 \cdot 10^{+233}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{+130}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -9.5 \cdot 10^{-53}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-160}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 10^{+53}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{+133}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* a b) (* y j)))) (t_2 (* b (- (* a i) (* z c)))))
   (if (<= b -1.45e+233)
     t_2
     (if (<= b -6.2e+130)
       t_1
       (if (<= b -9.5e-53)
         t_2
         (if (<= b 2.7e-160)
           (* x (- (* y z) (* t a)))
           (if (<= b 1e+53)
             (* t (- (* c j) (* x a)))
             (if (<= b 4e+96)
               t_1
               (if (<= b 2.2e+133) (* c (- (* t j) (* z b))) t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.45e+233) {
		tmp = t_2;
	} else if (b <= -6.2e+130) {
		tmp = t_1;
	} else if (b <= -9.5e-53) {
		tmp = t_2;
	} else if (b <= 2.7e-160) {
		tmp = x * ((y * z) - (t * a));
	} else if (b <= 1e+53) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= 4e+96) {
		tmp = t_1;
	} else if (b <= 2.2e+133) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i * ((a * b) - (y * j))
    t_2 = b * ((a * i) - (z * c))
    if (b <= (-1.45d+233)) then
        tmp = t_2
    else if (b <= (-6.2d+130)) then
        tmp = t_1
    else if (b <= (-9.5d-53)) then
        tmp = t_2
    else if (b <= 2.7d-160) then
        tmp = x * ((y * z) - (t * a))
    else if (b <= 1d+53) then
        tmp = t * ((c * j) - (x * a))
    else if (b <= 4d+96) then
        tmp = t_1
    else if (b <= 2.2d+133) then
        tmp = c * ((t * j) - (z * b))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.45e+233) {
		tmp = t_2;
	} else if (b <= -6.2e+130) {
		tmp = t_1;
	} else if (b <= -9.5e-53) {
		tmp = t_2;
	} else if (b <= 2.7e-160) {
		tmp = x * ((y * z) - (t * a));
	} else if (b <= 1e+53) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= 4e+96) {
		tmp = t_1;
	} else if (b <= 2.2e+133) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((a * b) - (y * j))
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -1.45e+233:
		tmp = t_2
	elif b <= -6.2e+130:
		tmp = t_1
	elif b <= -9.5e-53:
		tmp = t_2
	elif b <= 2.7e-160:
		tmp = x * ((y * z) - (t * a))
	elif b <= 1e+53:
		tmp = t * ((c * j) - (x * a))
	elif b <= 4e+96:
		tmp = t_1
	elif b <= 2.2e+133:
		tmp = c * ((t * j) - (z * b))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -1.45e+233)
		tmp = t_2;
	elseif (b <= -6.2e+130)
		tmp = t_1;
	elseif (b <= -9.5e-53)
		tmp = t_2;
	elseif (b <= 2.7e-160)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (b <= 1e+53)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (b <= 4e+96)
		tmp = t_1;
	elseif (b <= 2.2e+133)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((a * b) - (y * j));
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -1.45e+233)
		tmp = t_2;
	elseif (b <= -6.2e+130)
		tmp = t_1;
	elseif (b <= -9.5e-53)
		tmp = t_2;
	elseif (b <= 2.7e-160)
		tmp = x * ((y * z) - (t * a));
	elseif (b <= 1e+53)
		tmp = t * ((c * j) - (x * a));
	elseif (b <= 4e+96)
		tmp = t_1;
	elseif (b <= 2.2e+133)
		tmp = c * ((t * j) - (z * b));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.45e+233], t$95$2, If[LessEqual[b, -6.2e+130], t$95$1, If[LessEqual[b, -9.5e-53], t$95$2, If[LessEqual[b, 2.7e-160], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1e+53], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4e+96], t$95$1, If[LessEqual[b, 2.2e+133], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.45000000000000006e233 or -6.1999999999999999e130 < b < -9.5000000000000008e-53 or 2.2e133 < b

   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 69.0%

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

      1. *-commutative 69.0%

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

   5. Simplified 69.0%

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

   if -1.45000000000000006e233 < b < -6.1999999999999999e130 or 9.9999999999999999e52 < b < 4.0000000000000002e96

   1. Initial program 73.6%

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

   3. Taylor expanded in y around 0 70.8%

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

   4. Taylor expanded in x around inf 65.0%

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

      1. +-commutative 65.0%

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

      2. mul-1-neg 65.0%

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

      3. unsub-neg 65.0%

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

      4. associate-/l* 62.2%

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

   6. Simplified 62.2%

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

   7. Taylor expanded in y around 0 59.4%

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

   9. Simplified 53.1%

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

   10. Taylor expanded in i around inf 73.7%

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

       1. sub-neg 73.7%

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

       2. neg-mul-1 73.7%

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

       3. mul-1-neg 73.7%

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

       4. remove-double-neg 73.7%

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

       5. +-commutative 73.7%

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

       6. unsub-neg 73.7%

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

       7. *-commutative 73.7%

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

   12. Simplified 73.7%

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

   if -9.5000000000000008e-53 < b < 2.7000000000000001e-160

   1. Initial program 73.6%

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

   3. Taylor expanded in y around 0 76.0%

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

   4. Taylor expanded in x around inf 57.9%

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

      1. mul-1-neg 57.9%

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

      2. *-commutative 57.9%

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

      3. +-commutative 57.9%

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

      4. sub-neg 57.9%

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

   6. Simplified 57.9%

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

   if 2.7000000000000001e-160 < b < 9.9999999999999999e52

   1. Initial program 86.0%

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

   3. Taylor expanded in t around inf 60.5%

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

      1. +-commutative 60.5%

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

      2. mul-1-neg 60.5%

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

      3. unsub-neg 60.5%

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

      4. *-commutative 60.5%

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

      5. *-commutative 60.5%

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

   5. Simplified 60.5%

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

   if 4.0000000000000002e96 < b < 2.2e133

   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 c around inf 80.4%

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

      1. *-commutative 80.4%

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

      2. *-commutative 80.4%

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

   5. Simplified 80.4%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.45 \cdot 10^{+233}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{+130}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq -9.5 \cdot 10^{-53}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-160}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 10^{+53}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+96}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{+133}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right) - \left(i \cdot \left(y \cdot j\right) - c \cdot \left(t \cdot j\right)\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;x \leq -1.6 \cdot 10^{-45}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+101}:\\ \;\;\;\;\left(y \cdot \left(x \cdot z - i \cdot j\right) - a \cdot \left(x \cdot t\right)\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+145}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{+182}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* b (- (* a i) (* z c))) (- (* i (* y j)) (* c (* t j)))))
        (t_2 (+ (* t (- (* c j) (* x a))) (* z (- (* x y) (* b c))))))
   (if (<= x -1.6e-45)
     t_2
     (if (<= x 1.4e-61)
       t_1
       (if (<= x 5.6e+101)
         (+ (- (* y (- (* x z) (* i j))) (* a (* x t))) (* a (* b i)))
         (if (<= x 1.15e+145)
           t_1
           (if (<= x 1.08e+182)
             t_2
             (- (* j (- (* t c) (* y i))) (* x (- (* t a) (* y z)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (b * ((a * i) - (z * c))) - ((i * (y * j)) - (c * (t * j)));
	double t_2 = (t * ((c * j) - (x * a))) + (z * ((x * y) - (b * c)));
	double tmp;
	if (x <= -1.6e-45) {
		tmp = t_2;
	} else if (x <= 1.4e-61) {
		tmp = t_1;
	} else if (x <= 5.6e+101) {
		tmp = ((y * ((x * z) - (i * j))) - (a * (x * t))) + (a * (b * i));
	} else if (x <= 1.15e+145) {
		tmp = t_1;
	} else if (x <= 1.08e+182) {
		tmp = t_2;
	} else {
		tmp = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * ((a * i) - (z * c))) - ((i * (y * j)) - (c * (t * j)))
    t_2 = (t * ((c * j) - (x * a))) + (z * ((x * y) - (b * c)))
    if (x <= (-1.6d-45)) then
        tmp = t_2
    else if (x <= 1.4d-61) then
        tmp = t_1
    else if (x <= 5.6d+101) then
        tmp = ((y * ((x * z) - (i * j))) - (a * (x * t))) + (a * (b * i))
    else if (x <= 1.15d+145) then
        tmp = t_1
    else if (x <= 1.08d+182) then
        tmp = t_2
    else
        tmp = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (b * ((a * i) - (z * c))) - ((i * (y * j)) - (c * (t * j)));
	double t_2 = (t * ((c * j) - (x * a))) + (z * ((x * y) - (b * c)));
	double tmp;
	if (x <= -1.6e-45) {
		tmp = t_2;
	} else if (x <= 1.4e-61) {
		tmp = t_1;
	} else if (x <= 5.6e+101) {
		tmp = ((y * ((x * z) - (i * j))) - (a * (x * t))) + (a * (b * i));
	} else if (x <= 1.15e+145) {
		tmp = t_1;
	} else if (x <= 1.08e+182) {
		tmp = t_2;
	} else {
		tmp = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (b * ((a * i) - (z * c))) - ((i * (y * j)) - (c * (t * j)))
	t_2 = (t * ((c * j) - (x * a))) + (z * ((x * y) - (b * c)))
	tmp = 0
	if x <= -1.6e-45:
		tmp = t_2
	elif x <= 1.4e-61:
		tmp = t_1
	elif x <= 5.6e+101:
		tmp = ((y * ((x * z) - (i * j))) - (a * (x * t))) + (a * (b * i))
	elif x <= 1.15e+145:
		tmp = t_1
	elif x <= 1.08e+182:
		tmp = t_2
	else:
		tmp = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(b * Float64(Float64(a * i) - Float64(z * c))) - Float64(Float64(i * Float64(y * j)) - Float64(c * Float64(t * j))))
	t_2 = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) + Float64(z * Float64(Float64(x * y) - Float64(b * c))))
	tmp = 0.0
	if (x <= -1.6e-45)
		tmp = t_2;
	elseif (x <= 1.4e-61)
		tmp = t_1;
	elseif (x <= 5.6e+101)
		tmp = Float64(Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) - Float64(a * Float64(x * t))) + Float64(a * Float64(b * i)));
	elseif (x <= 1.15e+145)
		tmp = t_1;
	elseif (x <= 1.08e+182)
		tmp = t_2;
	else
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) - Float64(x * Float64(Float64(t * a) - Float64(y * z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (b * ((a * i) - (z * c))) - ((i * (y * j)) - (c * (t * j)));
	t_2 = (t * ((c * j) - (x * a))) + (z * ((x * y) - (b * c)));
	tmp = 0.0;
	if (x <= -1.6e-45)
		tmp = t_2;
	elseif (x <= 1.4e-61)
		tmp = t_1;
	elseif (x <= 5.6e+101)
		tmp = ((y * ((x * z) - (i * j))) - (a * (x * t))) + (a * (b * i));
	elseif (x <= 1.15e+145)
		tmp = t_1;
	elseif (x <= 1.08e+182)
		tmp = t_2;
	else
		tmp = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision] - N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.6e-45], t$95$2, If[LessEqual[x, 1.4e-61], t$95$1, If[LessEqual[x, 5.6e+101], N[(N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.15e+145], t$95$1, If[LessEqual[x, 1.08e+182], t$95$2, N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.60000000000000004e-45 or 1.15e145 < x < 1.08000000000000003e182

   1. Initial program 67.9%

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

   3. Taylor expanded in y around 0 66.4%

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

   4. Taylor expanded in x around inf 67.8%

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

      1. +-commutative 67.8%

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

      2. mul-1-neg 67.8%

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

      3. unsub-neg 67.8%

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

      4. associate-/l* 67.8%

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

   6. Simplified 67.8%

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

   7. Taylor expanded in i around 0 63.5%

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

      1. sub-neg 63.5%

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

      2. associate-+r+ 63.5%

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

      3. associate-+l+ 63.5%

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

      4. +-commutative 63.5%

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

      5. mul-1-neg 63.5%

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

      6. associate-*r* 65.1%

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

      7. *-commutative 65.1%

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

      8. associate-*r* 68.1%

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

      9. distribute-lft-neg-in 68.1%

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

      10. mul-1-neg 68.1%

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

      11. distribute-rgt-in 69.6%

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

      12. mul-1-neg 69.6%

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

      13. unsub-neg 69.6%

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

      14. *-commutative 69.6%

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

      15. *-commutative 69.6%

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

   9. Simplified 74.2%

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

   if -1.60000000000000004e-45 < x < 1.4000000000000001e-61 or 5.59999999999999962e101 < x < 1.15e145

   1. Initial program 72.0%

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

   3. Taylor expanded in y around 0 83.8%

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

   4. Taylor expanded in x around 0 77.6%

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

   if 1.4000000000000001e-61 < x < 5.59999999999999962e101

   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 77.6%

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

   4. Taylor expanded in c around 0 82.3%

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

   if 1.08000000000000003e182 < x

   1. Initial program 96.3%

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

   3. Taylor expanded in b around 0 92.4%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-45}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-61}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - \left(i \cdot \left(y \cdot j\right) - c \cdot \left(t \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+101}:\\ \;\;\;\;\left(y \cdot \left(x \cdot z - i \cdot j\right) - a \cdot \left(x \cdot t\right)\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+145}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - \left(i \cdot \left(y \cdot j\right) - c \cdot \left(t \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{+182}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{-51}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{-64} \lor \neg \left(x \leq 1.6 \cdot 10^{+32}\right) \land x \leq 4.6 \cdot 10^{+143}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - \left(i \cdot \left(y \cdot j\right) - c \cdot \left(t \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x -7.5e-51)
   (+ (* t (- (* c j) (* x a))) (* z (- (* x y) (* b c))))
   (if (or (<= x 2.55e-64) (and (not (<= x 1.6e+32)) (<= x 4.6e+143)))
     (- (* b (- (* a i) (* z c))) (- (* i (* y j)) (* c (* t j))))
     (- (* j (- (* t c) (* y i))) (* x (- (* t a) (* y z)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -7.5e-51) {
		tmp = (t * ((c * j) - (x * a))) + (z * ((x * y) - (b * c)));
	} else if ((x <= 2.55e-64) || (!(x <= 1.6e+32) && (x <= 4.6e+143))) {
		tmp = (b * ((a * i) - (z * c))) - ((i * (y * j)) - (c * (t * j)));
	} else {
		tmp = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (x <= (-7.5d-51)) then
        tmp = (t * ((c * j) - (x * a))) + (z * ((x * y) - (b * c)))
    else if ((x <= 2.55d-64) .or. (.not. (x <= 1.6d+32)) .and. (x <= 4.6d+143)) then
        tmp = (b * ((a * i) - (z * c))) - ((i * (y * j)) - (c * (t * j)))
    else
        tmp = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -7.5e-51) {
		tmp = (t * ((c * j) - (x * a))) + (z * ((x * y) - (b * c)));
	} else if ((x <= 2.55e-64) || (!(x <= 1.6e+32) && (x <= 4.6e+143))) {
		tmp = (b * ((a * i) - (z * c))) - ((i * (y * j)) - (c * (t * j)));
	} else {
		tmp = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if x <= -7.5e-51:
		tmp = (t * ((c * j) - (x * a))) + (z * ((x * y) - (b * c)))
	elif (x <= 2.55e-64) or (not (x <= 1.6e+32) and (x <= 4.6e+143)):
		tmp = (b * ((a * i) - (z * c))) - ((i * (y * j)) - (c * (t * j)))
	else:
		tmp = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= -7.5e-51)
		tmp = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) + Float64(z * Float64(Float64(x * y) - Float64(b * c))));
	elseif ((x <= 2.55e-64) || (!(x <= 1.6e+32) && (x <= 4.6e+143)))
		tmp = Float64(Float64(b * Float64(Float64(a * i) - Float64(z * c))) - Float64(Float64(i * Float64(y * j)) - Float64(c * Float64(t * j))));
	else
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) - Float64(x * Float64(Float64(t * a) - Float64(y * z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (x <= -7.5e-51)
		tmp = (t * ((c * j) - (x * a))) + (z * ((x * y) - (b * c)));
	elseif ((x <= 2.55e-64) || (~((x <= 1.6e+32)) && (x <= 4.6e+143)))
		tmp = (b * ((a * i) - (z * c))) - ((i * (y * j)) - (c * (t * j)));
	else
		tmp = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, -7.5e-51], N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 2.55e-64], And[N[Not[LessEqual[x, 1.6e+32]], $MachinePrecision], LessEqual[x, 4.6e+143]]], N[(N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision] - N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.49999999999999976e-51

   1. Initial program 66.9%

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

   3. Taylor expanded in y around 0 65.2%

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

   4. Taylor expanded in x around inf 66.8%

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

      1. +-commutative 66.8%

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

      2. mul-1-neg 66.8%

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

      3. unsub-neg 66.8%

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

      4. associate-/l* 66.7%

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

   6. Simplified 66.7%

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

   7. Taylor expanded in i around 0 62.1%

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

      1. sub-neg 62.1%

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

      2. associate-+r+ 62.1%

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

      3. associate-+l+ 62.1%

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

      4. +-commutative 62.1%

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

      5. mul-1-neg 62.1%

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

      6. associate-*r* 63.8%

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

      7. *-commutative 63.8%

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

      8. associate-*r* 65.5%

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

      9. distribute-lft-neg-in 65.5%

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

      10. mul-1-neg 65.5%

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

      11. distribute-rgt-in 67.1%

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

      12. mul-1-neg 67.1%

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

      13. unsub-neg 67.1%

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

      14. *-commutative 67.1%

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

      15. *-commutative 67.1%

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

   9. Simplified 72.1%

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

   if -7.49999999999999976e-51 < x < 2.54999999999999992e-64 or 1.5999999999999999e32 < x < 4.5999999999999999e143

   1. Initial program 71.8%

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

   3. Taylor expanded in y around 0 82.5%

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

   4. Taylor expanded in x around 0 76.7%

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

   if 2.54999999999999992e-64 < x < 1.5999999999999999e32 or 4.5999999999999999e143 < x

   1. Initial program 90.8%

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

   3. Taylor expanded in b around 0 86.5%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{-51}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{-64} \lor \neg \left(x \leq 1.6 \cdot 10^{+32}\right) \land x \leq 4.6 \cdot 10^{+143}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - \left(i \cdot \left(y \cdot j\right) - c \cdot \left(t \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 49.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -9.5 \cdot 10^{+232}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -9.5 \cdot 10^{+130}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3.2 \cdot 10^{-82}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{+52}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+132}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* a b) (* y j)))) (t_2 (* b (- (* a i) (* z c)))))
   (if (<= b -9.5e+232)
     t_2
     (if (<= b -9.5e+130)
       t_1
       (if (<= b -3.2e-82)
         t_2
         (if (<= b 2.25e+52)
           (* t (- (* c j) (* x a)))
           (if (<= b 4.2e+96)
             t_1
             (if (<= b 1.5e+132) (* c (- (* t j) (* z b))) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -9.5e+232) {
		tmp = t_2;
	} else if (b <= -9.5e+130) {
		tmp = t_1;
	} else if (b <= -3.2e-82) {
		tmp = t_2;
	} else if (b <= 2.25e+52) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= 4.2e+96) {
		tmp = t_1;
	} else if (b <= 1.5e+132) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i * ((a * b) - (y * j))
    t_2 = b * ((a * i) - (z * c))
    if (b <= (-9.5d+232)) then
        tmp = t_2
    else if (b <= (-9.5d+130)) then
        tmp = t_1
    else if (b <= (-3.2d-82)) then
        tmp = t_2
    else if (b <= 2.25d+52) then
        tmp = t * ((c * j) - (x * a))
    else if (b <= 4.2d+96) then
        tmp = t_1
    else if (b <= 1.5d+132) then
        tmp = c * ((t * j) - (z * b))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -9.5e+232) {
		tmp = t_2;
	} else if (b <= -9.5e+130) {
		tmp = t_1;
	} else if (b <= -3.2e-82) {
		tmp = t_2;
	} else if (b <= 2.25e+52) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= 4.2e+96) {
		tmp = t_1;
	} else if (b <= 1.5e+132) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((a * b) - (y * j))
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -9.5e+232:
		tmp = t_2
	elif b <= -9.5e+130:
		tmp = t_1
	elif b <= -3.2e-82:
		tmp = t_2
	elif b <= 2.25e+52:
		tmp = t * ((c * j) - (x * a))
	elif b <= 4.2e+96:
		tmp = t_1
	elif b <= 1.5e+132:
		tmp = c * ((t * j) - (z * b))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -9.5e+232)
		tmp = t_2;
	elseif (b <= -9.5e+130)
		tmp = t_1;
	elseif (b <= -3.2e-82)
		tmp = t_2;
	elseif (b <= 2.25e+52)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (b <= 4.2e+96)
		tmp = t_1;
	elseif (b <= 1.5e+132)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((a * b) - (y * j));
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -9.5e+232)
		tmp = t_2;
	elseif (b <= -9.5e+130)
		tmp = t_1;
	elseif (b <= -3.2e-82)
		tmp = t_2;
	elseif (b <= 2.25e+52)
		tmp = t * ((c * j) - (x * a));
	elseif (b <= 4.2e+96)
		tmp = t_1;
	elseif (b <= 1.5e+132)
		tmp = c * ((t * j) - (z * b));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9.5e+232], t$95$2, If[LessEqual[b, -9.5e+130], t$95$1, If[LessEqual[b, -3.2e-82], t$95$2, If[LessEqual[b, 2.25e+52], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.2e+96], t$95$1, If[LessEqual[b, 1.5e+132], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -9.4999999999999996e232 or -9.5000000000000009e130 < b < -3.2000000000000001e-82 or 1.4999999999999999e132 < b

   1. Initial program 70.3%

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

   3. Taylor expanded in b around inf 67.4%

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

      1. *-commutative 67.4%

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

   5. Simplified 67.4%

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

   if -9.4999999999999996e232 < b < -9.5000000000000009e130 or 2.25e52 < b < 4.2000000000000002e96

   1. Initial program 73.6%

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

   3. Taylor expanded in y around 0 70.8%

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

   4. Taylor expanded in x around inf 65.0%

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

      1. +-commutative 65.0%

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

      2. mul-1-neg 65.0%

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

      3. unsub-neg 65.0%

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

      4. associate-/l* 62.2%

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

   6. Simplified 62.2%

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

   7. Taylor expanded in y around 0 59.4%

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

   9. Simplified 53.1%

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

   10. Taylor expanded in i around inf 73.7%

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

       1. sub-neg 73.7%

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

       2. neg-mul-1 73.7%

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

       3. mul-1-neg 73.7%

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

       4. remove-double-neg 73.7%

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

       5. +-commutative 73.7%

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

       6. unsub-neg 73.7%

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

       7. *-commutative 73.7%

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

   12. Simplified 73.7%

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

   if -3.2000000000000001e-82 < b < 2.25e52

   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 t around inf 55.9%

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

      1. +-commutative 55.9%

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

      2. mul-1-neg 55.9%

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

      3. unsub-neg 55.9%

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

      4. *-commutative 55.9%

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

      5. *-commutative 55.9%

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

   5. Simplified 55.9%

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

   if 4.2000000000000002e96 < b < 1.4999999999999999e132

   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 c around inf 80.4%

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

      1. *-commutative 80.4%

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

      2. *-commutative 80.4%

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

   5. Simplified 80.4%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{+232}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -9.5 \cdot 10^{+130}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq -3.2 \cdot 10^{-82}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{+52}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{+96}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+132}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 38.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := z \cdot \left(x \cdot y\right)\\ t_3 := i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{if}\;x \leq -2.9 \cdot 10^{-25}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-301}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-236}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 4.45 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+78}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+150}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c))))
        (t_2 (* z (* x y)))
        (t_3 (* i (* y (- j)))))
   (if (<= x -2.9e-25)
     t_2
     (if (<= x 1.8e-301)
       t_1
       (if (<= x 5e-236)
         t_3
         (if (<= x 4.45e-7)
           t_1
           (if (<= x 3e+78) t_3 (if (<= x 1.6e+150) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = z * (x * y);
	double t_3 = i * (y * -j);
	double tmp;
	if (x <= -2.9e-25) {
		tmp = t_2;
	} else if (x <= 1.8e-301) {
		tmp = t_1;
	} else if (x <= 5e-236) {
		tmp = t_3;
	} else if (x <= 4.45e-7) {
		tmp = t_1;
	} else if (x <= 3e+78) {
		tmp = t_3;
	} else if (x <= 1.6e+150) {
		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) :: t_3
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = z * (x * y)
    t_3 = i * (y * -j)
    if (x <= (-2.9d-25)) then
        tmp = t_2
    else if (x <= 1.8d-301) then
        tmp = t_1
    else if (x <= 5d-236) then
        tmp = t_3
    else if (x <= 4.45d-7) then
        tmp = t_1
    else if (x <= 3d+78) then
        tmp = t_3
    else if (x <= 1.6d+150) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = z * (x * y);
	double t_3 = i * (y * -j);
	double tmp;
	if (x <= -2.9e-25) {
		tmp = t_2;
	} else if (x <= 1.8e-301) {
		tmp = t_1;
	} else if (x <= 5e-236) {
		tmp = t_3;
	} else if (x <= 4.45e-7) {
		tmp = t_1;
	} else if (x <= 3e+78) {
		tmp = t_3;
	} else if (x <= 1.6e+150) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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)
	t_3 = i * (y * -j)
	tmp = 0
	if x <= -2.9e-25:
		tmp = t_2
	elif x <= 1.8e-301:
		tmp = t_1
	elif x <= 5e-236:
		tmp = t_3
	elif x <= 4.45e-7:
		tmp = t_1
	elif x <= 3e+78:
		tmp = t_3
	elif x <= 1.6e+150:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(z * Float64(x * y))
	t_3 = Float64(i * Float64(y * Float64(-j)))
	tmp = 0.0
	if (x <= -2.9e-25)
		tmp = t_2;
	elseif (x <= 1.8e-301)
		tmp = t_1;
	elseif (x <= 5e-236)
		tmp = t_3;
	elseif (x <= 4.45e-7)
		tmp = t_1;
	elseif (x <= 3e+78)
		tmp = t_3;
	elseif (x <= 1.6e+150)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = z * (x * y);
	t_3 = i * (y * -j);
	tmp = 0.0;
	if (x <= -2.9e-25)
		tmp = t_2;
	elseif (x <= 1.8e-301)
		tmp = t_1;
	elseif (x <= 5e-236)
		tmp = t_3;
	elseif (x <= 4.45e-7)
		tmp = t_1;
	elseif (x <= 3e+78)
		tmp = t_3;
	elseif (x <= 1.6e+150)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.9e-25], t$95$2, If[LessEqual[x, 1.8e-301], t$95$1, If[LessEqual[x, 5e-236], t$95$3, If[LessEqual[x, 4.45e-7], t$95$1, If[LessEqual[x, 3e+78], t$95$3, If[LessEqual[x, 1.6e+150], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.9000000000000001e-25 or 1.60000000000000008e150 < x

   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 z around inf 54.5%

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

      1. *-commutative 54.5%

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

   5. Simplified 54.5%

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

   6. Taylor expanded in x around inf 51.1%

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

      1. *-commutative 51.1%

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

   8. Simplified 51.1%

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

   if -2.9000000000000001e-25 < x < 1.80000000000000004e-301 or 4.9999999999999998e-236 < x < 4.45e-7 or 2.99999999999999982e78 < x < 1.60000000000000008e150

   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 54.6%

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

      1. *-commutative 54.6%

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

   5. Simplified 54.6%

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

   if 1.80000000000000004e-301 < x < 4.9999999999999998e-236 or 4.45e-7 < x < 2.99999999999999982e78

   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 y around 0 81.6%

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

   4. Taylor expanded in x around inf 71.4%

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

      1. +-commutative 71.4%

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

      2. mul-1-neg 71.4%

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

      3. unsub-neg 71.4%

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

      4. associate-/l* 71.4%

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

   6. Simplified 71.4%

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

   7. Taylor expanded in i around inf 68.0%

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

      1. sub-neg 68.0%

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

      2. associate-*r* 68.0%

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

      3. mul-1-neg 68.0%

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

      4. neg-mul-1 68.0%

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

      5. remove-double-neg 68.0%

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

      6. *-commutative 68.0%

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

   9. Simplified 68.0%

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

   10. Taylor expanded in j around inf 56.9%

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

       1. neg-mul-1 56.9%

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

       2. *-commutative 56.9%

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

   12. Simplified 56.9%

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

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{-25}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-301}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-236}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;x \leq 4.45 \cdot 10^{-7}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+78}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+150}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -7 \cdot 10^{+174}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{+152}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -4.3 \cdot 10^{+108}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+102}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* j (- (* t c) (* y i))) (* x (- (* t a) (* y z)))))
        (t_2 (* a (- (* b i) (* x t)))))
   (if (<= a -7e+174)
     t_2
     (if (<= a -1.1e+152)
       t_1
       (if (<= a -4.3e+108)
         (* b (- (* a i) (* z c)))
         (if (<= a 3.3e+102) 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))) - (x * ((t * a) - (y * z)));
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -7e+174) {
		tmp = t_2;
	} else if (a <= -1.1e+152) {
		tmp = t_1;
	} else if (a <= -4.3e+108) {
		tmp = b * ((a * i) - (z * c));
	} else if (a <= 3.3e+102) {
		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))) - (x * ((t * a) - (y * z)))
    t_2 = a * ((b * i) - (x * t))
    if (a <= (-7d+174)) then
        tmp = t_2
    else if (a <= (-1.1d+152)) then
        tmp = t_1
    else if (a <= (-4.3d+108)) then
        tmp = b * ((a * i) - (z * c))
    else if (a <= 3.3d+102) 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))) - (x * ((t * a) - (y * z)));
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -7e+174) {
		tmp = t_2;
	} else if (a <= -1.1e+152) {
		tmp = t_1;
	} else if (a <= -4.3e+108) {
		tmp = b * ((a * i) - (z * c));
	} else if (a <= 3.3e+102) {
		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))) - (x * ((t * a) - (y * z)))
	t_2 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -7e+174:
		tmp = t_2
	elif a <= -1.1e+152:
		tmp = t_1
	elif a <= -4.3e+108:
		tmp = b * ((a * i) - (z * c))
	elif a <= 3.3e+102:
		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(j * Float64(Float64(t * c) - Float64(y * i))) - Float64(x * Float64(Float64(t * a) - Float64(y * z))))
	t_2 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -7e+174)
		tmp = t_2;
	elseif (a <= -1.1e+152)
		tmp = t_1;
	elseif (a <= -4.3e+108)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (a <= 3.3e+102)
		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))) - (x * ((t * a) - (y * z)));
	t_2 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -7e+174)
		tmp = t_2;
	elseif (a <= -1.1e+152)
		tmp = t_1;
	elseif (a <= -4.3e+108)
		tmp = b * ((a * i) - (z * c));
	elseif (a <= 3.3e+102)
		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[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7e+174], t$95$2, If[LessEqual[a, -1.1e+152], t$95$1, If[LessEqual[a, -4.3e+108], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.3e+102], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.0000000000000003e174 or 3.29999999999999999e102 < a

   1. Initial program 65.5%

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

   3. Taylor expanded in a around inf 80.8%

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

      1. distribute-lft-out-- 80.8%

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

      2. *-commutative 80.8%

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

      3. *-commutative 80.8%

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

   5. Simplified 80.8%

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

   if -7.0000000000000003e174 < a < -1.0999999999999999e152 or -4.29999999999999996e108 < a < 3.29999999999999999e102

   1. Initial program 78.8%

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

   3. Taylor expanded in b around 0 69.3%

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

   if -1.0999999999999999e152 < a < -4.29999999999999996e108

   1. Initial program 55.4%

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

   3. Taylor expanded in b around inf 89.2%

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

      1. *-commutative 89.2%

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

   5. Simplified 89.2%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{+174}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{+152}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;a \leq -4.3 \cdot 10^{+108}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+102}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3.9 \cdot 10^{+52}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -120:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;c \leq -3.7 \cdot 10^{-147}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 1.5 \cdot 10^{-64}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 4.8 \cdot 10^{+37}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(b \cdot \left(j \cdot \frac{t}{b} - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -3.9e+52)
   (* c (- (* t j) (* z b)))
   (if (<= c -120.0)
     (* t (- (* c j) (* x a)))
     (if (<= c -3.7e-147)
       (* y (- (* x z) (* i j)))
       (if (<= c 1.5e-64)
         (* a (- (* b i) (* x t)))
         (if (<= c 4.8e+37)
           (* i (- (* a b) (* y j)))
           (* c (* b (- (* j (/ t b)) z)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -3.9e+52) {
		tmp = c * ((t * j) - (z * b));
	} else if (c <= -120.0) {
		tmp = t * ((c * j) - (x * a));
	} else if (c <= -3.7e-147) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 1.5e-64) {
		tmp = a * ((b * i) - (x * t));
	} else if (c <= 4.8e+37) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = c * (b * ((j * (t / b)) - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (c <= (-3.9d+52)) then
        tmp = c * ((t * j) - (z * b))
    else if (c <= (-120.0d0)) then
        tmp = t * ((c * j) - (x * a))
    else if (c <= (-3.7d-147)) then
        tmp = y * ((x * z) - (i * j))
    else if (c <= 1.5d-64) then
        tmp = a * ((b * i) - (x * t))
    else if (c <= 4.8d+37) then
        tmp = i * ((a * b) - (y * j))
    else
        tmp = c * (b * ((j * (t / b)) - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -3.9e+52) {
		tmp = c * ((t * j) - (z * b));
	} else if (c <= -120.0) {
		tmp = t * ((c * j) - (x * a));
	} else if (c <= -3.7e-147) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 1.5e-64) {
		tmp = a * ((b * i) - (x * t));
	} else if (c <= 4.8e+37) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = c * (b * ((j * (t / b)) - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -3.9e+52:
		tmp = c * ((t * j) - (z * b))
	elif c <= -120.0:
		tmp = t * ((c * j) - (x * a))
	elif c <= -3.7e-147:
		tmp = y * ((x * z) - (i * j))
	elif c <= 1.5e-64:
		tmp = a * ((b * i) - (x * t))
	elif c <= 4.8e+37:
		tmp = i * ((a * b) - (y * j))
	else:
		tmp = c * (b * ((j * (t / b)) - z))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -3.9e+52)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (c <= -120.0)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (c <= -3.7e-147)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (c <= 1.5e-64)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (c <= 4.8e+37)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	else
		tmp = Float64(c * Float64(b * Float64(Float64(j * Float64(t / b)) - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -3.9e+52)
		tmp = c * ((t * j) - (z * b));
	elseif (c <= -120.0)
		tmp = t * ((c * j) - (x * a));
	elseif (c <= -3.7e-147)
		tmp = y * ((x * z) - (i * j));
	elseif (c <= 1.5e-64)
		tmp = a * ((b * i) - (x * t));
	elseif (c <= 4.8e+37)
		tmp = i * ((a * b) - (y * j));
	else
		tmp = c * (b * ((j * (t / b)) - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -3.9e+52], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -120.0], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -3.7e-147], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.5e-64], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.8e+37], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(b * N[(N[(j * N[(t / b), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -3.9e52

   1. Initial program 63.0%

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

   3. Taylor expanded in c around inf 65.9%

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

      1. *-commutative 65.9%

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

      2. *-commutative 65.9%

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

   5. Simplified 65.9%

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

   if -3.9e52 < c < -120

   1. Initial program 78.3%

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

   3. Taylor expanded in t around inf 66.1%

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

      1. +-commutative 66.1%

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

      2. mul-1-neg 66.1%

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

      3. unsub-neg 66.1%

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

      4. *-commutative 66.1%

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

      5. *-commutative 66.1%

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

   5. Simplified 66.1%

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

   if -120 < c < -3.7000000000000002e-147

   1. Initial program 79.6%

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

   3. Taylor expanded in y around 0 82.8%

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

   4. Taylor expanded in y around inf 70.6%

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

      1. +-commutative 70.6%

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

      2. mul-1-neg 70.6%

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

      3. unsub-neg 70.6%

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

      4. *-commutative 70.6%

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

   6. Simplified 70.6%

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

   if -3.7000000000000002e-147 < c < 1.5e-64

   1. Initial program 77.4%

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

   3. Taylor expanded in a around inf 59.8%

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

      1. distribute-lft-out-- 59.8%

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

      2. *-commutative 59.8%

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

      3. *-commutative 59.8%

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

   5. Simplified 59.8%

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

   if 1.5e-64 < c < 4.8e37

   1. Initial program 87.8%

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

   3. Taylor expanded in y around 0 71.6%

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

   4. Taylor expanded in x around inf 75.8%

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

      1. +-commutative 75.8%

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

      2. mul-1-neg 75.8%

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

      3. unsub-neg 75.8%

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

      4. associate-/l* 75.8%

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

   6. Simplified 75.8%

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

   7. Taylor expanded in y around 0 64.0%

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

   9. Simplified 71.4%

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

   10. Taylor expanded in i around inf 70.2%

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

       1. sub-neg 70.2%

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

       2. neg-mul-1 70.2%

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

       3. mul-1-neg 70.2%

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

       4. remove-double-neg 70.2%

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

       5. +-commutative 70.2%

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

       6. unsub-neg 70.2%

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

       7. *-commutative 70.2%

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

   12. Simplified 70.2%

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

   if 4.8e37 < c

   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 c around inf 66.8%

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

      1. *-commutative 66.8%

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

      2. *-commutative 66.8%

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

   5. Simplified 66.8%

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

   6. Taylor expanded in b around inf 66.8%

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

      1. associate-/l* 68.6%

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

   8. Simplified 68.6%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.9 \cdot 10^{+52}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -120:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;c \leq -3.7 \cdot 10^{-147}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 1.5 \cdot 10^{-64}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 4.8 \cdot 10^{+37}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(b \cdot \left(j \cdot \frac{t}{b} - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -3.7 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -112:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;c \leq -6 \cdot 10^{-146}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{-67}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 2.75 \cdot 10^{+38}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))))
   (if (<= c -3.7e+52)
     t_1
     (if (<= c -112.0)
       (* t (- (* c j) (* x a)))
       (if (<= c -6e-146)
         (* y (- (* x z) (* i j)))
         (if (<= c 1.25e-67)
           (* a (- (* b i) (* x t)))
           (if (<= c 2.75e+38) (* i (- (* a b) (* y j))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -3.7e+52) {
		tmp = t_1;
	} else if (c <= -112.0) {
		tmp = t * ((c * j) - (x * a));
	} else if (c <= -6e-146) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 1.25e-67) {
		tmp = a * ((b * i) - (x * t));
	} else if (c <= 2.75e+38) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((t * j) - (z * b))
    if (c <= (-3.7d+52)) then
        tmp = t_1
    else if (c <= (-112.0d0)) then
        tmp = t * ((c * j) - (x * a))
    else if (c <= (-6d-146)) then
        tmp = y * ((x * z) - (i * j))
    else if (c <= 1.25d-67) then
        tmp = a * ((b * i) - (x * t))
    else if (c <= 2.75d+38) then
        tmp = i * ((a * b) - (y * j))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -3.7e+52) {
		tmp = t_1;
	} else if (c <= -112.0) {
		tmp = t * ((c * j) - (x * a));
	} else if (c <= -6e-146) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 1.25e-67) {
		tmp = a * ((b * i) - (x * t));
	} else if (c <= 2.75e+38) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -3.7e+52:
		tmp = t_1
	elif c <= -112.0:
		tmp = t * ((c * j) - (x * a))
	elif c <= -6e-146:
		tmp = y * ((x * z) - (i * j))
	elif c <= 1.25e-67:
		tmp = a * ((b * i) - (x * t))
	elif c <= 2.75e+38:
		tmp = i * ((a * b) - (y * j))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -3.7e+52)
		tmp = t_1;
	elseif (c <= -112.0)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (c <= -6e-146)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (c <= 1.25e-67)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (c <= 2.75e+38)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -3.7e+52)
		tmp = t_1;
	elseif (c <= -112.0)
		tmp = t * ((c * j) - (x * a));
	elseif (c <= -6e-146)
		tmp = y * ((x * z) - (i * j));
	elseif (c <= 1.25e-67)
		tmp = a * ((b * i) - (x * t));
	elseif (c <= 2.75e+38)
		tmp = i * ((a * b) - (y * j));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.7e+52], t$95$1, If[LessEqual[c, -112.0], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -6e-146], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.25e-67], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.75e+38], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -3.7e52 or 2.7500000000000002e38 < c

   1. Initial program 67.3%

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

   3. Taylor expanded in c around inf 66.4%

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

      1. *-commutative 66.4%

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

      2. *-commutative 66.4%

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

   5. Simplified 66.4%

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

   if -3.7e52 < c < -112

   1. Initial program 78.3%

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

   3. Taylor expanded in t around inf 66.1%

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

      1. +-commutative 66.1%

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

      2. mul-1-neg 66.1%

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

      3. unsub-neg 66.1%

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

      4. *-commutative 66.1%

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

      5. *-commutative 66.1%

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

   5. Simplified 66.1%

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

   if -112 < c < -6.00000000000000038e-146

   1. Initial program 79.6%

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

   3. Taylor expanded in y around 0 82.8%

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

   4. Taylor expanded in y around inf 70.6%

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

      1. +-commutative 70.6%

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

      2. mul-1-neg 70.6%

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

      3. unsub-neg 70.6%

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

      4. *-commutative 70.6%

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

   6. Simplified 70.6%

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

   if -6.00000000000000038e-146 < c < 1.25e-67

   1. Initial program 77.4%

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

   3. Taylor expanded in a around inf 59.8%

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

      1. distribute-lft-out-- 59.8%

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

      2. *-commutative 59.8%

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

      3. *-commutative 59.8%

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

   5. Simplified 59.8%

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

   if 1.25e-67 < c < 2.7500000000000002e38

   1. Initial program 87.8%

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

   3. Taylor expanded in y around 0 71.6%

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

   4. Taylor expanded in x around inf 75.8%

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

      1. +-commutative 75.8%

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

      2. mul-1-neg 75.8%

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

      3. unsub-neg 75.8%

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

      4. associate-/l* 75.8%

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

   6. Simplified 75.8%

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

   7. Taylor expanded in y around 0 64.0%

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

   9. Simplified 71.4%

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

   10. Taylor expanded in i around inf 70.2%

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

       1. sub-neg 70.2%

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

       2. neg-mul-1 70.2%

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

       3. mul-1-neg 70.2%

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

       4. remove-double-neg 70.2%

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

       5. +-commutative 70.2%

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

       6. unsub-neg 70.2%

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

       7. *-commutative 70.2%

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

   12. Simplified 70.2%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.7 \cdot 10^{+52}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -112:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;c \leq -6 \cdot 10^{-146}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{-67}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 2.75 \cdot 10^{+38}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 65.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := t\_1 - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{if}\;j \leq -6.5 \cdot 10^{+17}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 3.4 \cdot 10^{+17}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 5.5 \cdot 10^{+194}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i))))
        (t_2 (- t_1 (* x (- (* t a) (* y z))))))
   (if (<= j -6.5e+17)
     t_2
     (if (<= j 3.4e+17)
       (+ (* t (- (* c j) (* x a))) (* z (- (* x y) (* b c))))
       (if (<= j 5.5e+194) t_2 t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = t_1 - (x * ((t * a) - (y * z)));
	double tmp;
	if (j <= -6.5e+17) {
		tmp = t_2;
	} else if (j <= 3.4e+17) {
		tmp = (t * ((c * j) - (x * a))) + (z * ((x * y) - (b * c)));
	} else if (j <= 5.5e+194) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = t_1 - (x * ((t * a) - (y * z)))
    if (j <= (-6.5d+17)) then
        tmp = t_2
    else if (j <= 3.4d+17) then
        tmp = (t * ((c * j) - (x * a))) + (z * ((x * y) - (b * c)))
    else if (j <= 5.5d+194) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = t_1 - (x * ((t * a) - (y * z)));
	double tmp;
	if (j <= -6.5e+17) {
		tmp = t_2;
	} else if (j <= 3.4e+17) {
		tmp = (t * ((c * j) - (x * a))) + (z * ((x * y) - (b * c)));
	} else if (j <= 5.5e+194) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = t_1 - (x * ((t * a) - (y * z)))
	tmp = 0
	if j <= -6.5e+17:
		tmp = t_2
	elif j <= 3.4e+17:
		tmp = (t * ((c * j) - (x * a))) + (z * ((x * y) - (b * c)))
	elif j <= 5.5e+194:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(t_1 - Float64(x * Float64(Float64(t * a) - Float64(y * z))))
	tmp = 0.0
	if (j <= -6.5e+17)
		tmp = t_2;
	elseif (j <= 3.4e+17)
		tmp = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) + Float64(z * Float64(Float64(x * y) - Float64(b * c))));
	elseif (j <= 5.5e+194)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = t_1 - (x * ((t * a) - (y * z)));
	tmp = 0.0;
	if (j <= -6.5e+17)
		tmp = t_2;
	elseif (j <= 3.4e+17)
		tmp = (t * ((c * j) - (x * a))) + (z * ((x * y) - (b * c)));
	elseif (j <= 5.5e+194)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -6.5e+17], t$95$2, If[LessEqual[j, 3.4e+17], N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.5e+194], t$95$2, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -6.5e17 or 3.4e17 < j < 5.4999999999999999e194

   1. Initial program 78.3%

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

   3. Taylor expanded in b around 0 77.9%

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

   if -6.5e17 < j < 3.4e17

   1. Initial program 72.7%

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

   3. Taylor expanded in y around 0 81.6%

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

   4. Taylor expanded in x around inf 77.5%

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

      1. +-commutative 77.5%

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

      2. mul-1-neg 77.5%

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

      3. unsub-neg 77.5%

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

      4. associate-/l* 77.5%

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

   6. Simplified 77.5%

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

   7. Taylor expanded in i around 0 62.0%

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

      1. sub-neg 62.0%

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

      2. associate-+r+ 62.0%

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

      3. associate-+l+ 62.0%

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

      4. +-commutative 62.0%

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

      5. mul-1-neg 62.0%

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

      6. associate-*r* 61.8%

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

      7. *-commutative 61.8%

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

      8. associate-*r* 64.3%

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

      9. distribute-lft-neg-in 64.3%

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

      10. mul-1-neg 64.3%

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

      11. distribute-rgt-in 64.3%

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

      12. mul-1-neg 64.3%

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

      13. unsub-neg 64.3%

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

      14. *-commutative 64.3%

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

      15. *-commutative 64.3%

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

   9. Simplified 72.5%

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

   if 5.4999999999999999e194 < j

   1. Initial program 69.0%

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

   3. Taylor expanded in j around inf 67.9%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -6.5 \cdot 10^{+17}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;j \leq 3.4 \cdot 10^{+17}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 5.5 \cdot 10^{+194}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 29.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j\right)\\ \mathbf{if}\;c \leq -3 \cdot 10^{+141}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -6 \cdot 10^{-160}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 5 \cdot 10^{+73}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{+208} \lor \neg \left(c \leq 10^{+267}\right):\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (* c j))))
   (if (<= c -3e+141)
     t_1
     (if (<= c -6e-160)
       (* z (* x y))
       (if (<= c 5e+73)
         (* b (* a i))
         (if (or (<= c 8.5e+208) (not (<= c 1e+267)))
           (* c (* z (- b)))
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (c * j);
	double tmp;
	if (c <= -3e+141) {
		tmp = t_1;
	} else if (c <= -6e-160) {
		tmp = z * (x * y);
	} else if (c <= 5e+73) {
		tmp = b * (a * i);
	} else if ((c <= 8.5e+208) || !(c <= 1e+267)) {
		tmp = c * (z * -b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (c * j)
    if (c <= (-3d+141)) then
        tmp = t_1
    else if (c <= (-6d-160)) then
        tmp = z * (x * y)
    else if (c <= 5d+73) then
        tmp = b * (a * i)
    else if ((c <= 8.5d+208) .or. (.not. (c <= 1d+267))) then
        tmp = c * (z * -b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (c * j);
	double tmp;
	if (c <= -3e+141) {
		tmp = t_1;
	} else if (c <= -6e-160) {
		tmp = z * (x * y);
	} else if (c <= 5e+73) {
		tmp = b * (a * i);
	} else if ((c <= 8.5e+208) || !(c <= 1e+267)) {
		tmp = c * (z * -b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * (c * j)
	tmp = 0
	if c <= -3e+141:
		tmp = t_1
	elif c <= -6e-160:
		tmp = z * (x * y)
	elif c <= 5e+73:
		tmp = b * (a * i)
	elif (c <= 8.5e+208) or not (c <= 1e+267):
		tmp = c * (z * -b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(c * j))
	tmp = 0.0
	if (c <= -3e+141)
		tmp = t_1;
	elseif (c <= -6e-160)
		tmp = Float64(z * Float64(x * y));
	elseif (c <= 5e+73)
		tmp = Float64(b * Float64(a * i));
	elseif ((c <= 8.5e+208) || !(c <= 1e+267))
		tmp = Float64(c * Float64(z * Float64(-b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * (c * j);
	tmp = 0.0;
	if (c <= -3e+141)
		tmp = t_1;
	elseif (c <= -6e-160)
		tmp = z * (x * y);
	elseif (c <= 5e+73)
		tmp = b * (a * i);
	elseif ((c <= 8.5e+208) || ~((c <= 1e+267)))
		tmp = c * (z * -b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3e+141], t$95$1, If[LessEqual[c, -6e-160], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5e+73], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[c, 8.5e+208], N[Not[LessEqual[c, 1e+267]], $MachinePrecision]], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -2.9999999999999999e141 or 8.4999999999999992e208 < c < 9.9999999999999997e266

   1. Initial program 61.4%

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

   3. Taylor expanded in c around inf 73.1%

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

      1. *-commutative 73.1%

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

      2. *-commutative 73.1%

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

   5. Simplified 73.1%

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

   6. Taylor expanded in t around inf 53.9%

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

      1. associate-*r* 57.9%

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

      2. *-commutative 57.9%

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

   8. Simplified 57.9%

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

   if -2.9999999999999999e141 < c < -5.99999999999999993e-160

   1. Initial program 80.1%

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

   3. Taylor expanded in z around inf 46.8%

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

      1. *-commutative 46.8%

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

   5. Simplified 46.8%

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

   6. Taylor expanded in x around inf 32.4%

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

      1. *-commutative 32.4%

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

   8. Simplified 32.4%

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

   if -5.99999999999999993e-160 < c < 4.99999999999999976e73

   1. Initial program 79.7%

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

   3. Taylor expanded in b around inf 39.0%

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

      1. *-commutative 39.0%

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

   5. Simplified 39.0%

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

   6. Taylor expanded in a around inf 34.9%

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

      1. *-commutative 34.9%

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

   8. Simplified 34.9%

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

   if 4.99999999999999976e73 < c < 8.4999999999999992e208 or 9.9999999999999997e266 < c

   1. Initial program 66.9%

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

   3. Taylor expanded in c around inf 63.0%

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

      1. *-commutative 63.0%

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

      2. *-commutative 63.0%

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

   5. Simplified 63.0%

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

   6. Taylor expanded in t around 0 55.0%

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

      1. mul-1-neg 55.0%

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

      2. *-commutative 55.0%

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

      3. distribute-rgt-neg-in 55.0%

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

   8. Simplified 55.0%

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

4. Final simplification 41.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3 \cdot 10^{+141}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq -6 \cdot 10^{-160}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 5 \cdot 10^{+73}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{+208} \lor \neg \left(c \leq 10^{+267}\right):\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 30.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(y \cdot \left(-j\right)\right)\\ t_2 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;x \leq -1.72 \cdot 10^{-28}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-264}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-170}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-60}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+83}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* y (- j)))) (t_2 (* z (* x y))))
   (if (<= x -1.72e-28)
     t_2
     (if (<= x 2.5e-264)
       (* c (* t j))
       (if (<= x 2.9e-170)
         t_1
         (if (<= x 2.1e-60) (* b (* a i)) (if (<= x 9.5e+83) 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 = i * (y * -j);
	double t_2 = z * (x * y);
	double tmp;
	if (x <= -1.72e-28) {
		tmp = t_2;
	} else if (x <= 2.5e-264) {
		tmp = c * (t * j);
	} else if (x <= 2.9e-170) {
		tmp = t_1;
	} else if (x <= 2.1e-60) {
		tmp = b * (a * i);
	} else if (x <= 9.5e+83) {
		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 = i * (y * -j)
    t_2 = z * (x * y)
    if (x <= (-1.72d-28)) then
        tmp = t_2
    else if (x <= 2.5d-264) then
        tmp = c * (t * j)
    else if (x <= 2.9d-170) then
        tmp = t_1
    else if (x <= 2.1d-60) then
        tmp = b * (a * i)
    else if (x <= 9.5d+83) 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 = i * (y * -j);
	double t_2 = z * (x * y);
	double tmp;
	if (x <= -1.72e-28) {
		tmp = t_2;
	} else if (x <= 2.5e-264) {
		tmp = c * (t * j);
	} else if (x <= 2.9e-170) {
		tmp = t_1;
	} else if (x <= 2.1e-60) {
		tmp = b * (a * i);
	} else if (x <= 9.5e+83) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (y * -j)
	t_2 = z * (x * y)
	tmp = 0
	if x <= -1.72e-28:
		tmp = t_2
	elif x <= 2.5e-264:
		tmp = c * (t * j)
	elif x <= 2.9e-170:
		tmp = t_1
	elif x <= 2.1e-60:
		tmp = b * (a * i)
	elif x <= 9.5e+83:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(y * Float64(-j)))
	t_2 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (x <= -1.72e-28)
		tmp = t_2;
	elseif (x <= 2.5e-264)
		tmp = Float64(c * Float64(t * j));
	elseif (x <= 2.9e-170)
		tmp = t_1;
	elseif (x <= 2.1e-60)
		tmp = Float64(b * Float64(a * i));
	elseif (x <= 9.5e+83)
		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 = i * (y * -j);
	t_2 = z * (x * y);
	tmp = 0.0;
	if (x <= -1.72e-28)
		tmp = t_2;
	elseif (x <= 2.5e-264)
		tmp = c * (t * j);
	elseif (x <= 2.9e-170)
		tmp = t_1;
	elseif (x <= 2.1e-60)
		tmp = b * (a * i);
	elseif (x <= 9.5e+83)
		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[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.72e-28], t$95$2, If[LessEqual[x, 2.5e-264], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.9e-170], t$95$1, If[LessEqual[x, 2.1e-60], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.5e+83], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.7199999999999999e-28 or 9.5000000000000002e83 < x

   1. Initial program 75.2%

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

   3. Taylor expanded in z around inf 54.1%

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

      1. *-commutative 54.1%

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

   5. Simplified 54.1%

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

   6. Taylor expanded in x around inf 48.2%

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

      1. *-commutative 48.2%

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

   8. Simplified 48.2%

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

   if -1.7199999999999999e-28 < x < 2.5e-264

   1. Initial program 72.2%

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

   3. Taylor expanded in b around 0 48.7%

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

   4. Taylor expanded in c around inf 35.3%

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

   if 2.5e-264 < x < 2.9e-170 or 2.09999999999999991e-60 < x < 9.5000000000000002e83

   1. Initial program 76.4%

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

   3. Taylor expanded in y around 0 79.0%

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

   4. Taylor expanded in x around inf 74.6%

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

      1. +-commutative 74.6%

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

      2. mul-1-neg 74.6%

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

      3. unsub-neg 74.6%

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

      4. associate-/l* 73.0%

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

   6. Simplified 73.0%

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

   7. Taylor expanded in i around inf 57.5%

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

      1. sub-neg 57.5%

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

      2. associate-*r* 57.5%

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

      3. mul-1-neg 57.5%

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

      4. neg-mul-1 57.5%

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

      5. remove-double-neg 57.5%

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

      6. *-commutative 57.5%

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

   9. Simplified 57.5%

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

   10. Taylor expanded in j around inf 44.4%

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

       1. neg-mul-1 44.4%

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

       2. *-commutative 44.4%

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

   12. Simplified 44.4%

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

   if 2.9e-170 < x < 2.09999999999999991e-60

   1. Initial program 73.7%

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

   3. Taylor expanded in b around inf 54.6%

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

      1. *-commutative 54.6%

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

   5. Simplified 54.6%

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

   6. Taylor expanded in a around inf 44.5%

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

      1. *-commutative 44.5%

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

   8. Simplified 44.5%

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

4. Final simplification 43.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.72 \cdot 10^{-28}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-264}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-170}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-60}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+83}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 29.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ t_2 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;x \leq -2.8 \cdot 10^{-27}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+39}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{+72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{+140}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j))) (t_2 (* z (* x y))))
   (if (<= x -2.8e-27)
     t_2
     (if (<= x 6.5e-119)
       t_1
       (if (<= x 1.9e+39)
         (* a (* b i))
         (if (<= x 1.22e+72) t_1 (if (<= x 7.6e+140) (* b (* a i)) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double t_2 = z * (x * y);
	double tmp;
	if (x <= -2.8e-27) {
		tmp = t_2;
	} else if (x <= 6.5e-119) {
		tmp = t_1;
	} else if (x <= 1.9e+39) {
		tmp = a * (b * i);
	} else if (x <= 1.22e+72) {
		tmp = t_1;
	} else if (x <= 7.6e+140) {
		tmp = b * (a * i);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * (t * j)
    t_2 = z * (x * y)
    if (x <= (-2.8d-27)) then
        tmp = t_2
    else if (x <= 6.5d-119) then
        tmp = t_1
    else if (x <= 1.9d+39) then
        tmp = a * (b * i)
    else if (x <= 1.22d+72) then
        tmp = t_1
    else if (x <= 7.6d+140) then
        tmp = b * (a * i)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double t_2 = z * (x * y);
	double tmp;
	if (x <= -2.8e-27) {
		tmp = t_2;
	} else if (x <= 6.5e-119) {
		tmp = t_1;
	} else if (x <= 1.9e+39) {
		tmp = a * (b * i);
	} else if (x <= 1.22e+72) {
		tmp = t_1;
	} else if (x <= 7.6e+140) {
		tmp = b * (a * i);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (t * j)
	t_2 = z * (x * y)
	tmp = 0
	if x <= -2.8e-27:
		tmp = t_2
	elif x <= 6.5e-119:
		tmp = t_1
	elif x <= 1.9e+39:
		tmp = a * (b * i)
	elif x <= 1.22e+72:
		tmp = t_1
	elif x <= 7.6e+140:
		tmp = b * (a * i)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(t * j))
	t_2 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (x <= -2.8e-27)
		tmp = t_2;
	elseif (x <= 6.5e-119)
		tmp = t_1;
	elseif (x <= 1.9e+39)
		tmp = Float64(a * Float64(b * i));
	elseif (x <= 1.22e+72)
		tmp = t_1;
	elseif (x <= 7.6e+140)
		tmp = Float64(b * Float64(a * i));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (t * j);
	t_2 = z * (x * y);
	tmp = 0.0;
	if (x <= -2.8e-27)
		tmp = t_2;
	elseif (x <= 6.5e-119)
		tmp = t_1;
	elseif (x <= 1.9e+39)
		tmp = a * (b * i);
	elseif (x <= 1.22e+72)
		tmp = t_1;
	elseif (x <= 7.6e+140)
		tmp = b * (a * i);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.8e-27], t$95$2, If[LessEqual[x, 6.5e-119], t$95$1, If[LessEqual[x, 1.9e+39], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.22e+72], t$95$1, If[LessEqual[x, 7.6e+140], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.8e-27 or 7.6000000000000002e140 < x

   1. Initial program 76.9%

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

   3. Taylor expanded in z around inf 54.4%

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

      1. *-commutative 54.4%

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

   5. Simplified 54.4%

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

   6. Taylor expanded in x around inf 51.1%

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

      1. *-commutative 51.1%

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

   8. Simplified 51.1%

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

   if -2.8e-27 < x < 6.5e-119 or 1.8999999999999999e39 < x < 1.2200000000000001e72

   1. Initial program 71.3%

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

   3. Taylor expanded in b around 0 52.9%

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

   4. Taylor expanded in c around inf 35.1%

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

   if 6.5e-119 < x < 1.8999999999999999e39

   1. Initial program 83.2%

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

   3. Taylor expanded in b around inf 47.7%

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

      1. *-commutative 47.7%

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

   5. Simplified 47.7%

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

   6. Taylor expanded in a around inf 38.9%

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

      1. *-commutative 38.9%

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

   8. Simplified 38.9%

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

   if 1.2200000000000001e72 < x < 7.6000000000000002e140

   1. Initial program 66.6%

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

   3. Taylor expanded in b around inf 56.4%

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

      1. *-commutative 56.4%

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

   5. Simplified 56.4%

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

   6. Taylor expanded in a around inf 29.3%

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

      1. *-commutative 29.3%

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

   8. Simplified 29.3%

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

4. Final simplification 40.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-27}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-119}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+39}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{+72}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{+140}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 51.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -6.4 \cdot 10^{+103} \lor \neg \left(i \leq -1.9 \cdot 10^{+56} \lor \neg \left(i \leq -1.3 \cdot 10^{-33}\right) \land i \leq 9.5 \cdot 10^{+73}\right):\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -6.4e+103)
         (not (or (<= i -1.9e+56) (and (not (<= i -1.3e-33)) (<= i 9.5e+73)))))
   (* i (- (* a b) (* y j)))
   (* 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 ((i <= -6.4e+103) || !((i <= -1.9e+56) || (!(i <= -1.3e-33) && (i <= 9.5e+73)))) {
		tmp = i * ((a * b) - (y * j));
	} 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 ((i <= (-6.4d+103)) .or. (.not. (i <= (-1.9d+56)) .or. (.not. (i <= (-1.3d-33))) .and. (i <= 9.5d+73))) then
        tmp = i * ((a * b) - (y * j))
    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 ((i <= -6.4e+103) || !((i <= -1.9e+56) || (!(i <= -1.3e-33) && (i <= 9.5e+73)))) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = c * ((t * j) - (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (i <= -6.4e+103) or not ((i <= -1.9e+56) or (not (i <= -1.3e-33) and (i <= 9.5e+73))):
		tmp = i * ((a * b) - (y * j))
	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 ((i <= -6.4e+103) || !((i <= -1.9e+56) || (!(i <= -1.3e-33) && (i <= 9.5e+73))))
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	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 ((i <= -6.4e+103) || ~(((i <= -1.9e+56) || (~((i <= -1.3e-33)) && (i <= 9.5e+73)))))
		tmp = i * ((a * b) - (y * j));
	else
		tmp = c * ((t * j) - (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[i, -6.4e+103], N[Not[Or[LessEqual[i, -1.9e+56], And[N[Not[LessEqual[i, -1.3e-33]], $MachinePrecision], LessEqual[i, 9.5e+73]]]], $MachinePrecision]], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -6.39999999999999985e103 or -1.89999999999999998e56 < i < -1.29999999999999997e-33 or 9.4999999999999996e73 < i

   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 y around 0 67.2%

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

   4. Taylor expanded in x around inf 62.8%

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

      1. +-commutative 62.8%

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

      2. mul-1-neg 62.8%

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

      3. unsub-neg 62.8%

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

      4. associate-/l* 62.8%

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

   6. Simplified 62.8%

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

   7. Taylor expanded in y around 0 61.3%

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

   9. Simplified 64.7%

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

   10. Taylor expanded in i around inf 64.7%

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

       1. sub-neg 64.7%

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

       2. neg-mul-1 64.7%

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

       3. mul-1-neg 64.7%

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

       4. remove-double-neg 64.7%

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

       5. +-commutative 64.7%

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

       6. unsub-neg 64.7%

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

       7. *-commutative 64.7%

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

   12. Simplified 64.7%

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

   if -6.39999999999999985e103 < i < -1.89999999999999998e56 or -1.29999999999999997e-33 < i < 9.4999999999999996e73

   1. Initial program 78.2%

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

   3. Taylor expanded in c around inf 50.9%

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

      1. *-commutative 50.9%

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

      2. *-commutative 50.9%

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

   5. Simplified 50.9%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -6.4 \cdot 10^{+103} \lor \neg \left(i \leq -1.9 \cdot 10^{+56} \lor \neg \left(i \leq -1.3 \cdot 10^{-33}\right) \land i \leq 9.5 \cdot 10^{+73}\right):\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 43.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{-101}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-266}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-23}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+187}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -5.3e-101)
   (* c (- (* t j) (* z b)))
   (if (<= z -9.5e-266)
     (* i (- (* a b) (* y j)))
     (if (<= z 8.2e-23)
       (* j (- (* t c) (* y i)))
       (if (<= z 1.9e+187) (* b (- (* a i) (* z c))) (* z (* x y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -5.3e-101) {
		tmp = c * ((t * j) - (z * b));
	} else if (z <= -9.5e-266) {
		tmp = i * ((a * b) - (y * j));
	} else if (z <= 8.2e-23) {
		tmp = j * ((t * c) - (y * i));
	} else if (z <= 1.9e+187) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-5.3d-101)) then
        tmp = c * ((t * j) - (z * b))
    else if (z <= (-9.5d-266)) then
        tmp = i * ((a * b) - (y * j))
    else if (z <= 8.2d-23) then
        tmp = j * ((t * c) - (y * i))
    else if (z <= 1.9d+187) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -5.3e-101) {
		tmp = c * ((t * j) - (z * b));
	} else if (z <= -9.5e-266) {
		tmp = i * ((a * b) - (y * j));
	} else if (z <= 8.2e-23) {
		tmp = j * ((t * c) - (y * i));
	} else if (z <= 1.9e+187) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -5.3e-101:
		tmp = c * ((t * j) - (z * b))
	elif z <= -9.5e-266:
		tmp = i * ((a * b) - (y * j))
	elif z <= 8.2e-23:
		tmp = j * ((t * c) - (y * i))
	elif z <= 1.9e+187:
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -5.3e-101)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (z <= -9.5e-266)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (z <= 8.2e-23)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (z <= 1.9e+187)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -5.3e-101)
		tmp = c * ((t * j) - (z * b));
	elseif (z <= -9.5e-266)
		tmp = i * ((a * b) - (y * j));
	elseif (z <= 8.2e-23)
		tmp = j * ((t * c) - (y * i));
	elseif (z <= 1.9e+187)
		tmp = b * ((a * i) - (z * c));
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -5.3e-101], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9.5e-266], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e-23], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e+187], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -5.3000000000000003e-101

   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 c around inf 51.0%

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

      1. *-commutative 51.0%

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

      2. *-commutative 51.0%

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

   5. Simplified 51.0%

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

   if -5.3000000000000003e-101 < z < -9.49999999999999951e-266

   1. Initial program 80.6%

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

   3. Taylor expanded in y around 0 87.0%

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

   4. Taylor expanded in x around inf 80.7%

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

      1. +-commutative 80.7%

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

      2. mul-1-neg 80.7%

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

      3. unsub-neg 80.7%

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

      4. associate-/l* 80.7%

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

   6. Simplified 80.7%

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

   7. Taylor expanded in y around 0 80.7%

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

   9. Simplified 76.1%

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

   10. Taylor expanded in i around inf 65.2%

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

       1. sub-neg 65.2%

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

       2. neg-mul-1 65.2%

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

       3. mul-1-neg 65.2%

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

       4. remove-double-neg 65.2%

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

       5. +-commutative 65.2%

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

       6. unsub-neg 65.2%

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

       7. *-commutative 65.2%

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

   12. Simplified 65.2%

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

   if -9.49999999999999951e-266 < z < 8.20000000000000059e-23

   1. Initial program 85.4%

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

   3. Taylor expanded in j around inf 56.7%

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

   if 8.20000000000000059e-23 < z < 1.9e187

   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 b around inf 61.5%

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

      1. *-commutative 61.5%

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

   5. Simplified 61.5%

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

   if 1.9e187 < z

   1. Initial program 52.6%

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

   3. Taylor expanded in z around inf 72.3%

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

      1. *-commutative 72.3%

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

   5. Simplified 72.3%

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

   6. Taylor expanded in x around inf 54.9%

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

      1. *-commutative 54.9%

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

   8. Simplified 54.9%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{-101}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-266}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-23}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+187}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 45.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -6.5 \cdot 10^{-65} \lor \neg \left(c \leq 4.4 \cdot 10^{+30}\right):\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -6.5e-65) (not (<= c 4.4e+30)))
   (* c (- (* t j) (* z b)))
   (* 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 ((c <= -6.5e-65) || !(c <= 4.4e+30)) {
		tmp = c * ((t * j) - (z * b));
	} 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 ((c <= (-6.5d-65)) .or. (.not. (c <= 4.4d+30))) then
        tmp = c * ((t * j) - (z * b))
    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 ((c <= -6.5e-65) || !(c <= 4.4e+30)) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = b * ((a * i) - (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -6.5e-65) or not (c <= 4.4e+30):
		tmp = c * ((t * j) - (z * b))
	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 ((c <= -6.5e-65) || !(c <= 4.4e+30))
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	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 ((c <= -6.5e-65) || ~((c <= 4.4e+30)))
		tmp = c * ((t * j) - (z * b));
	else
		tmp = b * ((a * i) - (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -6.5e-65], N[Not[LessEqual[c, 4.4e+30]], $MachinePrecision]], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -6.5e-65 or 4.4e30 < c

   1. Initial program 71.3%

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

   3. Taylor expanded in c around inf 60.1%

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

      1. *-commutative 60.1%

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

      2. *-commutative 60.1%

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

   5. Simplified 60.1%

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

   if -6.5e-65 < c < 4.4e30

   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 b around inf 38.9%

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

      1. *-commutative 38.9%

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

   5. Simplified 38.9%

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

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.5 \cdot 10^{-65} \lor \neg \left(c \leq 4.4 \cdot 10^{+30}\right):\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 30.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3 \cdot 10^{-64} \lor \neg \left(c \leq 8.8 \cdot 10^{+36}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -3e-64) (not (<= c 8.8e+36))) (* c (* t j)) (* b (* a i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -3e-64) || !(c <= 8.8e+36)) {
		tmp = c * (t * j);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((c <= (-3d-64)) .or. (.not. (c <= 8.8d+36))) then
        tmp = c * (t * j)
    else
        tmp = b * (a * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -3e-64) || !(c <= 8.8e+36)) {
		tmp = c * (t * j);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -3e-64) or not (c <= 8.8e+36):
		tmp = c * (t * j)
	else:
		tmp = b * (a * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -3e-64) || !(c <= 8.8e+36))
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(b * Float64(a * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -3e-64) || ~((c <= 8.8e+36)))
		tmp = c * (t * j);
	else
		tmp = b * (a * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -3e-64], N[Not[LessEqual[c, 8.8e+36]], $MachinePrecision]], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -3.0000000000000001e-64 or 8.80000000000000002e36 < c

   1. Initial program 71.3%

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

   3. Taylor expanded in b around 0 64.7%

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

   4. Taylor expanded in c around inf 33.3%

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

   if -3.0000000000000001e-64 < c < 8.80000000000000002e36

   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 b around inf 38.9%

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

      1. *-commutative 38.9%

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

   5. Simplified 38.9%

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

   6. Taylor expanded in a around inf 32.9%

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

      1. *-commutative 32.9%

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

   8. Simplified 32.9%

      \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 33.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3 \cdot 10^{-64} \lor \neg \left(c \leq 8.8 \cdot 10^{+36}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 23.2% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ b \cdot \left(a \cdot i\right) \end{array} \]

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]

Derivation

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 b around inf 39.3%

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

   1. *-commutative 39.3%

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

5. Simplified 39.3%

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

6. Taylor expanded in a around inf 22.1%

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

   1. *-commutative 22.1%

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

8. Simplified 22.1%

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

9. Final simplification 22.1%

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

Alternative 23: 22.8% 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 74.6%

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

3. Taylor expanded in b around inf 39.3%

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

   1. *-commutative 39.3%

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

5. Simplified 39.3%

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

6. Taylor expanded in a around inf 21.1%

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

   1. *-commutative 21.1%

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

8. Simplified 21.1%

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

9. Final simplification 21.1%

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

Developer target: 68.7% 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 2024096 
(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)))))