Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.5% → 83.3%

Time: 19.4s

Alternatives: 20

Speedup: 0.5×

• 58.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 83.3% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(Float64(t * c) - Float64(y * i))
	tmp = 0.0
	if (Float64(Float64(t_1 - Float64(x * Float64(Float64(t * a) - Float64(y * z)))) + Float64(j * t_2)) <= Inf)
		tmp = fma(j, t_2, Float64(Float64(x * fma(y, z, Float64(t * Float64(-a)))) + t_1));
	else
		tmp = Float64(i * Float64(b * Float64(a - Float64(j * Float64(y / b)))));
	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[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(t$95$1 - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * t$95$2), $MachinePrecision]), $MachinePrecision], Infinity], N[(j * t$95$2 + N[(N[(x * N[(y * z + N[(t * (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(i * N[(b * N[(a - N[(j * N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 93.9%

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

      1. +-commutative 93.9%

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

      2. fma-define 93.9%

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

      3. *-commutative 93.9%

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

      4. *-commutative 93.9%

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

      5. cancel-sign-sub-inv 93.9%

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

      6. cancel-sign-sub 93.9%

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

      7. sub-neg 93.9%

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

      8. sub-neg 93.9%

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

      9. *-commutative 93.9%

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

      10. fma-neg 93.9%

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

      11. *-commutative 93.9%

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

      12. distribute-rgt-neg-out 93.9%

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

      13. remove-double-neg 93.9%

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

      14. *-commutative 93.9%

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

      15. *-commutative 93.9%

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

   3. Simplified 93.9%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in i around inf 55.4%

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

      1. distribute-lft-out-- 55.4%

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

      2. *-commutative 55.4%

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

   5. Simplified 55.4%

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

   6. Taylor expanded in b around inf 34.7%

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

      1. +-commutative 34.7%

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

      2. *-commutative 34.7%

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

      3. mul-1-neg 34.7%

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

      4. unsub-neg 34.7%

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

      5. *-commutative 34.7%

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

      6. associate-/l* 47.8%

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

      7. *-commutative 47.8%

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

   8. Simplified 47.8%

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

   9. Taylor expanded in b around inf 34.7%

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

       1. mul-1-neg 34.7%

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

       2. distribute-frac-neg 34.7%

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

       3. distribute-lft-neg-in 34.7%

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

       4. associate-*r/ 47.8%

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

       5. *-commutative 47.8%

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

       6. associate-*r/ 47.9%

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

       7. distribute-lft-neg-in 47.9%

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

       8. +-commutative 47.9%

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

       9. distribute-lft-in 38.4%

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

       10. *-commutative 38.4%

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

       11. associate-*r* 45.7%

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

       12. distribute-rgt-neg-in 45.7%

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

       13. associate-*r* 32.7%

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

       14. distribute-lft-in 61.0%

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

       15. associate-*r/ 60.9%

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

       16. *-commutative 60.9%

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

   11. Simplified 61.0%

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

4. Final simplification 87.1%

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

Alternative 2: 83.3% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 93.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   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 i around inf 55.4%

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

      1. distribute-lft-out-- 55.4%

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

      2. *-commutative 55.4%

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

   5. Simplified 55.4%

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

   6. Taylor expanded in b around inf 34.7%

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

      1. +-commutative 34.7%

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

      2. *-commutative 34.7%

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

      3. mul-1-neg 34.7%

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

      4. unsub-neg 34.7%

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

      5. *-commutative 34.7%

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

      6. associate-/l* 47.8%

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

      7. *-commutative 47.8%

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

   8. Simplified 47.8%

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

   9. Taylor expanded in b around inf 34.7%

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

       1. mul-1-neg 34.7%

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

       2. distribute-frac-neg 34.7%

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

       3. distribute-lft-neg-in 34.7%

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

       4. associate-*r/ 47.8%

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

       5. *-commutative 47.8%

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

       6. associate-*r/ 47.9%

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

       7. distribute-lft-neg-in 47.9%

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

       8. +-commutative 47.9%

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

       9. distribute-lft-in 38.4%

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

       10. *-commutative 38.4%

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

       11. associate-*r* 45.7%

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

       12. distribute-rgt-neg-in 45.7%

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

       13. associate-*r* 32.7%

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

       14. distribute-lft-in 61.0%

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

       15. associate-*r/ 60.9%

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

       16. *-commutative 60.9%

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

   11. Simplified 61.0%

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

4. Final simplification 87.1%

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

Alternative 3: 51.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ t_3 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -1.9 \cdot 10^{+134}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq -6 \cdot 10^{+102}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -8.6 \cdot 10^{+50}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;c \leq -1.45 \cdot 10^{-9}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq -3.9 \cdot 10^{-122}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -3.5 \cdot 10^{-197}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -2.2 \cdot 10^{-263}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 7.8 \cdot 10^{-196}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 3.1 \cdot 10^{+41}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j))))
        (t_2 (* b (* z (- (* a (/ i z)) c))))
        (t_3 (* c (- (* t j) (* z b)))))
   (if (<= c -1.9e+134)
     t_3
     (if (<= c -6e+102)
       t_2
       (if (<= c -8.6e+50)
         (* z (- (* x y) (* b c)))
         (if (<= c -1.45e-9)
           (* x (- (* y z) (* t a)))
           (if (<= c -3.9e-122)
             t_1
             (if (<= c -3.5e-197)
               t_2
               (if (<= c -2.2e-263)
                 (* i (- (* a b) (* y j)))
                 (if (<= c 7.8e-196)
                   t_1
                   (if (<= c 3.1e+41) (* a (- (* b i) (* x t))) t_3)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double t_2 = b * (z * ((a * (i / z)) - c));
	double t_3 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -1.9e+134) {
		tmp = t_3;
	} else if (c <= -6e+102) {
		tmp = t_2;
	} else if (c <= -8.6e+50) {
		tmp = z * ((x * y) - (b * c));
	} else if (c <= -1.45e-9) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= -3.9e-122) {
		tmp = t_1;
	} else if (c <= -3.5e-197) {
		tmp = t_2;
	} else if (c <= -2.2e-263) {
		tmp = i * ((a * b) - (y * j));
	} else if (c <= 7.8e-196) {
		tmp = t_1;
	} else if (c <= 3.1e+41) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y * ((x * z) - (i * j))
    t_2 = b * (z * ((a * (i / z)) - c))
    t_3 = c * ((t * j) - (z * b))
    if (c <= (-1.9d+134)) then
        tmp = t_3
    else if (c <= (-6d+102)) then
        tmp = t_2
    else if (c <= (-8.6d+50)) then
        tmp = z * ((x * y) - (b * c))
    else if (c <= (-1.45d-9)) then
        tmp = x * ((y * z) - (t * a))
    else if (c <= (-3.9d-122)) then
        tmp = t_1
    else if (c <= (-3.5d-197)) then
        tmp = t_2
    else if (c <= (-2.2d-263)) then
        tmp = i * ((a * b) - (y * j))
    else if (c <= 7.8d-196) then
        tmp = t_1
    else if (c <= 3.1d+41) then
        tmp = a * ((b * i) - (x * t))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double t_2 = b * (z * ((a * (i / z)) - c));
	double t_3 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -1.9e+134) {
		tmp = t_3;
	} else if (c <= -6e+102) {
		tmp = t_2;
	} else if (c <= -8.6e+50) {
		tmp = z * ((x * y) - (b * c));
	} else if (c <= -1.45e-9) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= -3.9e-122) {
		tmp = t_1;
	} else if (c <= -3.5e-197) {
		tmp = t_2;
	} else if (c <= -2.2e-263) {
		tmp = i * ((a * b) - (y * j));
	} else if (c <= 7.8e-196) {
		tmp = t_1;
	} else if (c <= 3.1e+41) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	t_2 = b * (z * ((a * (i / z)) - c))
	t_3 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -1.9e+134:
		tmp = t_3
	elif c <= -6e+102:
		tmp = t_2
	elif c <= -8.6e+50:
		tmp = z * ((x * y) - (b * c))
	elif c <= -1.45e-9:
		tmp = x * ((y * z) - (t * a))
	elif c <= -3.9e-122:
		tmp = t_1
	elif c <= -3.5e-197:
		tmp = t_2
	elif c <= -2.2e-263:
		tmp = i * ((a * b) - (y * j))
	elif c <= 7.8e-196:
		tmp = t_1
	elif c <= 3.1e+41:
		tmp = a * ((b * i) - (x * t))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_2 = Float64(b * Float64(z * Float64(Float64(a * Float64(i / z)) - c)))
	t_3 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -1.9e+134)
		tmp = t_3;
	elseif (c <= -6e+102)
		tmp = t_2;
	elseif (c <= -8.6e+50)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (c <= -1.45e-9)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (c <= -3.9e-122)
		tmp = t_1;
	elseif (c <= -3.5e-197)
		tmp = t_2;
	elseif (c <= -2.2e-263)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (c <= 7.8e-196)
		tmp = t_1;
	elseif (c <= 3.1e+41)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((x * z) - (i * j));
	t_2 = b * (z * ((a * (i / z)) - c));
	t_3 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -1.9e+134)
		tmp = t_3;
	elseif (c <= -6e+102)
		tmp = t_2;
	elseif (c <= -8.6e+50)
		tmp = z * ((x * y) - (b * c));
	elseif (c <= -1.45e-9)
		tmp = x * ((y * z) - (t * a));
	elseif (c <= -3.9e-122)
		tmp = t_1;
	elseif (c <= -3.5e-197)
		tmp = t_2;
	elseif (c <= -2.2e-263)
		tmp = i * ((a * b) - (y * j));
	elseif (c <= 7.8e-196)
		tmp = t_1;
	elseif (c <= 3.1e+41)
		tmp = a * ((b * i) - (x * t));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(z * N[(N[(a * N[(i / z), $MachinePrecision]), $MachinePrecision] - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.9e+134], t$95$3, If[LessEqual[c, -6e+102], t$95$2, If[LessEqual[c, -8.6e+50], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.45e-9], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -3.9e-122], t$95$1, If[LessEqual[c, -3.5e-197], t$95$2, If[LessEqual[c, -2.2e-263], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 7.8e-196], t$95$1, If[LessEqual[c, 3.1e+41], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if c < -1.89999999999999999e134 or 3.1e41 < c

   1. Initial program 63.1%

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

   3. Taylor expanded in c around inf 73.2%

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

   if -1.89999999999999999e134 < c < -5.9999999999999996e102 or -3.8999999999999999e-122 < c < -3.4999999999999998e-197

   1. Initial program 75.8%

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

   3. Taylor expanded in b around inf 60.8%

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

   4. Taylor expanded in z around inf 72.4%

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

      1. associate-/l* 76.4%

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

   6. Simplified 76.4%

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

   if -5.9999999999999996e102 < c < -8.5999999999999994e50

   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 z around inf 70.3%

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

      1. *-commutative 70.3%

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

   5. Simplified 70.3%

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

   if -8.5999999999999994e50 < c < -1.44999999999999996e-9

   1. Initial program 92.9%

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

   3. Taylor expanded in x around inf 75.4%

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

      1. *-commutative 75.4%

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

   5. Simplified 75.4%

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

   if -1.44999999999999996e-9 < c < -3.8999999999999999e-122 or -2.2e-263 < c < 7.80000000000000031e-196

   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 y around inf 68.2%

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

      1. +-commutative 68.2%

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

      2. mul-1-neg 68.2%

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

      3. unsub-neg 68.2%

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

      4. *-commutative 68.2%

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

   5. Simplified 68.2%

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

   if -3.4999999999999998e-197 < c < -2.2e-263

   1. Initial program 82.4%

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

   3. Taylor expanded in i around inf 73.3%

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

      1. distribute-lft-out-- 73.3%

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

      2. *-commutative 73.3%

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

   5. Simplified 73.3%

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

   if 7.80000000000000031e-196 < c < 3.1e41

   1. Initial program 88.0%

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

   3. Taylor expanded in a around inf 66.5%

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

      1. distribute-lft-out-- 66.5%

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

   5. Simplified 66.5%

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

   6. Taylor expanded in t around 0 66.5%

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

      1. +-commutative 66.5%

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

      2. mul-1-neg 66.5%

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

      3. distribute-rgt-neg-in 66.5%

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

      4. distribute-lft-out 66.5%

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

      5. unsub-neg 66.5%

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

   8. Simplified 66.5%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.9 \cdot 10^{+134}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -6 \cdot 10^{+102}:\\ \;\;\;\;b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \mathbf{elif}\;c \leq -8.6 \cdot 10^{+50}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;c \leq -1.45 \cdot 10^{-9}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq -3.9 \cdot 10^{-122}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq -3.5 \cdot 10^{-197}:\\ \;\;\;\;b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \mathbf{elif}\;c \leq -2.2 \cdot 10^{-263}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 7.8 \cdot 10^{-196}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 3.1 \cdot 10^{+41}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 66.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_3 := t\_2 - x \cdot \left(t \cdot a - y \cdot z\right)\\ t_4 := t\_2 + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -3.1 \cdot 10^{+253}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{+184}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{+178}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;b \leq -53000:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-28}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 6 \cdot 10^{+140}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;b \leq 6.1 \cdot 10^{+205}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* z (- (* a (/ i z)) c))))
        (t_2 (* j (- (* t c) (* y i))))
        (t_3 (- t_2 (* x (- (* t a) (* y z)))))
        (t_4 (+ t_2 (* b (- (* a i) (* z c))))))
   (if (<= b -3.1e+253)
     (* x (- (* y z) (* t a)))
     (if (<= b -1.75e+184)
       t_1
       (if (<= b -8.5e+178)
         (* a (- (* b i) (* x t)))
         (if (<= b -53000.0)
           t_4
           (if (<= b 1.6e-28)
             t_3
             (if (<= b 6e+140) t_4 (if (<= b 6.1e+205) t_3 t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (z * ((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_2 + (b * ((a * i) - (z * c)));
	double tmp;
	if (b <= -3.1e+253) {
		tmp = x * ((y * z) - (t * a));
	} else if (b <= -1.75e+184) {
		tmp = t_1;
	} else if (b <= -8.5e+178) {
		tmp = a * ((b * i) - (x * t));
	} else if (b <= -53000.0) {
		tmp = t_4;
	} else if (b <= 1.6e-28) {
		tmp = t_3;
	} else if (b <= 6e+140) {
		tmp = t_4;
	} else if (b <= 6.1e+205) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = b * (z * ((a * (i / z)) - c))
    t_2 = j * ((t * c) - (y * i))
    t_3 = t_2 - (x * ((t * a) - (y * z)))
    t_4 = t_2 + (b * ((a * i) - (z * c)))
    if (b <= (-3.1d+253)) then
        tmp = x * ((y * z) - (t * a))
    else if (b <= (-1.75d+184)) then
        tmp = t_1
    else if (b <= (-8.5d+178)) then
        tmp = a * ((b * i) - (x * t))
    else if (b <= (-53000.0d0)) then
        tmp = t_4
    else if (b <= 1.6d-28) then
        tmp = t_3
    else if (b <= 6d+140) then
        tmp = t_4
    else if (b <= 6.1d+205) then
        tmp = t_3
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (z * ((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_2 + (b * ((a * i) - (z * c)));
	double tmp;
	if (b <= -3.1e+253) {
		tmp = x * ((y * z) - (t * a));
	} else if (b <= -1.75e+184) {
		tmp = t_1;
	} else if (b <= -8.5e+178) {
		tmp = a * ((b * i) - (x * t));
	} else if (b <= -53000.0) {
		tmp = t_4;
	} else if (b <= 1.6e-28) {
		tmp = t_3;
	} else if (b <= 6e+140) {
		tmp = t_4;
	} else if (b <= 6.1e+205) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (z * ((a * (i / z)) - c))
	t_2 = j * ((t * c) - (y * i))
	t_3 = t_2 - (x * ((t * a) - (y * z)))
	t_4 = t_2 + (b * ((a * i) - (z * c)))
	tmp = 0
	if b <= -3.1e+253:
		tmp = x * ((y * z) - (t * a))
	elif b <= -1.75e+184:
		tmp = t_1
	elif b <= -8.5e+178:
		tmp = a * ((b * i) - (x * t))
	elif b <= -53000.0:
		tmp = t_4
	elif b <= 1.6e-28:
		tmp = t_3
	elif b <= 6e+140:
		tmp = t_4
	elif b <= 6.1e+205:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(z * Float64(Float64(a * Float64(i / 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(t_2 + Float64(b * Float64(Float64(a * i) - Float64(z * c))))
	tmp = 0.0
	if (b <= -3.1e+253)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (b <= -1.75e+184)
		tmp = t_1;
	elseif (b <= -8.5e+178)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (b <= -53000.0)
		tmp = t_4;
	elseif (b <= 1.6e-28)
		tmp = t_3;
	elseif (b <= 6e+140)
		tmp = t_4;
	elseif (b <= 6.1e+205)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (z * ((a * (i / z)) - c));
	t_2 = j * ((t * c) - (y * i));
	t_3 = t_2 - (x * ((t * a) - (y * z)));
	t_4 = t_2 + (b * ((a * i) - (z * c)));
	tmp = 0.0;
	if (b <= -3.1e+253)
		tmp = x * ((y * z) - (t * a));
	elseif (b <= -1.75e+184)
		tmp = t_1;
	elseif (b <= -8.5e+178)
		tmp = a * ((b * i) - (x * t));
	elseif (b <= -53000.0)
		tmp = t_4;
	elseif (b <= 1.6e-28)
		tmp = t_3;
	elseif (b <= 6e+140)
		tmp = t_4;
	elseif (b <= 6.1e+205)
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(z * N[(N[(a * N[(i / z), $MachinePrecision]), $MachinePrecision] - 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[(t$95$2 + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.1e+253], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.75e+184], t$95$1, If[LessEqual[b, -8.5e+178], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -53000.0], t$95$4, If[LessEqual[b, 1.6e-28], t$95$3, If[LessEqual[b, 6e+140], t$95$4, If[LessEqual[b, 6.1e+205], t$95$3, t$95$1]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -3.10000000000000006e253

   1. Initial program 57.1%

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

   3. Taylor expanded in x around inf 85.7%

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

      1. *-commutative 85.7%

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

   5. Simplified 85.7%

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

   if -3.10000000000000006e253 < b < -1.74999999999999989e184 or 6.0999999999999997e205 < b

   1. Initial program 62.1%

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

   3. Taylor expanded in b around inf 84.1%

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

   4. Taylor expanded in z around inf 86.8%

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

      1. associate-/l* 89.5%

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

   6. Simplified 89.5%

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

   if -1.74999999999999989e184 < b < -8.49999999999999991e178

   1. Initial program 99.2%

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

   3. Taylor expanded in a around inf 100.0%

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

      1. distribute-lft-out-- 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in t around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. distribute-rgt-neg-in 100.0%

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

      4. distribute-lft-out 100.0%

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

      5. unsub-neg 100.0%

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

   8. Simplified 100.0%

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

   if -8.49999999999999991e178 < b < -53000 or 1.59999999999999991e-28 < b < 5.99999999999999993e140

   1. Initial program 83.5%

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

   3. Taylor expanded in x around 0 82.3%

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

   if -53000 < b < 1.59999999999999991e-28 or 5.99999999999999993e140 < b < 6.0999999999999997e205

   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 b around 0 73.9%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.1 \cdot 10^{+253}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{+184}:\\ \;\;\;\;b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{+178}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;b \leq -53000:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-28}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;b \leq 6 \cdot 10^{+140}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 6.1 \cdot 10^{+205}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -3.1 \cdot 10^{+134}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -2.9 \cdot 10^{+102}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -5.8 \cdot 10^{+62}:\\ \;\;\;\;\left(z \cdot j\right) \cdot \frac{x \cdot y - b \cdot c}{j}\\ \mathbf{elif}\;c \leq -1.9 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq -2.3 \cdot 10^{-119}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(x \cdot \frac{z}{j} - i\right)\\ \mathbf{elif}\;c \leq -4.6 \cdot 10^{-196}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 4.8 \cdot 10^{-196}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 8.2 \cdot 10^{+40}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* z (- (* a (/ i z)) c)))) (t_2 (* c (- (* t j) (* z b)))))
   (if (<= c -3.1e+134)
     t_2
     (if (<= c -2.9e+102)
       t_1
       (if (<= c -5.8e+62)
         (* (* z j) (/ (- (* x y) (* b c)) j))
         (if (<= c -1.9e-10)
           (* x (- (* y z) (* t a)))
           (if (<= c -2.3e-119)
             (* (* y j) (- (* x (/ z j)) i))
             (if (<= c -4.6e-196)
               t_1
               (if (<= c 4.8e-196)
                 (* y (- (* x z) (* i j)))
                 (if (<= c 8.2e+40) (* a (- (* b i) (* x t))) t_2))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (z * ((a * (i / z)) - c));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -3.1e+134) {
		tmp = t_2;
	} else if (c <= -2.9e+102) {
		tmp = t_1;
	} else if (c <= -5.8e+62) {
		tmp = (z * j) * (((x * y) - (b * c)) / j);
	} else if (c <= -1.9e-10) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= -2.3e-119) {
		tmp = (y * j) * ((x * (z / j)) - i);
	} else if (c <= -4.6e-196) {
		tmp = t_1;
	} else if (c <= 4.8e-196) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 8.2e+40) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (z * ((a * (i / z)) - c))
    t_2 = c * ((t * j) - (z * b))
    if (c <= (-3.1d+134)) then
        tmp = t_2
    else if (c <= (-2.9d+102)) then
        tmp = t_1
    else if (c <= (-5.8d+62)) then
        tmp = (z * j) * (((x * y) - (b * c)) / j)
    else if (c <= (-1.9d-10)) then
        tmp = x * ((y * z) - (t * a))
    else if (c <= (-2.3d-119)) then
        tmp = (y * j) * ((x * (z / j)) - i)
    else if (c <= (-4.6d-196)) then
        tmp = t_1
    else if (c <= 4.8d-196) then
        tmp = y * ((x * z) - (i * j))
    else if (c <= 8.2d+40) then
        tmp = a * ((b * i) - (x * t))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (z * ((a * (i / z)) - c));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -3.1e+134) {
		tmp = t_2;
	} else if (c <= -2.9e+102) {
		tmp = t_1;
	} else if (c <= -5.8e+62) {
		tmp = (z * j) * (((x * y) - (b * c)) / j);
	} else if (c <= -1.9e-10) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= -2.3e-119) {
		tmp = (y * j) * ((x * (z / j)) - i);
	} else if (c <= -4.6e-196) {
		tmp = t_1;
	} else if (c <= 4.8e-196) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 8.2e+40) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (z * ((a * (i / z)) - c))
	t_2 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -3.1e+134:
		tmp = t_2
	elif c <= -2.9e+102:
		tmp = t_1
	elif c <= -5.8e+62:
		tmp = (z * j) * (((x * y) - (b * c)) / j)
	elif c <= -1.9e-10:
		tmp = x * ((y * z) - (t * a))
	elif c <= -2.3e-119:
		tmp = (y * j) * ((x * (z / j)) - i)
	elif c <= -4.6e-196:
		tmp = t_1
	elif c <= 4.8e-196:
		tmp = y * ((x * z) - (i * j))
	elif c <= 8.2e+40:
		tmp = a * ((b * i) - (x * t))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(z * Float64(Float64(a * Float64(i / z)) - c)))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -3.1e+134)
		tmp = t_2;
	elseif (c <= -2.9e+102)
		tmp = t_1;
	elseif (c <= -5.8e+62)
		tmp = Float64(Float64(z * j) * Float64(Float64(Float64(x * y) - Float64(b * c)) / j));
	elseif (c <= -1.9e-10)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (c <= -2.3e-119)
		tmp = Float64(Float64(y * j) * Float64(Float64(x * Float64(z / j)) - i));
	elseif (c <= -4.6e-196)
		tmp = t_1;
	elseif (c <= 4.8e-196)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (c <= 8.2e+40)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (z * ((a * (i / z)) - c));
	t_2 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -3.1e+134)
		tmp = t_2;
	elseif (c <= -2.9e+102)
		tmp = t_1;
	elseif (c <= -5.8e+62)
		tmp = (z * j) * (((x * y) - (b * c)) / j);
	elseif (c <= -1.9e-10)
		tmp = x * ((y * z) - (t * a));
	elseif (c <= -2.3e-119)
		tmp = (y * j) * ((x * (z / j)) - i);
	elseif (c <= -4.6e-196)
		tmp = t_1;
	elseif (c <= 4.8e-196)
		tmp = y * ((x * z) - (i * j));
	elseif (c <= 8.2e+40)
		tmp = a * ((b * i) - (x * t));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(z * N[(N[(a * N[(i / z), $MachinePrecision]), $MachinePrecision] - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.1e+134], t$95$2, If[LessEqual[c, -2.9e+102], t$95$1, If[LessEqual[c, -5.8e+62], N[(N[(z * j), $MachinePrecision] * N[(N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision] / j), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.9e-10], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.3e-119], N[(N[(y * j), $MachinePrecision] * N[(N[(x * N[(z / j), $MachinePrecision]), $MachinePrecision] - i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -4.6e-196], t$95$1, If[LessEqual[c, 4.8e-196], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 8.2e+40], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if c < -3.09999999999999982e134 or 8.2000000000000003e40 < c

   1. Initial program 63.1%

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

   3. Taylor expanded in c around inf 73.2%

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

   if -3.09999999999999982e134 < c < -2.9000000000000002e102 or -2.29999999999999993e-119 < c < -4.6000000000000004e-196

   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 b around inf 64.8%

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

   4. Taylor expanded in z around inf 76.4%

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

      1. associate-/l* 76.3%

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

   6. Simplified 76.3%

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

   if -2.9000000000000002e102 < c < -5.79999999999999968e62

   1. Initial program 64.9%

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

   3. Taylor expanded in j around inf 48.1%

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

      1. associate--l+ 48.1%

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

      2. sub-neg 48.1%

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

      3. mul-1-neg 48.1%

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

      4. +-commutative 48.1%

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

      5. +-commutative 48.1%

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

      6. associate--r+ 48.1%

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

   5. Simplified 57.2%

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

   6. Taylor expanded in z around inf 57.5%

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

      1. associate-*r* 65.2%

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

      2. *-commutative 65.2%

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

      3. div-sub 74.3%

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

      4. *-commutative 74.3%

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

   8. Simplified 74.3%

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

   if -5.79999999999999968e62 < c < -1.8999999999999999e-10

   1. Initial program 93.9%

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

   3. Taylor expanded in x around inf 72.0%

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

      1. *-commutative 72.0%

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

   5. Simplified 72.0%

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

   if -1.8999999999999999e-10 < c < -2.29999999999999993e-119

   1. Initial program 75.7%

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

   3. Taylor expanded in j around inf 71.8%

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

      1. associate--l+ 71.8%

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

      2. sub-neg 71.8%

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

      3. mul-1-neg 71.8%

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

      4. +-commutative 71.8%

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

      5. +-commutative 71.8%

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

      6. associate--r+ 71.8%

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

   5. Simplified 71.8%

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

   6. Taylor expanded in y around inf 64.1%

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

      1. associate-*r* 71.9%

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

      2. *-commutative 71.9%

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

      3. associate-/l* 71.5%

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

   8. Simplified 71.5%

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

   if -4.6000000000000004e-196 < c < 4.80000000000000041e-196

   1. Initial program 81.5%

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

   3. Taylor expanded in y around inf 65.5%

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

      1. +-commutative 65.5%

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

      2. mul-1-neg 65.5%

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

      3. unsub-neg 65.5%

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

      4. *-commutative 65.5%

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

   5. Simplified 65.5%

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

   if 4.80000000000000041e-196 < c < 8.2000000000000003e40

   1. Initial program 88.0%

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

   3. Taylor expanded in a around inf 66.5%

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

      1. distribute-lft-out-- 66.5%

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

   5. Simplified 66.5%

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

   6. Taylor expanded in t around 0 66.5%

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

      1. +-commutative 66.5%

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

      2. mul-1-neg 66.5%

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

      3. distribute-rgt-neg-in 66.5%

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

      4. distribute-lft-out 66.5%

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

      5. unsub-neg 66.5%

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

   8. Simplified 66.5%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.1 \cdot 10^{+134}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -2.9 \cdot 10^{+102}:\\ \;\;\;\;b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \mathbf{elif}\;c \leq -5.8 \cdot 10^{+62}:\\ \;\;\;\;\left(z \cdot j\right) \cdot \frac{x \cdot y - b \cdot c}{j}\\ \mathbf{elif}\;c \leq -1.9 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq -2.3 \cdot 10^{-119}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(x \cdot \frac{z}{j} - i\right)\\ \mathbf{elif}\;c \leq -4.6 \cdot 10^{-196}:\\ \;\;\;\;b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \mathbf{elif}\;c \leq 4.8 \cdot 10^{-196}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 8.2 \cdot 10^{+40}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -2 \cdot 10^{+134}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -7.2 \cdot 10^{+102}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -2 \cdot 10^{+51}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;c \leq -1.02 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq -1.45 \cdot 10^{-119}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(x \cdot \frac{z}{j} - i\right)\\ \mathbf{elif}\;c \leq -1.25 \cdot 10^{-195}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{-196}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 3.7 \cdot 10^{+41}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* z (- (* a (/ i z)) c)))) (t_2 (* c (- (* t j) (* z b)))))
   (if (<= c -2e+134)
     t_2
     (if (<= c -7.2e+102)
       t_1
       (if (<= c -2e+51)
         (* z (- (* x y) (* b c)))
         (if (<= c -1.02e-10)
           (* x (- (* y z) (* t a)))
           (if (<= c -1.45e-119)
             (* (* y j) (- (* x (/ z j)) i))
             (if (<= c -1.25e-195)
               t_1
               (if (<= c 3.2e-196)
                 (* y (- (* x z) (* i j)))
                 (if (<= c 3.7e+41) (* a (- (* b i) (* x t))) t_2))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (z * ((a * (i / z)) - c));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -2e+134) {
		tmp = t_2;
	} else if (c <= -7.2e+102) {
		tmp = t_1;
	} else if (c <= -2e+51) {
		tmp = z * ((x * y) - (b * c));
	} else if (c <= -1.02e-10) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= -1.45e-119) {
		tmp = (y * j) * ((x * (z / j)) - i);
	} else if (c <= -1.25e-195) {
		tmp = t_1;
	} else if (c <= 3.2e-196) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 3.7e+41) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (z * ((a * (i / z)) - c))
    t_2 = c * ((t * j) - (z * b))
    if (c <= (-2d+134)) then
        tmp = t_2
    else if (c <= (-7.2d+102)) then
        tmp = t_1
    else if (c <= (-2d+51)) then
        tmp = z * ((x * y) - (b * c))
    else if (c <= (-1.02d-10)) then
        tmp = x * ((y * z) - (t * a))
    else if (c <= (-1.45d-119)) then
        tmp = (y * j) * ((x * (z / j)) - i)
    else if (c <= (-1.25d-195)) then
        tmp = t_1
    else if (c <= 3.2d-196) then
        tmp = y * ((x * z) - (i * j))
    else if (c <= 3.7d+41) then
        tmp = a * ((b * i) - (x * t))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (z * ((a * (i / z)) - c));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -2e+134) {
		tmp = t_2;
	} else if (c <= -7.2e+102) {
		tmp = t_1;
	} else if (c <= -2e+51) {
		tmp = z * ((x * y) - (b * c));
	} else if (c <= -1.02e-10) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= -1.45e-119) {
		tmp = (y * j) * ((x * (z / j)) - i);
	} else if (c <= -1.25e-195) {
		tmp = t_1;
	} else if (c <= 3.2e-196) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 3.7e+41) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (z * ((a * (i / z)) - c))
	t_2 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -2e+134:
		tmp = t_2
	elif c <= -7.2e+102:
		tmp = t_1
	elif c <= -2e+51:
		tmp = z * ((x * y) - (b * c))
	elif c <= -1.02e-10:
		tmp = x * ((y * z) - (t * a))
	elif c <= -1.45e-119:
		tmp = (y * j) * ((x * (z / j)) - i)
	elif c <= -1.25e-195:
		tmp = t_1
	elif c <= 3.2e-196:
		tmp = y * ((x * z) - (i * j))
	elif c <= 3.7e+41:
		tmp = a * ((b * i) - (x * t))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(z * Float64(Float64(a * Float64(i / z)) - c)))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -2e+134)
		tmp = t_2;
	elseif (c <= -7.2e+102)
		tmp = t_1;
	elseif (c <= -2e+51)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (c <= -1.02e-10)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (c <= -1.45e-119)
		tmp = Float64(Float64(y * j) * Float64(Float64(x * Float64(z / j)) - i));
	elseif (c <= -1.25e-195)
		tmp = t_1;
	elseif (c <= 3.2e-196)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (c <= 3.7e+41)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (z * ((a * (i / z)) - c));
	t_2 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -2e+134)
		tmp = t_2;
	elseif (c <= -7.2e+102)
		tmp = t_1;
	elseif (c <= -2e+51)
		tmp = z * ((x * y) - (b * c));
	elseif (c <= -1.02e-10)
		tmp = x * ((y * z) - (t * a));
	elseif (c <= -1.45e-119)
		tmp = (y * j) * ((x * (z / j)) - i);
	elseif (c <= -1.25e-195)
		tmp = t_1;
	elseif (c <= 3.2e-196)
		tmp = y * ((x * z) - (i * j));
	elseif (c <= 3.7e+41)
		tmp = a * ((b * i) - (x * t));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(z * N[(N[(a * N[(i / z), $MachinePrecision]), $MachinePrecision] - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2e+134], t$95$2, If[LessEqual[c, -7.2e+102], t$95$1, If[LessEqual[c, -2e+51], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.02e-10], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.45e-119], N[(N[(y * j), $MachinePrecision] * N[(N[(x * N[(z / j), $MachinePrecision]), $MachinePrecision] - i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.25e-195], t$95$1, If[LessEqual[c, 3.2e-196], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.7e+41], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if c < -1.99999999999999984e134 or 3.69999999999999981e41 < c

   1. Initial program 63.1%

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

   3. Taylor expanded in c around inf 73.2%

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

   if -1.99999999999999984e134 < c < -7.2000000000000003e102 or -1.45e-119 < c < -1.25000000000000002e-195

   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 b around inf 64.8%

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

   4. Taylor expanded in z around inf 76.4%

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

      1. associate-/l* 76.3%

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

   6. Simplified 76.3%

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

   if -7.2000000000000003e102 < c < -2e51

   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 z around inf 70.3%

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

      1. *-commutative 70.3%

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

   5. Simplified 70.3%

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

   if -2e51 < c < -1.01999999999999997e-10

   1. Initial program 92.9%

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

   3. Taylor expanded in x around inf 75.4%

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

      1. *-commutative 75.4%

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

   5. Simplified 75.4%

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

   if -1.01999999999999997e-10 < c < -1.45e-119

   1. Initial program 75.7%

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

   3. Taylor expanded in j around inf 71.8%

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

      1. associate--l+ 71.8%

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

      2. sub-neg 71.8%

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

      3. mul-1-neg 71.8%

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

      4. +-commutative 71.8%

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

      5. +-commutative 71.8%

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

      6. associate--r+ 71.8%

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

   5. Simplified 71.8%

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

   6. Taylor expanded in y around inf 64.1%

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

      1. associate-*r* 71.9%

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

      2. *-commutative 71.9%

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

      3. associate-/l* 71.5%

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

   8. Simplified 71.5%

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

   if -1.25000000000000002e-195 < c < 3.2e-196

   1. Initial program 81.5%

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

   3. Taylor expanded in y around inf 65.5%

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

      1. +-commutative 65.5%

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

      2. mul-1-neg 65.5%

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

      3. unsub-neg 65.5%

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

      4. *-commutative 65.5%

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

   5. Simplified 65.5%

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

   if 3.2e-196 < c < 3.69999999999999981e41

   1. Initial program 88.0%

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

   3. Taylor expanded in a around inf 66.5%

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

      1. distribute-lft-out-- 66.5%

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

   5. Simplified 66.5%

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

   6. Taylor expanded in t around 0 66.5%

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

      1. +-commutative 66.5%

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

      2. mul-1-neg 66.5%

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

      3. distribute-rgt-neg-in 66.5%

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

      4. distribute-lft-out 66.5%

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

      5. unsub-neg 66.5%

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

   8. Simplified 66.5%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2 \cdot 10^{+134}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -7.2 \cdot 10^{+102}:\\ \;\;\;\;b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \mathbf{elif}\;c \leq -2 \cdot 10^{+51}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;c \leq -1.02 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq -1.45 \cdot 10^{-119}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(x \cdot \frac{z}{j} - i\right)\\ \mathbf{elif}\;c \leq -1.25 \cdot 10^{-195}:\\ \;\;\;\;b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{-196}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 3.7 \cdot 10^{+41}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ t_3 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -3.2 \cdot 10^{+134}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq -2.9 \cdot 10^{+102}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -6.8 \cdot 10^{+50}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;c \leq -4.6 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq -2.6 \cdot 10^{-123}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -1.9 \cdot 10^{-195}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 6.8 \cdot 10^{-196}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 4.1 \cdot 10^{+40}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j))))
        (t_2 (* b (* z (- (* a (/ i z)) c))))
        (t_3 (* c (- (* t j) (* z b)))))
   (if (<= c -3.2e+134)
     t_3
     (if (<= c -2.9e+102)
       t_2
       (if (<= c -6.8e+50)
         (* z (- (* x y) (* b c)))
         (if (<= c -4.6e-11)
           (* x (- (* y z) (* t a)))
           (if (<= c -2.6e-123)
             t_1
             (if (<= c -1.9e-195)
               t_2
               (if (<= c 6.8e-196)
                 t_1
                 (if (<= c 4.1e+40) (* a (- (* b i) (* x t))) t_3))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double t_2 = b * (z * ((a * (i / z)) - c));
	double t_3 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -3.2e+134) {
		tmp = t_3;
	} else if (c <= -2.9e+102) {
		tmp = t_2;
	} else if (c <= -6.8e+50) {
		tmp = z * ((x * y) - (b * c));
	} else if (c <= -4.6e-11) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= -2.6e-123) {
		tmp = t_1;
	} else if (c <= -1.9e-195) {
		tmp = t_2;
	} else if (c <= 6.8e-196) {
		tmp = t_1;
	} else if (c <= 4.1e+40) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y * ((x * z) - (i * j))
    t_2 = b * (z * ((a * (i / z)) - c))
    t_3 = c * ((t * j) - (z * b))
    if (c <= (-3.2d+134)) then
        tmp = t_3
    else if (c <= (-2.9d+102)) then
        tmp = t_2
    else if (c <= (-6.8d+50)) then
        tmp = z * ((x * y) - (b * c))
    else if (c <= (-4.6d-11)) then
        tmp = x * ((y * z) - (t * a))
    else if (c <= (-2.6d-123)) then
        tmp = t_1
    else if (c <= (-1.9d-195)) then
        tmp = t_2
    else if (c <= 6.8d-196) then
        tmp = t_1
    else if (c <= 4.1d+40) then
        tmp = a * ((b * i) - (x * t))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double t_2 = b * (z * ((a * (i / z)) - c));
	double t_3 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -3.2e+134) {
		tmp = t_3;
	} else if (c <= -2.9e+102) {
		tmp = t_2;
	} else if (c <= -6.8e+50) {
		tmp = z * ((x * y) - (b * c));
	} else if (c <= -4.6e-11) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= -2.6e-123) {
		tmp = t_1;
	} else if (c <= -1.9e-195) {
		tmp = t_2;
	} else if (c <= 6.8e-196) {
		tmp = t_1;
	} else if (c <= 4.1e+40) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	t_2 = b * (z * ((a * (i / z)) - c))
	t_3 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -3.2e+134:
		tmp = t_3
	elif c <= -2.9e+102:
		tmp = t_2
	elif c <= -6.8e+50:
		tmp = z * ((x * y) - (b * c))
	elif c <= -4.6e-11:
		tmp = x * ((y * z) - (t * a))
	elif c <= -2.6e-123:
		tmp = t_1
	elif c <= -1.9e-195:
		tmp = t_2
	elif c <= 6.8e-196:
		tmp = t_1
	elif c <= 4.1e+40:
		tmp = a * ((b * i) - (x * t))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_2 = Float64(b * Float64(z * Float64(Float64(a * Float64(i / z)) - c)))
	t_3 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -3.2e+134)
		tmp = t_3;
	elseif (c <= -2.9e+102)
		tmp = t_2;
	elseif (c <= -6.8e+50)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (c <= -4.6e-11)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (c <= -2.6e-123)
		tmp = t_1;
	elseif (c <= -1.9e-195)
		tmp = t_2;
	elseif (c <= 6.8e-196)
		tmp = t_1;
	elseif (c <= 4.1e+40)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((x * z) - (i * j));
	t_2 = b * (z * ((a * (i / z)) - c));
	t_3 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -3.2e+134)
		tmp = t_3;
	elseif (c <= -2.9e+102)
		tmp = t_2;
	elseif (c <= -6.8e+50)
		tmp = z * ((x * y) - (b * c));
	elseif (c <= -4.6e-11)
		tmp = x * ((y * z) - (t * a));
	elseif (c <= -2.6e-123)
		tmp = t_1;
	elseif (c <= -1.9e-195)
		tmp = t_2;
	elseif (c <= 6.8e-196)
		tmp = t_1;
	elseif (c <= 4.1e+40)
		tmp = a * ((b * i) - (x * t));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(z * N[(N[(a * N[(i / z), $MachinePrecision]), $MachinePrecision] - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.2e+134], t$95$3, If[LessEqual[c, -2.9e+102], t$95$2, If[LessEqual[c, -6.8e+50], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -4.6e-11], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.6e-123], t$95$1, If[LessEqual[c, -1.9e-195], t$95$2, If[LessEqual[c, 6.8e-196], t$95$1, If[LessEqual[c, 4.1e+40], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -3.2000000000000001e134 or 4.1000000000000002e40 < c

   1. Initial program 63.1%

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

   3. Taylor expanded in c around inf 73.2%

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

   if -3.2000000000000001e134 < c < -2.9000000000000002e102 or -2.59999999999999995e-123 < c < -1.90000000000000006e-195

   1. Initial program 74.8%

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

   3. Taylor expanded in b around inf 63.3%

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

   4. Taylor expanded in z around inf 75.4%

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

      1. associate-/l* 79.5%

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

   6. Simplified 79.5%

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

   if -2.9000000000000002e102 < c < -6.7999999999999997e50

   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 z around inf 70.3%

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

      1. *-commutative 70.3%

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

   5. Simplified 70.3%

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

   if -6.7999999999999997e50 < c < -4.60000000000000027e-11

   1. Initial program 92.9%

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

   3. Taylor expanded in x around inf 75.4%

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

      1. *-commutative 75.4%

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

   5. Simplified 75.4%

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

   if -4.60000000000000027e-11 < c < -2.59999999999999995e-123 or -1.90000000000000006e-195 < c < 6.8e-196

   1. Initial program 78.5%

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

   3. Taylor expanded in y around inf 65.4%

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

      1. +-commutative 65.4%

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

      2. mul-1-neg 65.4%

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

      3. unsub-neg 65.4%

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

      4. *-commutative 65.4%

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

   5. Simplified 65.4%

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

   if 6.8e-196 < c < 4.1000000000000002e40

   1. Initial program 88.0%

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

   3. Taylor expanded in a around inf 66.5%

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

      1. distribute-lft-out-- 66.5%

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

   5. Simplified 66.5%

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

   6. Taylor expanded in t around 0 66.5%

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

      1. +-commutative 66.5%

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

      2. mul-1-neg 66.5%

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

      3. distribute-rgt-neg-in 66.5%

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

      4. distribute-lft-out 66.5%

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

      5. unsub-neg 66.5%

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

   8. Simplified 66.5%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.2 \cdot 10^{+134}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -2.9 \cdot 10^{+102}:\\ \;\;\;\;b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \mathbf{elif}\;c \leq -6.8 \cdot 10^{+50}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;c \leq -4.6 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq -2.6 \cdot 10^{-123}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq -1.9 \cdot 10^{-195}:\\ \;\;\;\;b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \mathbf{elif}\;c \leq 6.8 \cdot 10^{-196}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 4.1 \cdot 10^{+40}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -1.05 \cdot 10^{+85}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -4.8 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq -3.6 \cdot 10^{-119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -1.5 \cdot 10^{-195}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq 6.4 \cdot 10^{-196}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 6.8 \cdot 10^{+40}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j)))) (t_2 (* c (- (* t j) (* z b)))))
   (if (<= c -1.05e+85)
     t_2
     (if (<= c -4.8e-10)
       (* x (- (* y z) (* t a)))
       (if (<= c -3.6e-119)
         t_1
         (if (<= c -1.5e-195)
           (* b (- (* a i) (* z c)))
           (if (<= c 6.4e-196)
             t_1
             (if (<= c 6.8e+40) (* a (- (* b i) (* x t))) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -1.05e+85) {
		tmp = t_2;
	} else if (c <= -4.8e-10) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= -3.6e-119) {
		tmp = t_1;
	} else if (c <= -1.5e-195) {
		tmp = b * ((a * i) - (z * c));
	} else if (c <= 6.4e-196) {
		tmp = t_1;
	} else if (c <= 6.8e+40) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((x * z) - (i * j))
    t_2 = c * ((t * j) - (z * b))
    if (c <= (-1.05d+85)) then
        tmp = t_2
    else if (c <= (-4.8d-10)) then
        tmp = x * ((y * z) - (t * a))
    else if (c <= (-3.6d-119)) then
        tmp = t_1
    else if (c <= (-1.5d-195)) then
        tmp = b * ((a * i) - (z * c))
    else if (c <= 6.4d-196) then
        tmp = t_1
    else if (c <= 6.8d+40) then
        tmp = a * ((b * i) - (x * t))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -1.05e+85) {
		tmp = t_2;
	} else if (c <= -4.8e-10) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= -3.6e-119) {
		tmp = t_1;
	} else if (c <= -1.5e-195) {
		tmp = b * ((a * i) - (z * c));
	} else if (c <= 6.4e-196) {
		tmp = t_1;
	} else if (c <= 6.8e+40) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	t_2 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -1.05e+85:
		tmp = t_2
	elif c <= -4.8e-10:
		tmp = x * ((y * z) - (t * a))
	elif c <= -3.6e-119:
		tmp = t_1
	elif c <= -1.5e-195:
		tmp = b * ((a * i) - (z * c))
	elif c <= 6.4e-196:
		tmp = t_1
	elif c <= 6.8e+40:
		tmp = a * ((b * i) - (x * t))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -1.05e+85)
		tmp = t_2;
	elseif (c <= -4.8e-10)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (c <= -3.6e-119)
		tmp = t_1;
	elseif (c <= -1.5e-195)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (c <= 6.4e-196)
		tmp = t_1;
	elseif (c <= 6.8e+40)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((x * z) - (i * j));
	t_2 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -1.05e+85)
		tmp = t_2;
	elseif (c <= -4.8e-10)
		tmp = x * ((y * z) - (t * a));
	elseif (c <= -3.6e-119)
		tmp = t_1;
	elseif (c <= -1.5e-195)
		tmp = b * ((a * i) - (z * c));
	elseif (c <= 6.4e-196)
		tmp = t_1;
	elseif (c <= 6.8e+40)
		tmp = a * ((b * i) - (x * t));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.05e+85], t$95$2, If[LessEqual[c, -4.8e-10], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -3.6e-119], t$95$1, If[LessEqual[c, -1.5e-195], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.4e-196], t$95$1, If[LessEqual[c, 6.8e+40], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -1.05000000000000005e85 or 6.79999999999999977e40 < c

   1. Initial program 62.6%

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

   3. Taylor expanded in c around inf 69.7%

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

   if -1.05000000000000005e85 < c < -4.8e-10

   1. Initial program 86.7%

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

   3. Taylor expanded in x around inf 66.1%

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

      1. *-commutative 66.1%

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

   5. Simplified 66.1%

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

   if -4.8e-10 < c < -3.6e-119 or -1.5e-195 < c < 6.3999999999999999e-196

   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 inf 66.3%

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

      1. +-commutative 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%

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

   5. Simplified 66.3%

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

   if -3.6e-119 < c < -1.5e-195

   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 b around inf 67.3%

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

   if 6.3999999999999999e-196 < c < 6.79999999999999977e40

   1. Initial program 88.0%

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

   3. Taylor expanded in a around inf 66.5%

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

      1. distribute-lft-out-- 66.5%

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

   5. Simplified 66.5%

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

   6. Taylor expanded in t around 0 66.5%

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

      1. +-commutative 66.5%

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

      2. mul-1-neg 66.5%

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

      3. distribute-rgt-neg-in 66.5%

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

      4. distribute-lft-out 66.5%

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

      5. unsub-neg 66.5%

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

   8. Simplified 66.5%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.05 \cdot 10^{+85}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -4.8 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq -3.6 \cdot 10^{-119}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq -1.5 \cdot 10^{-195}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq 6.4 \cdot 10^{-196}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 6.8 \cdot 10^{+40}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 67.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_3 := t\_2 - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{if}\;j \leq -4.1 \cdot 10^{+96}:\\ \;\;\;\;j \cdot \left(t \cdot c + i \cdot \left(a \cdot \frac{b}{j} - y\right)\right)\\ \mathbf{elif}\;j \leq -2.3 \cdot 10^{+17}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq -6.9 \cdot 10^{-74}:\\ \;\;\;\;t\_2 + t\_1\\ \mathbf{elif}\;j \leq 5.6 \cdot 10^{-73}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c))))
        (t_2 (* j (- (* t c) (* y i))))
        (t_3 (- t_2 (* x (- (* t a) (* y z))))))
   (if (<= j -4.1e+96)
     (* j (+ (* t c) (* i (- (* a (/ b j)) y))))
     (if (<= j -2.3e+17)
       t_3
       (if (<= j -6.9e-74)
         (+ t_2 t_1)
         (if (<= j 5.6e-73) (+ (* t (- (* c j) (* x a))) t_1) t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = j * ((t * c) - (y * i));
	double t_3 = t_2 - (x * ((t * a) - (y * z)));
	double tmp;
	if (j <= -4.1e+96) {
		tmp = j * ((t * c) + (i * ((a * (b / j)) - y)));
	} else if (j <= -2.3e+17) {
		tmp = t_3;
	} else if (j <= -6.9e-74) {
		tmp = t_2 + t_1;
	} else if (j <= 5.6e-73) {
		tmp = (t * ((c * j) - (x * a))) + t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = j * ((t * c) - (y * i))
    t_3 = t_2 - (x * ((t * a) - (y * z)))
    if (j <= (-4.1d+96)) then
        tmp = j * ((t * c) + (i * ((a * (b / j)) - y)))
    else if (j <= (-2.3d+17)) then
        tmp = t_3
    else if (j <= (-6.9d-74)) then
        tmp = t_2 + t_1
    else if (j <= 5.6d-73) then
        tmp = (t * ((c * j) - (x * a))) + t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = j * ((t * c) - (y * i));
	double t_3 = t_2 - (x * ((t * a) - (y * z)));
	double tmp;
	if (j <= -4.1e+96) {
		tmp = j * ((t * c) + (i * ((a * (b / j)) - y)));
	} else if (j <= -2.3e+17) {
		tmp = t_3;
	} else if (j <= -6.9e-74) {
		tmp = t_2 + t_1;
	} else if (j <= 5.6e-73) {
		tmp = (t * ((c * j) - (x * a))) + t_1;
	} else {
		tmp = t_3;
	}
	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)))
	tmp = 0
	if j <= -4.1e+96:
		tmp = j * ((t * c) + (i * ((a * (b / j)) - y)))
	elif j <= -2.3e+17:
		tmp = t_3
	elif j <= -6.9e-74:
		tmp = t_2 + t_1
	elif j <= 5.6e-73:
		tmp = (t * ((c * j) - (x * a))) + t_1
	else:
		tmp = t_3
	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))))
	tmp = 0.0
	if (j <= -4.1e+96)
		tmp = Float64(j * Float64(Float64(t * c) + Float64(i * Float64(Float64(a * Float64(b / j)) - y))));
	elseif (j <= -2.3e+17)
		tmp = t_3;
	elseif (j <= -6.9e-74)
		tmp = Float64(t_2 + t_1);
	elseif (j <= 5.6e-73)
		tmp = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) + t_1);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = j * ((t * c) - (y * i));
	t_3 = t_2 - (x * ((t * a) - (y * z)));
	tmp = 0.0;
	if (j <= -4.1e+96)
		tmp = j * ((t * c) + (i * ((a * (b / j)) - y)));
	elseif (j <= -2.3e+17)
		tmp = t_3;
	elseif (j <= -6.9e-74)
		tmp = t_2 + t_1;
	elseif (j <= 5.6e-73)
		tmp = (t * ((c * j) - (x * a))) + t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(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]}, If[LessEqual[j, -4.1e+96], N[(j * N[(N[(t * c), $MachinePrecision] + N[(i * N[(N[(a * N[(b / j), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.3e+17], t$95$3, If[LessEqual[j, -6.9e-74], N[(t$95$2 + t$95$1), $MachinePrecision], If[LessEqual[j, 5.6e-73], N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], t$95$3]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -4.09999999999999998e96

   1. Initial program 58.8%

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

   3. Taylor expanded in j around inf 63.2%

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

      1. associate--l+ 63.2%

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

      2. sub-neg 63.2%

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

      3. mul-1-neg 63.2%

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

      4. +-commutative 63.2%

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

      5. +-commutative 63.2%

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

      6. associate--r+ 63.2%

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

   5. Simplified 63.2%

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

   6. Taylor expanded in i around inf 81.3%

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

      1. associate-*r* 77.7%

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

   8. Simplified 77.7%

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

   9. Taylor expanded in a around 0 81.3%

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

       1. sub-neg 81.3%

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

       2. *-commutative 81.3%

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

       3. associate-*r* 75.1%

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

       4. *-commutative 75.1%

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

       5. associate-*r* 77.7%

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

       6. associate-*r/ 79.9%

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

       7. distribute-rgt-neg-in 79.9%

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

       8. distribute-lft-in 79.9%

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

       9. sub-neg 79.9%

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

       10. associate-/l* 79.3%

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

   11. Simplified 79.3%

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

   if -4.09999999999999998e96 < j < -2.3e17 or 5.60000000000000023e-73 < j

   1. Initial program 80.5%

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

   3. Taylor expanded in b around 0 77.3%

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

   if -2.3e17 < j < -6.89999999999999981e-74

   1. Initial program 95.7%

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

   3. Taylor expanded in x around 0 87.2%

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

   if -6.89999999999999981e-74 < j < 5.60000000000000023e-73

   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 72.3%

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

      1. associate-*r* 72.3%

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

      2. *-commutative 72.3%

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

      3. associate-*r* 71.3%

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

      4. associate-*r* 71.3%

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

      5. associate-*r* 71.3%

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

      6. distribute-rgt-in 71.3%

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

      7. +-commutative 71.3%

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

      8. mul-1-neg 71.3%

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

      9. unsub-neg 71.3%

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

   5. Simplified 71.3%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4.1 \cdot 10^{+96}:\\ \;\;\;\;j \cdot \left(t \cdot c + i \cdot \left(a \cdot \frac{b}{j} - y\right)\right)\\ \mathbf{elif}\;j \leq -2.3 \cdot 10^{+17}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;j \leq -6.9 \cdot 10^{-74}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 5.6 \cdot 10^{-73}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{if}\;c \leq -4 \cdot 10^{+91}:\\ \;\;\;\;j \cdot \left(t \cdot c + i \cdot \left(a \cdot \frac{b}{j} - y\right)\right)\\ \mathbf{elif}\;c \leq -1.6 \cdot 10^{-119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -2 \cdot 10^{-195}:\\ \;\;\;\;b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \mathbf{elif}\;c \leq 2.3 \cdot 10^{+167}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* j (- (* t c) (* y i))) (* x (- (* t a) (* y z))))))
   (if (<= c -4e+91)
     (* j (+ (* t c) (* i (- (* a (/ b j)) y))))
     (if (<= c -1.6e-119)
       t_1
       (if (<= c -2e-195)
         (* b (* z (- (* a (/ i z)) c)))
         (if (<= c 2.3e+167) t_1 (* c (- (* t j) (* z b)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)));
	double tmp;
	if (c <= -4e+91) {
		tmp = j * ((t * c) + (i * ((a * (b / j)) - y)));
	} else if (c <= -1.6e-119) {
		tmp = t_1;
	} else if (c <= -2e-195) {
		tmp = b * (z * ((a * (i / z)) - c));
	} else if (c <= 2.3e+167) {
		tmp = t_1;
	} else {
		tmp = c * ((t * j) - (z * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)))
    if (c <= (-4d+91)) then
        tmp = j * ((t * c) + (i * ((a * (b / j)) - y)))
    else if (c <= (-1.6d-119)) then
        tmp = t_1
    else if (c <= (-2d-195)) then
        tmp = b * (z * ((a * (i / z)) - c))
    else if (c <= 2.3d+167) then
        tmp = t_1
    else
        tmp = c * ((t * j) - (z * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)));
	double tmp;
	if (c <= -4e+91) {
		tmp = j * ((t * c) + (i * ((a * (b / j)) - y)));
	} else if (c <= -1.6e-119) {
		tmp = t_1;
	} else if (c <= -2e-195) {
		tmp = b * (z * ((a * (i / z)) - c));
	} else if (c <= 2.3e+167) {
		tmp = t_1;
	} else {
		tmp = c * ((t * j) - (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)))
	tmp = 0
	if c <= -4e+91:
		tmp = j * ((t * c) + (i * ((a * (b / j)) - y)))
	elif c <= -1.6e-119:
		tmp = t_1
	elif c <= -2e-195:
		tmp = b * (z * ((a * (i / z)) - c))
	elif c <= 2.3e+167:
		tmp = t_1
	else:
		tmp = c * ((t * j) - (z * b))
	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))))
	tmp = 0.0
	if (c <= -4e+91)
		tmp = Float64(j * Float64(Float64(t * c) + Float64(i * Float64(Float64(a * Float64(b / j)) - y))));
	elseif (c <= -1.6e-119)
		tmp = t_1;
	elseif (c <= -2e-195)
		tmp = Float64(b * Float64(z * Float64(Float64(a * Float64(i / z)) - c)));
	elseif (c <= 2.3e+167)
		tmp = t_1;
	else
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)));
	tmp = 0.0;
	if (c <= -4e+91)
		tmp = j * ((t * c) + (i * ((a * (b / j)) - y)));
	elseif (c <= -1.6e-119)
		tmp = t_1;
	elseif (c <= -2e-195)
		tmp = b * (z * ((a * (i / z)) - c));
	elseif (c <= 2.3e+167)
		tmp = t_1;
	else
		tmp = c * ((t * j) - (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(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]}, If[LessEqual[c, -4e+91], N[(j * N[(N[(t * c), $MachinePrecision] + N[(i * N[(N[(a * N[(b / j), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.6e-119], t$95$1, If[LessEqual[c, -2e-195], N[(b * N[(z * N[(N[(a * N[(i / z), $MachinePrecision]), $MachinePrecision] - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.3e+167], t$95$1, N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -4.00000000000000032e91

   1. Initial program 54.3%

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

   3. Taylor expanded in j around inf 46.0%

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

      1. associate--l+ 46.0%

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

      2. sub-neg 46.0%

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

      3. mul-1-neg 46.0%

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

      4. +-commutative 46.0%

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

      5. +-commutative 46.0%

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

      6. associate--r+ 46.0%

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

   5. Simplified 48.2%

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

   6. Taylor expanded in i around inf 57.0%

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

      1. associate-*r* 59.2%

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

   8. Simplified 59.2%

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

   9. Taylor expanded in a around 0 57.0%

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

       1. sub-neg 57.0%

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

       2. *-commutative 57.0%

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

       3. associate-*r* 57.0%

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

       4. *-commutative 57.0%

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

       5. associate-*r* 59.2%

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

       6. associate-*r/ 61.2%

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

       7. distribute-rgt-neg-in 61.2%

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

       8. distribute-lft-in 63.4%

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

       9. sub-neg 63.4%

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

       10. associate-/l* 65.6%

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

   11. Simplified 65.6%

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

   if -4.00000000000000032e91 < c < -1.59999999999999997e-119 or -2.0000000000000002e-195 < c < 2.29999999999999988e167

   1. Initial program 83.0%

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

   3. Taylor expanded in b around 0 72.3%

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

   if -1.59999999999999997e-119 < c < -2.0000000000000002e-195

   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 b around inf 67.3%

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

   4. Taylor expanded in z around inf 72.5%

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

      1. associate-/l* 72.4%

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

   6. Simplified 72.4%

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

   if 2.29999999999999988e167 < c

   1. Initial program 52.3%

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

   3. Taylor expanded in c around inf 92.0%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4 \cdot 10^{+91}:\\ \;\;\;\;j \cdot \left(t \cdot c + i \cdot \left(a \cdot \frac{b}{j} - y\right)\right)\\ \mathbf{elif}\;c \leq -1.6 \cdot 10^{-119}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;c \leq -2 \cdot 10^{-195}:\\ \;\;\;\;b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \mathbf{elif}\;c \leq 2.3 \cdot 10^{+167}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 30.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{if}\;y \leq -2.8 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-28}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-121}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-261}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-121}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{+67}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* y (- j)))))
   (if (<= y -2.8e+100)
     t_1
     (if (<= y -7e-28)
       (* y (* x z))
       (if (<= y -2.8e-121)
         (* j (* t c))
         (if (<= y 4.1e-261)
           (* a (* b i))
           (if (<= y 7.2e-121)
             (* x (* t (- a)))
             (if (<= y 8.4e+67) (* b (* a i)) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (y * -j);
	double tmp;
	if (y <= -2.8e+100) {
		tmp = t_1;
	} else if (y <= -7e-28) {
		tmp = y * (x * z);
	} else if (y <= -2.8e-121) {
		tmp = j * (t * c);
	} else if (y <= 4.1e-261) {
		tmp = a * (b * i);
	} else if (y <= 7.2e-121) {
		tmp = x * (t * -a);
	} else if (y <= 8.4e+67) {
		tmp = b * (a * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * (y * -j)
    if (y <= (-2.8d+100)) then
        tmp = t_1
    else if (y <= (-7d-28)) then
        tmp = y * (x * z)
    else if (y <= (-2.8d-121)) then
        tmp = j * (t * c)
    else if (y <= 4.1d-261) then
        tmp = a * (b * i)
    else if (y <= 7.2d-121) then
        tmp = x * (t * -a)
    else if (y <= 8.4d+67) then
        tmp = b * (a * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (y * -j);
	double tmp;
	if (y <= -2.8e+100) {
		tmp = t_1;
	} else if (y <= -7e-28) {
		tmp = y * (x * z);
	} else if (y <= -2.8e-121) {
		tmp = j * (t * c);
	} else if (y <= 4.1e-261) {
		tmp = a * (b * i);
	} else if (y <= 7.2e-121) {
		tmp = x * (t * -a);
	} else if (y <= 8.4e+67) {
		tmp = b * (a * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (y * -j)
	tmp = 0
	if y <= -2.8e+100:
		tmp = t_1
	elif y <= -7e-28:
		tmp = y * (x * z)
	elif y <= -2.8e-121:
		tmp = j * (t * c)
	elif y <= 4.1e-261:
		tmp = a * (b * i)
	elif y <= 7.2e-121:
		tmp = x * (t * -a)
	elif y <= 8.4e+67:
		tmp = b * (a * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(y * Float64(-j)))
	tmp = 0.0
	if (y <= -2.8e+100)
		tmp = t_1;
	elseif (y <= -7e-28)
		tmp = Float64(y * Float64(x * z));
	elseif (y <= -2.8e-121)
		tmp = Float64(j * Float64(t * c));
	elseif (y <= 4.1e-261)
		tmp = Float64(a * Float64(b * i));
	elseif (y <= 7.2e-121)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (y <= 8.4e+67)
		tmp = Float64(b * Float64(a * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * (y * -j);
	tmp = 0.0;
	if (y <= -2.8e+100)
		tmp = t_1;
	elseif (y <= -7e-28)
		tmp = y * (x * z);
	elseif (y <= -2.8e-121)
		tmp = j * (t * c);
	elseif (y <= 4.1e-261)
		tmp = a * (b * i);
	elseif (y <= 7.2e-121)
		tmp = x * (t * -a);
	elseif (y <= 8.4e+67)
		tmp = b * (a * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.8e+100], t$95$1, If[LessEqual[y, -7e-28], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.8e-121], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.1e-261], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.2e-121], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.4e+67], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -2.7999999999999998e100 or 8.4000000000000005e67 < y

   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 i around inf 60.7%

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

      1. distribute-lft-out-- 60.7%

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

      2. *-commutative 60.7%

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

   5. Simplified 60.7%

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

   6. Taylor expanded in j around inf 54.9%

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

      1. associate-*r* 54.9%

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

      2. mul-1-neg 54.9%

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

      3. *-commutative 54.9%

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

   8. Simplified 54.9%

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

   if -2.7999999999999998e100 < y < -6.9999999999999999e-28

   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 y around inf 46.6%

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

      1. +-commutative 46.6%

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

      2. mul-1-neg 46.6%

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

      3. unsub-neg 46.6%

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

      4. *-commutative 46.6%

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

   5. Simplified 46.6%

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

   6. Taylor expanded in z around inf 41.5%

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

      1. *-commutative 41.5%

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

      2. associate-*l* 46.0%

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

   8. Simplified 46.0%

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

   if -6.9999999999999999e-28 < y < -2.8000000000000001e-121

   1. Initial program 99.9%

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

   3. Taylor expanded in j around inf 83.7%

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

      1. associate--l+ 83.7%

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

      2. sub-neg 83.7%

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

      3. mul-1-neg 83.7%

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

      4. +-commutative 83.7%

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

      5. +-commutative 83.7%

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

      6. associate--r+ 83.7%

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

   5. Simplified 88.5%

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

   6. Taylor expanded in i around inf 59.0%

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

      1. associate-*r* 63.2%

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

   8. Simplified 63.2%

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

   9. Taylor expanded in c around inf 35.3%

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

       1. associate-*r* 31.4%

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

       2. *-commutative 31.4%

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

       3. associate-*r* 39.3%

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

   11. Simplified 39.3%

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

   if -2.8000000000000001e-121 < y < 4.10000000000000015e-261

   1. Initial program 80.5%

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

   3. Taylor expanded in b around inf 61.9%

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

   4. Taylor expanded in a around inf 38.9%

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

   if 4.10000000000000015e-261 < y < 7.19999999999999967e-121

   1. Initial program 96.1%

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

   3. Taylor expanded in x around inf 64.4%

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

      1. *-commutative 64.4%

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

   5. Simplified 64.4%

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

   6. Taylor expanded in z around 0 50.9%

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

      1. neg-mul-1 50.9%

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

      2. distribute-lft-neg-in 50.9%

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

      3. *-commutative 50.9%

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

   8. Simplified 50.9%

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

   if 7.19999999999999967e-121 < y < 8.4000000000000005e67

   1. Initial program 70.7%

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

   3. Taylor expanded in b around inf 50.2%

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

   4. Taylor expanded in a around inf 41.9%

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

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+100}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-28}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-121}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-261}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-121}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{+67}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 30.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i\right)\\ \mathbf{if}\;a \leq -3.6 \cdot 10^{+231}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{+129}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{+69}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-25}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq -1.08 \cdot 10^{-213}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq 54000000000:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* a i))))
   (if (<= a -3.6e+231)
     t_1
     (if (<= a -8.5e+129)
       (* x (* t (- a)))
       (if (<= a -2.9e+69)
         (* a (* b i))
         (if (<= a -1e-25)
           (* y (* x z))
           (if (<= a -1.08e-213)
             (* b (* z (- c)))
             (if (<= a 54000000000.0) (* c (* t j)) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (a * i);
	double tmp;
	if (a <= -3.6e+231) {
		tmp = t_1;
	} else if (a <= -8.5e+129) {
		tmp = x * (t * -a);
	} else if (a <= -2.9e+69) {
		tmp = a * (b * i);
	} else if (a <= -1e-25) {
		tmp = y * (x * z);
	} else if (a <= -1.08e-213) {
		tmp = b * (z * -c);
	} else if (a <= 54000000000.0) {
		tmp = c * (t * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a * i)
    if (a <= (-3.6d+231)) then
        tmp = t_1
    else if (a <= (-8.5d+129)) then
        tmp = x * (t * -a)
    else if (a <= (-2.9d+69)) then
        tmp = a * (b * i)
    else if (a <= (-1d-25)) then
        tmp = y * (x * z)
    else if (a <= (-1.08d-213)) then
        tmp = b * (z * -c)
    else if (a <= 54000000000.0d0) then
        tmp = c * (t * j)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (a * i);
	double tmp;
	if (a <= -3.6e+231) {
		tmp = t_1;
	} else if (a <= -8.5e+129) {
		tmp = x * (t * -a);
	} else if (a <= -2.9e+69) {
		tmp = a * (b * i);
	} else if (a <= -1e-25) {
		tmp = y * (x * z);
	} else if (a <= -1.08e-213) {
		tmp = b * (z * -c);
	} else if (a <= 54000000000.0) {
		tmp = c * (t * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (a * i)
	tmp = 0
	if a <= -3.6e+231:
		tmp = t_1
	elif a <= -8.5e+129:
		tmp = x * (t * -a)
	elif a <= -2.9e+69:
		tmp = a * (b * i)
	elif a <= -1e-25:
		tmp = y * (x * z)
	elif a <= -1.08e-213:
		tmp = b * (z * -c)
	elif a <= 54000000000.0:
		tmp = c * (t * j)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(a * i))
	tmp = 0.0
	if (a <= -3.6e+231)
		tmp = t_1;
	elseif (a <= -8.5e+129)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (a <= -2.9e+69)
		tmp = Float64(a * Float64(b * i));
	elseif (a <= -1e-25)
		tmp = Float64(y * Float64(x * z));
	elseif (a <= -1.08e-213)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (a <= 54000000000.0)
		tmp = Float64(c * Float64(t * j));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (a * i);
	tmp = 0.0;
	if (a <= -3.6e+231)
		tmp = t_1;
	elseif (a <= -8.5e+129)
		tmp = x * (t * -a);
	elseif (a <= -2.9e+69)
		tmp = a * (b * i);
	elseif (a <= -1e-25)
		tmp = y * (x * z);
	elseif (a <= -1.08e-213)
		tmp = b * (z * -c);
	elseif (a <= 54000000000.0)
		tmp = c * (t * j);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.6e+231], t$95$1, If[LessEqual[a, -8.5e+129], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.9e+69], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1e-25], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.08e-213], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 54000000000.0], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -3.5999999999999999e231 or 5.4e10 < a

   1. Initial program 68.3%

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

   3. Taylor expanded in b around inf 52.4%

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

   4. Taylor expanded in a around inf 49.4%

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

   if -3.5999999999999999e231 < a < -8.5000000000000001e129

   1. Initial program 69.6%

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

   3. Taylor expanded in x around inf 63.7%

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

      1. *-commutative 63.7%

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

   5. Simplified 63.7%

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

   6. Taylor expanded in z around 0 49.3%

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

      1. neg-mul-1 49.3%

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

      2. distribute-lft-neg-in 49.3%

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

      3. *-commutative 49.3%

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

   8. Simplified 49.3%

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

   if -8.5000000000000001e129 < a < -2.8999999999999998e69

   1. Initial program 67.2%

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

   3. Taylor expanded in b around inf 51.7%

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

   4. Taylor expanded in a around inf 51.8%

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

   if -2.8999999999999998e69 < a < -1.00000000000000004e-25

   1. Initial program 84.6%

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

   3. Taylor expanded in y around inf 54.7%

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

      1. +-commutative 54.7%

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

      2. mul-1-neg 54.7%

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

      3. unsub-neg 54.7%

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

      4. *-commutative 54.7%

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

   5. Simplified 54.7%

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

   6. Taylor expanded in z around inf 39.6%

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

      1. *-commutative 39.6%

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

      2. associate-*l* 39.9%

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

   8. Simplified 39.9%

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

   if -1.00000000000000004e-25 < a < -1.08e-213

   1. Initial program 82.6%

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

   3. Taylor expanded in b around inf 44.3%

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

   4. Taylor expanded in a around 0 42.0%

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

      1. mul-1-neg 42.0%

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

      2. distribute-lft-neg-out 42.0%

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

      3. *-commutative 42.0%

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

   6. Simplified 42.0%

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

   if -1.08e-213 < a < 5.4e10

   1. Initial program 77.3%

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

   3. Taylor expanded in j around inf 72.5%

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

      1. associate--l+ 72.5%

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

      2. sub-neg 72.5%

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

      3. mul-1-neg 72.5%

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

      4. +-commutative 72.5%

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

      5. +-commutative 72.5%

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

      6. associate--r+ 72.5%

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

   5. Simplified 73.9%

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

   6. Taylor expanded in i around inf 58.8%

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

      1. associate-*r* 61.5%

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

   8. Simplified 61.5%

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

   9. Taylor expanded in c around inf 33.4%

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

4. Final simplification 42.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{+231}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{+129}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{+69}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-25}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq -1.08 \cdot 10^{-213}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq 54000000000:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 30.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(z \cdot \left(-c\right)\right)\\ t_2 := b \cdot \left(a \cdot i\right)\\ \mathbf{if}\;a \leq -2.2 \cdot 10^{+53}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-211}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -7.8 \cdot 10^{-302}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;a \leq 1.52 \cdot 10^{-287}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-91}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 46000000000:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* z (- c)))) (t_2 (* b (* a i))))
   (if (<= a -2.2e+53)
     t_2
     (if (<= a -1e-211)
       t_1
       (if (<= a -7.8e-302)
         (* c (* t j))
         (if (<= a 1.52e-287)
           t_1
           (if (<= a 1.45e-91)
             (* z (* x y))
             (if (<= a 46000000000.0) (* j (* t 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 = b * (z * -c);
	double t_2 = b * (a * i);
	double tmp;
	if (a <= -2.2e+53) {
		tmp = t_2;
	} else if (a <= -1e-211) {
		tmp = t_1;
	} else if (a <= -7.8e-302) {
		tmp = c * (t * j);
	} else if (a <= 1.52e-287) {
		tmp = t_1;
	} else if (a <= 1.45e-91) {
		tmp = z * (x * y);
	} else if (a <= 46000000000.0) {
		tmp = j * (t * 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 = b * (z * -c)
    t_2 = b * (a * i)
    if (a <= (-2.2d+53)) then
        tmp = t_2
    else if (a <= (-1d-211)) then
        tmp = t_1
    else if (a <= (-7.8d-302)) then
        tmp = c * (t * j)
    else if (a <= 1.52d-287) then
        tmp = t_1
    else if (a <= 1.45d-91) then
        tmp = z * (x * y)
    else if (a <= 46000000000.0d0) then
        tmp = j * (t * 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 = b * (z * -c);
	double t_2 = b * (a * i);
	double tmp;
	if (a <= -2.2e+53) {
		tmp = t_2;
	} else if (a <= -1e-211) {
		tmp = t_1;
	} else if (a <= -7.8e-302) {
		tmp = c * (t * j);
	} else if (a <= 1.52e-287) {
		tmp = t_1;
	} else if (a <= 1.45e-91) {
		tmp = z * (x * y);
	} else if (a <= 46000000000.0) {
		tmp = j * (t * c);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (z * -c)
	t_2 = b * (a * i)
	tmp = 0
	if a <= -2.2e+53:
		tmp = t_2
	elif a <= -1e-211:
		tmp = t_1
	elif a <= -7.8e-302:
		tmp = c * (t * j)
	elif a <= 1.52e-287:
		tmp = t_1
	elif a <= 1.45e-91:
		tmp = z * (x * y)
	elif a <= 46000000000.0:
		tmp = j * (t * c)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(z * Float64(-c)))
	t_2 = Float64(b * Float64(a * i))
	tmp = 0.0
	if (a <= -2.2e+53)
		tmp = t_2;
	elseif (a <= -1e-211)
		tmp = t_1;
	elseif (a <= -7.8e-302)
		tmp = Float64(c * Float64(t * j));
	elseif (a <= 1.52e-287)
		tmp = t_1;
	elseif (a <= 1.45e-91)
		tmp = Float64(z * Float64(x * y));
	elseif (a <= 46000000000.0)
		tmp = Float64(j * Float64(t * 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 = b * (z * -c);
	t_2 = b * (a * i);
	tmp = 0.0;
	if (a <= -2.2e+53)
		tmp = t_2;
	elseif (a <= -1e-211)
		tmp = t_1;
	elseif (a <= -7.8e-302)
		tmp = c * (t * j);
	elseif (a <= 1.52e-287)
		tmp = t_1;
	elseif (a <= 1.45e-91)
		tmp = z * (x * y);
	elseif (a <= 46000000000.0)
		tmp = j * (t * 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[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.2e+53], t$95$2, If[LessEqual[a, -1e-211], t$95$1, If[LessEqual[a, -7.8e-302], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.52e-287], t$95$1, If[LessEqual[a, 1.45e-91], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 46000000000.0], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.19999999999999999e53 or 4.6e10 < a

   1. Initial program 68.1%

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

   3. Taylor expanded in b around inf 48.7%

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

   4. Taylor expanded in a around inf 43.5%

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

   if -2.19999999999999999e53 < a < -1.00000000000000009e-211 or -7.7999999999999998e-302 < a < 1.5199999999999999e-287

   1. Initial program 82.2%

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

   3. Taylor expanded in b around inf 42.8%

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

   4. Taylor expanded in a around 0 41.1%

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

      1. mul-1-neg 41.1%

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

      2. distribute-lft-neg-out 41.1%

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

      3. *-commutative 41.1%

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

   6. Simplified 41.1%

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

   if -1.00000000000000009e-211 < a < -7.7999999999999998e-302

   1. Initial program 65.1%

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

   3. Taylor expanded in j around inf 65.1%

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

      1. associate--l+ 65.1%

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

      2. sub-neg 65.1%

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

      3. mul-1-neg 65.1%

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

      4. +-commutative 65.1%

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

      5. +-commutative 65.1%

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

      6. associate--r+ 65.1%

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

   5. Simplified 65.1%

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

   6. Taylor expanded in i around inf 86.2%

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

      1. associate-*r* 86.7%

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

   8. Simplified 86.7%

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

   9. Taylor expanded in c around inf 51.3%

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

   if 1.5199999999999999e-287 < a < 1.45e-91

   1. Initial program 77.0%

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

   3. Taylor expanded in j around inf 77.2%

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

      1. associate--l+ 77.2%

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

      2. sub-neg 77.2%

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

      3. mul-1-neg 77.2%

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

      4. +-commutative 77.2%

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

      5. +-commutative 77.2%

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

      6. associate--r+ 77.2%

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

   5. Simplified 77.2%

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

   6. Taylor expanded in z around inf 35.3%

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

      1. associate-*r* 41.1%

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

      2. *-commutative 41.1%

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

      3. div-sub 41.1%

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

      4. *-commutative 41.1%

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

   8. Simplified 41.1%

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

   9. Taylor expanded in x around inf 39.2%

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

       1. *-commutative 39.2%

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

       2. *-commutative 39.2%

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

       3. associate-*l* 42.1%

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

   11. Simplified 42.1%

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

   if 1.45e-91 < a < 4.6e10

   1. Initial program 86.6%

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

   3. Taylor expanded in j around inf 73.3%

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

      1. associate--l+ 73.3%

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

      2. sub-neg 73.3%

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

      3. mul-1-neg 73.3%

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

      4. +-commutative 73.3%

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

      5. +-commutative 73.3%

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

      6. associate--r+ 73.3%

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

   5. Simplified 77.1%

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

   6. Taylor expanded in i around inf 56.5%

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

      1. associate-*r* 60.0%

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

   8. Simplified 60.0%

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

   9. Taylor expanded in c around inf 29.0%

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

       1. associate-*r* 32.3%

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

       2. *-commutative 32.3%

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

       3. associate-*r* 32.2%

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

   11. Simplified 32.2%

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

4. Final simplification 41.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{+53}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-211}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq -7.8 \cdot 10^{-302}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;a \leq 1.52 \cdot 10^{-287}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-91}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 46000000000:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 41.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{if}\;y \leq -2.75 \cdot 10^{+100}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{-140}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-272}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+67}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))) (t_2 (* i (* y (- j)))))
   (if (<= y -2.75e+100)
     t_2
     (if (<= y -7.8e-140)
       t_1
       (if (<= y 1.85e-272)
         (* b (- (* a i) (* z c)))
         (if (<= y 1.15e+67) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double t_2 = i * (y * -j);
	double tmp;
	if (y <= -2.75e+100) {
		tmp = t_2;
	} else if (y <= -7.8e-140) {
		tmp = t_1;
	} else if (y <= 1.85e-272) {
		tmp = b * ((a * i) - (z * c));
	} else if (y <= 1.15e+67) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((b * i) - (x * t))
    t_2 = i * (y * -j)
    if (y <= (-2.75d+100)) then
        tmp = t_2
    else if (y <= (-7.8d-140)) then
        tmp = t_1
    else if (y <= 1.85d-272) then
        tmp = b * ((a * i) - (z * c))
    else if (y <= 1.15d+67) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double t_2 = i * (y * -j);
	double tmp;
	if (y <= -2.75e+100) {
		tmp = t_2;
	} else if (y <= -7.8e-140) {
		tmp = t_1;
	} else if (y <= 1.85e-272) {
		tmp = b * ((a * i) - (z * c));
	} else if (y <= 1.15e+67) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	t_2 = i * (y * -j)
	tmp = 0
	if y <= -2.75e+100:
		tmp = t_2
	elif y <= -7.8e-140:
		tmp = t_1
	elif y <= 1.85e-272:
		tmp = b * ((a * i) - (z * c))
	elif y <= 1.15e+67:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	t_2 = Float64(i * Float64(y * Float64(-j)))
	tmp = 0.0
	if (y <= -2.75e+100)
		tmp = t_2;
	elseif (y <= -7.8e-140)
		tmp = t_1;
	elseif (y <= 1.85e-272)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (y <= 1.15e+67)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((b * i) - (x * t));
	t_2 = i * (y * -j);
	tmp = 0.0;
	if (y <= -2.75e+100)
		tmp = t_2;
	elseif (y <= -7.8e-140)
		tmp = t_1;
	elseif (y <= 1.85e-272)
		tmp = b * ((a * i) - (z * c));
	elseif (y <= 1.15e+67)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.75e+100], t$95$2, If[LessEqual[y, -7.8e-140], t$95$1, If[LessEqual[y, 1.85e-272], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e+67], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.7500000000000001e100 or 1.1499999999999999e67 < y

   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 i around inf 60.7%

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

      1. distribute-lft-out-- 60.7%

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

      2. *-commutative 60.7%

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

   5. Simplified 60.7%

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

   6. Taylor expanded in j around inf 54.9%

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

      1. associate-*r* 54.9%

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

      2. mul-1-neg 54.9%

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

      3. *-commutative 54.9%

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

   8. Simplified 54.9%

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

   if -2.7500000000000001e100 < y < -7.80000000000000038e-140 or 1.8499999999999998e-272 < y < 1.1499999999999999e67

   1. Initial program 82.4%

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

   3. Taylor expanded in a around inf 48.9%

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

      1. distribute-lft-out-- 48.9%

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

   5. Simplified 48.9%

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

   6. Taylor expanded in t around 0 48.9%

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

      1. +-commutative 48.9%

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

      2. mul-1-neg 48.9%

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

      3. distribute-rgt-neg-in 48.9%

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

      4. distribute-lft-out 48.9%

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

      5. unsub-neg 48.9%

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

   8. Simplified 48.9%

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

   if -7.80000000000000038e-140 < y < 1.8499999999999998e-272

   1. Initial program 81.2%

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

   3. Taylor expanded in b around inf 66.6%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{+100}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{-140}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-272}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+67}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 41.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{if}\;y \leq -5 \cdot 10^{+101}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-228}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-299}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+68}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))) (t_2 (* i (* y (- j)))))
   (if (<= y -5e+101)
     t_2
     (if (<= y -2.4e-228)
       t_1
       (if (<= y -1.7e-299) (* b (* z (- c))) (if (<= y 9.2e+68) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double t_2 = i * (y * -j);
	double tmp;
	if (y <= -5e+101) {
		tmp = t_2;
	} else if (y <= -2.4e-228) {
		tmp = t_1;
	} else if (y <= -1.7e-299) {
		tmp = b * (z * -c);
	} else if (y <= 9.2e+68) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((b * i) - (x * t))
    t_2 = i * (y * -j)
    if (y <= (-5d+101)) then
        tmp = t_2
    else if (y <= (-2.4d-228)) then
        tmp = t_1
    else if (y <= (-1.7d-299)) then
        tmp = b * (z * -c)
    else if (y <= 9.2d+68) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double t_2 = i * (y * -j);
	double tmp;
	if (y <= -5e+101) {
		tmp = t_2;
	} else if (y <= -2.4e-228) {
		tmp = t_1;
	} else if (y <= -1.7e-299) {
		tmp = b * (z * -c);
	} else if (y <= 9.2e+68) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	t_2 = i * (y * -j)
	tmp = 0
	if y <= -5e+101:
		tmp = t_2
	elif y <= -2.4e-228:
		tmp = t_1
	elif y <= -1.7e-299:
		tmp = b * (z * -c)
	elif y <= 9.2e+68:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	t_2 = Float64(i * Float64(y * Float64(-j)))
	tmp = 0.0
	if (y <= -5e+101)
		tmp = t_2;
	elseif (y <= -2.4e-228)
		tmp = t_1;
	elseif (y <= -1.7e-299)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (y <= 9.2e+68)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((b * i) - (x * t));
	t_2 = i * (y * -j);
	tmp = 0.0;
	if (y <= -5e+101)
		tmp = t_2;
	elseif (y <= -2.4e-228)
		tmp = t_1;
	elseif (y <= -1.7e-299)
		tmp = b * (z * -c);
	elseif (y <= 9.2e+68)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5e+101], t$95$2, If[LessEqual[y, -2.4e-228], t$95$1, If[LessEqual[y, -1.7e-299], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.2e+68], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.99999999999999989e101 or 9.1999999999999999e68 < y

   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 i around inf 60.7%

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

      1. distribute-lft-out-- 60.7%

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

      2. *-commutative 60.7%

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

   5. Simplified 60.7%

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

   6. Taylor expanded in j around inf 54.9%

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

      1. associate-*r* 54.9%

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

      2. mul-1-neg 54.9%

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

      3. *-commutative 54.9%

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

   8. Simplified 54.9%

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

   if -4.99999999999999989e101 < y < -2.40000000000000002e-228 or -1.6999999999999999e-299 < y < 9.1999999999999999e68

   1. Initial program 82.8%

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

   3. Taylor expanded in a around inf 49.9%

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

      1. distribute-lft-out-- 49.9%

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

   5. Simplified 49.9%

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

   6. Taylor expanded in t around 0 49.9%

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

      1. +-commutative 49.9%

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

      2. mul-1-neg 49.9%

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

      3. distribute-rgt-neg-in 49.9%

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

      4. distribute-lft-out 49.9%

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

      5. unsub-neg 49.9%

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

   8. Simplified 49.9%

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

   if -2.40000000000000002e-228 < y < -1.6999999999999999e-299

   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 b around inf 81.9%

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

   4. Taylor expanded in a around 0 73.0%

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

      1. mul-1-neg 73.0%

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

      2. distribute-lft-neg-out 73.0%

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

      3. *-commutative 73.0%

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

   6. Simplified 73.0%

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

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+101}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-228}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-299}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+68}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 60.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+171} \lor \neg \left(z \leq 3.5 \cdot 10^{+41}\right):\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c + i \cdot \left(a \cdot \frac{b}{j} - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= z -3.5e+171) (not (<= z 3.5e+41)))
   (* z (- (* x y) (* b c)))
   (* j (+ (* t c) (* i (- (* a (/ b j)) 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 <= -3.5e+171) || !(z <= 3.5e+41)) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = j * ((t * c) + (i * ((a * (b / j)) - 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 <= (-3.5d+171)) .or. (.not. (z <= 3.5d+41))) then
        tmp = z * ((x * y) - (b * c))
    else
        tmp = j * ((t * c) + (i * ((a * (b / j)) - 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 <= -3.5e+171) || !(z <= 3.5e+41)) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = j * ((t * c) + (i * ((a * (b / j)) - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (z <= -3.5e+171) or not (z <= 3.5e+41):
		tmp = z * ((x * y) - (b * c))
	else:
		tmp = j * ((t * c) + (i * ((a * (b / j)) - y)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((z <= -3.5e+171) || !(z <= 3.5e+41))
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	else
		tmp = Float64(j * Float64(Float64(t * c) + Float64(i * Float64(Float64(a * Float64(b / j)) - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((z <= -3.5e+171) || ~((z <= 3.5e+41)))
		tmp = z * ((x * y) - (b * c));
	else
		tmp = j * ((t * c) + (i * ((a * (b / j)) - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[z, -3.5e+171], N[Not[LessEqual[z, 3.5e+41]], $MachinePrecision]], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(N[(t * c), $MachinePrecision] + N[(i * N[(N[(a * N[(b / j), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.4999999999999999e171 or 3.4999999999999999e41 < z

   1. Initial program 62.3%

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

   3. Taylor expanded in z around inf 71.8%

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

      1. *-commutative 71.8%

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

   5. Simplified 71.8%

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

   if -3.4999999999999999e171 < z < 3.4999999999999999e41

   1. Initial program 81.5%

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

   3. Taylor expanded in j around inf 75.0%

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

      1. associate--l+ 75.0%

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

      2. sub-neg 75.0%

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

      3. mul-1-neg 75.0%

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

      4. +-commutative 75.0%

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

      5. +-commutative 75.0%

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

      6. associate--r+ 75.0%

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

   5. Simplified 77.5%

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

   6. Taylor expanded in i around inf 61.6%

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

      1. associate-*r* 62.0%

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

   8. Simplified 62.0%

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

   9. Taylor expanded in a around 0 61.6%

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

       1. sub-neg 61.6%

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

       2. *-commutative 61.6%

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

       3. associate-*r* 62.9%

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

       4. *-commutative 62.9%

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

       5. associate-*r* 62.0%

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

       6. associate-*r/ 63.8%

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

       7. distribute-rgt-neg-in 63.8%

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

       8. distribute-lft-in 65.6%

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

       9. sub-neg 65.6%

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

       10. associate-/l* 65.3%

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

   11. Simplified 65.3%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+171} \lor \neg \left(z \leq 3.5 \cdot 10^{+41}\right):\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c + i \cdot \left(a \cdot \frac{b}{j} - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 52.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -9.6 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-269}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 16200000000:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))))
   (if (<= a -9.6e+33)
     t_1
     (if (<= a 3.2e-269)
       (* c (- (* t j) (* z b)))
       (if (<= a 16200000000.0) (* j (- (* t c) (* y i))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -9.6e+33) {
		tmp = t_1;
	} else if (a <= 3.2e-269) {
		tmp = c * ((t * j) - (z * b));
	} else if (a <= 16200000000.0) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((b * i) - (x * t))
    if (a <= (-9.6d+33)) then
        tmp = t_1
    else if (a <= 3.2d-269) then
        tmp = c * ((t * j) - (z * b))
    else if (a <= 16200000000.0d0) then
        tmp = j * ((t * c) - (y * i))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -9.6e+33) {
		tmp = t_1;
	} else if (a <= 3.2e-269) {
		tmp = c * ((t * j) - (z * b));
	} else if (a <= 16200000000.0) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -9.6e+33:
		tmp = t_1
	elif a <= 3.2e-269:
		tmp = c * ((t * j) - (z * b))
	elif a <= 16200000000.0:
		tmp = j * ((t * c) - (y * i))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -9.6e+33)
		tmp = t_1;
	elseif (a <= 3.2e-269)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (a <= 16200000000.0)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -9.6e+33)
		tmp = t_1;
	elseif (a <= 3.2e-269)
		tmp = c * ((t * j) - (z * b));
	elseif (a <= 16200000000.0)
		tmp = j * ((t * c) - (y * i));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9.6e+33], t$95$1, If[LessEqual[a, 3.2e-269], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 16200000000.0], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.5999999999999999e33 or 1.62e10 < a

   1. Initial program 68.6%

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

   3. Taylor expanded in a around inf 63.3%

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

      1. distribute-lft-out-- 63.3%

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

   5. Simplified 63.3%

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

   6. Taylor expanded in t around 0 63.3%

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

      1. +-commutative 63.3%

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

      2. mul-1-neg 63.3%

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

      3. distribute-rgt-neg-in 63.3%

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

      4. distribute-lft-out 63.3%

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

      5. unsub-neg 63.3%

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

   8. Simplified 63.3%

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

   if -9.5999999999999999e33 < a < 3.2000000000000001e-269

   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 c around inf 56.0%

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

   if 3.2000000000000001e-269 < a < 1.62e10

   1. Initial program 82.2%

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

   3. Taylor expanded in j around inf 61.2%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.6 \cdot 10^{+33}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-269}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 16200000000:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 52.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.3 \cdot 10^{+19} \lor \neg \left(a \leq 2.25 \cdot 10^{+15}\right):\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -6.3e+19) (not (<= a 2.25e+15)))
   (* a (- (* b i) (* x t)))
   (* c (- (* t j) (* z b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -6.3e+19) || !(a <= 2.25e+15)) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = c * ((t * j) - (z * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((a <= (-6.3d+19)) .or. (.not. (a <= 2.25d+15))) then
        tmp = a * ((b * i) - (x * t))
    else
        tmp = c * ((t * j) - (z * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -6.3e+19) || !(a <= 2.25e+15)) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = c * ((t * j) - (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (a <= -6.3e+19) or not (a <= 2.25e+15):
		tmp = a * ((b * i) - (x * t))
	else:
		tmp = c * ((t * j) - (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -6.3e+19) || !(a <= 2.25e+15))
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	else
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((a <= -6.3e+19) || ~((a <= 2.25e+15)))
		tmp = a * ((b * i) - (x * t));
	else
		tmp = c * ((t * j) - (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -6.3e+19], N[Not[LessEqual[a, 2.25e+15]], $MachinePrecision]], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $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 a < -6.3e19 or 2.25e15 < a

   1. Initial program 68.7%

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

   3. Taylor expanded in a around inf 63.2%

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

      1. distribute-lft-out-- 63.2%

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

   5. Simplified 63.2%

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

   6. Taylor expanded in t around 0 63.2%

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

      1. +-commutative 63.2%

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

      2. mul-1-neg 63.2%

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

      3. distribute-rgt-neg-in 63.2%

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

      4. distribute-lft-out 63.2%

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

      5. unsub-neg 63.2%

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

   8. Simplified 63.2%

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

   if -6.3e19 < a < 2.25e15

   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 c around inf 51.1%

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

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.3 \cdot 10^{+19} \lor \neg \left(a \leq 2.25 \cdot 10^{+15}\right):\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 30.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.12 \cdot 10^{+64} \lor \neg \left(a \leq 12500000000\right):\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -1.12e+64) (not (<= a 12500000000.0)))
   (* b (* a i))
   (* c (* t j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -1.12e+64) || !(a <= 12500000000.0)) {
		tmp = b * (a * i);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((a <= (-1.12d+64)) .or. (.not. (a <= 12500000000.0d0))) then
        tmp = b * (a * i)
    else
        tmp = c * (t * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -1.12e+64) || !(a <= 12500000000.0)) {
		tmp = b * (a * i);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (a <= -1.12e+64) or not (a <= 12500000000.0):
		tmp = b * (a * i)
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -1.12e+64) || !(a <= 12500000000.0))
		tmp = Float64(b * Float64(a * i));
	else
		tmp = Float64(c * Float64(t * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((a <= -1.12e+64) || ~((a <= 12500000000.0)))
		tmp = b * (a * i);
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -1.12e+64], N[Not[LessEqual[a, 12500000000.0]], $MachinePrecision]], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.11999999999999995e64 or 1.25e10 < a

   1. Initial program 68.4%

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

   3. Taylor expanded in b around inf 49.6%

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

   4. Taylor expanded in a around inf 44.2%

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

   if -1.11999999999999995e64 < a < 1.25e10

   1. Initial program 79.8%

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

   3. Taylor expanded in j around inf 72.1%

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

      1. associate--l+ 72.1%

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

      2. sub-neg 72.1%

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

      3. mul-1-neg 72.1%

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

      4. +-commutative 72.1%

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

      5. +-commutative 72.1%

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

      6. associate--r+ 72.1%

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

   5. Simplified 75.1%

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

   6. Taylor expanded in i around inf 50.3%

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

      1. associate-*r* 52.6%

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

   8. Simplified 52.6%

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

   9. Taylor expanded in c around inf 29.7%

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

4. Final simplification 36.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.12 \cdot 10^{+64} \lor \neg \left(a \leq 12500000000\right):\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 22.4% 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 74.4%

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

3. Taylor expanded in b around inf 40.6%

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

4. Taylor expanded in a around inf 25.2%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
5. 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 2024107 
(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)))))