Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.5% → 83.3%

Time: 28.4s

Alternatives: 33

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

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

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 (<= (+ (+ (* x (- (* y z) (* t a))) t_1) (* 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 ((((x * ((y * z) - (t * a))) + t_1) + (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(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_1) + 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[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $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%

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

Alternative 2: 48.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_3 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -4.3 \cdot 10^{+151}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq -9.5 \cdot 10^{+104}:\\ \;\;\;\;i \cdot \left(y \cdot \left(b \cdot \frac{a}{y} - j\right)\right)\\ \mathbf{elif}\;c \leq -1.52 \cdot 10^{+58}:\\ \;\;\;\;\left(z \cdot j\right) \cdot \frac{x \cdot y - b \cdot c}{j}\\ \mathbf{elif}\;c \leq -5.1 \cdot 10^{+48}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;c \leq -2 \cdot 10^{-118}:\\ \;\;\;\;x \cdot \left(y \cdot z - i \cdot \left(j \cdot \frac{y}{x}\right)\right)\\ \mathbf{elif}\;c \leq -1.7 \cdot 10^{-195}:\\ \;\;\;\;b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \mathbf{elif}\;c \leq 3.9 \cdot 10^{-196}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 3 \cdot 10^{-130}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 4.7 \cdot 10^{-61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 1.16 \cdot 10^{+40}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 2.65 \cdot 10^{+48} \lor \neg \left(c \leq 1.22 \cdot 10^{+119}\right):\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - a \cdot \left(t \cdot \frac{x}{c}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j))))
        (t_2 (* a (- (* b i) (* x t))))
        (t_3 (* c (- (* t j) (* z b)))))
   (if (<= c -4.3e+151)
     t_3
     (if (<= c -9.5e+104)
       (* i (* y (- (* b (/ a y)) j)))
       (if (<= c -1.52e+58)
         (* (* z j) (/ (- (* x y) (* b c)) j))
         (if (<= c -5.1e+48)
           (* a (* t (- x)))
           (if (<= c -2e-118)
             (* x (- (* y z) (* i (* j (/ y x)))))
             (if (<= c -1.7e-195)
               (* b (* z (- (* a (/ i z)) c)))
               (if (<= c 3.9e-196)
                 t_1
                 (if (<= c 3e-130)
                   t_2
                   (if (<= c 4.7e-61)
                     t_1
                     (if (<= c 1.16e+40)
                       t_2
                       (if (or (<= c 2.65e+48) (not (<= c 1.22e+119)))
                         t_3
                         (* c (- (* t j) (* a (* t (/ x c))))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double t_2 = a * ((b * i) - (x * t));
	double t_3 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -4.3e+151) {
		tmp = t_3;
	} else if (c <= -9.5e+104) {
		tmp = i * (y * ((b * (a / y)) - j));
	} else if (c <= -1.52e+58) {
		tmp = (z * j) * (((x * y) - (b * c)) / j);
	} else if (c <= -5.1e+48) {
		tmp = a * (t * -x);
	} else if (c <= -2e-118) {
		tmp = x * ((y * z) - (i * (j * (y / x))));
	} else if (c <= -1.7e-195) {
		tmp = b * (z * ((a * (i / z)) - c));
	} else if (c <= 3.9e-196) {
		tmp = t_1;
	} else if (c <= 3e-130) {
		tmp = t_2;
	} else if (c <= 4.7e-61) {
		tmp = t_1;
	} else if (c <= 1.16e+40) {
		tmp = t_2;
	} else if ((c <= 2.65e+48) || !(c <= 1.22e+119)) {
		tmp = t_3;
	} else {
		tmp = c * ((t * j) - (a * (t * (x / c))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y * ((x * z) - (i * j))
    t_2 = a * ((b * i) - (x * t))
    t_3 = c * ((t * j) - (z * b))
    if (c <= (-4.3d+151)) then
        tmp = t_3
    else if (c <= (-9.5d+104)) then
        tmp = i * (y * ((b * (a / y)) - j))
    else if (c <= (-1.52d+58)) then
        tmp = (z * j) * (((x * y) - (b * c)) / j)
    else if (c <= (-5.1d+48)) then
        tmp = a * (t * -x)
    else if (c <= (-2d-118)) then
        tmp = x * ((y * z) - (i * (j * (y / x))))
    else if (c <= (-1.7d-195)) then
        tmp = b * (z * ((a * (i / z)) - c))
    else if (c <= 3.9d-196) then
        tmp = t_1
    else if (c <= 3d-130) then
        tmp = t_2
    else if (c <= 4.7d-61) then
        tmp = t_1
    else if (c <= 1.16d+40) then
        tmp = t_2
    else if ((c <= 2.65d+48) .or. (.not. (c <= 1.22d+119))) then
        tmp = t_3
    else
        tmp = c * ((t * j) - (a * (t * (x / c))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double t_2 = a * ((b * i) - (x * t));
	double t_3 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -4.3e+151) {
		tmp = t_3;
	} else if (c <= -9.5e+104) {
		tmp = i * (y * ((b * (a / y)) - j));
	} else if (c <= -1.52e+58) {
		tmp = (z * j) * (((x * y) - (b * c)) / j);
	} else if (c <= -5.1e+48) {
		tmp = a * (t * -x);
	} else if (c <= -2e-118) {
		tmp = x * ((y * z) - (i * (j * (y / x))));
	} else if (c <= -1.7e-195) {
		tmp = b * (z * ((a * (i / z)) - c));
	} else if (c <= 3.9e-196) {
		tmp = t_1;
	} else if (c <= 3e-130) {
		tmp = t_2;
	} else if (c <= 4.7e-61) {
		tmp = t_1;
	} else if (c <= 1.16e+40) {
		tmp = t_2;
	} else if ((c <= 2.65e+48) || !(c <= 1.22e+119)) {
		tmp = t_3;
	} else {
		tmp = c * ((t * j) - (a * (t * (x / c))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	t_2 = a * ((b * i) - (x * t))
	t_3 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -4.3e+151:
		tmp = t_3
	elif c <= -9.5e+104:
		tmp = i * (y * ((b * (a / y)) - j))
	elif c <= -1.52e+58:
		tmp = (z * j) * (((x * y) - (b * c)) / j)
	elif c <= -5.1e+48:
		tmp = a * (t * -x)
	elif c <= -2e-118:
		tmp = x * ((y * z) - (i * (j * (y / x))))
	elif c <= -1.7e-195:
		tmp = b * (z * ((a * (i / z)) - c))
	elif c <= 3.9e-196:
		tmp = t_1
	elif c <= 3e-130:
		tmp = t_2
	elif c <= 4.7e-61:
		tmp = t_1
	elif c <= 1.16e+40:
		tmp = t_2
	elif (c <= 2.65e+48) or not (c <= 1.22e+119):
		tmp = t_3
	else:
		tmp = c * ((t * j) - (a * (t * (x / c))))
	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(a * Float64(Float64(b * i) - Float64(x * t)))
	t_3 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -4.3e+151)
		tmp = t_3;
	elseif (c <= -9.5e+104)
		tmp = Float64(i * Float64(y * Float64(Float64(b * Float64(a / y)) - j)));
	elseif (c <= -1.52e+58)
		tmp = Float64(Float64(z * j) * Float64(Float64(Float64(x * y) - Float64(b * c)) / j));
	elseif (c <= -5.1e+48)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (c <= -2e-118)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(i * Float64(j * Float64(y / x)))));
	elseif (c <= -1.7e-195)
		tmp = Float64(b * Float64(z * Float64(Float64(a * Float64(i / z)) - c)));
	elseif (c <= 3.9e-196)
		tmp = t_1;
	elseif (c <= 3e-130)
		tmp = t_2;
	elseif (c <= 4.7e-61)
		tmp = t_1;
	elseif (c <= 1.16e+40)
		tmp = t_2;
	elseif ((c <= 2.65e+48) || !(c <= 1.22e+119))
		tmp = t_3;
	else
		tmp = Float64(c * Float64(Float64(t * j) - Float64(a * Float64(t * Float64(x / c)))));
	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 = a * ((b * i) - (x * t));
	t_3 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -4.3e+151)
		tmp = t_3;
	elseif (c <= -9.5e+104)
		tmp = i * (y * ((b * (a / y)) - j));
	elseif (c <= -1.52e+58)
		tmp = (z * j) * (((x * y) - (b * c)) / j);
	elseif (c <= -5.1e+48)
		tmp = a * (t * -x);
	elseif (c <= -2e-118)
		tmp = x * ((y * z) - (i * (j * (y / x))));
	elseif (c <= -1.7e-195)
		tmp = b * (z * ((a * (i / z)) - c));
	elseif (c <= 3.9e-196)
		tmp = t_1;
	elseif (c <= 3e-130)
		tmp = t_2;
	elseif (c <= 4.7e-61)
		tmp = t_1;
	elseif (c <= 1.16e+40)
		tmp = t_2;
	elseif ((c <= 2.65e+48) || ~((c <= 1.22e+119)))
		tmp = t_3;
	else
		tmp = c * ((t * j) - (a * (t * (x / c))));
	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[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4.3e+151], t$95$3, If[LessEqual[c, -9.5e+104], N[(i * N[(y * N[(N[(b * N[(a / y), $MachinePrecision]), $MachinePrecision] - j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.52e+58], N[(N[(z * j), $MachinePrecision] * N[(N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision] / j), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -5.1e+48], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2e-118], N[(x * N[(N[(y * z), $MachinePrecision] - N[(i * N[(j * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.7e-195], N[(b * N[(z * N[(N[(a * N[(i / z), $MachinePrecision]), $MachinePrecision] - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.9e-196], t$95$1, If[LessEqual[c, 3e-130], t$95$2, If[LessEqual[c, 4.7e-61], t$95$1, If[LessEqual[c, 1.16e+40], t$95$2, If[Or[LessEqual[c, 2.65e+48], N[Not[LessEqual[c, 1.22e+119]], $MachinePrecision]], t$95$3, N[(c * N[(N[(t * j), $MachinePrecision] - N[(a * N[(t * N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if c < -4.29999999999999983e151 or 1.16000000000000012e40 < c < 2.65e48 or 1.2200000000000001e119 < c

   1. Initial program 59.8%

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

   3. Taylor expanded in c around inf 75.6%

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

   if -4.29999999999999983e151 < c < -9.5e104

   1. Initial program 58.3%

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

   3. Taylor expanded in i around inf 67.6%

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

      1. distribute-lft-out-- 67.6%

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

      2. *-commutative 67.6%

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

   5. Simplified 67.6%

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

   6. Taylor expanded in b around inf 59.7%

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

      1. +-commutative 59.7%

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

      2. *-commutative 59.7%

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

      3. mul-1-neg 59.7%

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

      4. unsub-neg 59.7%

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

      5. *-commutative 59.7%

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

      6. associate-/l* 68.1%

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

      7. *-commutative 68.1%

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

   8. Simplified 68.1%

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

   9. Taylor expanded in b around inf 59.7%

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

       1. mul-1-neg 59.7%

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

       2. distribute-frac-neg 59.7%

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

       3. distribute-lft-neg-in 59.7%

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

       4. associate-*r/ 68.1%

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

       5. *-commutative 68.1%

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

       6. associate-*r/ 60.2%

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

       7. distribute-lft-neg-in 60.2%

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

       8. +-commutative 60.2%

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

       9. distribute-lft-in 60.2%

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

       10. *-commutative 60.2%

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

       11. associate-*r* 60.2%

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

       12. distribute-rgt-neg-in 60.2%

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

       13. associate-*r* 35.2%

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

       14. distribute-lft-in 60.2%

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

       15. associate-*r/ 68.1%

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

       16. *-commutative 68.1%

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

   11. Simplified 67.6%

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

   12. Taylor expanded in y around inf 67.5%

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

       1. neg-mul-1 67.5%

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

       2. +-commutative 67.5%

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

       3. unsub-neg 67.5%

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

       4. *-commutative 67.5%

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

       5. associate-/l* 75.6%

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

   14. Simplified 75.6%

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

   if -9.5e104 < c < -1.5199999999999999e58

   1. Initial program 67.8%

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

   3. Taylor expanded in j around inf 52.5%

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

      1. associate--l+ 52.5%

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

      2. sub-neg 52.5%

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

      3. mul-1-neg 52.5%

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

      4. +-commutative 52.5%

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

      5. +-commutative 52.5%

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

      6. associate--r+ 52.5%

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

   5. Simplified 60.8%

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

   6. Taylor expanded in z around inf 52.8%

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

      1. associate-*r* 59.9%

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

      2. *-commutative 59.9%

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

      3. div-sub 68.3%

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

      4. *-commutative 68.3%

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

   8. Simplified 68.3%

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

   if -1.5199999999999999e58 < c < -5.0999999999999998e48

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 80.1%

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

      1. distribute-lft-out-- 80.1%

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

   5. Simplified 80.1%

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

   6. Taylor expanded in t around inf 80.4%

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

      1. mul-1-neg 80.4%

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

      2. distribute-rgt-neg-in 80.4%

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

      3. distribute-rgt-neg-in 80.4%

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

   8. Simplified 80.4%

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

   if -5.0999999999999998e48 < c < -1.99999999999999997e-118

   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 j around inf 73.7%

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

      1. associate--l+ 73.7%

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

      2. sub-neg 73.7%

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

      3. mul-1-neg 73.7%

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

      4. +-commutative 73.7%

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

      5. +-commutative 73.7%

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

      6. associate--r+ 73.7%

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

   5. Simplified 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 y around inf 48.1%

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

      1. associate-*r* 53.5%

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

      2. *-commutative 53.5%

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

      3. associate-/l* 55.9%

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

   8. Simplified 55.9%

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

   9. Taylor expanded in x around inf 62.1%

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

       1. +-commutative 62.1%

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

       2. mul-1-neg 62.1%

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

       3. unsub-neg 62.1%

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

       4. associate-/l* 62.0%

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

       5. associate-/l* 59.2%

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

   11. Simplified 59.2%

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

   if -1.99999999999999997e-118 < c < -1.70000000000000001e-195

   1. Initial program 78.7%

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

   3. Taylor expanded in b around inf 63.7%

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

   4. Taylor expanded in z around inf 68.7%

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

      1. associate-/l* 68.6%

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

   6. Simplified 68.6%

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

   if -1.70000000000000001e-195 < c < 3.90000000000000016e-196 or 2.99999999999999986e-130 < c < 4.6999999999999997e-61

   1. Initial program 79.7%

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

   3. Taylor expanded in y around inf 66.5%

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

      1. +-commutative 66.5%

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

      2. mul-1-neg 66.5%

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

      3. unsub-neg 66.5%

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

      4. *-commutative 66.5%

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

   5. Simplified 66.5%

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

   if 3.90000000000000016e-196 < c < 2.99999999999999986e-130 or 4.6999999999999997e-61 < c < 1.16000000000000012e40

   1. Initial program 93.2%

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

   3. Taylor expanded in a around inf 73.7%

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

      1. distribute-lft-out-- 73.7%

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

   5. Simplified 73.7%

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

   6. Taylor expanded in t around 0 73.7%

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

      1. +-commutative 73.7%

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

      2. mul-1-neg 73.7%

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

      3. distribute-rgt-neg-in 73.7%

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

      4. distribute-lft-out 73.7%

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

      5. unsub-neg 73.7%

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

   8. Simplified 73.7%

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

   if 2.65e48 < c < 1.2200000000000001e119

   1. Initial program 80.0%

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

   3. Taylor expanded in t around inf 73.6%

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

      1. +-commutative 73.6%

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

      2. mul-1-neg 73.6%

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

      3. unsub-neg 73.6%

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

   5. Simplified 73.6%

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

   6. Taylor expanded in c around inf 73.9%

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

      1. +-commutative 73.9%

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

      2. mul-1-neg 73.9%

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

      3. unsub-neg 73.9%

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

      4. associate-/l* 73.8%

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

      5. associate-/l* 73.8%

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

   8. Simplified 73.8%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - a \cdot \left(t \cdot \frac{x}{c}\right)\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.3 \cdot 10^{+151}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -9.5 \cdot 10^{+104}:\\ \;\;\;\;i \cdot \left(y \cdot \left(b \cdot \frac{a}{y} - j\right)\right)\\ \mathbf{elif}\;c \leq -1.52 \cdot 10^{+58}:\\ \;\;\;\;\left(z \cdot j\right) \cdot \frac{x \cdot y - b \cdot c}{j}\\ \mathbf{elif}\;c \leq -5.1 \cdot 10^{+48}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;c \leq -2 \cdot 10^{-118}:\\ \;\;\;\;x \cdot \left(y \cdot z - i \cdot \left(j \cdot \frac{y}{x}\right)\right)\\ \mathbf{elif}\;c \leq -1.7 \cdot 10^{-195}:\\ \;\;\;\;b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \mathbf{elif}\;c \leq 3.9 \cdot 10^{-196}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 3 \cdot 10^{-130}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 4.7 \cdot 10^{-61}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 1.16 \cdot 10^{+40}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 2.65 \cdot 10^{+48} \lor \neg \left(c \leq 1.22 \cdot 10^{+119}\right):\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - a \cdot \left(t \cdot \frac{x}{c}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 49.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_3 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -2.45 \cdot 10^{+151}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq -2.5 \cdot 10^{+105}:\\ \;\;\;\;i \cdot \left(y \cdot \left(b \cdot \frac{a}{y} - j\right)\right)\\ \mathbf{elif}\;c \leq -2.8 \cdot 10^{+57}:\\ \;\;\;\;\left(z \cdot j\right) \cdot \frac{x \cdot y - b \cdot c}{j}\\ \mathbf{elif}\;c \leq -4.4 \cdot 10^{+48}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;c \leq -2.4 \cdot 10^{-118}:\\ \;\;\;\;x \cdot \left(y \cdot z - i \cdot \left(j \cdot \frac{y}{x}\right)\right)\\ \mathbf{elif}\;c \leq -9 \cdot 10^{-197}:\\ \;\;\;\;b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \mathbf{elif}\;c \leq 5.5 \cdot 10^{-196}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 9.6 \cdot 10^{-129}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 3.7 \cdot 10^{-62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 6.4 \cdot 10^{+39}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 4.4 \cdot 10^{+47}:\\ \;\;\;\;j \cdot \left(\frac{b \cdot \left(z \cdot c\right)}{-j} - y \cdot i\right)\\ \mathbf{elif}\;c \leq 4.3 \cdot 10^{+73}:\\ \;\;\;\;c \cdot \left(t \cdot j - a \cdot \left(t \cdot \frac{x}{c}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j))))
        (t_2 (* a (- (* b i) (* x t))))
        (t_3 (* c (- (* t j) (* z b)))))
   (if (<= c -2.45e+151)
     t_3
     (if (<= c -2.5e+105)
       (* i (* y (- (* b (/ a y)) j)))
       (if (<= c -2.8e+57)
         (* (* z j) (/ (- (* x y) (* b c)) j))
         (if (<= c -4.4e+48)
           (* a (* t (- x)))
           (if (<= c -2.4e-118)
             (* x (- (* y z) (* i (* j (/ y x)))))
             (if (<= c -9e-197)
               (* b (* z (- (* a (/ i z)) c)))
               (if (<= c 5.5e-196)
                 t_1
                 (if (<= c 9.6e-129)
                   t_2
                   (if (<= c 3.7e-62)
                     t_1
                     (if (<= c 6.4e+39)
                       t_2
                       (if (<= c 4.4e+47)
                         (* j (- (/ (* b (* z c)) (- j)) (* y i)))
                         (if (<= c 4.3e+73)
                           (* c (- (* t j) (* a (* t (/ x c)))))
                           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 = a * ((b * i) - (x * t));
	double t_3 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -2.45e+151) {
		tmp = t_3;
	} else if (c <= -2.5e+105) {
		tmp = i * (y * ((b * (a / y)) - j));
	} else if (c <= -2.8e+57) {
		tmp = (z * j) * (((x * y) - (b * c)) / j);
	} else if (c <= -4.4e+48) {
		tmp = a * (t * -x);
	} else if (c <= -2.4e-118) {
		tmp = x * ((y * z) - (i * (j * (y / x))));
	} else if (c <= -9e-197) {
		tmp = b * (z * ((a * (i / z)) - c));
	} else if (c <= 5.5e-196) {
		tmp = t_1;
	} else if (c <= 9.6e-129) {
		tmp = t_2;
	} else if (c <= 3.7e-62) {
		tmp = t_1;
	} else if (c <= 6.4e+39) {
		tmp = t_2;
	} else if (c <= 4.4e+47) {
		tmp = j * (((b * (z * c)) / -j) - (y * i));
	} else if (c <= 4.3e+73) {
		tmp = c * ((t * j) - (a * (t * (x / c))));
	} 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 = a * ((b * i) - (x * t))
    t_3 = c * ((t * j) - (z * b))
    if (c <= (-2.45d+151)) then
        tmp = t_3
    else if (c <= (-2.5d+105)) then
        tmp = i * (y * ((b * (a / y)) - j))
    else if (c <= (-2.8d+57)) then
        tmp = (z * j) * (((x * y) - (b * c)) / j)
    else if (c <= (-4.4d+48)) then
        tmp = a * (t * -x)
    else if (c <= (-2.4d-118)) then
        tmp = x * ((y * z) - (i * (j * (y / x))))
    else if (c <= (-9d-197)) then
        tmp = b * (z * ((a * (i / z)) - c))
    else if (c <= 5.5d-196) then
        tmp = t_1
    else if (c <= 9.6d-129) then
        tmp = t_2
    else if (c <= 3.7d-62) then
        tmp = t_1
    else if (c <= 6.4d+39) then
        tmp = t_2
    else if (c <= 4.4d+47) then
        tmp = j * (((b * (z * c)) / -j) - (y * i))
    else if (c <= 4.3d+73) then
        tmp = c * ((t * j) - (a * (t * (x / c))))
    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 = a * ((b * i) - (x * t));
	double t_3 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -2.45e+151) {
		tmp = t_3;
	} else if (c <= -2.5e+105) {
		tmp = i * (y * ((b * (a / y)) - j));
	} else if (c <= -2.8e+57) {
		tmp = (z * j) * (((x * y) - (b * c)) / j);
	} else if (c <= -4.4e+48) {
		tmp = a * (t * -x);
	} else if (c <= -2.4e-118) {
		tmp = x * ((y * z) - (i * (j * (y / x))));
	} else if (c <= -9e-197) {
		tmp = b * (z * ((a * (i / z)) - c));
	} else if (c <= 5.5e-196) {
		tmp = t_1;
	} else if (c <= 9.6e-129) {
		tmp = t_2;
	} else if (c <= 3.7e-62) {
		tmp = t_1;
	} else if (c <= 6.4e+39) {
		tmp = t_2;
	} else if (c <= 4.4e+47) {
		tmp = j * (((b * (z * c)) / -j) - (y * i));
	} else if (c <= 4.3e+73) {
		tmp = c * ((t * j) - (a * (t * (x / c))));
	} 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 = a * ((b * i) - (x * t))
	t_3 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -2.45e+151:
		tmp = t_3
	elif c <= -2.5e+105:
		tmp = i * (y * ((b * (a / y)) - j))
	elif c <= -2.8e+57:
		tmp = (z * j) * (((x * y) - (b * c)) / j)
	elif c <= -4.4e+48:
		tmp = a * (t * -x)
	elif c <= -2.4e-118:
		tmp = x * ((y * z) - (i * (j * (y / x))))
	elif c <= -9e-197:
		tmp = b * (z * ((a * (i / z)) - c))
	elif c <= 5.5e-196:
		tmp = t_1
	elif c <= 9.6e-129:
		tmp = t_2
	elif c <= 3.7e-62:
		tmp = t_1
	elif c <= 6.4e+39:
		tmp = t_2
	elif c <= 4.4e+47:
		tmp = j * (((b * (z * c)) / -j) - (y * i))
	elif c <= 4.3e+73:
		tmp = c * ((t * j) - (a * (t * (x / c))))
	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(a * Float64(Float64(b * i) - Float64(x * t)))
	t_3 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -2.45e+151)
		tmp = t_3;
	elseif (c <= -2.5e+105)
		tmp = Float64(i * Float64(y * Float64(Float64(b * Float64(a / y)) - j)));
	elseif (c <= -2.8e+57)
		tmp = Float64(Float64(z * j) * Float64(Float64(Float64(x * y) - Float64(b * c)) / j));
	elseif (c <= -4.4e+48)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (c <= -2.4e-118)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(i * Float64(j * Float64(y / x)))));
	elseif (c <= -9e-197)
		tmp = Float64(b * Float64(z * Float64(Float64(a * Float64(i / z)) - c)));
	elseif (c <= 5.5e-196)
		tmp = t_1;
	elseif (c <= 9.6e-129)
		tmp = t_2;
	elseif (c <= 3.7e-62)
		tmp = t_1;
	elseif (c <= 6.4e+39)
		tmp = t_2;
	elseif (c <= 4.4e+47)
		tmp = Float64(j * Float64(Float64(Float64(b * Float64(z * c)) / Float64(-j)) - Float64(y * i)));
	elseif (c <= 4.3e+73)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(a * Float64(t * Float64(x / c)))));
	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 = a * ((b * i) - (x * t));
	t_3 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -2.45e+151)
		tmp = t_3;
	elseif (c <= -2.5e+105)
		tmp = i * (y * ((b * (a / y)) - j));
	elseif (c <= -2.8e+57)
		tmp = (z * j) * (((x * y) - (b * c)) / j);
	elseif (c <= -4.4e+48)
		tmp = a * (t * -x);
	elseif (c <= -2.4e-118)
		tmp = x * ((y * z) - (i * (j * (y / x))));
	elseif (c <= -9e-197)
		tmp = b * (z * ((a * (i / z)) - c));
	elseif (c <= 5.5e-196)
		tmp = t_1;
	elseif (c <= 9.6e-129)
		tmp = t_2;
	elseif (c <= 3.7e-62)
		tmp = t_1;
	elseif (c <= 6.4e+39)
		tmp = t_2;
	elseif (c <= 4.4e+47)
		tmp = j * (((b * (z * c)) / -j) - (y * i));
	elseif (c <= 4.3e+73)
		tmp = c * ((t * j) - (a * (t * (x / c))));
	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[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.45e+151], t$95$3, If[LessEqual[c, -2.5e+105], N[(i * N[(y * N[(N[(b * N[(a / y), $MachinePrecision]), $MachinePrecision] - j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.8e+57], N[(N[(z * j), $MachinePrecision] * N[(N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision] / j), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -4.4e+48], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.4e-118], N[(x * N[(N[(y * z), $MachinePrecision] - N[(i * N[(j * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -9e-197], N[(b * N[(z * N[(N[(a * N[(i / z), $MachinePrecision]), $MachinePrecision] - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.5e-196], t$95$1, If[LessEqual[c, 9.6e-129], t$95$2, If[LessEqual[c, 3.7e-62], t$95$1, If[LessEqual[c, 6.4e+39], t$95$2, If[LessEqual[c, 4.4e+47], N[(j * N[(N[(N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision] / (-j)), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.3e+73], N[(c * N[(N[(t * j), $MachinePrecision] - N[(a * N[(t * N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if c < -2.45e151 or 4.30000000000000013e73 < c

   1. Initial program 61.4%

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

   3. Taylor expanded in c around inf 73.9%

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

   if -2.45e151 < c < -2.50000000000000023e105

   1. Initial program 58.3%

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

   3. Taylor expanded in i around inf 67.6%

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

      1. distribute-lft-out-- 67.6%

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

      2. *-commutative 67.6%

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

   5. Simplified 67.6%

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

   6. Taylor expanded in b around inf 59.7%

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

      1. +-commutative 59.7%

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

      2. *-commutative 59.7%

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

      3. mul-1-neg 59.7%

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

      4. unsub-neg 59.7%

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

      5. *-commutative 59.7%

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

      6. associate-/l* 68.1%

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

      7. *-commutative 68.1%

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

   8. Simplified 68.1%

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

   9. Taylor expanded in b around inf 59.7%

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

       1. mul-1-neg 59.7%

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

       2. distribute-frac-neg 59.7%

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

       3. distribute-lft-neg-in 59.7%

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

       4. associate-*r/ 68.1%

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

       5. *-commutative 68.1%

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

       6. associate-*r/ 60.2%

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

       7. distribute-lft-neg-in 60.2%

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

       8. +-commutative 60.2%

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

       9. distribute-lft-in 60.2%

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

       10. *-commutative 60.2%

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

       11. associate-*r* 60.2%

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

       12. distribute-rgt-neg-in 60.2%

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

       13. associate-*r* 35.2%

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

       14. distribute-lft-in 60.2%

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

       15. associate-*r/ 68.1%

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

       16. *-commutative 68.1%

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

   11. Simplified 67.6%

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

   12. Taylor expanded in y around inf 67.5%

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

       1. neg-mul-1 67.5%

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

       2. +-commutative 67.5%

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

       3. unsub-neg 67.5%

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

       4. *-commutative 67.5%

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

       5. associate-/l* 75.6%

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

   14. Simplified 75.6%

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

   if -2.50000000000000023e105 < c < -2.8e57

   1. Initial program 67.8%

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

   3. Taylor expanded in j around inf 52.5%

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

      1. associate--l+ 52.5%

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

      2. sub-neg 52.5%

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

      3. mul-1-neg 52.5%

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

      4. +-commutative 52.5%

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

      5. +-commutative 52.5%

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

      6. associate--r+ 52.5%

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

   5. Simplified 60.8%

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

   6. Taylor expanded in z around inf 52.8%

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

      1. associate-*r* 59.9%

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

      2. *-commutative 59.9%

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

      3. div-sub 68.3%

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

      4. *-commutative 68.3%

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

   8. Simplified 68.3%

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

   if -2.8e57 < c < -4.3999999999999999e48

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 80.1%

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

      1. distribute-lft-out-- 80.1%

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

   5. Simplified 80.1%

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

   6. Taylor expanded in t around inf 80.4%

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

      1. mul-1-neg 80.4%

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

      2. distribute-rgt-neg-in 80.4%

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

      3. distribute-rgt-neg-in 80.4%

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

   8. Simplified 80.4%

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

   if -4.3999999999999999e48 < c < -2.4000000000000001e-118

   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 j around inf 73.7%

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

      1. associate--l+ 73.7%

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

      2. sub-neg 73.7%

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

      3. mul-1-neg 73.7%

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

      4. +-commutative 73.7%

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

      5. +-commutative 73.7%

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

      6. associate--r+ 73.7%

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

   5. Simplified 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 y around inf 48.1%

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

      1. associate-*r* 53.5%

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

      2. *-commutative 53.5%

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

      3. associate-/l* 55.9%

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

   8. Simplified 55.9%

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

   9. Taylor expanded in x around inf 62.1%

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

       1. +-commutative 62.1%

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

       2. mul-1-neg 62.1%

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

       3. unsub-neg 62.1%

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

       4. associate-/l* 62.0%

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

       5. associate-/l* 59.2%

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

   11. Simplified 59.2%

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

   if -2.4000000000000001e-118 < c < -9.0000000000000002e-197

   1. Initial program 78.7%

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

   3. Taylor expanded in b around inf 63.7%

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

   4. Taylor expanded in z around inf 68.7%

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

      1. associate-/l* 68.6%

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

   6. Simplified 68.6%

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

   if -9.0000000000000002e-197 < c < 5.50000000000000014e-196 or 9.59999999999999954e-129 < c < 3.6999999999999998e-62

   1. Initial program 79.7%

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

   3. Taylor expanded in y around inf 66.5%

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

      1. +-commutative 66.5%

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

      2. mul-1-neg 66.5%

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

      3. unsub-neg 66.5%

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

      4. *-commutative 66.5%

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

   5. Simplified 66.5%

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

   if 5.50000000000000014e-196 < c < 9.59999999999999954e-129 or 3.6999999999999998e-62 < c < 6.39999999999999986e39

   1. Initial program 93.2%

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

   3. Taylor expanded in a around inf 73.7%

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

      1. distribute-lft-out-- 73.7%

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

   5. Simplified 73.7%

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

   6. Taylor expanded in t around 0 73.7%

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

      1. +-commutative 73.7%

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

      2. mul-1-neg 73.7%

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

      3. distribute-rgt-neg-in 73.7%

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

      4. distribute-lft-out 73.7%

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

      5. unsub-neg 73.7%

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

   8. Simplified 73.7%

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

   if 6.39999999999999986e39 < c < 4.3999999999999999e47

   1. Initial program 83.9%

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

   3. Taylor expanded in j around inf 83.9%

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

      1. associate--l+ 83.9%

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

      2. sub-neg 83.9%

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

      3. mul-1-neg 83.9%

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

      4. +-commutative 83.9%

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

      5. +-commutative 83.9%

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

      6. associate--r+ 83.9%

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

   5. Simplified 83.9%

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

   6. Taylor expanded in c around inf 83.9%

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

      1. associate-*r/ 83.9%

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

      2. associate-*r* 83.9%

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

      3. neg-mul-1 83.9%

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

      4. *-commutative 83.9%

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

   8. Simplified 83.9%

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

   9. Taylor expanded in t around 0 83.9%

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

       1. associate-*r/ 83.9%

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

       2. neg-mul-1 83.9%

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

       3. distribute-lft-neg-in 83.9%

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

   11. Simplified 83.9%

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

   if 4.3999999999999999e47 < c < 4.30000000000000013e73

   1. Initial program 66.7%

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

   3. Taylor expanded in t around inf 83.4%

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

      1. +-commutative 83.4%

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

      2. mul-1-neg 83.4%

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

      3. unsub-neg 83.4%

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

   5. Simplified 83.4%

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

   6. Taylor expanded in c around inf 99.7%

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

      1. +-commutative 99.7%

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

      2. mul-1-neg 99.7%

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

      3. unsub-neg 99.7%

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

      4. associate-/l* 99.5%

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

      5. associate-/l* 99.5%

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

   8. Simplified 99.5%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - a \cdot \left(t \cdot \frac{x}{c}\right)\right)} \]
3. Recombined 10 regimes into one program.

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.45 \cdot 10^{+151}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -2.5 \cdot 10^{+105}:\\ \;\;\;\;i \cdot \left(y \cdot \left(b \cdot \frac{a}{y} - j\right)\right)\\ \mathbf{elif}\;c \leq -2.8 \cdot 10^{+57}:\\ \;\;\;\;\left(z \cdot j\right) \cdot \frac{x \cdot y - b \cdot c}{j}\\ \mathbf{elif}\;c \leq -4.4 \cdot 10^{+48}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;c \leq -2.4 \cdot 10^{-118}:\\ \;\;\;\;x \cdot \left(y \cdot z - i \cdot \left(j \cdot \frac{y}{x}\right)\right)\\ \mathbf{elif}\;c \leq -9 \cdot 10^{-197}:\\ \;\;\;\;b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \mathbf{elif}\;c \leq 5.5 \cdot 10^{-196}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 9.6 \cdot 10^{-129}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 3.7 \cdot 10^{-62}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 6.4 \cdot 10^{+39}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 4.4 \cdot 10^{+47}:\\ \;\;\;\;j \cdot \left(\frac{b \cdot \left(z \cdot c\right)}{-j} - y \cdot i\right)\\ \mathbf{elif}\;c \leq 4.3 \cdot 10^{+73}:\\ \;\;\;\;c \cdot \left(t \cdot j - a \cdot \left(t \cdot \frac{x}{c}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -6.6 \cdot 10^{+25}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -3.95 \cdot 10^{-19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -6.1 \cdot 10^{-50}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-165}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-197}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 42000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+49}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 10^{+61}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+124} \lor \neg \left(a \leq 2.15 \cdot 10^{+186}\right) \land a \leq 1.3 \cdot 10^{+190}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))) (t_2 (* a (- (* b i) (* x t)))))
   (if (<= a -6.6e+25)
     t_2
     (if (<= a -3.95e-19)
       t_1
       (if (<= a -6.1e-50)
         t_2
         (if (<= a -2e-165)
           (* c (- (* t j) (* z b)))
           (if (<= a -4.4e-197)
             (* x (* y z))
             (if (<= a 42000000000.0)
               t_1
               (if (<= a 1.1e+49)
                 t_2
                 (if (<= a 1e+61)
                   (* b (- (* a i) (* z c)))
                   (if (or (<= a 1.05e+124)
                           (and (not (<= a 2.15e+186)) (<= a 1.3e+190)))
                     t_1
                     t_2)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -6.6e+25) {
		tmp = t_2;
	} else if (a <= -3.95e-19) {
		tmp = t_1;
	} else if (a <= -6.1e-50) {
		tmp = t_2;
	} else if (a <= -2e-165) {
		tmp = c * ((t * j) - (z * b));
	} else if (a <= -4.4e-197) {
		tmp = x * (y * z);
	} else if (a <= 42000000000.0) {
		tmp = t_1;
	} else if (a <= 1.1e+49) {
		tmp = t_2;
	} else if (a <= 1e+61) {
		tmp = b * ((a * i) - (z * c));
	} else if ((a <= 1.05e+124) || (!(a <= 2.15e+186) && (a <= 1.3e+190))) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = a * ((b * i) - (x * t))
    if (a <= (-6.6d+25)) then
        tmp = t_2
    else if (a <= (-3.95d-19)) then
        tmp = t_1
    else if (a <= (-6.1d-50)) then
        tmp = t_2
    else if (a <= (-2d-165)) then
        tmp = c * ((t * j) - (z * b))
    else if (a <= (-4.4d-197)) then
        tmp = x * (y * z)
    else if (a <= 42000000000.0d0) then
        tmp = t_1
    else if (a <= 1.1d+49) then
        tmp = t_2
    else if (a <= 1d+61) then
        tmp = b * ((a * i) - (z * c))
    else if ((a <= 1.05d+124) .or. (.not. (a <= 2.15d+186)) .and. (a <= 1.3d+190)) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -6.6e+25) {
		tmp = t_2;
	} else if (a <= -3.95e-19) {
		tmp = t_1;
	} else if (a <= -6.1e-50) {
		tmp = t_2;
	} else if (a <= -2e-165) {
		tmp = c * ((t * j) - (z * b));
	} else if (a <= -4.4e-197) {
		tmp = x * (y * z);
	} else if (a <= 42000000000.0) {
		tmp = t_1;
	} else if (a <= 1.1e+49) {
		tmp = t_2;
	} else if (a <= 1e+61) {
		tmp = b * ((a * i) - (z * c));
	} else if ((a <= 1.05e+124) || (!(a <= 2.15e+186) && (a <= 1.3e+190))) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -6.6e+25:
		tmp = t_2
	elif a <= -3.95e-19:
		tmp = t_1
	elif a <= -6.1e-50:
		tmp = t_2
	elif a <= -2e-165:
		tmp = c * ((t * j) - (z * b))
	elif a <= -4.4e-197:
		tmp = x * (y * z)
	elif a <= 42000000000.0:
		tmp = t_1
	elif a <= 1.1e+49:
		tmp = t_2
	elif a <= 1e+61:
		tmp = b * ((a * i) - (z * c))
	elif (a <= 1.05e+124) or (not (a <= 2.15e+186) and (a <= 1.3e+190)):
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -6.6e+25)
		tmp = t_2;
	elseif (a <= -3.95e-19)
		tmp = t_1;
	elseif (a <= -6.1e-50)
		tmp = t_2;
	elseif (a <= -2e-165)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (a <= -4.4e-197)
		tmp = Float64(x * Float64(y * z));
	elseif (a <= 42000000000.0)
		tmp = t_1;
	elseif (a <= 1.1e+49)
		tmp = t_2;
	elseif (a <= 1e+61)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif ((a <= 1.05e+124) || (!(a <= 2.15e+186) && (a <= 1.3e+190)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -6.6e+25)
		tmp = t_2;
	elseif (a <= -3.95e-19)
		tmp = t_1;
	elseif (a <= -6.1e-50)
		tmp = t_2;
	elseif (a <= -2e-165)
		tmp = c * ((t * j) - (z * b));
	elseif (a <= -4.4e-197)
		tmp = x * (y * z);
	elseif (a <= 42000000000.0)
		tmp = t_1;
	elseif (a <= 1.1e+49)
		tmp = t_2;
	elseif (a <= 1e+61)
		tmp = b * ((a * i) - (z * c));
	elseif ((a <= 1.05e+124) || (~((a <= 2.15e+186)) && (a <= 1.3e+190)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.6e+25], t$95$2, If[LessEqual[a, -3.95e-19], t$95$1, If[LessEqual[a, -6.1e-50], t$95$2, If[LessEqual[a, -2e-165], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.4e-197], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 42000000000.0], t$95$1, If[LessEqual[a, 1.1e+49], t$95$2, If[LessEqual[a, 1e+61], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 1.05e+124], And[N[Not[LessEqual[a, 2.15e+186]], $MachinePrecision], LessEqual[a, 1.3e+190]]], t$95$1, t$95$2]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -6.6000000000000002e25 or -3.9500000000000002e-19 < a < -6.0999999999999996e-50 or 4.2e10 < a < 1.1e49 or 1.05000000000000006e124 < a < 2.15e186 or 1.30000000000000005e190 < 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 66.6%

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

      1. distribute-lft-out-- 66.6%

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

   5. Simplified 66.6%

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

   6. Taylor expanded in t around 0 66.6%

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

      1. +-commutative 66.6%

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

      2. mul-1-neg 66.6%

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

      3. distribute-rgt-neg-in 66.6%

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

      4. distribute-lft-out 66.6%

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

      5. unsub-neg 66.6%

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

   8. Simplified 66.6%

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

   if -6.6000000000000002e25 < a < -3.9500000000000002e-19 or -4.4000000000000001e-197 < a < 4.2e10 or 9.99999999999999949e60 < a < 1.05000000000000006e124 or 2.15e186 < a < 1.30000000000000005e190

   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 j around inf 60.7%

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

   if -6.0999999999999996e-50 < a < -2e-165

   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 c around inf 63.7%

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

   if -2e-165 < a < -4.4000000000000001e-197

   1. Initial program 71.2%

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

   3. Taylor expanded in x around inf 71.3%

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

      1. *-commutative 71.3%

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

   5. Simplified 71.3%

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

   6. Taylor expanded in z around inf 71.3%

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

   if 1.1e49 < a < 9.99999999999999949e60

   1. Initial program 99.5%

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

   3. Taylor expanded in b around inf 89.3%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.6 \cdot 10^{+25}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -3.95 \cdot 10^{-19}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq -6.1 \cdot 10^{-50}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-165}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-197}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 42000000000:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+49}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq 10^{+61}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+124} \lor \neg \left(a \leq 2.15 \cdot 10^{+186}\right) \land a \leq 1.3 \cdot 10^{+190}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 62.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := j \cdot \left(t \cdot c - y \cdot i\right) + t\_2\\ \mathbf{if}\;b \leq -3.1 \cdot 10^{+253}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{+119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{+97}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -80000:\\ \;\;\;\;j \cdot \left(t \cdot c - \left(y \cdot i + \frac{b \cdot \left(z \cdot c\right)}{j}\right)\right)\\ \mathbf{elif}\;b \leq -7 \cdot 10^{-38}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{-99}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+38}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{+97}:\\ \;\;\;\;c \cdot \left(\frac{i \cdot \left(a \cdot b\right)}{c} - z \cdot b\right)\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{+204}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* z (- (* a (/ i z)) c))))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (+ (* j (- (* t c) (* y i))) t_2)))
   (if (<= b -3.1e+253)
     t_2
     (if (<= b -6.2e+119)
       t_1
       (if (<= b -2.7e+97)
         t_3
         (if (<= b -80000.0)
           (* j (- (* t c) (+ (* y i) (/ (* b (* z c)) j))))
           (if (<= b -7e-38)
             t_3
             (if (<= b -1.2e-99)
               (* y (- (* x z) (* i j)))
               (if (<= b 6.5e+38)
                 t_3
                 (if (<= b 5.6e+97)
                   (* c (- (/ (* i (* a b)) c) (* z b)))
                   (if (<= b 2.25e+204) 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 = x * ((y * z) - (t * a));
	double t_3 = (j * ((t * c) - (y * i))) + t_2;
	double tmp;
	if (b <= -3.1e+253) {
		tmp = t_2;
	} else if (b <= -6.2e+119) {
		tmp = t_1;
	} else if (b <= -2.7e+97) {
		tmp = t_3;
	} else if (b <= -80000.0) {
		tmp = j * ((t * c) - ((y * i) + ((b * (z * c)) / j)));
	} else if (b <= -7e-38) {
		tmp = t_3;
	} else if (b <= -1.2e-99) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 6.5e+38) {
		tmp = t_3;
	} else if (b <= 5.6e+97) {
		tmp = c * (((i * (a * b)) / c) - (z * b));
	} else if (b <= 2.25e+204) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = b * (z * ((a * (i / z)) - c))
    t_2 = x * ((y * z) - (t * a))
    t_3 = (j * ((t * c) - (y * i))) + t_2
    if (b <= (-3.1d+253)) then
        tmp = t_2
    else if (b <= (-6.2d+119)) then
        tmp = t_1
    else if (b <= (-2.7d+97)) then
        tmp = t_3
    else if (b <= (-80000.0d0)) then
        tmp = j * ((t * c) - ((y * i) + ((b * (z * c)) / j)))
    else if (b <= (-7d-38)) then
        tmp = t_3
    else if (b <= (-1.2d-99)) then
        tmp = y * ((x * z) - (i * j))
    else if (b <= 6.5d+38) then
        tmp = t_3
    else if (b <= 5.6d+97) then
        tmp = c * (((i * (a * b)) / c) - (z * b))
    else if (b <= 2.25d+204) 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 = x * ((y * z) - (t * a));
	double t_3 = (j * ((t * c) - (y * i))) + t_2;
	double tmp;
	if (b <= -3.1e+253) {
		tmp = t_2;
	} else if (b <= -6.2e+119) {
		tmp = t_1;
	} else if (b <= -2.7e+97) {
		tmp = t_3;
	} else if (b <= -80000.0) {
		tmp = j * ((t * c) - ((y * i) + ((b * (z * c)) / j)));
	} else if (b <= -7e-38) {
		tmp = t_3;
	} else if (b <= -1.2e-99) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 6.5e+38) {
		tmp = t_3;
	} else if (b <= 5.6e+97) {
		tmp = c * (((i * (a * b)) / c) - (z * b));
	} else if (b <= 2.25e+204) {
		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 = x * ((y * z) - (t * a))
	t_3 = (j * ((t * c) - (y * i))) + t_2
	tmp = 0
	if b <= -3.1e+253:
		tmp = t_2
	elif b <= -6.2e+119:
		tmp = t_1
	elif b <= -2.7e+97:
		tmp = t_3
	elif b <= -80000.0:
		tmp = j * ((t * c) - ((y * i) + ((b * (z * c)) / j)))
	elif b <= -7e-38:
		tmp = t_3
	elif b <= -1.2e-99:
		tmp = y * ((x * z) - (i * j))
	elif b <= 6.5e+38:
		tmp = t_3
	elif b <= 5.6e+97:
		tmp = c * (((i * (a * b)) / c) - (z * b))
	elif b <= 2.25e+204:
		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(x * Float64(Float64(y * z) - Float64(t * a)))
	t_3 = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + t_2)
	tmp = 0.0
	if (b <= -3.1e+253)
		tmp = t_2;
	elseif (b <= -6.2e+119)
		tmp = t_1;
	elseif (b <= -2.7e+97)
		tmp = t_3;
	elseif (b <= -80000.0)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(Float64(y * i) + Float64(Float64(b * Float64(z * c)) / j))));
	elseif (b <= -7e-38)
		tmp = t_3;
	elseif (b <= -1.2e-99)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (b <= 6.5e+38)
		tmp = t_3;
	elseif (b <= 5.6e+97)
		tmp = Float64(c * Float64(Float64(Float64(i * Float64(a * b)) / c) - Float64(z * b)));
	elseif (b <= 2.25e+204)
		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 = x * ((y * z) - (t * a));
	t_3 = (j * ((t * c) - (y * i))) + t_2;
	tmp = 0.0;
	if (b <= -3.1e+253)
		tmp = t_2;
	elseif (b <= -6.2e+119)
		tmp = t_1;
	elseif (b <= -2.7e+97)
		tmp = t_3;
	elseif (b <= -80000.0)
		tmp = j * ((t * c) - ((y * i) + ((b * (z * c)) / j)));
	elseif (b <= -7e-38)
		tmp = t_3;
	elseif (b <= -1.2e-99)
		tmp = y * ((x * z) - (i * j));
	elseif (b <= 6.5e+38)
		tmp = t_3;
	elseif (b <= 5.6e+97)
		tmp = c * (((i * (a * b)) / c) - (z * b));
	elseif (b <= 2.25e+204)
		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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]}, If[LessEqual[b, -3.1e+253], t$95$2, If[LessEqual[b, -6.2e+119], t$95$1, If[LessEqual[b, -2.7e+97], t$95$3, If[LessEqual[b, -80000.0], N[(j * N[(N[(t * c), $MachinePrecision] - N[(N[(y * i), $MachinePrecision] + N[(N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision] / j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -7e-38], t$95$3, If[LessEqual[b, -1.2e-99], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.5e+38], t$95$3, If[LessEqual[b, 5.6e+97], N[(c * N[(N[(N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.25e+204], t$95$3, t$95$1]]]]]]]]]]]]

Derivation

1. Split input into 6 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 < -6.1999999999999999e119 or 2.25000000000000001e204 < b

   1. Initial program 66.6%

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

   3. Taylor expanded in b around inf 80.7%

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

   4. Taylor expanded in z around inf 82.7%

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

      1. associate-/l* 84.6%

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

   6. Simplified 84.6%

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

   if -6.1999999999999999e119 < b < -2.69999999999999993e97 or -8e4 < b < -7.0000000000000003e-38 or -1.2e-99 < b < 6.5e38 or 5.5999999999999998e97 < b < 2.25000000000000001e204

   1. Initial program 78.3%

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

   3. Taylor expanded in b around 0 76.3%

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

   if -2.69999999999999993e97 < b < -8e4

   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 j around inf 82.8%

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

      1. associate--l+ 82.8%

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

      2. sub-neg 82.8%

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

      3. mul-1-neg 82.8%

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

      4. +-commutative 82.8%

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

      5. +-commutative 82.8%

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

      6. associate--r+ 82.8%

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

   5. Simplified 83.2%

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

   6. Taylor expanded in c around inf 71.3%

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

      1. associate-*r/ 71.3%

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

      2. associate-*r* 71.3%

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

      3. neg-mul-1 71.3%

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

      4. *-commutative 71.3%

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

   8. Simplified 71.3%

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

   if -7.0000000000000003e-38 < b < -1.2e-99

   1. Initial program 49.0%

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

   3. Taylor expanded in y around inf 59.9%

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

      1. +-commutative 59.9%

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

      2. mul-1-neg 59.9%

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

      3. unsub-neg 59.9%

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

      4. *-commutative 59.9%

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

   5. Simplified 59.9%

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

   if 6.5e38 < b < 5.5999999999999998e97

   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 b around inf 78.8%

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

   4. Taylor expanded in c around inf 79.0%

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

      1. mul-1-neg 79.0%

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

      2. +-commutative 79.0%

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

      3. unsub-neg 79.0%

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

      4. associate-*r* 79.0%

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

      5. *-commutative 79.0%

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

   6. Simplified 79.0%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.1 \cdot 10^{+253}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{+119}:\\ \;\;\;\;b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{+97}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq -80000:\\ \;\;\;\;j \cdot \left(t \cdot c - \left(y \cdot i + \frac{b \cdot \left(z \cdot c\right)}{j}\right)\right)\\ \mathbf{elif}\;b \leq -7 \cdot 10^{-38}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{-99}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+38}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{+97}:\\ \;\;\;\;c \cdot \left(\frac{i \cdot \left(a \cdot b\right)}{c} - z \cdot b\right)\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{+204}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.3% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (+ (* x (- (* y z) (* t a))) (* b (- (* a i) (* z c))))
          (* 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 = ((x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))) + (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 = ((x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))) + (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 = ((x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))) + (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(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(a * i) - Float64(z * c)))) + 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 = ((x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))) + (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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $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%

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

Alternative 7: 29.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := j \cdot \left(t \cdot c\right)\\ \mathbf{if}\;c \leq -7.5 \cdot 10^{+143}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -2.9 \cdot 10^{+90}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq -1.35 \cdot 10^{+81}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -1.5 \cdot 10^{+46}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{-219}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{-194}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 2.45 \cdot 10^{-135}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq 3.6 \cdot 10^{-61}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{+73}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{+142}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq 3.4 \cdot 10^{+232}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))) (t_2 (* j (* t c))))
   (if (<= c -7.5e+143)
     t_2
     (if (<= c -2.9e+90)
       (* b (* z (- c)))
       (if (<= c -1.35e+81)
         t_1
         (if (<= c -1.5e+46)
           (* x (* t (- a)))
           (if (<= c 2.2e-219)
             (* i (* j (- y)))
             (if (<= c 1.7e-194)
               t_1
               (if (<= c 2.45e-135)
                 (* a (* b i))
                 (if (<= c 3.6e-61)
                   (* z (* x y))
                   (if (<= c 1.1e+73)
                     (* a (* t (- x)))
                     (if (<= c 2.5e+142)
                       (* t (* c j))
                       (if (<= c 3.4e+232) (* z (* b (- 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 = x * (y * z);
	double t_2 = j * (t * c);
	double tmp;
	if (c <= -7.5e+143) {
		tmp = t_2;
	} else if (c <= -2.9e+90) {
		tmp = b * (z * -c);
	} else if (c <= -1.35e+81) {
		tmp = t_1;
	} else if (c <= -1.5e+46) {
		tmp = x * (t * -a);
	} else if (c <= 2.2e-219) {
		tmp = i * (j * -y);
	} else if (c <= 1.7e-194) {
		tmp = t_1;
	} else if (c <= 2.45e-135) {
		tmp = a * (b * i);
	} else if (c <= 3.6e-61) {
		tmp = z * (x * y);
	} else if (c <= 1.1e+73) {
		tmp = a * (t * -x);
	} else if (c <= 2.5e+142) {
		tmp = t * (c * j);
	} else if (c <= 3.4e+232) {
		tmp = z * (b * -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 = x * (y * z)
    t_2 = j * (t * c)
    if (c <= (-7.5d+143)) then
        tmp = t_2
    else if (c <= (-2.9d+90)) then
        tmp = b * (z * -c)
    else if (c <= (-1.35d+81)) then
        tmp = t_1
    else if (c <= (-1.5d+46)) then
        tmp = x * (t * -a)
    else if (c <= 2.2d-219) then
        tmp = i * (j * -y)
    else if (c <= 1.7d-194) then
        tmp = t_1
    else if (c <= 2.45d-135) then
        tmp = a * (b * i)
    else if (c <= 3.6d-61) then
        tmp = z * (x * y)
    else if (c <= 1.1d+73) then
        tmp = a * (t * -x)
    else if (c <= 2.5d+142) then
        tmp = t * (c * j)
    else if (c <= 3.4d+232) then
        tmp = z * (b * -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 = x * (y * z);
	double t_2 = j * (t * c);
	double tmp;
	if (c <= -7.5e+143) {
		tmp = t_2;
	} else if (c <= -2.9e+90) {
		tmp = b * (z * -c);
	} else if (c <= -1.35e+81) {
		tmp = t_1;
	} else if (c <= -1.5e+46) {
		tmp = x * (t * -a);
	} else if (c <= 2.2e-219) {
		tmp = i * (j * -y);
	} else if (c <= 1.7e-194) {
		tmp = t_1;
	} else if (c <= 2.45e-135) {
		tmp = a * (b * i);
	} else if (c <= 3.6e-61) {
		tmp = z * (x * y);
	} else if (c <= 1.1e+73) {
		tmp = a * (t * -x);
	} else if (c <= 2.5e+142) {
		tmp = t * (c * j);
	} else if (c <= 3.4e+232) {
		tmp = z * (b * -c);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	t_2 = j * (t * c)
	tmp = 0
	if c <= -7.5e+143:
		tmp = t_2
	elif c <= -2.9e+90:
		tmp = b * (z * -c)
	elif c <= -1.35e+81:
		tmp = t_1
	elif c <= -1.5e+46:
		tmp = x * (t * -a)
	elif c <= 2.2e-219:
		tmp = i * (j * -y)
	elif c <= 1.7e-194:
		tmp = t_1
	elif c <= 2.45e-135:
		tmp = a * (b * i)
	elif c <= 3.6e-61:
		tmp = z * (x * y)
	elif c <= 1.1e+73:
		tmp = a * (t * -x)
	elif c <= 2.5e+142:
		tmp = t * (c * j)
	elif c <= 3.4e+232:
		tmp = z * (b * -c)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(y * z))
	t_2 = Float64(j * Float64(t * c))
	tmp = 0.0
	if (c <= -7.5e+143)
		tmp = t_2;
	elseif (c <= -2.9e+90)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (c <= -1.35e+81)
		tmp = t_1;
	elseif (c <= -1.5e+46)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (c <= 2.2e-219)
		tmp = Float64(i * Float64(j * Float64(-y)));
	elseif (c <= 1.7e-194)
		tmp = t_1;
	elseif (c <= 2.45e-135)
		tmp = Float64(a * Float64(b * i));
	elseif (c <= 3.6e-61)
		tmp = Float64(z * Float64(x * y));
	elseif (c <= 1.1e+73)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (c <= 2.5e+142)
		tmp = Float64(t * Float64(c * j));
	elseif (c <= 3.4e+232)
		tmp = Float64(z * Float64(b * Float64(-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 = x * (y * z);
	t_2 = j * (t * c);
	tmp = 0.0;
	if (c <= -7.5e+143)
		tmp = t_2;
	elseif (c <= -2.9e+90)
		tmp = b * (z * -c);
	elseif (c <= -1.35e+81)
		tmp = t_1;
	elseif (c <= -1.5e+46)
		tmp = x * (t * -a);
	elseif (c <= 2.2e-219)
		tmp = i * (j * -y);
	elseif (c <= 1.7e-194)
		tmp = t_1;
	elseif (c <= 2.45e-135)
		tmp = a * (b * i);
	elseif (c <= 3.6e-61)
		tmp = z * (x * y);
	elseif (c <= 1.1e+73)
		tmp = a * (t * -x);
	elseif (c <= 2.5e+142)
		tmp = t * (c * j);
	elseif (c <= 3.4e+232)
		tmp = z * (b * -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[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -7.5e+143], t$95$2, If[LessEqual[c, -2.9e+90], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.35e+81], t$95$1, If[LessEqual[c, -1.5e+46], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.2e-219], N[(i * N[(j * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.7e-194], t$95$1, If[LessEqual[c, 2.45e-135], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.6e-61], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.1e+73], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.5e+142], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.4e+232], N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if c < -7.49999999999999974e143 or 3.3999999999999998e232 < c

   1. Initial program 53.1%

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

   3. Taylor expanded in j around inf 47.3%

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

      1. associate--l+ 47.3%

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

      2. sub-neg 47.3%

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

      3. mul-1-neg 47.3%

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

      4. +-commutative 47.3%

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

      5. +-commutative 47.3%

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

      6. associate--r+ 47.3%

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

   5. Simplified 51.4%

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

   6. Taylor expanded in i around inf 61.5%

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

      1. associate-*r* 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 55.9%

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

       1. associate-*r* 54.1%

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

       2. *-commutative 54.1%

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

       3. associate-*r* 59.8%

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

   11. Simplified 59.8%

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

   if -7.49999999999999974e143 < c < -2.9000000000000001e90

   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 b around inf 57.9%

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

   4. Taylor expanded in a around 0 42.2%

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

      1. mul-1-neg 42.2%

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

      2. distribute-lft-neg-out 42.2%

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

      3. *-commutative 42.2%

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

   6. Simplified 42.2%

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

   if -2.9000000000000001e90 < c < -1.35e81 or 2.1999999999999999e-219 < c < 1.70000000000000005e-194

   1. Initial program 74.7%

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

   3. Taylor expanded in x around inf 68.9%

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

      1. *-commutative 68.9%

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

   5. Simplified 68.9%

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

   6. Taylor expanded in z around inf 69.1%

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

   if -1.35e81 < c < -1.50000000000000012e46

   1. Initial program 90.4%

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

   3. Taylor expanded in x around inf 56.4%

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

      1. *-commutative 56.4%

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

   5. Simplified 56.4%

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

   6. Taylor expanded in z around 0 45.9%

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

      1. neg-mul-1 45.9%

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

      2. distribute-lft-neg-in 45.9%

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

      3. *-commutative 45.9%

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

   8. Simplified 45.9%

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

   if -1.50000000000000012e46 < c < 2.1999999999999999e-219

   1. Initial program 81.0%

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

   3. Taylor expanded in i around inf 58.7%

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

      1. distribute-lft-out-- 58.7%

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

      2. *-commutative 58.7%

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

   5. Simplified 58.7%

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

   6. Taylor expanded in j around inf 38.1%

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

      1. associate-*r* 38.1%

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

      2. mul-1-neg 38.1%

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

      3. *-commutative 38.1%

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

   8. Simplified 38.1%

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

   if 1.70000000000000005e-194 < c < 2.4500000000000001e-135

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf 46.0%

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

   4. Taylor expanded in a around inf 46.0%

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

   if 2.4500000000000001e-135 < c < 3.60000000000000014e-61

   1. Initial program 74.0%

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

   3. Taylor expanded in j around inf 74.0%

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

      1. associate--l+ 74.0%

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

      2. sub-neg 74.0%

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

      3. mul-1-neg 74.0%

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

      4. +-commutative 74.0%

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

      5. +-commutative 74.0%

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

      6. associate--r+ 74.0%

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

   5. Simplified 74.0%

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

   6. Taylor expanded in z around inf 39.9%

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

      1. associate-*r* 55.5%

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

      2. *-commutative 55.5%

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

      3. div-sub 64.6%

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

      4. *-commutative 64.6%

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

   8. Simplified 64.6%

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

   9. Taylor expanded in x around inf 40.2%

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

       1. *-commutative 40.2%

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

       2. *-commutative 40.2%

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

       3. associate-*l* 57.3%

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

   11. Simplified 57.3%

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

   if 3.60000000000000014e-61 < c < 1.1e73

   1. Initial program 83.8%

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

   3. Taylor expanded in a around inf 65.2%

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

      1. distribute-lft-out-- 65.2%

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

   5. Simplified 65.2%

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

   6. Taylor expanded in t around inf 43.1%

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

      1. mul-1-neg 43.1%

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

      2. distribute-rgt-neg-in 43.1%

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

      3. distribute-rgt-neg-in 43.1%

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

   8. Simplified 43.1%

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

   if 1.1e73 < c < 2.5000000000000001e142

   1. Initial program 92.3%

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

   3. Taylor expanded in t around inf 61.9%

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

      1. +-commutative 61.9%

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

      2. mul-1-neg 61.9%

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

      3. unsub-neg 61.9%

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

   5. Simplified 61.9%

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

   6. Taylor expanded in c around inf 54.4%

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

   if 2.5000000000000001e142 < c < 3.3999999999999998e232

   1. Initial program 59.9%

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

   3. Taylor expanded in j around inf 66.6%

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

      1. associate--l+ 66.6%

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

      2. sub-neg 66.6%

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

      3. mul-1-neg 66.6%

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

      4. +-commutative 66.6%

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

      5. +-commutative 66.6%

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

      6. associate--r+ 66.6%

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

   5. Simplified 66.6%

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

   6. Taylor expanded in c around inf 66.7%

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

      1. associate-*r/ 66.7%

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

      2. associate-*r* 66.7%

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

      3. neg-mul-1 66.7%

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

      4. *-commutative 66.7%

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

   8. Simplified 66.7%

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

   9. Taylor expanded in j around 0 66.9%

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

       1. neg-mul-1 66.9%

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

       2. *-commutative 66.9%

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

       3. associate-*r* 66.9%

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

       4. *-commutative 66.9%

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

       5. associate-*r* 66.9%

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

       6. distribute-rgt-neg-out 66.9%

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

       7. distribute-rgt-neg-in 66.9%

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

   11. Simplified 66.9%

       \[\leadsto \color{blue}{z \cdot \left(b \cdot \left(-c\right)\right)} \]
3. Recombined 10 regimes into one program.

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -7.5 \cdot 10^{+143}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq -2.9 \cdot 10^{+90}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq -1.35 \cdot 10^{+81}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq -1.5 \cdot 10^{+46}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{-219}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{-194}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 2.45 \cdot 10^{-135}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq 3.6 \cdot 10^{-61}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{+73}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{+142}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq 3.4 \cdot 10^{+232}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 49.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{+51}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-48}:\\ \;\;\;\;c \cdot \left(t \cdot j - a \cdot \left(t \cdot \frac{x}{c}\right)\right)\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-91}:\\ \;\;\;\;j \cdot \left(t \cdot c + a \cdot \left(b \cdot \frac{i}{j}\right)\right)\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-118}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-229}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-164}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-164}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+121}:\\ \;\;\;\;i \cdot \left(y \cdot \left(b \cdot \frac{a}{y} - j\right)\right)\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+146}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(x \cdot \frac{z}{j} - i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* z (- (* a (/ i z)) c)))))
   (if (<= y -4.5e+51)
     (* y (- (* x z) (* i j)))
     (if (<= y -1.8e-48)
       (* c (- (* t j) (* a (* t (/ x c)))))
       (if (<= y -3.5e-71)
         t_1
         (if (<= y -1.3e-91)
           (* j (+ (* t c) (* a (* b (/ i j)))))
           (if (<= y -6.8e-118)
             (* t (- (* c j) (* x a)))
             (if (<= y 2.6e-229)
               t_1
               (if (<= y 1.45e-164)
                 (* x (- (* y z) (* t a)))
                 (if (<= y 2.8e-164)
                   (* c (* t j))
                   (if (<= y 3.3e+121)
                     (* i (* y (- (* b (/ a y)) j)))
                     (if (<= y 1.75e+146)
                       (* z (- (* x y) (* b c)))
                       (* (* y j) (- (* x (/ z j)) i))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (z * ((a * (i / z)) - c));
	double tmp;
	if (y <= -4.5e+51) {
		tmp = y * ((x * z) - (i * j));
	} else if (y <= -1.8e-48) {
		tmp = c * ((t * j) - (a * (t * (x / c))));
	} else if (y <= -3.5e-71) {
		tmp = t_1;
	} else if (y <= -1.3e-91) {
		tmp = j * ((t * c) + (a * (b * (i / j))));
	} else if (y <= -6.8e-118) {
		tmp = t * ((c * j) - (x * a));
	} else if (y <= 2.6e-229) {
		tmp = t_1;
	} else if (y <= 1.45e-164) {
		tmp = x * ((y * z) - (t * a));
	} else if (y <= 2.8e-164) {
		tmp = c * (t * j);
	} else if (y <= 3.3e+121) {
		tmp = i * (y * ((b * (a / y)) - j));
	} else if (y <= 1.75e+146) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = (y * j) * ((x * (z / j)) - i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (z * ((a * (i / z)) - c))
    if (y <= (-4.5d+51)) then
        tmp = y * ((x * z) - (i * j))
    else if (y <= (-1.8d-48)) then
        tmp = c * ((t * j) - (a * (t * (x / c))))
    else if (y <= (-3.5d-71)) then
        tmp = t_1
    else if (y <= (-1.3d-91)) then
        tmp = j * ((t * c) + (a * (b * (i / j))))
    else if (y <= (-6.8d-118)) then
        tmp = t * ((c * j) - (x * a))
    else if (y <= 2.6d-229) then
        tmp = t_1
    else if (y <= 1.45d-164) then
        tmp = x * ((y * z) - (t * a))
    else if (y <= 2.8d-164) then
        tmp = c * (t * j)
    else if (y <= 3.3d+121) then
        tmp = i * (y * ((b * (a / y)) - j))
    else if (y <= 1.75d+146) then
        tmp = z * ((x * y) - (b * c))
    else
        tmp = (y * j) * ((x * (z / j)) - i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (z * ((a * (i / z)) - c));
	double tmp;
	if (y <= -4.5e+51) {
		tmp = y * ((x * z) - (i * j));
	} else if (y <= -1.8e-48) {
		tmp = c * ((t * j) - (a * (t * (x / c))));
	} else if (y <= -3.5e-71) {
		tmp = t_1;
	} else if (y <= -1.3e-91) {
		tmp = j * ((t * c) + (a * (b * (i / j))));
	} else if (y <= -6.8e-118) {
		tmp = t * ((c * j) - (x * a));
	} else if (y <= 2.6e-229) {
		tmp = t_1;
	} else if (y <= 1.45e-164) {
		tmp = x * ((y * z) - (t * a));
	} else if (y <= 2.8e-164) {
		tmp = c * (t * j);
	} else if (y <= 3.3e+121) {
		tmp = i * (y * ((b * (a / y)) - j));
	} else if (y <= 1.75e+146) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = (y * j) * ((x * (z / j)) - i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (z * ((a * (i / z)) - c))
	tmp = 0
	if y <= -4.5e+51:
		tmp = y * ((x * z) - (i * j))
	elif y <= -1.8e-48:
		tmp = c * ((t * j) - (a * (t * (x / c))))
	elif y <= -3.5e-71:
		tmp = t_1
	elif y <= -1.3e-91:
		tmp = j * ((t * c) + (a * (b * (i / j))))
	elif y <= -6.8e-118:
		tmp = t * ((c * j) - (x * a))
	elif y <= 2.6e-229:
		tmp = t_1
	elif y <= 1.45e-164:
		tmp = x * ((y * z) - (t * a))
	elif y <= 2.8e-164:
		tmp = c * (t * j)
	elif y <= 3.3e+121:
		tmp = i * (y * ((b * (a / y)) - j))
	elif y <= 1.75e+146:
		tmp = z * ((x * y) - (b * c))
	else:
		tmp = (y * j) * ((x * (z / j)) - i)
	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)))
	tmp = 0.0
	if (y <= -4.5e+51)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (y <= -1.8e-48)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(a * Float64(t * Float64(x / c)))));
	elseif (y <= -3.5e-71)
		tmp = t_1;
	elseif (y <= -1.3e-91)
		tmp = Float64(j * Float64(Float64(t * c) + Float64(a * Float64(b * Float64(i / j)))));
	elseif (y <= -6.8e-118)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (y <= 2.6e-229)
		tmp = t_1;
	elseif (y <= 1.45e-164)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (y <= 2.8e-164)
		tmp = Float64(c * Float64(t * j));
	elseif (y <= 3.3e+121)
		tmp = Float64(i * Float64(y * Float64(Float64(b * Float64(a / y)) - j)));
	elseif (y <= 1.75e+146)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	else
		tmp = Float64(Float64(y * j) * Float64(Float64(x * Float64(z / j)) - i));
	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));
	tmp = 0.0;
	if (y <= -4.5e+51)
		tmp = y * ((x * z) - (i * j));
	elseif (y <= -1.8e-48)
		tmp = c * ((t * j) - (a * (t * (x / c))));
	elseif (y <= -3.5e-71)
		tmp = t_1;
	elseif (y <= -1.3e-91)
		tmp = j * ((t * c) + (a * (b * (i / j))));
	elseif (y <= -6.8e-118)
		tmp = t * ((c * j) - (x * a));
	elseif (y <= 2.6e-229)
		tmp = t_1;
	elseif (y <= 1.45e-164)
		tmp = x * ((y * z) - (t * a));
	elseif (y <= 2.8e-164)
		tmp = c * (t * j);
	elseif (y <= 3.3e+121)
		tmp = i * (y * ((b * (a / y)) - j));
	elseif (y <= 1.75e+146)
		tmp = z * ((x * y) - (b * c));
	else
		tmp = (y * j) * ((x * (z / j)) - i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(z * N[(N[(a * N[(i / z), $MachinePrecision]), $MachinePrecision] - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.5e+51], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.8e-48], N[(c * N[(N[(t * j), $MachinePrecision] - N[(a * N[(t * N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.5e-71], t$95$1, If[LessEqual[y, -1.3e-91], N[(j * N[(N[(t * c), $MachinePrecision] + N[(a * N[(b * N[(i / j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.8e-118], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.6e-229], t$95$1, If[LessEqual[y, 1.45e-164], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e-164], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.3e+121], N[(i * N[(y * N[(N[(b * N[(a / y), $MachinePrecision]), $MachinePrecision] - j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.75e+146], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * j), $MachinePrecision] * N[(N[(x * N[(z / j), $MachinePrecision]), $MachinePrecision] - i), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if y < -4.5e51

   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 y around inf 72.7%

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

      1. +-commutative 72.7%

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

      2. mul-1-neg 72.7%

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

      3. unsub-neg 72.7%

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

      4. *-commutative 72.7%

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

   5. Simplified 72.7%

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

   if -4.5e51 < y < -1.8000000000000001e-48

   1. Initial program 85.5%

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

   3. Taylor expanded in t around inf 38.6%

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

      1. +-commutative 38.6%

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

      2. mul-1-neg 38.6%

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

      3. unsub-neg 38.6%

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

   5. Simplified 38.6%

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

   6. Taylor expanded in c around inf 45.3%

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

      1. +-commutative 45.3%

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

      2. mul-1-neg 45.3%

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

      3. unsub-neg 45.3%

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

      4. associate-/l* 59.1%

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

      5. associate-/l* 66.0%

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

   8. Simplified 66.0%

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

   if -1.8000000000000001e-48 < y < -3.4999999999999999e-71 or -6.79999999999999981e-118 < y < 2.6000000000000001e-229

   1. Initial program 82.3%

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

   3. Taylor expanded in b around inf 62.1%

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

   4. Taylor expanded in z around inf 63.7%

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

      1. associate-/l* 65.2%

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

   6. Simplified 65.2%

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

   if -3.4999999999999999e-71 < y < -1.30000000000000007e-91

   1. Initial program 99.8%

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

   3. Taylor expanded in j around inf 87.5%

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

      1. associate--l+ 87.5%

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

      2. sub-neg 87.5%

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

      3. mul-1-neg 87.5%

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

      4. +-commutative 87.5%

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

      5. +-commutative 87.5%

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

      6. associate--r+ 87.5%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in i around inf 70.1%

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

      1. associate-*r* 82.6%

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

   8. Simplified 82.6%

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

   9. Taylor expanded in a around 0 70.1%

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

       1. sub-neg 70.1%

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

       2. *-commutative 70.1%

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

       3. associate-*r* 82.6%

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

       4. *-commutative 82.6%

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

       5. associate-*r* 82.6%

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

       6. associate-*r/ 82.6%

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

       7. distribute-rgt-neg-in 82.6%

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

       8. distribute-lft-in 82.6%

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

       9. sub-neg 82.6%

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

       10. associate-/l* 82.6%

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

   11. Simplified 82.6%

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

   12. Taylor expanded in a around inf 50.4%

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

       1. associate-/l* 50.4%

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

       2. *-commutative 50.4%

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

       3. associate-/l* 62.8%

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

   14. Simplified 62.8%

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

   15. Taylor expanded in i around 0 50.4%

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

       1. associate-/l* 62.9%

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

   17. Simplified 62.9%

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

   if -1.30000000000000007e-91 < y < -6.79999999999999981e-118

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 86.1%

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

      1. +-commutative 86.1%

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

      2. mul-1-neg 86.1%

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

      3. unsub-neg 86.1%

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

   5. Simplified 86.1%

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

   if 2.6000000000000001e-229 < y < 1.45e-164

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 80.4%

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

      1. *-commutative 80.4%

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

   5. Simplified 80.4%

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

   if 1.45e-164 < y < 2.8000000000000001e-164

   1. Initial program 100.0%

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

   3. Taylor expanded in j around inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. sub-neg 100.0%

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

      3. mul-1-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. +-commutative 100.0%

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

      6. associate--r+ 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in i around inf 100.0%

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

      1. associate-*r* 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in c around inf 100.0%

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

   if 2.8000000000000001e-164 < y < 3.29999999999999979e121

   1. Initial program 74.3%

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

   3. Taylor expanded in i around inf 49.8%

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

      1. distribute-lft-out-- 49.8%

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

      2. *-commutative 49.8%

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

   5. Simplified 49.8%

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

   6. Taylor expanded in b around inf 41.7%

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

      1. +-commutative 41.7%

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

      2. *-commutative 41.7%

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

      3. mul-1-neg 41.7%

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

      4. unsub-neg 41.7%

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

      5. *-commutative 41.7%

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

      6. associate-/l* 45.7%

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

      7. *-commutative 45.7%

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

   8. Simplified 45.7%

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

   9. Taylor expanded in b around inf 41.7%

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

       1. mul-1-neg 41.7%

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

       2. distribute-frac-neg 41.7%

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

       3. distribute-lft-neg-in 41.7%

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

       4. associate-*r/ 45.7%

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

       5. *-commutative 45.7%

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

       6. associate-*r/ 45.7%

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

       7. distribute-lft-neg-in 45.7%

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

       8. +-commutative 45.7%

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

       9. distribute-lft-in 41.7%

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

       10. *-commutative 41.7%

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

       11. associate-*r* 42.0%

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

       12. distribute-rgt-neg-in 42.0%

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

       13. associate-*r* 39.9%

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

       14. distribute-lft-in 47.9%

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

       15. associate-*r/ 48.0%

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

       16. *-commutative 48.0%

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

   11. Simplified 47.9%

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

   12. Taylor expanded in y around inf 49.8%

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

       1. neg-mul-1 49.8%

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

       2. +-commutative 49.8%

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

       3. unsub-neg 49.8%

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

       4. *-commutative 49.8%

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

       5. associate-/l* 55.5%

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

   14. Simplified 55.5%

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

   if 3.29999999999999979e121 < y < 1.7500000000000001e146

   1. Initial program 67.8%

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

   3. Taylor expanded in z around inf 84.2%

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

      1. *-commutative 84.2%

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

   5. Simplified 84.2%

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

   if 1.7500000000000001e146 < y

   1. Initial program 56.1%

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

   3. Taylor expanded in j around inf 56.6%

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

      1. associate--l+ 56.6%

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

      2. sub-neg 56.6%

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

      3. mul-1-neg 56.6%

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

      4. +-commutative 56.6%

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

      5. +-commutative 56.6%

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

      6. associate--r+ 56.6%

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

   5. Simplified 56.6%

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

   6. Taylor expanded in y around inf 73.8%

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

      1. associate-*r* 73.7%

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

      2. *-commutative 73.7%

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

      3. associate-/l* 73.7%

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

   8. Simplified 73.7%

      \[\leadsto \color{blue}{\left(y \cdot j\right) \cdot \left(x \cdot \frac{z}{j} - i\right)} \]
3. Recombined 10 regimes into one program.

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+51}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-48}:\\ \;\;\;\;c \cdot \left(t \cdot j - a \cdot \left(t \cdot \frac{x}{c}\right)\right)\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-71}:\\ \;\;\;\;b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-91}:\\ \;\;\;\;j \cdot \left(t \cdot c + a \cdot \left(b \cdot \frac{i}{j}\right)\right)\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-118}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-229}:\\ \;\;\;\;b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-164}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-164}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+121}:\\ \;\;\;\;i \cdot \left(y \cdot \left(b \cdot \frac{a}{y} - j\right)\right)\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+146}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(x \cdot \frac{z}{j} - i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 50.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;a \leq -4 \cdot 10^{+74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-51}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-160}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-198}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 56000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{+60}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+124} \lor \neg \left(a \leq 1.65 \cdot 10^{+186}\right) \land a \leq 1.35 \cdot 10^{+190}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))) (t_2 (* j (- (* t c) (* y i)))))
   (if (<= a -4e+74)
     t_1
     (if (<= a -5.5e-51)
       (* t (- (* c j) (* x a)))
       (if (<= a -4.8e-160)
         (* c (- (* t j) (* z b)))
         (if (<= a -7.5e-198)
           (* x (* y z))
           (if (<= a 56000000000.0)
             t_2
             (if (<= a 7e+49)
               t_1
               (if (<= a 4.7e+60)
                 (* b (- (* a i) (* z c)))
                 (if (or (<= a 1.05e+124)
                         (and (not (<= a 1.65e+186)) (<= a 1.35e+190)))
                   t_2
                   t_1))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (a <= -4e+74) {
		tmp = t_1;
	} else if (a <= -5.5e-51) {
		tmp = t * ((c * j) - (x * a));
	} else if (a <= -4.8e-160) {
		tmp = c * ((t * j) - (z * b));
	} else if (a <= -7.5e-198) {
		tmp = x * (y * z);
	} else if (a <= 56000000000.0) {
		tmp = t_2;
	} else if (a <= 7e+49) {
		tmp = t_1;
	} else if (a <= 4.7e+60) {
		tmp = b * ((a * i) - (z * c));
	} else if ((a <= 1.05e+124) || (!(a <= 1.65e+186) && (a <= 1.35e+190))) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((b * i) - (x * t))
    t_2 = j * ((t * c) - (y * i))
    if (a <= (-4d+74)) then
        tmp = t_1
    else if (a <= (-5.5d-51)) then
        tmp = t * ((c * j) - (x * a))
    else if (a <= (-4.8d-160)) then
        tmp = c * ((t * j) - (z * b))
    else if (a <= (-7.5d-198)) then
        tmp = x * (y * z)
    else if (a <= 56000000000.0d0) then
        tmp = t_2
    else if (a <= 7d+49) then
        tmp = t_1
    else if (a <= 4.7d+60) then
        tmp = b * ((a * i) - (z * c))
    else if ((a <= 1.05d+124) .or. (.not. (a <= 1.65d+186)) .and. (a <= 1.35d+190)) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (a <= -4e+74) {
		tmp = t_1;
	} else if (a <= -5.5e-51) {
		tmp = t * ((c * j) - (x * a));
	} else if (a <= -4.8e-160) {
		tmp = c * ((t * j) - (z * b));
	} else if (a <= -7.5e-198) {
		tmp = x * (y * z);
	} else if (a <= 56000000000.0) {
		tmp = t_2;
	} else if (a <= 7e+49) {
		tmp = t_1;
	} else if (a <= 4.7e+60) {
		tmp = b * ((a * i) - (z * c));
	} else if ((a <= 1.05e+124) || (!(a <= 1.65e+186) && (a <= 1.35e+190))) {
		tmp = t_2;
	} 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))
	t_2 = j * ((t * c) - (y * i))
	tmp = 0
	if a <= -4e+74:
		tmp = t_1
	elif a <= -5.5e-51:
		tmp = t * ((c * j) - (x * a))
	elif a <= -4.8e-160:
		tmp = c * ((t * j) - (z * b))
	elif a <= -7.5e-198:
		tmp = x * (y * z)
	elif a <= 56000000000.0:
		tmp = t_2
	elif a <= 7e+49:
		tmp = t_1
	elif a <= 4.7e+60:
		tmp = b * ((a * i) - (z * c))
	elif (a <= 1.05e+124) or (not (a <= 1.65e+186) and (a <= 1.35e+190)):
		tmp = t_2
	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)))
	t_2 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (a <= -4e+74)
		tmp = t_1;
	elseif (a <= -5.5e-51)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (a <= -4.8e-160)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (a <= -7.5e-198)
		tmp = Float64(x * Float64(y * z));
	elseif (a <= 56000000000.0)
		tmp = t_2;
	elseif (a <= 7e+49)
		tmp = t_1;
	elseif (a <= 4.7e+60)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif ((a <= 1.05e+124) || (!(a <= 1.65e+186) && (a <= 1.35e+190)))
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((b * i) - (x * t));
	t_2 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (a <= -4e+74)
		tmp = t_1;
	elseif (a <= -5.5e-51)
		tmp = t * ((c * j) - (x * a));
	elseif (a <= -4.8e-160)
		tmp = c * ((t * j) - (z * b));
	elseif (a <= -7.5e-198)
		tmp = x * (y * z);
	elseif (a <= 56000000000.0)
		tmp = t_2;
	elseif (a <= 7e+49)
		tmp = t_1;
	elseif (a <= 4.7e+60)
		tmp = b * ((a * i) - (z * c));
	elseif ((a <= 1.05e+124) || (~((a <= 1.65e+186)) && (a <= 1.35e+190)))
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4e+74], t$95$1, If[LessEqual[a, -5.5e-51], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.8e-160], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -7.5e-198], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 56000000000.0], t$95$2, If[LessEqual[a, 7e+49], t$95$1, If[LessEqual[a, 4.7e+60], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 1.05e+124], And[N[Not[LessEqual[a, 1.65e+186]], $MachinePrecision], LessEqual[a, 1.35e+190]]], t$95$2, t$95$1]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -3.99999999999999981e74 or 5.6e10 < a < 6.9999999999999995e49 or 1.05000000000000006e124 < a < 1.65000000000000012e186 or 1.35000000000000002e190 < a

   1. Initial program 66.8%

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

   3. Taylor expanded in a around inf 68.6%

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

      1. distribute-lft-out-- 68.6%

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

   5. Simplified 68.6%

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

   6. Taylor expanded in t around 0 68.6%

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

      1. +-commutative 68.6%

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

      2. mul-1-neg 68.6%

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

      3. distribute-rgt-neg-in 68.6%

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

      4. distribute-lft-out 68.6%

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

      5. unsub-neg 68.6%

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

   8. Simplified 68.6%

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

   if -3.99999999999999981e74 < a < -5.4999999999999997e-51

   1. Initial program 84.0%

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

   3. Taylor expanded in t around inf 59.0%

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

      1. +-commutative 59.0%

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

      2. mul-1-neg 59.0%

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

      3. unsub-neg 59.0%

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

   5. Simplified 59.0%

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

   if -5.4999999999999997e-51 < a < -4.79999999999999982e-160

   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 c around inf 63.7%

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

   if -4.79999999999999982e-160 < a < -7.50000000000000064e-198

   1. Initial program 71.2%

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

   3. Taylor expanded in x around inf 71.3%

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

      1. *-commutative 71.3%

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

   5. Simplified 71.3%

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

   6. Taylor expanded in z around inf 71.3%

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

   if -7.50000000000000064e-198 < a < 5.6e10 or 4.6999999999999998e60 < a < 1.05000000000000006e124 or 1.65000000000000012e186 < a < 1.35000000000000002e190

   1. Initial program 76.8%

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

   3. Taylor expanded in j around inf 59.9%

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

   if 6.9999999999999995e49 < a < 4.6999999999999998e60

   1. Initial program 99.5%

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

   3. Taylor expanded in b around inf 89.3%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{+74}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-51}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-160}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-198}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 56000000000:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+49}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{+60}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+124} \lor \neg \left(a \leq 1.65 \cdot 10^{+186}\right) \land a \leq 1.35 \cdot 10^{+190}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 50.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_3 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -2.2 \cdot 10^{+85}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq -9 \cdot 10^{-12}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq -2.4 \cdot 10^{-118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -1.85 \cdot 10^{-191}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq 2.1 \cdot 10^{-195}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 9 \cdot 10^{-128}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 7.5 \cdot 10^{-63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{+40}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 2 \cdot 10^{+40}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{+167}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j))))
        (t_2 (* a (- (* b i) (* x t))))
        (t_3 (* c (- (* t j) (* z b)))))
   (if (<= c -2.2e+85)
     t_3
     (if (<= c -9e-12)
       (* x (- (* y z) (* t a)))
       (if (<= c -2.4e-118)
         t_1
         (if (<= c -1.85e-191)
           (* b (- (* a i) (* z c)))
           (if (<= c 2.1e-195)
             t_1
             (if (<= c 9e-128)
               t_2
               (if (<= c 7.5e-63)
                 t_1
                 (if (<= c 1.1e+40)
                   t_2
                   (if (<= c 2e+40)
                     (* i (* j (- y)))
                     (if (<= c 2.2e+167)
                       (* t (- (* c j) (* x a)))
                       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 = a * ((b * i) - (x * t));
	double t_3 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -2.2e+85) {
		tmp = t_3;
	} else if (c <= -9e-12) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= -2.4e-118) {
		tmp = t_1;
	} else if (c <= -1.85e-191) {
		tmp = b * ((a * i) - (z * c));
	} else if (c <= 2.1e-195) {
		tmp = t_1;
	} else if (c <= 9e-128) {
		tmp = t_2;
	} else if (c <= 7.5e-63) {
		tmp = t_1;
	} else if (c <= 1.1e+40) {
		tmp = t_2;
	} else if (c <= 2e+40) {
		tmp = i * (j * -y);
	} else if (c <= 2.2e+167) {
		tmp = t * ((c * j) - (x * a));
	} 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 = a * ((b * i) - (x * t))
    t_3 = c * ((t * j) - (z * b))
    if (c <= (-2.2d+85)) then
        tmp = t_3
    else if (c <= (-9d-12)) then
        tmp = x * ((y * z) - (t * a))
    else if (c <= (-2.4d-118)) then
        tmp = t_1
    else if (c <= (-1.85d-191)) then
        tmp = b * ((a * i) - (z * c))
    else if (c <= 2.1d-195) then
        tmp = t_1
    else if (c <= 9d-128) then
        tmp = t_2
    else if (c <= 7.5d-63) then
        tmp = t_1
    else if (c <= 1.1d+40) then
        tmp = t_2
    else if (c <= 2d+40) then
        tmp = i * (j * -y)
    else if (c <= 2.2d+167) then
        tmp = t * ((c * j) - (x * a))
    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 = a * ((b * i) - (x * t));
	double t_3 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -2.2e+85) {
		tmp = t_3;
	} else if (c <= -9e-12) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= -2.4e-118) {
		tmp = t_1;
	} else if (c <= -1.85e-191) {
		tmp = b * ((a * i) - (z * c));
	} else if (c <= 2.1e-195) {
		tmp = t_1;
	} else if (c <= 9e-128) {
		tmp = t_2;
	} else if (c <= 7.5e-63) {
		tmp = t_1;
	} else if (c <= 1.1e+40) {
		tmp = t_2;
	} else if (c <= 2e+40) {
		tmp = i * (j * -y);
	} else if (c <= 2.2e+167) {
		tmp = t * ((c * j) - (x * a));
	} 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 = a * ((b * i) - (x * t))
	t_3 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -2.2e+85:
		tmp = t_3
	elif c <= -9e-12:
		tmp = x * ((y * z) - (t * a))
	elif c <= -2.4e-118:
		tmp = t_1
	elif c <= -1.85e-191:
		tmp = b * ((a * i) - (z * c))
	elif c <= 2.1e-195:
		tmp = t_1
	elif c <= 9e-128:
		tmp = t_2
	elif c <= 7.5e-63:
		tmp = t_1
	elif c <= 1.1e+40:
		tmp = t_2
	elif c <= 2e+40:
		tmp = i * (j * -y)
	elif c <= 2.2e+167:
		tmp = t * ((c * j) - (x * a))
	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(a * Float64(Float64(b * i) - Float64(x * t)))
	t_3 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -2.2e+85)
		tmp = t_3;
	elseif (c <= -9e-12)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (c <= -2.4e-118)
		tmp = t_1;
	elseif (c <= -1.85e-191)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (c <= 2.1e-195)
		tmp = t_1;
	elseif (c <= 9e-128)
		tmp = t_2;
	elseif (c <= 7.5e-63)
		tmp = t_1;
	elseif (c <= 1.1e+40)
		tmp = t_2;
	elseif (c <= 2e+40)
		tmp = Float64(i * Float64(j * Float64(-y)));
	elseif (c <= 2.2e+167)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	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 = a * ((b * i) - (x * t));
	t_3 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -2.2e+85)
		tmp = t_3;
	elseif (c <= -9e-12)
		tmp = x * ((y * z) - (t * a));
	elseif (c <= -2.4e-118)
		tmp = t_1;
	elseif (c <= -1.85e-191)
		tmp = b * ((a * i) - (z * c));
	elseif (c <= 2.1e-195)
		tmp = t_1;
	elseif (c <= 9e-128)
		tmp = t_2;
	elseif (c <= 7.5e-63)
		tmp = t_1;
	elseif (c <= 1.1e+40)
		tmp = t_2;
	elseif (c <= 2e+40)
		tmp = i * (j * -y);
	elseif (c <= 2.2e+167)
		tmp = t * ((c * j) - (x * a));
	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[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.2e+85], t$95$3, If[LessEqual[c, -9e-12], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.4e-118], t$95$1, If[LessEqual[c, -1.85e-191], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.1e-195], t$95$1, If[LessEqual[c, 9e-128], t$95$2, If[LessEqual[c, 7.5e-63], t$95$1, If[LessEqual[c, 1.1e+40], t$95$2, If[LessEqual[c, 2e+40], N[(i * N[(j * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.2e+167], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if c < -2.2000000000000002e85 or 2.20000000000000003e167 < c

   1. Initial program 56.0%

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

   3. Taylor expanded in c around inf 72.4%

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

   if -2.2000000000000002e85 < c < -8.99999999999999962e-12

   1. Initial program 82.8%

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

   3. Taylor expanded in x around inf 67.6%

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

      1. *-commutative 67.6%

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

   5. Simplified 67.6%

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

   if -8.99999999999999962e-12 < c < -2.4000000000000001e-118 or -1.8499999999999998e-191 < c < 2.1e-195 or 8.9999999999999998e-128 < c < 7.5000000000000003e-63

   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 y around inf 65.6%

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

      1. +-commutative 65.6%

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

      2. mul-1-neg 65.6%

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

      3. unsub-neg 65.6%

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

      4. *-commutative 65.6%

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

   5. Simplified 65.6%

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

   if -2.4000000000000001e-118 < c < -1.8499999999999998e-191

   1. Initial program 76.3%

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

   3. Taylor expanded in b around inf 59.6%

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

   if 2.1e-195 < c < 8.9999999999999998e-128 or 7.5000000000000003e-63 < c < 1.0999999999999999e40

   1. Initial program 93.2%

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

   3. Taylor expanded in a around inf 73.7%

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

      1. distribute-lft-out-- 73.7%

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

   5. Simplified 73.7%

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

   6. Taylor expanded in t around 0 73.7%

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

      1. +-commutative 73.7%

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

      2. mul-1-neg 73.7%

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

      3. distribute-rgt-neg-in 73.7%

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

      4. distribute-lft-out 73.7%

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

      5. unsub-neg 73.7%

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

   8. Simplified 73.7%

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

   if 1.0999999999999999e40 < c < 2.00000000000000006e40

   1. Initial program 98.4%

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

   3. Taylor expanded in i around inf 100.0%

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

      1. distribute-lft-out-- 100.0%

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

      2. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in j around inf 100.0%

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

      1. associate-*r* 100.0%

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

      2. mul-1-neg 100.0%

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

      3. *-commutative 100.0%

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

   8. Simplified 100.0%

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

   if 2.00000000000000006e40 < c < 2.20000000000000003e167

   1. Initial program 79.5%

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

   3. Taylor expanded in t around inf 66.0%

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

      1. +-commutative 66.0%

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

      2. mul-1-neg 66.0%

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

      3. unsub-neg 66.0%

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

   5. Simplified 66.0%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.2 \cdot 10^{+85}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -9 \cdot 10^{-12}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq -2.4 \cdot 10^{-118}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq -1.85 \cdot 10^{-191}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq 2.1 \cdot 10^{-195}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 9 \cdot 10^{-128}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 7.5 \cdot 10^{-63}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{+40}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 2 \cdot 10^{+40}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{+167}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 29.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(z \cdot \left(-c\right)\right)\\ t_2 := x \cdot \left(y \cdot z\right)\\ t_3 := j \cdot \left(t \cdot c\right)\\ t_4 := a \cdot \left(b \cdot i\right)\\ \mathbf{if}\;c \leq -1 \cdot 10^{+149}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq -1.45 \cdot 10^{+90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -4.4 \cdot 10^{+80}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -1.65 \cdot 10^{+48}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq -3.3 \cdot 10^{-118}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 6.2 \cdot 10^{-257}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;c \leq 2.8 \cdot 10^{-61}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{+14}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;c \leq 3.4 \cdot 10^{+120}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{+238}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* z (- c))))
        (t_2 (* x (* y z)))
        (t_3 (* j (* t c)))
        (t_4 (* a (* b i))))
   (if (<= c -1e+149)
     t_3
     (if (<= c -1.45e+90)
       t_1
       (if (<= c -4.4e+80)
         t_2
         (if (<= c -1.65e+48)
           (* x (* t (- a)))
           (if (<= c -3.3e-118)
             t_2
             (if (<= c 6.2e-257)
               t_4
               (if (<= c 2.8e-61)
                 (* z (* x y))
                 (if (<= c 1.25e+14)
                   t_4
                   (if (<= c 3.4e+120)
                     (* t (* c j))
                     (if (<= c 3.2e+238) 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 * (z * -c);
	double t_2 = x * (y * z);
	double t_3 = j * (t * c);
	double t_4 = a * (b * i);
	double tmp;
	if (c <= -1e+149) {
		tmp = t_3;
	} else if (c <= -1.45e+90) {
		tmp = t_1;
	} else if (c <= -4.4e+80) {
		tmp = t_2;
	} else if (c <= -1.65e+48) {
		tmp = x * (t * -a);
	} else if (c <= -3.3e-118) {
		tmp = t_2;
	} else if (c <= 6.2e-257) {
		tmp = t_4;
	} else if (c <= 2.8e-61) {
		tmp = z * (x * y);
	} else if (c <= 1.25e+14) {
		tmp = t_4;
	} else if (c <= 3.4e+120) {
		tmp = t * (c * j);
	} else if (c <= 3.2e+238) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = b * (z * -c)
    t_2 = x * (y * z)
    t_3 = j * (t * c)
    t_4 = a * (b * i)
    if (c <= (-1d+149)) then
        tmp = t_3
    else if (c <= (-1.45d+90)) then
        tmp = t_1
    else if (c <= (-4.4d+80)) then
        tmp = t_2
    else if (c <= (-1.65d+48)) then
        tmp = x * (t * -a)
    else if (c <= (-3.3d-118)) then
        tmp = t_2
    else if (c <= 6.2d-257) then
        tmp = t_4
    else if (c <= 2.8d-61) then
        tmp = z * (x * y)
    else if (c <= 1.25d+14) then
        tmp = t_4
    else if (c <= 3.4d+120) then
        tmp = t * (c * j)
    else if (c <= 3.2d+238) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (z * -c);
	double t_2 = x * (y * z);
	double t_3 = j * (t * c);
	double t_4 = a * (b * i);
	double tmp;
	if (c <= -1e+149) {
		tmp = t_3;
	} else if (c <= -1.45e+90) {
		tmp = t_1;
	} else if (c <= -4.4e+80) {
		tmp = t_2;
	} else if (c <= -1.65e+48) {
		tmp = x * (t * -a);
	} else if (c <= -3.3e-118) {
		tmp = t_2;
	} else if (c <= 6.2e-257) {
		tmp = t_4;
	} else if (c <= 2.8e-61) {
		tmp = z * (x * y);
	} else if (c <= 1.25e+14) {
		tmp = t_4;
	} else if (c <= 3.4e+120) {
		tmp = t * (c * j);
	} else if (c <= 3.2e+238) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (z * -c)
	t_2 = x * (y * z)
	t_3 = j * (t * c)
	t_4 = a * (b * i)
	tmp = 0
	if c <= -1e+149:
		tmp = t_3
	elif c <= -1.45e+90:
		tmp = t_1
	elif c <= -4.4e+80:
		tmp = t_2
	elif c <= -1.65e+48:
		tmp = x * (t * -a)
	elif c <= -3.3e-118:
		tmp = t_2
	elif c <= 6.2e-257:
		tmp = t_4
	elif c <= 2.8e-61:
		tmp = z * (x * y)
	elif c <= 1.25e+14:
		tmp = t_4
	elif c <= 3.4e+120:
		tmp = t * (c * j)
	elif c <= 3.2e+238:
		tmp = 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(z * Float64(-c)))
	t_2 = Float64(x * Float64(y * z))
	t_3 = Float64(j * Float64(t * c))
	t_4 = Float64(a * Float64(b * i))
	tmp = 0.0
	if (c <= -1e+149)
		tmp = t_3;
	elseif (c <= -1.45e+90)
		tmp = t_1;
	elseif (c <= -4.4e+80)
		tmp = t_2;
	elseif (c <= -1.65e+48)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (c <= -3.3e-118)
		tmp = t_2;
	elseif (c <= 6.2e-257)
		tmp = t_4;
	elseif (c <= 2.8e-61)
		tmp = Float64(z * Float64(x * y));
	elseif (c <= 1.25e+14)
		tmp = t_4;
	elseif (c <= 3.4e+120)
		tmp = Float64(t * Float64(c * j));
	elseif (c <= 3.2e+238)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (z * -c);
	t_2 = x * (y * z);
	t_3 = j * (t * c);
	t_4 = a * (b * i);
	tmp = 0.0;
	if (c <= -1e+149)
		tmp = t_3;
	elseif (c <= -1.45e+90)
		tmp = t_1;
	elseif (c <= -4.4e+80)
		tmp = t_2;
	elseif (c <= -1.65e+48)
		tmp = x * (t * -a);
	elseif (c <= -3.3e-118)
		tmp = t_2;
	elseif (c <= 6.2e-257)
		tmp = t_4;
	elseif (c <= 2.8e-61)
		tmp = z * (x * y);
	elseif (c <= 1.25e+14)
		tmp = t_4;
	elseif (c <= 3.4e+120)
		tmp = t * (c * j);
	elseif (c <= 3.2e+238)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1e+149], t$95$3, If[LessEqual[c, -1.45e+90], t$95$1, If[LessEqual[c, -4.4e+80], t$95$2, If[LessEqual[c, -1.65e+48], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -3.3e-118], t$95$2, If[LessEqual[c, 6.2e-257], t$95$4, If[LessEqual[c, 2.8e-61], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.25e+14], t$95$4, If[LessEqual[c, 3.4e+120], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.2e+238], t$95$1, t$95$3]]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if c < -1.00000000000000005e149 or 3.19999999999999981e238 < c

   1. Initial program 54.2%

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

   3. Taylor expanded in j around inf 46.2%

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

      1. associate--l+ 46.2%

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

      2. sub-neg 46.2%

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

      3. mul-1-neg 46.2%

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

      4. +-commutative 46.2%

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

      5. +-commutative 46.2%

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

      6. associate--r+ 46.2%

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

   5. Simplified 50.4%

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

   6. Taylor expanded in i around inf 60.7%

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

      1. associate-*r* 60.7%

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

   8. Simplified 60.7%

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

   9. Taylor expanded in c around inf 57.1%

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

       1. associate-*r* 55.2%

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

       2. *-commutative 55.2%

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

       3. associate-*r* 61.0%

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

   11. Simplified 61.0%

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

   if -1.00000000000000005e149 < c < -1.4500000000000001e90 or 3.39999999999999999e120 < c < 3.19999999999999981e238

   1. Initial program 60.6%

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

   3. Taylor expanded in b around inf 64.1%

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

   4. Taylor expanded in a around 0 54.5%

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

      1. mul-1-neg 54.5%

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

      2. distribute-lft-neg-out 54.5%

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

      3. *-commutative 54.5%

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

   6. Simplified 54.5%

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

   if -1.4500000000000001e90 < c < -4.40000000000000005e80 or -1.65000000000000011e48 < c < -3.3e-118

   1. Initial program 79.1%

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

   3. Taylor expanded in x around inf 52.5%

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

      1. *-commutative 52.5%

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

   5. Simplified 52.5%

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

   6. Taylor expanded in z around inf 42.9%

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

   if -4.40000000000000005e80 < c < -1.65000000000000011e48

   1. Initial program 90.4%

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

   3. Taylor expanded in x around inf 56.4%

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

      1. *-commutative 56.4%

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

   5. Simplified 56.4%

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

   6. Taylor expanded in z around 0 45.9%

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

      1. neg-mul-1 45.9%

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

      2. distribute-lft-neg-in 45.9%

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

      3. *-commutative 45.9%

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

   8. Simplified 45.9%

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

   if -3.3e-118 < c < 6.20000000000000016e-257 or 2.8000000000000001e-61 < c < 1.25e14

   1. Initial program 84.9%

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

   3. Taylor expanded in b around inf 40.2%

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

   4. Taylor expanded in a around inf 35.0%

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

   if 6.20000000000000016e-257 < c < 2.8000000000000001e-61

   1. Initial program 78.1%

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

   3. Taylor expanded in j around inf 78.2%

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

      1. associate--l+ 78.2%

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

      2. sub-neg 78.2%

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

      3. mul-1-neg 78.2%

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

      4. +-commutative 78.2%

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

      5. +-commutative 78.2%

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

      6. associate--r+ 78.2%

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

   5. Simplified 78.2%

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

   6. Taylor expanded in z around inf 42.3%

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

      1. associate-*r* 42.2%

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

      2. *-commutative 42.2%

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

      3. div-sub 45.0%

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

      4. *-commutative 45.0%

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

   8. Simplified 45.0%

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

   9. Taylor expanded in x around inf 33.3%

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

       1. *-commutative 33.3%

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

       2. *-commutative 33.3%

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

       3. associate-*l* 37.3%

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

   11. Simplified 37.3%

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

   if 1.25e14 < c < 3.39999999999999999e120

   1. Initial program 85.3%

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

   3. Taylor expanded in t around inf 63.8%

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

      1. +-commutative 63.8%

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

      2. mul-1-neg 63.8%

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

      3. unsub-neg 63.8%

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

   5. Simplified 63.8%

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

   6. Taylor expanded in c around inf 42.1%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot j\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 45.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1 \cdot 10^{+149}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq -1.45 \cdot 10^{+90}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq -4.4 \cdot 10^{+80}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq -1.65 \cdot 10^{+48}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq -3.3 \cdot 10^{-118}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 6.2 \cdot 10^{-257}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq 2.8 \cdot 10^{-61}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{+14}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq 3.4 \cdot 10^{+120}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{+238}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 29.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(z \cdot \left(-c\right)\right)\\ t_2 := x \cdot \left(y \cdot z\right)\\ t_3 := j \cdot \left(t \cdot c\right)\\ t_4 := a \cdot \left(b \cdot i\right)\\ \mathbf{if}\;c \leq -2.8 \cdot 10^{+145}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq -8.2 \cdot 10^{+89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -2.8 \cdot 10^{+82}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -4.2 \cdot 10^{+47}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;c \leq -4 \cdot 10^{-118}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{-258}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;c \leq 4.7 \cdot 10^{-61}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 1.02 \cdot 10^{+24}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;c \leq 5.5 \cdot 10^{+158}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq 6.6 \cdot 10^{+238}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* z (- c))))
        (t_2 (* x (* y z)))
        (t_3 (* j (* t c)))
        (t_4 (* a (* b i))))
   (if (<= c -2.8e+145)
     t_3
     (if (<= c -8.2e+89)
       t_1
       (if (<= c -2.8e+82)
         t_2
         (if (<= c -4.2e+47)
           (* a (* t (- x)))
           (if (<= c -4e-118)
             t_2
             (if (<= c 1.25e-258)
               t_4
               (if (<= c 4.7e-61)
                 (* z (* x y))
                 (if (<= c 1.02e+24)
                   t_4
                   (if (<= c 5.5e+158)
                     (* t (* c j))
                     (if (<= c 6.6e+238) 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 * (z * -c);
	double t_2 = x * (y * z);
	double t_3 = j * (t * c);
	double t_4 = a * (b * i);
	double tmp;
	if (c <= -2.8e+145) {
		tmp = t_3;
	} else if (c <= -8.2e+89) {
		tmp = t_1;
	} else if (c <= -2.8e+82) {
		tmp = t_2;
	} else if (c <= -4.2e+47) {
		tmp = a * (t * -x);
	} else if (c <= -4e-118) {
		tmp = t_2;
	} else if (c <= 1.25e-258) {
		tmp = t_4;
	} else if (c <= 4.7e-61) {
		tmp = z * (x * y);
	} else if (c <= 1.02e+24) {
		tmp = t_4;
	} else if (c <= 5.5e+158) {
		tmp = t * (c * j);
	} else if (c <= 6.6e+238) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = b * (z * -c)
    t_2 = x * (y * z)
    t_3 = j * (t * c)
    t_4 = a * (b * i)
    if (c <= (-2.8d+145)) then
        tmp = t_3
    else if (c <= (-8.2d+89)) then
        tmp = t_1
    else if (c <= (-2.8d+82)) then
        tmp = t_2
    else if (c <= (-4.2d+47)) then
        tmp = a * (t * -x)
    else if (c <= (-4d-118)) then
        tmp = t_2
    else if (c <= 1.25d-258) then
        tmp = t_4
    else if (c <= 4.7d-61) then
        tmp = z * (x * y)
    else if (c <= 1.02d+24) then
        tmp = t_4
    else if (c <= 5.5d+158) then
        tmp = t * (c * j)
    else if (c <= 6.6d+238) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (z * -c);
	double t_2 = x * (y * z);
	double t_3 = j * (t * c);
	double t_4 = a * (b * i);
	double tmp;
	if (c <= -2.8e+145) {
		tmp = t_3;
	} else if (c <= -8.2e+89) {
		tmp = t_1;
	} else if (c <= -2.8e+82) {
		tmp = t_2;
	} else if (c <= -4.2e+47) {
		tmp = a * (t * -x);
	} else if (c <= -4e-118) {
		tmp = t_2;
	} else if (c <= 1.25e-258) {
		tmp = t_4;
	} else if (c <= 4.7e-61) {
		tmp = z * (x * y);
	} else if (c <= 1.02e+24) {
		tmp = t_4;
	} else if (c <= 5.5e+158) {
		tmp = t * (c * j);
	} else if (c <= 6.6e+238) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (z * -c)
	t_2 = x * (y * z)
	t_3 = j * (t * c)
	t_4 = a * (b * i)
	tmp = 0
	if c <= -2.8e+145:
		tmp = t_3
	elif c <= -8.2e+89:
		tmp = t_1
	elif c <= -2.8e+82:
		tmp = t_2
	elif c <= -4.2e+47:
		tmp = a * (t * -x)
	elif c <= -4e-118:
		tmp = t_2
	elif c <= 1.25e-258:
		tmp = t_4
	elif c <= 4.7e-61:
		tmp = z * (x * y)
	elif c <= 1.02e+24:
		tmp = t_4
	elif c <= 5.5e+158:
		tmp = t * (c * j)
	elif c <= 6.6e+238:
		tmp = 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(z * Float64(-c)))
	t_2 = Float64(x * Float64(y * z))
	t_3 = Float64(j * Float64(t * c))
	t_4 = Float64(a * Float64(b * i))
	tmp = 0.0
	if (c <= -2.8e+145)
		tmp = t_3;
	elseif (c <= -8.2e+89)
		tmp = t_1;
	elseif (c <= -2.8e+82)
		tmp = t_2;
	elseif (c <= -4.2e+47)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (c <= -4e-118)
		tmp = t_2;
	elseif (c <= 1.25e-258)
		tmp = t_4;
	elseif (c <= 4.7e-61)
		tmp = Float64(z * Float64(x * y));
	elseif (c <= 1.02e+24)
		tmp = t_4;
	elseif (c <= 5.5e+158)
		tmp = Float64(t * Float64(c * j));
	elseif (c <= 6.6e+238)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (z * -c);
	t_2 = x * (y * z);
	t_3 = j * (t * c);
	t_4 = a * (b * i);
	tmp = 0.0;
	if (c <= -2.8e+145)
		tmp = t_3;
	elseif (c <= -8.2e+89)
		tmp = t_1;
	elseif (c <= -2.8e+82)
		tmp = t_2;
	elseif (c <= -4.2e+47)
		tmp = a * (t * -x);
	elseif (c <= -4e-118)
		tmp = t_2;
	elseif (c <= 1.25e-258)
		tmp = t_4;
	elseif (c <= 4.7e-61)
		tmp = z * (x * y);
	elseif (c <= 1.02e+24)
		tmp = t_4;
	elseif (c <= 5.5e+158)
		tmp = t * (c * j);
	elseif (c <= 6.6e+238)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.8e+145], t$95$3, If[LessEqual[c, -8.2e+89], t$95$1, If[LessEqual[c, -2.8e+82], t$95$2, If[LessEqual[c, -4.2e+47], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -4e-118], t$95$2, If[LessEqual[c, 1.25e-258], t$95$4, If[LessEqual[c, 4.7e-61], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.02e+24], t$95$4, If[LessEqual[c, 5.5e+158], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.6e+238], t$95$1, t$95$3]]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if c < -2.7999999999999999e145 or 6.6000000000000001e238 < c

   1. Initial program 54.2%

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

   3. Taylor expanded in j around inf 46.2%

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

      1. associate--l+ 46.2%

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

      2. sub-neg 46.2%

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

      3. mul-1-neg 46.2%

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

      4. +-commutative 46.2%

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

      5. +-commutative 46.2%

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

      6. associate--r+ 46.2%

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

   5. Simplified 50.4%

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

   6. Taylor expanded in i around inf 60.7%

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

      1. associate-*r* 60.7%

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

   8. Simplified 60.7%

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

   9. Taylor expanded in c around inf 57.1%

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

       1. associate-*r* 55.2%

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

       2. *-commutative 55.2%

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

       3. associate-*r* 61.0%

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

   11. Simplified 61.0%

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

   if -2.7999999999999999e145 < c < -8.1999999999999997e89 or 5.4999999999999998e158 < c < 6.6000000000000001e238

   1. Initial program 53.5%

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

   3. Taylor expanded in b around inf 68.3%

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

   4. Taylor expanded in a around 0 56.9%

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

      1. mul-1-neg 56.9%

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

      2. distribute-lft-neg-out 56.9%

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

      3. *-commutative 56.9%

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

   6. Simplified 56.9%

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

   if -8.1999999999999997e89 < c < -2.8e82 or -4.2e47 < c < -3.99999999999999994e-118

   1. Initial program 79.1%

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

   3. Taylor expanded in x around inf 52.5%

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

      1. *-commutative 52.5%

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

   5. Simplified 52.5%

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

   6. Taylor expanded in z around inf 42.9%

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

   if -2.8e82 < c < -4.2e47

   1. Initial program 90.4%

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

   3. Taylor expanded in a around inf 67.5%

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

      1. distribute-lft-out-- 67.5%

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

   5. Simplified 67.5%

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

   6. Taylor expanded in t around inf 45.8%

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

      1. mul-1-neg 45.8%

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

      2. distribute-rgt-neg-in 45.8%

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

      3. distribute-rgt-neg-in 45.8%

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

   8. Simplified 45.8%

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

   if -3.99999999999999994e-118 < c < 1.25e-258 or 4.6999999999999997e-61 < c < 1.02000000000000004e24

   1. Initial program 84.9%

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

   3. Taylor expanded in b around inf 40.2%

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

   4. Taylor expanded in a around inf 35.0%

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

   if 1.25e-258 < c < 4.6999999999999997e-61

   1. Initial program 78.1%

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

   3. Taylor expanded in j around inf 78.2%

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

      1. associate--l+ 78.2%

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

      2. sub-neg 78.2%

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

      3. mul-1-neg 78.2%

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

      4. +-commutative 78.2%

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

      5. +-commutative 78.2%

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

      6. associate--r+ 78.2%

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

   5. Simplified 78.2%

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

   6. Taylor expanded in z around inf 42.3%

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

      1. associate-*r* 42.2%

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

      2. *-commutative 42.2%

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

      3. div-sub 45.0%

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

      4. *-commutative 45.0%

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

   8. Simplified 45.0%

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

   9. Taylor expanded in x around inf 33.3%

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

       1. *-commutative 33.3%

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

       2. *-commutative 33.3%

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

       3. associate-*l* 37.3%

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

   11. Simplified 37.3%

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

   if 1.02000000000000004e24 < c < 5.4999999999999998e158

   1. Initial program 87.6%

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

   3. Taylor expanded in t around inf 63.2%

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

      1. +-commutative 63.2%

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

      2. mul-1-neg 63.2%

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

      3. unsub-neg 63.2%

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

   5. Simplified 63.2%

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

   6. Taylor expanded in c around inf 44.9%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot j\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.8 \cdot 10^{+145}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq -8.2 \cdot 10^{+89}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq -2.8 \cdot 10^{+82}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq -4.2 \cdot 10^{+47}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;c \leq -4 \cdot 10^{-118}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{-258}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq 4.7 \cdot 10^{-61}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 1.02 \cdot 10^{+24}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq 5.5 \cdot 10^{+158}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq 6.6 \cdot 10^{+238}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 28.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b\right)\\ t_2 := x \cdot \left(y \cdot z\right)\\ t_3 := a \cdot \left(t \cdot \left(-x\right)\right)\\ t_4 := a \cdot \left(b \cdot i\right)\\ \mathbf{if}\;c \leq -6.2 \cdot 10^{+147}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq -5 \cdot 10^{+71}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq -2.95 \cdot 10^{+38}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq -2.9 \cdot 10^{+20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -3.2 \cdot 10^{-118}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -3.8 \cdot 10^{-158}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;c \leq -1.35 \cdot 10^{-174}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq 9 \cdot 10^{-254}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{-196}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 1.14 \cdot 10^{+21}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* a b)))
        (t_2 (* x (* y z)))
        (t_3 (* a (* t (- x))))
        (t_4 (* a (* b i))))
   (if (<= c -6.2e+147)
     (* j (* t c))
     (if (<= c -5e+71)
       (* z (* x y))
       (if (<= c -2.95e+38)
         t_3
         (if (<= c -2.9e+20)
           t_1
           (if (<= c -3.2e-118)
             t_2
             (if (<= c -3.8e-158)
               t_4
               (if (<= c -1.35e-174)
                 t_3
                 (if (<= c 9e-254)
                   t_1
                   (if (<= c 9.5e-196)
                     t_2
                     (if (<= c 1.14e+21) t_4 (* t (* c j))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (a * b);
	double t_2 = x * (y * z);
	double t_3 = a * (t * -x);
	double t_4 = a * (b * i);
	double tmp;
	if (c <= -6.2e+147) {
		tmp = j * (t * c);
	} else if (c <= -5e+71) {
		tmp = z * (x * y);
	} else if (c <= -2.95e+38) {
		tmp = t_3;
	} else if (c <= -2.9e+20) {
		tmp = t_1;
	} else if (c <= -3.2e-118) {
		tmp = t_2;
	} else if (c <= -3.8e-158) {
		tmp = t_4;
	} else if (c <= -1.35e-174) {
		tmp = t_3;
	} else if (c <= 9e-254) {
		tmp = t_1;
	} else if (c <= 9.5e-196) {
		tmp = t_2;
	} else if (c <= 1.14e+21) {
		tmp = t_4;
	} else {
		tmp = t * (c * 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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = i * (a * b)
    t_2 = x * (y * z)
    t_3 = a * (t * -x)
    t_4 = a * (b * i)
    if (c <= (-6.2d+147)) then
        tmp = j * (t * c)
    else if (c <= (-5d+71)) then
        tmp = z * (x * y)
    else if (c <= (-2.95d+38)) then
        tmp = t_3
    else if (c <= (-2.9d+20)) then
        tmp = t_1
    else if (c <= (-3.2d-118)) then
        tmp = t_2
    else if (c <= (-3.8d-158)) then
        tmp = t_4
    else if (c <= (-1.35d-174)) then
        tmp = t_3
    else if (c <= 9d-254) then
        tmp = t_1
    else if (c <= 9.5d-196) then
        tmp = t_2
    else if (c <= 1.14d+21) then
        tmp = t_4
    else
        tmp = t * (c * 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 t_1 = i * (a * b);
	double t_2 = x * (y * z);
	double t_3 = a * (t * -x);
	double t_4 = a * (b * i);
	double tmp;
	if (c <= -6.2e+147) {
		tmp = j * (t * c);
	} else if (c <= -5e+71) {
		tmp = z * (x * y);
	} else if (c <= -2.95e+38) {
		tmp = t_3;
	} else if (c <= -2.9e+20) {
		tmp = t_1;
	} else if (c <= -3.2e-118) {
		tmp = t_2;
	} else if (c <= -3.8e-158) {
		tmp = t_4;
	} else if (c <= -1.35e-174) {
		tmp = t_3;
	} else if (c <= 9e-254) {
		tmp = t_1;
	} else if (c <= 9.5e-196) {
		tmp = t_2;
	} else if (c <= 1.14e+21) {
		tmp = t_4;
	} else {
		tmp = t * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (a * b)
	t_2 = x * (y * z)
	t_3 = a * (t * -x)
	t_4 = a * (b * i)
	tmp = 0
	if c <= -6.2e+147:
		tmp = j * (t * c)
	elif c <= -5e+71:
		tmp = z * (x * y)
	elif c <= -2.95e+38:
		tmp = t_3
	elif c <= -2.9e+20:
		tmp = t_1
	elif c <= -3.2e-118:
		tmp = t_2
	elif c <= -3.8e-158:
		tmp = t_4
	elif c <= -1.35e-174:
		tmp = t_3
	elif c <= 9e-254:
		tmp = t_1
	elif c <= 9.5e-196:
		tmp = t_2
	elif c <= 1.14e+21:
		tmp = t_4
	else:
		tmp = t * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(a * b))
	t_2 = Float64(x * Float64(y * z))
	t_3 = Float64(a * Float64(t * Float64(-x)))
	t_4 = Float64(a * Float64(b * i))
	tmp = 0.0
	if (c <= -6.2e+147)
		tmp = Float64(j * Float64(t * c));
	elseif (c <= -5e+71)
		tmp = Float64(z * Float64(x * y));
	elseif (c <= -2.95e+38)
		tmp = t_3;
	elseif (c <= -2.9e+20)
		tmp = t_1;
	elseif (c <= -3.2e-118)
		tmp = t_2;
	elseif (c <= -3.8e-158)
		tmp = t_4;
	elseif (c <= -1.35e-174)
		tmp = t_3;
	elseif (c <= 9e-254)
		tmp = t_1;
	elseif (c <= 9.5e-196)
		tmp = t_2;
	elseif (c <= 1.14e+21)
		tmp = t_4;
	else
		tmp = Float64(t * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * (a * b);
	t_2 = x * (y * z);
	t_3 = a * (t * -x);
	t_4 = a * (b * i);
	tmp = 0.0;
	if (c <= -6.2e+147)
		tmp = j * (t * c);
	elseif (c <= -5e+71)
		tmp = z * (x * y);
	elseif (c <= -2.95e+38)
		tmp = t_3;
	elseif (c <= -2.9e+20)
		tmp = t_1;
	elseif (c <= -3.2e-118)
		tmp = t_2;
	elseif (c <= -3.8e-158)
		tmp = t_4;
	elseif (c <= -1.35e-174)
		tmp = t_3;
	elseif (c <= 9e-254)
		tmp = t_1;
	elseif (c <= 9.5e-196)
		tmp = t_2;
	elseif (c <= 1.14e+21)
		tmp = t_4;
	else
		tmp = t * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -6.2e+147], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -5e+71], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.95e+38], t$95$3, If[LessEqual[c, -2.9e+20], t$95$1, If[LessEqual[c, -3.2e-118], t$95$2, If[LessEqual[c, -3.8e-158], t$95$4, If[LessEqual[c, -1.35e-174], t$95$3, If[LessEqual[c, 9e-254], t$95$1, If[LessEqual[c, 9.5e-196], t$95$2, If[LessEqual[c, 1.14e+21], t$95$4, N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if c < -6.2000000000000001e147

   1. Initial program 54.5%

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

   3. Taylor expanded in j around inf 45.8%

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

      1. associate--l+ 45.8%

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

      2. sub-neg 45.8%

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

      3. mul-1-neg 45.8%

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

      4. +-commutative 45.8%

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

      5. +-commutative 45.8%

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

      6. associate--r+ 45.8%

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

   5. Simplified 48.9%

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

   6. Taylor expanded in i around inf 60.8%

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

      1. associate-*r* 63.9%

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

   8. Simplified 63.9%

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

   9. Taylor expanded in c around inf 52.3%

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

       1. associate-*r* 49.4%

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

       2. *-commutative 49.4%

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

       3. associate-*r* 55.1%

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

   11. Simplified 55.1%

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

   if -6.2000000000000001e147 < c < -4.99999999999999972e71

   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 51.0%

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

      1. associate--l+ 51.0%

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

      2. sub-neg 51.0%

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

      3. mul-1-neg 51.0%

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

      4. +-commutative 51.0%

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

      5. +-commutative 51.0%

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

      6. associate--r+ 51.0%

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

   5. Simplified 56.0%

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

   6. Taylor expanded in z around inf 36.4%

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

      1. associate-*r* 36.2%

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

      2. *-commutative 36.2%

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

      3. div-sub 41.2%

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

      4. *-commutative 41.2%

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

   8. Simplified 41.2%

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

   9. Taylor expanded in x around inf 41.0%

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

       1. *-commutative 41.0%

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

       2. *-commutative 41.0%

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

       3. associate-*l* 41.1%

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

   11. Simplified 41.1%

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

   if -4.99999999999999972e71 < c < -2.94999999999999991e38 or -3.7999999999999999e-158 < c < -1.34999999999999994e-174

   1. Initial program 92.7%

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

   3. Taylor expanded in a around inf 57.6%

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

      1. distribute-lft-out-- 57.6%

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

   5. Simplified 57.6%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x - b \cdot i\right)\right)} \]

   6. Taylor expanded in t around inf 49.6%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 49.6%

         \[\leadsto \color{blue}{-a \cdot \left(t \cdot x\right)} \]

      2. distribute-rgt-neg-in 49.6%

         \[\leadsto \color{blue}{a \cdot \left(-t \cdot x\right)} \]

      3. distribute-rgt-neg-in 49.6%

         \[\leadsto a \cdot \color{blue}{\left(t \cdot \left(-x\right)\right)} \]

   8. Simplified 49.6%

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \left(-x\right)\right)} \]

   if -2.94999999999999991e38 < c < -2.9e20 or -1.34999999999999994e-174 < c < 9e-254

   1. Initial program 89.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 34.0%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]

   4. Taylor expanded in a around inf 33.7%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 33.7%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot i} \]

   6. Simplified 33.7%

      \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot i} \]

   if -2.9e20 < c < -3.20000000000000004e-118 or 9e-254 < c < 9.50000000000000032e-196

   1. Initial program 71.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 51.0%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   4. Step-by-step derivation

      1. *-commutative 51.0%

         \[\leadsto x \cdot \left(\color{blue}{z \cdot y} - a \cdot t\right) \]

   5. Simplified 51.0%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y - a \cdot t\right)} \]

   6. Taylor expanded in z around inf 43.9%

      \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]

   if -3.20000000000000004e-118 < c < -3.7999999999999999e-158 or 9.50000000000000032e-196 < c < 1.14e21

   1. Initial program 82.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 47.1%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]

   4. Taylor expanded in a around inf 41.4%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

   if 1.14e21 < c

   1. Initial program 70.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 63.2%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 63.2%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 63.2%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 63.2%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   5. Simplified 63.2%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   6. Taylor expanded in c around inf 48.7%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot j\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.2 \cdot 10^{+147}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq -5 \cdot 10^{+71}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq -2.95 \cdot 10^{+38}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;c \leq -2.9 \cdot 10^{+20}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;c \leq -3.2 \cdot 10^{-118}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq -3.8 \cdot 10^{-158}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq -1.35 \cdot 10^{-174}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;c \leq 9 \cdot 10^{-254}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{-196}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 1.14 \cdot 10^{+21}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 50.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{-36}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-84}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-117}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-164}:\\ \;\;\;\;b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-259}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;y \leq 10^{-192}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{+31}:\\ \;\;\;\;i \cdot \left(y \cdot \left(b \cdot \frac{a}{y} - j\right)\right)\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+43}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a)))) (t_2 (* y (- (* x z) (* i j)))))
   (if (<= y -2.4e-36)
     t_2
     (if (<= y -1.45e-84)
       (* a (- (* b i) (* x t)))
       (if (<= y -7.5e-117)
         t_1
         (if (<= y -1.9e-164)
           (* b (* z (- (* a (/ i z)) c)))
           (if (<= y 7.2e-259)
             (+ (* c (* t j)) (* a (* b i)))
             (if (<= y 1e-192)
               (* z (- (* x y) (* b c)))
               (if (<= y 5.8e-90)
                 t_1
                 (if (<= y 2.75e+31)
                   (* i (* y (- (* b (/ a y)) j)))
                   (if (<= y 9.2e+43) (* b (* z (- c))) t_2)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -2.4e-36) {
		tmp = t_2;
	} else if (y <= -1.45e-84) {
		tmp = a * ((b * i) - (x * t));
	} else if (y <= -7.5e-117) {
		tmp = t_1;
	} else if (y <= -1.9e-164) {
		tmp = b * (z * ((a * (i / z)) - c));
	} else if (y <= 7.2e-259) {
		tmp = (c * (t * j)) + (a * (b * i));
	} else if (y <= 1e-192) {
		tmp = z * ((x * y) - (b * c));
	} else if (y <= 5.8e-90) {
		tmp = t_1;
	} else if (y <= 2.75e+31) {
		tmp = i * (y * ((b * (a / y)) - j));
	} else if (y <= 9.2e+43) {
		tmp = b * (z * -c);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((c * j) - (x * a))
    t_2 = y * ((x * z) - (i * j))
    if (y <= (-2.4d-36)) then
        tmp = t_2
    else if (y <= (-1.45d-84)) then
        tmp = a * ((b * i) - (x * t))
    else if (y <= (-7.5d-117)) then
        tmp = t_1
    else if (y <= (-1.9d-164)) then
        tmp = b * (z * ((a * (i / z)) - c))
    else if (y <= 7.2d-259) then
        tmp = (c * (t * j)) + (a * (b * i))
    else if (y <= 1d-192) then
        tmp = z * ((x * y) - (b * c))
    else if (y <= 5.8d-90) then
        tmp = t_1
    else if (y <= 2.75d+31) then
        tmp = i * (y * ((b * (a / y)) - j))
    else if (y <= 9.2d+43) then
        tmp = b * (z * -c)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -2.4e-36) {
		tmp = t_2;
	} else if (y <= -1.45e-84) {
		tmp = a * ((b * i) - (x * t));
	} else if (y <= -7.5e-117) {
		tmp = t_1;
	} else if (y <= -1.9e-164) {
		tmp = b * (z * ((a * (i / z)) - c));
	} else if (y <= 7.2e-259) {
		tmp = (c * (t * j)) + (a * (b * i));
	} else if (y <= 1e-192) {
		tmp = z * ((x * y) - (b * c));
	} else if (y <= 5.8e-90) {
		tmp = t_1;
	} else if (y <= 2.75e+31) {
		tmp = i * (y * ((b * (a / y)) - j));
	} else if (y <= 9.2e+43) {
		tmp = b * (z * -c);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	t_2 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -2.4e-36:
		tmp = t_2
	elif y <= -1.45e-84:
		tmp = a * ((b * i) - (x * t))
	elif y <= -7.5e-117:
		tmp = t_1
	elif y <= -1.9e-164:
		tmp = b * (z * ((a * (i / z)) - c))
	elif y <= 7.2e-259:
		tmp = (c * (t * j)) + (a * (b * i))
	elif y <= 1e-192:
		tmp = z * ((x * y) - (b * c))
	elif y <= 5.8e-90:
		tmp = t_1
	elif y <= 2.75e+31:
		tmp = i * (y * ((b * (a / y)) - j))
	elif y <= 9.2e+43:
		tmp = b * (z * -c)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -2.4e-36)
		tmp = t_2;
	elseif (y <= -1.45e-84)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (y <= -7.5e-117)
		tmp = t_1;
	elseif (y <= -1.9e-164)
		tmp = Float64(b * Float64(z * Float64(Float64(a * Float64(i / z)) - c)));
	elseif (y <= 7.2e-259)
		tmp = Float64(Float64(c * Float64(t * j)) + Float64(a * Float64(b * i)));
	elseif (y <= 1e-192)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (y <= 5.8e-90)
		tmp = t_1;
	elseif (y <= 2.75e+31)
		tmp = Float64(i * Float64(y * Float64(Float64(b * Float64(a / y)) - j)));
	elseif (y <= 9.2e+43)
		tmp = Float64(b * Float64(z * Float64(-c)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((c * j) - (x * a));
	t_2 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -2.4e-36)
		tmp = t_2;
	elseif (y <= -1.45e-84)
		tmp = a * ((b * i) - (x * t));
	elseif (y <= -7.5e-117)
		tmp = t_1;
	elseif (y <= -1.9e-164)
		tmp = b * (z * ((a * (i / z)) - c));
	elseif (y <= 7.2e-259)
		tmp = (c * (t * j)) + (a * (b * i));
	elseif (y <= 1e-192)
		tmp = z * ((x * y) - (b * c));
	elseif (y <= 5.8e-90)
		tmp = t_1;
	elseif (y <= 2.75e+31)
		tmp = i * (y * ((b * (a / y)) - j));
	elseif (y <= 9.2e+43)
		tmp = b * (z * -c);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.4e-36], t$95$2, If[LessEqual[y, -1.45e-84], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.5e-117], t$95$1, If[LessEqual[y, -1.9e-164], N[(b * N[(z * N[(N[(a * N[(i / z), $MachinePrecision]), $MachinePrecision] - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.2e-259], N[(N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision] + N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e-192], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.8e-90], t$95$1, If[LessEqual[y, 2.75e+31], N[(i * N[(y * N[(N[(b * N[(a / y), $MachinePrecision]), $MachinePrecision] - j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.2e+43], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y < -2.4e-36 or 9.200000000000001e43 < y

   1. Initial program 64.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 68.0%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 68.0%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 68.0%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 68.0%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 68.0%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   5. Simplified 68.0%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   if -2.4e-36 < y < -1.4500000000000001e-84

   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 a around inf 70.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 70.2%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x - b \cdot i\right)\right)} \]

   5. Simplified 70.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x - b \cdot i\right)\right)} \]

   6. Taylor expanded in t around 0 70.2%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(b \cdot i\right)} \]
   7. Step-by-step derivation

      1. +-commutative 70.2%

         \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 70.2%

         \[\leadsto a \cdot \left(b \cdot i\right) + \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} \]

      3. distribute-rgt-neg-in 70.2%

         \[\leadsto a \cdot \left(b \cdot i\right) + \color{blue}{a \cdot \left(-t \cdot x\right)} \]

      4. distribute-lft-out 70.2%

         \[\leadsto \color{blue}{a \cdot \left(b \cdot i + \left(-t \cdot x\right)\right)} \]

      5. unsub-neg 70.2%

         \[\leadsto a \cdot \color{blue}{\left(b \cdot i - t \cdot x\right)} \]

   8. Simplified 70.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   if -1.4500000000000001e-84 < y < -7.50000000000000066e-117 or 1.0000000000000001e-192 < y < 5.79999999999999967e-90

   1. Initial program 93.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 58.9%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 58.9%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 58.9%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 58.9%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   5. Simplified 58.9%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   if -7.50000000000000066e-117 < y < -1.89999999999999995e-164

   1. Initial program 85.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 51.0%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]

   4. Taylor expanded in z around inf 58.7%

      \[\leadsto b \cdot \color{blue}{\left(z \cdot \left(\frac{a \cdot i}{z} - c\right)\right)} \]
   5. Step-by-step derivation

      1. associate-/l* 66.3%

         \[\leadsto b \cdot \left(z \cdot \left(\color{blue}{a \cdot \frac{i}{z}} - c\right)\right) \]

   6. Simplified 66.3%

      \[\leadsto b \cdot \color{blue}{\left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)} \]

   if -1.89999999999999995e-164 < y < 7.1999999999999996e-259

   1. Initial program 80.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 75.2%

      \[\leadsto \color{blue}{j \cdot \left(\left(c \cdot t + \frac{x \cdot \left(y \cdot z - a \cdot t\right)}{j}\right) - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 75.2%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t + \left(\frac{x \cdot \left(y \cdot z - a \cdot t\right)}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right)} \]

      2. sub-neg 75.2%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \color{blue}{\left(y \cdot z + \left(-a \cdot t\right)\right)}}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right) \]

      3. mul-1-neg 75.2%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \left(y \cdot z + \color{blue}{-1 \cdot \left(a \cdot t\right)}\right)}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right) \]

      4. +-commutative 75.2%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \color{blue}{\left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)}}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right) \]

      5. +-commutative 75.2%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)}{j} - \color{blue}{\left(\frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j} + i \cdot y\right)}\right)\right) \]

      6. associate--r+ 75.2%

         \[\leadsto j \cdot \left(c \cdot t + \color{blue}{\left(\left(\frac{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)}{j} - \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right) - i \cdot y\right)}\right) \]

   5. Simplified 75.3%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t + \left(\frac{x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(c \cdot z - a \cdot i\right)}{j} - i \cdot y\right)\right)} \]

   6. Taylor expanded in i around inf 53.8%

      \[\leadsto j \cdot \left(c \cdot t + \left(\color{blue}{\frac{a \cdot \left(b \cdot i\right)}{j}} - i \cdot y\right)\right) \]
   7. Step-by-step derivation

      1. associate-*r* 51.4%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{\color{blue}{\left(a \cdot b\right) \cdot i}}{j} - i \cdot y\right)\right) \]

   8. Simplified 51.4%

      \[\leadsto j \cdot \left(c \cdot t + \left(\color{blue}{\frac{\left(a \cdot b\right) \cdot i}{j}} - i \cdot y\right)\right) \]

   9. Taylor expanded in a around 0 53.8%

      \[\leadsto j \cdot \left(c \cdot t + \color{blue}{\left(\frac{a \cdot \left(b \cdot i\right)}{j} - i \cdot y\right)}\right) \]
   10. Step-by-step derivation

       1. sub-neg 53.8%

          \[\leadsto j \cdot \left(c \cdot t + \color{blue}{\left(\frac{a \cdot \left(b \cdot i\right)}{j} + \left(-i \cdot y\right)\right)}\right) \]

       2. *-commutative 53.8%

          \[\leadsto j \cdot \left(c \cdot t + \left(\frac{a \cdot \color{blue}{\left(i \cdot b\right)}}{j} + \left(-i \cdot y\right)\right)\right) \]

       3. associate-*r* 51.5%

          \[\leadsto j \cdot \left(c \cdot t + \left(\frac{\color{blue}{\left(a \cdot i\right) \cdot b}}{j} + \left(-i \cdot y\right)\right)\right) \]

       4. *-commutative 51.5%

          \[\leadsto j \cdot \left(c \cdot t + \left(\frac{\color{blue}{\left(i \cdot a\right)} \cdot b}{j} + \left(-i \cdot y\right)\right)\right) \]

       5. associate-*r* 51.4%

          \[\leadsto j \cdot \left(c \cdot t + \left(\frac{\color{blue}{i \cdot \left(a \cdot b\right)}}{j} + \left(-i \cdot y\right)\right)\right) \]

       6. associate-*r/ 51.3%

          \[\leadsto j \cdot \left(c \cdot t + \left(\color{blue}{i \cdot \frac{a \cdot b}{j}} + \left(-i \cdot y\right)\right)\right) \]

       7. distribute-rgt-neg-in 51.3%

          \[\leadsto j \cdot \left(c \cdot t + \left(i \cdot \frac{a \cdot b}{j} + \color{blue}{i \cdot \left(-y\right)}\right)\right) \]

       8. distribute-lft-in 51.3%

          \[\leadsto j \cdot \left(c \cdot t + \color{blue}{i \cdot \left(\frac{a \cdot b}{j} + \left(-y\right)\right)}\right) \]

       9. sub-neg 51.3%

          \[\leadsto j \cdot \left(c \cdot t + i \cdot \color{blue}{\left(\frac{a \cdot b}{j} - y\right)}\right) \]

       10. associate-/l* 46.4%

           \[\leadsto j \cdot \left(c \cdot t + i \cdot \left(\color{blue}{a \cdot \frac{b}{j}} - y\right)\right) \]

   11. Simplified 46.4%

       \[\leadsto j \cdot \left(c \cdot t + \color{blue}{i \cdot \left(a \cdot \frac{b}{j} - y\right)}\right) \]

   12. Taylor expanded in a around inf 53.8%

       \[\leadsto j \cdot \left(c \cdot t + \color{blue}{\frac{a \cdot \left(b \cdot i\right)}{j}}\right) \]
   13. Step-by-step derivation

       1. associate-/l* 51.4%

          \[\leadsto j \cdot \left(c \cdot t + \color{blue}{a \cdot \frac{b \cdot i}{j}}\right) \]

       2. *-commutative 51.4%

          \[\leadsto j \cdot \left(c \cdot t + a \cdot \frac{\color{blue}{i \cdot b}}{j}\right) \]

       3. associate-/l* 46.6%

          \[\leadsto j \cdot \left(c \cdot t + a \cdot \color{blue}{\left(i \cdot \frac{b}{j}\right)}\right) \]

   14. Simplified 46.6%

       \[\leadsto j \cdot \left(c \cdot t + \color{blue}{a \cdot \left(i \cdot \frac{b}{j}\right)}\right) \]

   15. Taylor expanded in j around 0 63.4%

       \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right) + c \cdot \left(j \cdot t\right)} \]

   if 7.1999999999999996e-259 < y < 1.0000000000000001e-192

   1. Initial program 85.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 83.5%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 83.5%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

   5. Simplified 83.5%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - b \cdot c\right)} \]

   if 5.79999999999999967e-90 < y < 2.75000000000000001e31

   1. Initial program 72.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 57.2%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 57.2%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. *-commutative 57.2%

         \[\leadsto i \cdot \left(-1 \cdot \left(j \cdot y - \color{blue}{b \cdot a}\right)\right) \]

   5. Simplified 57.2%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - b \cdot a\right)\right)} \]

   6. Taylor expanded in b around inf 52.9%

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \frac{i \cdot \left(j \cdot y\right)}{b} + a \cdot i\right)} \]
   7. Step-by-step derivation

      1. +-commutative 52.9%

         \[\leadsto b \cdot \color{blue}{\left(a \cdot i + -1 \cdot \frac{i \cdot \left(j \cdot y\right)}{b}\right)} \]

      2. *-commutative 52.9%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} + -1 \cdot \frac{i \cdot \left(j \cdot y\right)}{b}\right) \]

      3. mul-1-neg 52.9%

         \[\leadsto b \cdot \left(i \cdot a + \color{blue}{\left(-\frac{i \cdot \left(j \cdot y\right)}{b}\right)}\right) \]

      4. unsub-neg 52.9%

         \[\leadsto b \cdot \color{blue}{\left(i \cdot a - \frac{i \cdot \left(j \cdot y\right)}{b}\right)} \]

      5. *-commutative 52.9%

         \[\leadsto b \cdot \left(\color{blue}{a \cdot i} - \frac{i \cdot \left(j \cdot y\right)}{b}\right) \]

      6. associate-/l* 56.9%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{i \cdot \frac{j \cdot y}{b}}\right) \]

      7. *-commutative 56.9%

         \[\leadsto b \cdot \left(a \cdot i - i \cdot \frac{\color{blue}{y \cdot j}}{b}\right) \]

   8. Simplified 56.9%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - i \cdot \frac{y \cdot j}{b}\right)} \]

   9. Taylor expanded in b around inf 52.9%

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \frac{i \cdot \left(j \cdot y\right)}{b} + a \cdot i\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 52.9%

          \[\leadsto b \cdot \left(\color{blue}{\left(-\frac{i \cdot \left(j \cdot y\right)}{b}\right)} + a \cdot i\right) \]

       2. distribute-frac-neg 52.9%

          \[\leadsto b \cdot \left(\color{blue}{\frac{-i \cdot \left(j \cdot y\right)}{b}} + a \cdot i\right) \]

       3. distribute-lft-neg-in 52.9%

          \[\leadsto b \cdot \left(\frac{\color{blue}{\left(-i\right) \cdot \left(j \cdot y\right)}}{b} + a \cdot i\right) \]

       4. associate-*r/ 56.9%

          \[\leadsto b \cdot \left(\color{blue}{\left(-i\right) \cdot \frac{j \cdot y}{b}} + a \cdot i\right) \]

       5. *-commutative 56.9%

          \[\leadsto b \cdot \left(\left(-i\right) \cdot \frac{\color{blue}{y \cdot j}}{b} + a \cdot i\right) \]

       6. associate-*r/ 56.9%

          \[\leadsto b \cdot \left(\left(-i\right) \cdot \color{blue}{\left(y \cdot \frac{j}{b}\right)} + a \cdot i\right) \]

       7. distribute-lft-neg-in 56.9%

          \[\leadsto b \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot \frac{j}{b}\right)\right)} + a \cdot i\right) \]

       8. +-commutative 56.9%

          \[\leadsto b \cdot \color{blue}{\left(a \cdot i + \left(-i \cdot \left(y \cdot \frac{j}{b}\right)\right)\right)} \]

       9. distribute-lft-in 52.9%

          \[\leadsto \color{blue}{b \cdot \left(a \cdot i\right) + b \cdot \left(-i \cdot \left(y \cdot \frac{j}{b}\right)\right)} \]

       10. *-commutative 52.9%

           \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} + b \cdot \left(-i \cdot \left(y \cdot \frac{j}{b}\right)\right) \]

       11. associate-*r* 53.1%

           \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot a} + b \cdot \left(-i \cdot \left(y \cdot \frac{j}{b}\right)\right) \]

       12. distribute-rgt-neg-in 53.1%

           \[\leadsto \left(b \cdot i\right) \cdot a + b \cdot \color{blue}{\left(i \cdot \left(-y \cdot \frac{j}{b}\right)\right)} \]

       13. associate-*r* 49.1%

           \[\leadsto \left(b \cdot i\right) \cdot a + \color{blue}{\left(b \cdot i\right) \cdot \left(-y \cdot \frac{j}{b}\right)} \]

       14. distribute-lft-in 57.1%

           \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot \left(a + \left(-y \cdot \frac{j}{b}\right)\right)} \]

       15. associate-*r/ 57.2%

           \[\leadsto \left(b \cdot i\right) \cdot \left(a + \left(-\color{blue}{\frac{y \cdot j}{b}}\right)\right) \]

       16. *-commutative 57.2%

           \[\leadsto \left(b \cdot i\right) \cdot \left(a + \left(-\frac{\color{blue}{j \cdot y}}{b}\right)\right) \]

   11. Simplified 57.1%

       \[\leadsto \color{blue}{i \cdot \left(b \cdot \left(a - j \cdot \frac{y}{b}\right)\right)} \]

   12. Taylor expanded in y around inf 57.2%

       \[\leadsto i \cdot \color{blue}{\left(y \cdot \left(-1 \cdot j + \frac{a \cdot b}{y}\right)\right)} \]
   13. Step-by-step derivation

       1. neg-mul-1 57.2%

          \[\leadsto i \cdot \left(y \cdot \left(\color{blue}{\left(-j\right)} + \frac{a \cdot b}{y}\right)\right) \]

       2. +-commutative 57.2%

          \[\leadsto i \cdot \left(y \cdot \color{blue}{\left(\frac{a \cdot b}{y} + \left(-j\right)\right)}\right) \]

       3. unsub-neg 57.2%

          \[\leadsto i \cdot \left(y \cdot \color{blue}{\left(\frac{a \cdot b}{y} - j\right)}\right) \]

       4. *-commutative 57.2%

          \[\leadsto i \cdot \left(y \cdot \left(\frac{\color{blue}{b \cdot a}}{y} - j\right)\right) \]

       5. associate-/l* 64.8%

          \[\leadsto i \cdot \left(y \cdot \left(\color{blue}{b \cdot \frac{a}{y}} - j\right)\right) \]

   14. Simplified 64.8%

       \[\leadsto i \cdot \color{blue}{\left(y \cdot \left(b \cdot \frac{a}{y} - j\right)\right)} \]

   if 2.75000000000000001e31 < y < 9.200000000000001e43

   1. Initial program 66.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 100.0%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]

   4. Taylor expanded in a around 0 100.0%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(c \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 100.0%

         \[\leadsto b \cdot \color{blue}{\left(-c \cdot z\right)} \]

      2. distribute-lft-neg-out 100.0%

         \[\leadsto b \cdot \color{blue}{\left(\left(-c\right) \cdot z\right)} \]

      3. *-commutative 100.0%

         \[\leadsto b \cdot \color{blue}{\left(z \cdot \left(-c\right)\right)} \]

   6. Simplified 100.0%

      \[\leadsto b \cdot \color{blue}{\left(z \cdot \left(-c\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-36}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-84}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-117}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-164}:\\ \;\;\;\;b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-259}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;y \leq 10^{-192}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-90}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{+31}:\\ \;\;\;\;i \cdot \left(y \cdot \left(b \cdot \frac{a}{y} - j\right)\right)\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+43}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 46.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(j \cdot \left(-y\right)\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_3 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -3.2 \cdot 10^{+86}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq -7.5 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq -6.5 \cdot 10^{-119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -3.9 \cdot 10^{-196}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq -2.9 \cdot 10^{-278}:\\ \;\;\;\;j \cdot \left(i \cdot \left(-y\right)\right)\\ \mathbf{elif}\;c \leq 7 \cdot 10^{-240}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 2 \cdot 10^{-219}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 2.45 \cdot 10^{+22}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{+167}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* j (- y))))
        (t_2 (* a (- (* b i) (* x t))))
        (t_3 (* c (- (* t j) (* z b)))))
   (if (<= c -3.2e+86)
     t_3
     (if (<= c -7.5e-13)
       (* x (- (* y z) (* t a)))
       (if (<= c -6.5e-119)
         t_1
         (if (<= c -3.9e-196)
           (* b (- (* a i) (* z c)))
           (if (<= c -2.9e-278)
             (* j (* i (- y)))
             (if (<= c 7e-240)
               t_2
               (if (<= c 2e-219)
                 t_1
                 (if (<= c 2.45e+22)
                   t_2
                   (if (<= c 2.2e+167) (* t (- (* c j) (* x a))) t_3)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (j * -y);
	double t_2 = a * ((b * i) - (x * t));
	double t_3 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -3.2e+86) {
		tmp = t_3;
	} else if (c <= -7.5e-13) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= -6.5e-119) {
		tmp = t_1;
	} else if (c <= -3.9e-196) {
		tmp = b * ((a * i) - (z * c));
	} else if (c <= -2.9e-278) {
		tmp = j * (i * -y);
	} else if (c <= 7e-240) {
		tmp = t_2;
	} else if (c <= 2e-219) {
		tmp = t_1;
	} else if (c <= 2.45e+22) {
		tmp = t_2;
	} else if (c <= 2.2e+167) {
		tmp = t * ((c * j) - (x * a));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = i * (j * -y)
    t_2 = a * ((b * i) - (x * t))
    t_3 = c * ((t * j) - (z * b))
    if (c <= (-3.2d+86)) then
        tmp = t_3
    else if (c <= (-7.5d-13)) then
        tmp = x * ((y * z) - (t * a))
    else if (c <= (-6.5d-119)) then
        tmp = t_1
    else if (c <= (-3.9d-196)) then
        tmp = b * ((a * i) - (z * c))
    else if (c <= (-2.9d-278)) then
        tmp = j * (i * -y)
    else if (c <= 7d-240) then
        tmp = t_2
    else if (c <= 2d-219) then
        tmp = t_1
    else if (c <= 2.45d+22) then
        tmp = t_2
    else if (c <= 2.2d+167) then
        tmp = t * ((c * j) - (x * a))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (j * -y);
	double t_2 = a * ((b * i) - (x * t));
	double t_3 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -3.2e+86) {
		tmp = t_3;
	} else if (c <= -7.5e-13) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= -6.5e-119) {
		tmp = t_1;
	} else if (c <= -3.9e-196) {
		tmp = b * ((a * i) - (z * c));
	} else if (c <= -2.9e-278) {
		tmp = j * (i * -y);
	} else if (c <= 7e-240) {
		tmp = t_2;
	} else if (c <= 2e-219) {
		tmp = t_1;
	} else if (c <= 2.45e+22) {
		tmp = t_2;
	} else if (c <= 2.2e+167) {
		tmp = t * ((c * j) - (x * a));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (j * -y)
	t_2 = a * ((b * i) - (x * t))
	t_3 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -3.2e+86:
		tmp = t_3
	elif c <= -7.5e-13:
		tmp = x * ((y * z) - (t * a))
	elif c <= -6.5e-119:
		tmp = t_1
	elif c <= -3.9e-196:
		tmp = b * ((a * i) - (z * c))
	elif c <= -2.9e-278:
		tmp = j * (i * -y)
	elif c <= 7e-240:
		tmp = t_2
	elif c <= 2e-219:
		tmp = t_1
	elif c <= 2.45e+22:
		tmp = t_2
	elif c <= 2.2e+167:
		tmp = t * ((c * j) - (x * a))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(j * Float64(-y)))
	t_2 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	t_3 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -3.2e+86)
		tmp = t_3;
	elseif (c <= -7.5e-13)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (c <= -6.5e-119)
		tmp = t_1;
	elseif (c <= -3.9e-196)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (c <= -2.9e-278)
		tmp = Float64(j * Float64(i * Float64(-y)));
	elseif (c <= 7e-240)
		tmp = t_2;
	elseif (c <= 2e-219)
		tmp = t_1;
	elseif (c <= 2.45e+22)
		tmp = t_2;
	elseif (c <= 2.2e+167)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * (j * -y);
	t_2 = a * ((b * i) - (x * t));
	t_3 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -3.2e+86)
		tmp = t_3;
	elseif (c <= -7.5e-13)
		tmp = x * ((y * z) - (t * a));
	elseif (c <= -6.5e-119)
		tmp = t_1;
	elseif (c <= -3.9e-196)
		tmp = b * ((a * i) - (z * c));
	elseif (c <= -2.9e-278)
		tmp = j * (i * -y);
	elseif (c <= 7e-240)
		tmp = t_2;
	elseif (c <= 2e-219)
		tmp = t_1;
	elseif (c <= 2.45e+22)
		tmp = t_2;
	elseif (c <= 2.2e+167)
		tmp = t * ((c * j) - (x * a));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(j * (-y)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $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+86], t$95$3, If[LessEqual[c, -7.5e-13], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -6.5e-119], t$95$1, If[LessEqual[c, -3.9e-196], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.9e-278], N[(j * N[(i * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 7e-240], t$95$2, If[LessEqual[c, 2e-219], t$95$1, If[LessEqual[c, 2.45e+22], t$95$2, If[LessEqual[c, 2.2e+167], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if c < -3.2e86 or 2.20000000000000003e167 < c

   1. Initial program 56.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 72.4%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

   if -3.2e86 < c < -7.5000000000000004e-13

   1. Initial program 82.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 67.6%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   4. Step-by-step derivation

      1. *-commutative 67.6%

         \[\leadsto x \cdot \left(\color{blue}{z \cdot y} - a \cdot t\right) \]

   5. Simplified 67.6%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y - a \cdot t\right)} \]

   if -7.5000000000000004e-13 < c < -6.5e-119 or 7.00000000000000032e-240 < c < 2.0000000000000001e-219

   1. Initial program 72.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 66.0%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 66.0%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. *-commutative 66.0%

         \[\leadsto i \cdot \left(-1 \cdot \left(j \cdot y - \color{blue}{b \cdot a}\right)\right) \]

   5. Simplified 66.0%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - b \cdot a\right)\right)} \]

   6. Taylor expanded in j around inf 55.3%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 55.3%

         \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(j \cdot y\right)} \]

      2. mul-1-neg 55.3%

         \[\leadsto \color{blue}{\left(-i\right)} \cdot \left(j \cdot y\right) \]

      3. *-commutative 55.3%

         \[\leadsto \left(-i\right) \cdot \color{blue}{\left(y \cdot j\right)} \]

   8. Simplified 55.3%

      \[\leadsto \color{blue}{\left(-i\right) \cdot \left(y \cdot j\right)} \]

   if -6.5e-119 < c < -3.90000000000000016e-196

   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 -3.90000000000000016e-196 < c < -2.9e-278

   1. Initial program 86.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 64.8%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 64.8%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. *-commutative 64.8%

         \[\leadsto i \cdot \left(-1 \cdot \left(j \cdot y - \color{blue}{b \cdot a}\right)\right) \]

   5. Simplified 64.8%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - b \cdot a\right)\right)} \]

   6. Taylor expanded in j around inf 43.6%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 43.6%

         \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(j \cdot y\right)} \]

      2. mul-1-neg 43.6%

         \[\leadsto \color{blue}{\left(-i\right)} \cdot \left(j \cdot y\right) \]

      3. *-commutative 43.6%

         \[\leadsto \left(-i\right) \cdot \color{blue}{\left(y \cdot j\right)} \]

   8. Simplified 43.6%

      \[\leadsto \color{blue}{\left(-i\right) \cdot \left(y \cdot j\right)} \]

   9. Taylor expanded in i around 0 43.6%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 43.6%

          \[\leadsto \color{blue}{-i \cdot \left(j \cdot y\right)} \]

       2. *-commutative 43.6%

          \[\leadsto -i \cdot \color{blue}{\left(y \cdot j\right)} \]

       3. associate-*l* 43.7%

          \[\leadsto -\color{blue}{\left(i \cdot y\right) \cdot j} \]

       4. distribute-rgt-neg-in 43.7%

          \[\leadsto \color{blue}{\left(i \cdot y\right) \cdot \left(-j\right)} \]

   11. Simplified 43.7%

       \[\leadsto \color{blue}{\left(i \cdot y\right) \cdot \left(-j\right)} \]

   if -2.9e-278 < c < 7.00000000000000032e-240 or 2.0000000000000001e-219 < c < 2.4499999999999999e22

   1. Initial program 86.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 53.9%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 53.9%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x - b \cdot i\right)\right)} \]

   5. Simplified 53.9%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x - b \cdot i\right)\right)} \]

   6. Taylor expanded in t around 0 53.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(b \cdot i\right)} \]
   7. Step-by-step derivation

      1. +-commutative 53.9%

         \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 53.9%

         \[\leadsto a \cdot \left(b \cdot i\right) + \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} \]

      3. distribute-rgt-neg-in 53.9%

         \[\leadsto a \cdot \left(b \cdot i\right) + \color{blue}{a \cdot \left(-t \cdot x\right)} \]

      4. distribute-lft-out 53.9%

         \[\leadsto \color{blue}{a \cdot \left(b \cdot i + \left(-t \cdot x\right)\right)} \]

      5. unsub-neg 53.9%

         \[\leadsto a \cdot \color{blue}{\left(b \cdot i - t \cdot x\right)} \]

   8. Simplified 53.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   if 2.4499999999999999e22 < c < 2.20000000000000003e167

   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 t around inf 66.3%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 66.3%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 66.3%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 66.3%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   5. Simplified 66.3%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.2 \cdot 10^{+86}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -7.5 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq -6.5 \cdot 10^{-119}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;c \leq -3.9 \cdot 10^{-196}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq -2.9 \cdot 10^{-278}:\\ \;\;\;\;j \cdot \left(i \cdot \left(-y\right)\right)\\ \mathbf{elif}\;c \leq 7 \cdot 10^{-240}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 2 \cdot 10^{-219}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;c \leq 2.45 \cdot 10^{+22}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{+167}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 43.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -4.9 \cdot 10^{+17}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.02 \cdot 10^{-78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-213}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq -2.35 \cdot 10^{-272}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-283}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{-287}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-220}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-13}:\\ \;\;\;\;j \cdot \left(i \cdot \left(-y\right)\right)\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))) (t_2 (* a (- (* b i) (* x t)))))
   (if (<= a -4.9e+17)
     t_2
     (if (<= a -1.02e-78)
       t_1
       (if (<= a -2.7e-213)
         (* z (* b (- c)))
         (if (<= a -2.35e-272)
           (* t (* c j))
           (if (<= a -8.5e-283)
             (* i (* j (- y)))
             (if (<= a 1.22e-287)
               (* b (* z (- c)))
               (if (<= a 2.7e-220)
                 (* y (* x z))
                 (if (<= a 1.2e-13)
                   (* j (* i (- y)))
                   (if (<= a 3.9e+18) t_1 t_2)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -4.9e+17) {
		tmp = t_2;
	} else if (a <= -1.02e-78) {
		tmp = t_1;
	} else if (a <= -2.7e-213) {
		tmp = z * (b * -c);
	} else if (a <= -2.35e-272) {
		tmp = t * (c * j);
	} else if (a <= -8.5e-283) {
		tmp = i * (j * -y);
	} else if (a <= 1.22e-287) {
		tmp = b * (z * -c);
	} else if (a <= 2.7e-220) {
		tmp = y * (x * z);
	} else if (a <= 1.2e-13) {
		tmp = j * (i * -y);
	} else if (a <= 3.9e+18) {
		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 = b * ((a * i) - (z * c))
    t_2 = a * ((b * i) - (x * t))
    if (a <= (-4.9d+17)) then
        tmp = t_2
    else if (a <= (-1.02d-78)) then
        tmp = t_1
    else if (a <= (-2.7d-213)) then
        tmp = z * (b * -c)
    else if (a <= (-2.35d-272)) then
        tmp = t * (c * j)
    else if (a <= (-8.5d-283)) then
        tmp = i * (j * -y)
    else if (a <= 1.22d-287) then
        tmp = b * (z * -c)
    else if (a <= 2.7d-220) then
        tmp = y * (x * z)
    else if (a <= 1.2d-13) then
        tmp = j * (i * -y)
    else if (a <= 3.9d+18) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -4.9e+17) {
		tmp = t_2;
	} else if (a <= -1.02e-78) {
		tmp = t_1;
	} else if (a <= -2.7e-213) {
		tmp = z * (b * -c);
	} else if (a <= -2.35e-272) {
		tmp = t * (c * j);
	} else if (a <= -8.5e-283) {
		tmp = i * (j * -y);
	} else if (a <= 1.22e-287) {
		tmp = b * (z * -c);
	} else if (a <= 2.7e-220) {
		tmp = y * (x * z);
	} else if (a <= 1.2e-13) {
		tmp = j * (i * -y);
	} else if (a <= 3.9e+18) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -4.9e+17:
		tmp = t_2
	elif a <= -1.02e-78:
		tmp = t_1
	elif a <= -2.7e-213:
		tmp = z * (b * -c)
	elif a <= -2.35e-272:
		tmp = t * (c * j)
	elif a <= -8.5e-283:
		tmp = i * (j * -y)
	elif a <= 1.22e-287:
		tmp = b * (z * -c)
	elif a <= 2.7e-220:
		tmp = y * (x * z)
	elif a <= 1.2e-13:
		tmp = j * (i * -y)
	elif a <= 3.9e+18:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -4.9e+17)
		tmp = t_2;
	elseif (a <= -1.02e-78)
		tmp = t_1;
	elseif (a <= -2.7e-213)
		tmp = Float64(z * Float64(b * Float64(-c)));
	elseif (a <= -2.35e-272)
		tmp = Float64(t * Float64(c * j));
	elseif (a <= -8.5e-283)
		tmp = Float64(i * Float64(j * Float64(-y)));
	elseif (a <= 1.22e-287)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (a <= 2.7e-220)
		tmp = Float64(y * Float64(x * z));
	elseif (a <= 1.2e-13)
		tmp = Float64(j * Float64(i * Float64(-y)));
	elseif (a <= 3.9e+18)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -4.9e+17)
		tmp = t_2;
	elseif (a <= -1.02e-78)
		tmp = t_1;
	elseif (a <= -2.7e-213)
		tmp = z * (b * -c);
	elseif (a <= -2.35e-272)
		tmp = t * (c * j);
	elseif (a <= -8.5e-283)
		tmp = i * (j * -y);
	elseif (a <= 1.22e-287)
		tmp = b * (z * -c);
	elseif (a <= 2.7e-220)
		tmp = y * (x * z);
	elseif (a <= 1.2e-13)
		tmp = j * (i * -y);
	elseif (a <= 3.9e+18)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.9e+17], t$95$2, If[LessEqual[a, -1.02e-78], t$95$1, If[LessEqual[a, -2.7e-213], N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.35e-272], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -8.5e-283], N[(i * N[(j * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.22e-287], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.7e-220], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.2e-13], N[(j * N[(i * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.9e+18], t$95$1, t$95$2]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if a < -4.9e17 or 3.9e18 < 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 -4.9e17 < a < -1.02e-78 or 1.1999999999999999e-13 < a < 3.9e18

   1. Initial program 87.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 53.0%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]

   if -1.02e-78 < a < -2.7000000000000001e-213

   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 73.8%

      \[\leadsto \color{blue}{j \cdot \left(\left(c \cdot t + \frac{x \cdot \left(y \cdot z - a \cdot t\right)}{j}\right) - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 73.8%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t + \left(\frac{x \cdot \left(y \cdot z - a \cdot t\right)}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right)} \]

      2. sub-neg 73.8%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \color{blue}{\left(y \cdot z + \left(-a \cdot t\right)\right)}}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right) \]

      3. mul-1-neg 73.8%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \left(y \cdot z + \color{blue}{-1 \cdot \left(a \cdot t\right)}\right)}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right) \]

      4. +-commutative 73.8%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \color{blue}{\left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)}}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right) \]

      5. +-commutative 73.8%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)}{j} - \color{blue}{\left(\frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j} + i \cdot y\right)}\right)\right) \]

      6. associate--r+ 73.8%

         \[\leadsto j \cdot \left(c \cdot t + \color{blue}{\left(\left(\frac{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)}{j} - \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right) - i \cdot y\right)}\right) \]

   5. Simplified 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 c around inf 65.5%

      \[\leadsto j \cdot \left(c \cdot t + \left(\color{blue}{-1 \cdot \frac{b \cdot \left(c \cdot z\right)}{j}} - i \cdot y\right)\right) \]
   7. Step-by-step derivation

      1. associate-*r/ 65.5%

         \[\leadsto j \cdot \left(c \cdot t + \left(\color{blue}{\frac{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)}{j}} - i \cdot y\right)\right) \]

      2. associate-*r* 65.5%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{\color{blue}{\left(-1 \cdot b\right) \cdot \left(c \cdot z\right)}}{j} - i \cdot y\right)\right) \]

      3. neg-mul-1 65.5%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{\color{blue}{\left(-b\right)} \cdot \left(c \cdot z\right)}{j} - i \cdot y\right)\right) \]

      4. *-commutative 65.5%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{\left(-b\right) \cdot \color{blue}{\left(z \cdot c\right)}}{j} - i \cdot y\right)\right) \]

   8. Simplified 65.5%

      \[\leadsto j \cdot \left(c \cdot t + \left(\color{blue}{\frac{\left(-b\right) \cdot \left(z \cdot c\right)}{j}} - i \cdot y\right)\right) \]

   9. Taylor expanded in j around 0 38.4%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. neg-mul-1 38.4%

          \[\leadsto \color{blue}{-b \cdot \left(c \cdot z\right)} \]

       2. *-commutative 38.4%

          \[\leadsto -b \cdot \color{blue}{\left(z \cdot c\right)} \]

       3. associate-*r* 38.4%

          \[\leadsto -\color{blue}{\left(b \cdot z\right) \cdot c} \]

       4. *-commutative 38.4%

          \[\leadsto -\color{blue}{\left(z \cdot b\right)} \cdot c \]

       5. associate-*r* 41.1%

          \[\leadsto -\color{blue}{z \cdot \left(b \cdot c\right)} \]

       6. distribute-rgt-neg-out 41.1%

          \[\leadsto \color{blue}{z \cdot \left(-b \cdot c\right)} \]

       7. distribute-rgt-neg-in 41.1%

          \[\leadsto z \cdot \color{blue}{\left(b \cdot \left(-c\right)\right)} \]

   11. Simplified 41.1%

       \[\leadsto \color{blue}{z \cdot \left(b \cdot \left(-c\right)\right)} \]

   if -2.7000000000000001e-213 < a < -2.3499999999999999e-272

   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 t around inf 86.0%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 86.0%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 86.0%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 86.0%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   5. Simplified 86.0%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   6. Taylor expanded in c around inf 86.0%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot j\right)} \]

   if -2.3499999999999999e-272 < a < -8.49999999999999997e-283

   1. Initial program 76.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 100.0%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 100.0%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. *-commutative 100.0%

         \[\leadsto i \cdot \left(-1 \cdot \left(j \cdot y - \color{blue}{b \cdot a}\right)\right) \]

   5. Simplified 100.0%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - b \cdot a\right)\right)} \]

   6. Taylor expanded in j around inf 75.9%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 75.9%

         \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(j \cdot y\right)} \]

      2. mul-1-neg 75.9%

         \[\leadsto \color{blue}{\left(-i\right)} \cdot \left(j \cdot y\right) \]

      3. *-commutative 75.9%

         \[\leadsto \left(-i\right) \cdot \color{blue}{\left(y \cdot j\right)} \]

   8. Simplified 75.9%

      \[\leadsto \color{blue}{\left(-i\right) \cdot \left(y \cdot j\right)} \]

   if -8.49999999999999997e-283 < a < 1.21999999999999996e-287

   1. Initial program 37.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 63.1%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]

   4. Taylor expanded in a around 0 63.1%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(c \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 63.1%

         \[\leadsto b \cdot \color{blue}{\left(-c \cdot z\right)} \]

      2. distribute-lft-neg-out 63.1%

         \[\leadsto b \cdot \color{blue}{\left(\left(-c\right) \cdot z\right)} \]

      3. *-commutative 63.1%

         \[\leadsto b \cdot \color{blue}{\left(z \cdot \left(-c\right)\right)} \]

   6. Simplified 63.1%

      \[\leadsto b \cdot \color{blue}{\left(z \cdot \left(-c\right)\right)} \]

   if 1.21999999999999996e-287 < a < 2.7e-220

   1. Initial program 67.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 75.8%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 75.8%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 75.8%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 75.8%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 75.8%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   5. Simplified 75.8%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   6. Taylor expanded in z around inf 43.4%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-commutative 43.4%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

      2. associate-*l* 51.1%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   8. Simplified 51.1%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if 2.7e-220 < a < 1.1999999999999999e-13

   1. Initial program 82.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 42.4%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 42.4%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. *-commutative 42.4%

         \[\leadsto i \cdot \left(-1 \cdot \left(j \cdot y - \color{blue}{b \cdot a}\right)\right) \]

   5. Simplified 42.4%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - b \cdot a\right)\right)} \]

   6. Taylor expanded in j around inf 42.1%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 42.1%

         \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(j \cdot y\right)} \]

      2. mul-1-neg 42.1%

         \[\leadsto \color{blue}{\left(-i\right)} \cdot \left(j \cdot y\right) \]

      3. *-commutative 42.1%

         \[\leadsto \left(-i\right) \cdot \color{blue}{\left(y \cdot j\right)} \]

   8. Simplified 42.1%

      \[\leadsto \color{blue}{\left(-i\right) \cdot \left(y \cdot j\right)} \]

   9. Taylor expanded in i around 0 42.1%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 42.1%

          \[\leadsto \color{blue}{-i \cdot \left(j \cdot y\right)} \]

       2. *-commutative 42.1%

          \[\leadsto -i \cdot \color{blue}{\left(y \cdot j\right)} \]

       3. associate-*l* 42.2%

          \[\leadsto -\color{blue}{\left(i \cdot y\right) \cdot j} \]

       4. distribute-rgt-neg-in 42.2%

          \[\leadsto \color{blue}{\left(i \cdot y\right) \cdot \left(-j\right)} \]

   11. Simplified 42.2%

       \[\leadsto \color{blue}{\left(i \cdot y\right) \cdot \left(-j\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.9 \cdot 10^{+17}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.02 \cdot 10^{-78}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-213}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq -2.35 \cdot 10^{-272}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-283}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{-287}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-220}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-13}:\\ \;\;\;\;j \cdot \left(i \cdot \left(-y\right)\right)\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{+18}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 46.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \mathbf{if}\;y \leq -2 \cdot 10^{+53}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-47}:\\ \;\;\;\;c \cdot \left(t \cdot j - a \cdot \left(t \cdot \frac{x}{c}\right)\right)\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-87}:\\ \;\;\;\;b \cdot \left(a \cdot i - a \cdot \left(t \cdot \frac{x}{b}\right)\right)\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-119}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-133}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-261}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{-169}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(b \cdot \frac{a}{y} - j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* z (- (* a (/ i z)) c)))))
   (if (<= y -2e+53)
     (* y (- (* x z) (* i j)))
     (if (<= y -3e-47)
       (* c (- (* t j) (* a (* t (/ x c)))))
       (if (<= y -3.1e-71)
         t_1
         (if (<= y -7.2e-87)
           (* b (- (* a i) (* a (* t (/ x b)))))
           (if (<= y -4.8e-119)
             (* t (- (* c j) (* x a)))
             (if (<= y -1.15e-133)
               t_1
               (if (<= y 1.65e-261)
                 (* b (- (* a i) (* z c)))
                 (if (<= y 9.6e-169)
                   (* x (- (* y z) (* t a)))
                   (* i (* y (- (* b (/ a y)) j)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (z * ((a * (i / z)) - c));
	double tmp;
	if (y <= -2e+53) {
		tmp = y * ((x * z) - (i * j));
	} else if (y <= -3e-47) {
		tmp = c * ((t * j) - (a * (t * (x / c))));
	} else if (y <= -3.1e-71) {
		tmp = t_1;
	} else if (y <= -7.2e-87) {
		tmp = b * ((a * i) - (a * (t * (x / b))));
	} else if (y <= -4.8e-119) {
		tmp = t * ((c * j) - (x * a));
	} else if (y <= -1.15e-133) {
		tmp = t_1;
	} else if (y <= 1.65e-261) {
		tmp = b * ((a * i) - (z * c));
	} else if (y <= 9.6e-169) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = i * (y * ((b * (a / y)) - 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) :: t_1
    real(8) :: tmp
    t_1 = b * (z * ((a * (i / z)) - c))
    if (y <= (-2d+53)) then
        tmp = y * ((x * z) - (i * j))
    else if (y <= (-3d-47)) then
        tmp = c * ((t * j) - (a * (t * (x / c))))
    else if (y <= (-3.1d-71)) then
        tmp = t_1
    else if (y <= (-7.2d-87)) then
        tmp = b * ((a * i) - (a * (t * (x / b))))
    else if (y <= (-4.8d-119)) then
        tmp = t * ((c * j) - (x * a))
    else if (y <= (-1.15d-133)) then
        tmp = t_1
    else if (y <= 1.65d-261) then
        tmp = b * ((a * i) - (z * c))
    else if (y <= 9.6d-169) then
        tmp = x * ((y * z) - (t * a))
    else
        tmp = i * (y * ((b * (a / y)) - 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 t_1 = b * (z * ((a * (i / z)) - c));
	double tmp;
	if (y <= -2e+53) {
		tmp = y * ((x * z) - (i * j));
	} else if (y <= -3e-47) {
		tmp = c * ((t * j) - (a * (t * (x / c))));
	} else if (y <= -3.1e-71) {
		tmp = t_1;
	} else if (y <= -7.2e-87) {
		tmp = b * ((a * i) - (a * (t * (x / b))));
	} else if (y <= -4.8e-119) {
		tmp = t * ((c * j) - (x * a));
	} else if (y <= -1.15e-133) {
		tmp = t_1;
	} else if (y <= 1.65e-261) {
		tmp = b * ((a * i) - (z * c));
	} else if (y <= 9.6e-169) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = i * (y * ((b * (a / y)) - j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (z * ((a * (i / z)) - c))
	tmp = 0
	if y <= -2e+53:
		tmp = y * ((x * z) - (i * j))
	elif y <= -3e-47:
		tmp = c * ((t * j) - (a * (t * (x / c))))
	elif y <= -3.1e-71:
		tmp = t_1
	elif y <= -7.2e-87:
		tmp = b * ((a * i) - (a * (t * (x / b))))
	elif y <= -4.8e-119:
		tmp = t * ((c * j) - (x * a))
	elif y <= -1.15e-133:
		tmp = t_1
	elif y <= 1.65e-261:
		tmp = b * ((a * i) - (z * c))
	elif y <= 9.6e-169:
		tmp = x * ((y * z) - (t * a))
	else:
		tmp = i * (y * ((b * (a / y)) - j))
	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)))
	tmp = 0.0
	if (y <= -2e+53)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (y <= -3e-47)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(a * Float64(t * Float64(x / c)))));
	elseif (y <= -3.1e-71)
		tmp = t_1;
	elseif (y <= -7.2e-87)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(a * Float64(t * Float64(x / b)))));
	elseif (y <= -4.8e-119)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (y <= -1.15e-133)
		tmp = t_1;
	elseif (y <= 1.65e-261)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (y <= 9.6e-169)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	else
		tmp = Float64(i * Float64(y * Float64(Float64(b * Float64(a / y)) - j)));
	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));
	tmp = 0.0;
	if (y <= -2e+53)
		tmp = y * ((x * z) - (i * j));
	elseif (y <= -3e-47)
		tmp = c * ((t * j) - (a * (t * (x / c))));
	elseif (y <= -3.1e-71)
		tmp = t_1;
	elseif (y <= -7.2e-87)
		tmp = b * ((a * i) - (a * (t * (x / b))));
	elseif (y <= -4.8e-119)
		tmp = t * ((c * j) - (x * a));
	elseif (y <= -1.15e-133)
		tmp = t_1;
	elseif (y <= 1.65e-261)
		tmp = b * ((a * i) - (z * c));
	elseif (y <= 9.6e-169)
		tmp = x * ((y * z) - (t * a));
	else
		tmp = i * (y * ((b * (a / y)) - j));
	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]}, If[LessEqual[y, -2e+53], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3e-47], N[(c * N[(N[(t * j), $MachinePrecision] - N[(a * N[(t * N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.1e-71], t$95$1, If[LessEqual[y, -7.2e-87], N[(b * N[(N[(a * i), $MachinePrecision] - N[(a * N[(t * N[(x / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.8e-119], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.15e-133], t$95$1, If[LessEqual[y, 1.65e-261], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.6e-169], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(y * N[(N[(b * N[(a / y), $MachinePrecision]), $MachinePrecision] - j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y < -2e53

   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 y around inf 72.7%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 72.7%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 72.7%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 72.7%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 72.7%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   5. Simplified 72.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   if -2e53 < y < -3.00000000000000017e-47

   1. Initial program 85.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 38.6%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 38.6%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 38.6%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 38.6%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   5. Simplified 38.6%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   6. Taylor expanded in c around inf 45.3%

      \[\leadsto \color{blue}{c \cdot \left(-1 \cdot \frac{a \cdot \left(t \cdot x\right)}{c} + j \cdot t\right)} \]
   7. Step-by-step derivation

      1. +-commutative 45.3%

         \[\leadsto c \cdot \color{blue}{\left(j \cdot t + -1 \cdot \frac{a \cdot \left(t \cdot x\right)}{c}\right)} \]

      2. mul-1-neg 45.3%

         \[\leadsto c \cdot \left(j \cdot t + \color{blue}{\left(-\frac{a \cdot \left(t \cdot x\right)}{c}\right)}\right) \]

      3. unsub-neg 45.3%

         \[\leadsto c \cdot \color{blue}{\left(j \cdot t - \frac{a \cdot \left(t \cdot x\right)}{c}\right)} \]

      4. associate-/l* 59.1%

         \[\leadsto c \cdot \left(j \cdot t - \color{blue}{a \cdot \frac{t \cdot x}{c}}\right) \]

      5. associate-/l* 66.0%

         \[\leadsto c \cdot \left(j \cdot t - a \cdot \color{blue}{\left(t \cdot \frac{x}{c}\right)}\right) \]

   8. Simplified 66.0%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - a \cdot \left(t \cdot \frac{x}{c}\right)\right)} \]

   if -3.00000000000000017e-47 < y < -3.10000000000000002e-71 or -4.80000000000000017e-119 < y < -1.15e-133

   1. Initial program 90.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 55.6%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]

   4. Taylor expanded in z around inf 72.9%

      \[\leadsto b \cdot \color{blue}{\left(z \cdot \left(\frac{a \cdot i}{z} - c\right)\right)} \]
   5. Step-by-step derivation

      1. associate-/l* 81.8%

         \[\leadsto b \cdot \left(z \cdot \left(\color{blue}{a \cdot \frac{i}{z}} - c\right)\right) \]

   6. Simplified 81.8%

      \[\leadsto b \cdot \color{blue}{\left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)} \]

   if -3.10000000000000002e-71 < y < -7.19999999999999986e-87

   1. Initial program 100.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 51.7%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 51.7%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x - b \cdot i\right)\right)} \]

   5. Simplified 51.7%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x - b \cdot i\right)\right)} \]

   6. Taylor expanded in b around inf 67.2%

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \frac{a \cdot \left(t \cdot x\right)}{b} + a \cdot i\right)} \]
   7. Step-by-step derivation

      1. +-commutative 67.2%

         \[\leadsto b \cdot \color{blue}{\left(a \cdot i + -1 \cdot \frac{a \cdot \left(t \cdot x\right)}{b}\right)} \]

      2. mul-1-neg 67.2%

         \[\leadsto b \cdot \left(a \cdot i + \color{blue}{\left(-\frac{a \cdot \left(t \cdot x\right)}{b}\right)}\right) \]

      3. unsub-neg 67.2%

         \[\leadsto b \cdot \color{blue}{\left(a \cdot i - \frac{a \cdot \left(t \cdot x\right)}{b}\right)} \]

      4. *-commutative 67.2%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - \frac{a \cdot \left(t \cdot x\right)}{b}\right) \]

      5. associate-/l* 67.2%

         \[\leadsto b \cdot \left(i \cdot a - \color{blue}{a \cdot \frac{t \cdot x}{b}}\right) \]

      6. associate-/l* 67.2%

         \[\leadsto b \cdot \left(i \cdot a - a \cdot \color{blue}{\left(t \cdot \frac{x}{b}\right)}\right) \]

   8. Simplified 67.2%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a - a \cdot \left(t \cdot \frac{x}{b}\right)\right)} \]

   if -7.19999999999999986e-87 < y < -4.80000000000000017e-119

   1. Initial program 99.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 67.8%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 67.8%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 67.8%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 67.8%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   5. Simplified 67.8%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   if -1.15e-133 < y < 1.6499999999999999e-261

   1. Initial program 82.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 67.0%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]

   if 1.6499999999999999e-261 < y < 9.60000000000000043e-169

   1. Initial program 88.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 63.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   4. Step-by-step derivation

      1. *-commutative 63.3%

         \[\leadsto x \cdot \left(\color{blue}{z \cdot y} - a \cdot t\right) \]

   5. Simplified 63.3%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y - a \cdot t\right)} \]

   if 9.60000000000000043e-169 < y

   1. Initial program 67.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 54.0%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 54.0%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. *-commutative 54.0%

         \[\leadsto i \cdot \left(-1 \cdot \left(j \cdot y - \color{blue}{b \cdot a}\right)\right) \]

   5. Simplified 54.0%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - b \cdot a\right)\right)} \]

   6. Taylor expanded in b around inf 43.0%

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \frac{i \cdot \left(j \cdot y\right)}{b} + a \cdot i\right)} \]
   7. Step-by-step derivation

      1. +-commutative 43.0%

         \[\leadsto b \cdot \color{blue}{\left(a \cdot i + -1 \cdot \frac{i \cdot \left(j \cdot y\right)}{b}\right)} \]

      2. *-commutative 43.0%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} + -1 \cdot \frac{i \cdot \left(j \cdot y\right)}{b}\right) \]

      3. mul-1-neg 43.0%

         \[\leadsto b \cdot \left(i \cdot a + \color{blue}{\left(-\frac{i \cdot \left(j \cdot y\right)}{b}\right)}\right) \]

      4. unsub-neg 43.0%

         \[\leadsto b \cdot \color{blue}{\left(i \cdot a - \frac{i \cdot \left(j \cdot y\right)}{b}\right)} \]

      5. *-commutative 43.0%

         \[\leadsto b \cdot \left(\color{blue}{a \cdot i} - \frac{i \cdot \left(j \cdot y\right)}{b}\right) \]

      6. associate-/l* 46.4%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{i \cdot \frac{j \cdot y}{b}}\right) \]

      7. *-commutative 46.4%

         \[\leadsto b \cdot \left(a \cdot i - i \cdot \frac{\color{blue}{y \cdot j}}{b}\right) \]

   8. Simplified 46.4%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - i \cdot \frac{y \cdot j}{b}\right)} \]

   9. Taylor expanded in b around inf 43.0%

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \frac{i \cdot \left(j \cdot y\right)}{b} + a \cdot i\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 43.0%

          \[\leadsto b \cdot \left(\color{blue}{\left(-\frac{i \cdot \left(j \cdot y\right)}{b}\right)} + a \cdot i\right) \]

       2. distribute-frac-neg 43.0%

          \[\leadsto b \cdot \left(\color{blue}{\frac{-i \cdot \left(j \cdot y\right)}{b}} + a \cdot i\right) \]

       3. distribute-lft-neg-in 43.0%

          \[\leadsto b \cdot \left(\frac{\color{blue}{\left(-i\right) \cdot \left(j \cdot y\right)}}{b} + a \cdot i\right) \]

       4. associate-*r/ 46.4%

          \[\leadsto b \cdot \left(\color{blue}{\left(-i\right) \cdot \frac{j \cdot y}{b}} + a \cdot i\right) \]

       5. *-commutative 46.4%

          \[\leadsto b \cdot \left(\left(-i\right) \cdot \frac{\color{blue}{y \cdot j}}{b} + a \cdot i\right) \]

       6. associate-*r/ 46.4%

          \[\leadsto b \cdot \left(\left(-i\right) \cdot \color{blue}{\left(y \cdot \frac{j}{b}\right)} + a \cdot i\right) \]

       7. distribute-lft-neg-in 46.4%

          \[\leadsto b \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot \frac{j}{b}\right)\right)} + a \cdot i\right) \]

       8. +-commutative 46.4%

          \[\leadsto b \cdot \color{blue}{\left(a \cdot i + \left(-i \cdot \left(y \cdot \frac{j}{b}\right)\right)\right)} \]

       9. distribute-lft-in 42.0%

          \[\leadsto \color{blue}{b \cdot \left(a \cdot i\right) + b \cdot \left(-i \cdot \left(y \cdot \frac{j}{b}\right)\right)} \]

       10. *-commutative 42.0%

           \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} + b \cdot \left(-i \cdot \left(y \cdot \frac{j}{b}\right)\right) \]

       11. associate-*r* 42.2%

           \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot a} + b \cdot \left(-i \cdot \left(y \cdot \frac{j}{b}\right)\right) \]

       12. distribute-rgt-neg-in 42.2%

           \[\leadsto \left(b \cdot i\right) \cdot a + b \cdot \color{blue}{\left(i \cdot \left(-y \cdot \frac{j}{b}\right)\right)} \]

       13. associate-*r* 34.5%

           \[\leadsto \left(b \cdot i\right) \cdot a + \color{blue}{\left(b \cdot i\right) \cdot \left(-y \cdot \frac{j}{b}\right)} \]

       14. distribute-lft-in 48.7%

           \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot \left(a + \left(-y \cdot \frac{j}{b}\right)\right)} \]

       15. associate-*r/ 48.8%

           \[\leadsto \left(b \cdot i\right) \cdot \left(a + \left(-\color{blue}{\frac{y \cdot j}{b}}\right)\right) \]

       16. *-commutative 48.8%

           \[\leadsto \left(b \cdot i\right) \cdot \left(a + \left(-\frac{\color{blue}{j \cdot y}}{b}\right)\right) \]

   11. Simplified 52.0%

       \[\leadsto \color{blue}{i \cdot \left(b \cdot \left(a - j \cdot \frac{y}{b}\right)\right)} \]

   12. Taylor expanded in y around inf 54.0%

       \[\leadsto i \cdot \color{blue}{\left(y \cdot \left(-1 \cdot j + \frac{a \cdot b}{y}\right)\right)} \]
   13. Step-by-step derivation

       1. neg-mul-1 54.0%

          \[\leadsto i \cdot \left(y \cdot \left(\color{blue}{\left(-j\right)} + \frac{a \cdot b}{y}\right)\right) \]

       2. +-commutative 54.0%

          \[\leadsto i \cdot \left(y \cdot \color{blue}{\left(\frac{a \cdot b}{y} + \left(-j\right)\right)}\right) \]

       3. unsub-neg 54.0%

          \[\leadsto i \cdot \left(y \cdot \color{blue}{\left(\frac{a \cdot b}{y} - j\right)}\right) \]

       4. *-commutative 54.0%

          \[\leadsto i \cdot \left(y \cdot \left(\frac{\color{blue}{b \cdot a}}{y} - j\right)\right) \]

       5. associate-/l* 58.2%

          \[\leadsto i \cdot \left(y \cdot \left(\color{blue}{b \cdot \frac{a}{y}} - j\right)\right) \]

   14. Simplified 58.2%

       \[\leadsto i \cdot \color{blue}{\left(y \cdot \left(b \cdot \frac{a}{y} - j\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+53}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-47}:\\ \;\;\;\;c \cdot \left(t \cdot j - a \cdot \left(t \cdot \frac{x}{c}\right)\right)\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-71}:\\ \;\;\;\;b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-87}:\\ \;\;\;\;b \cdot \left(a \cdot i - a \cdot \left(t \cdot \frac{x}{b}\right)\right)\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-119}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-133}:\\ \;\;\;\;b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-261}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{-169}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(b \cdot \frac{a}{y} - j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 48.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{-35}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-85}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-116}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-229}:\\ \;\;\;\;b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-164}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-164}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+118}:\\ \;\;\;\;i \cdot \left(y \cdot \left(b \cdot \frac{a}{y} - j\right)\right)\\ \mathbf{elif}\;y \leq 1.96 \cdot 10^{+145}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(x \cdot \frac{z}{j} - i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -1.22e-35)
   (* y (- (* x z) (* i j)))
   (if (<= y -5.2e-85)
     (* a (- (* b i) (* x t)))
     (if (<= y -1.3e-116)
       (* t (- (* c j) (* x a)))
       (if (<= y 2.5e-229)
         (* b (* z (- (* a (/ i z)) c)))
         (if (<= y 1.2e-164)
           (* x (- (* y z) (* t a)))
           (if (<= y 2.4e-164)
             (* c (* t j))
             (if (<= y 1.55e+118)
               (* i (* y (- (* b (/ a y)) j)))
               (if (<= y 1.96e+145)
                 (* z (- (* x y) (* b c)))
                 (* (* y j) (- (* x (/ z j)) i)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -1.22e-35) {
		tmp = y * ((x * z) - (i * j));
	} else if (y <= -5.2e-85) {
		tmp = a * ((b * i) - (x * t));
	} else if (y <= -1.3e-116) {
		tmp = t * ((c * j) - (x * a));
	} else if (y <= 2.5e-229) {
		tmp = b * (z * ((a * (i / z)) - c));
	} else if (y <= 1.2e-164) {
		tmp = x * ((y * z) - (t * a));
	} else if (y <= 2.4e-164) {
		tmp = c * (t * j);
	} else if (y <= 1.55e+118) {
		tmp = i * (y * ((b * (a / y)) - j));
	} else if (y <= 1.96e+145) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = (y * j) * ((x * (z / j)) - i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-1.22d-35)) then
        tmp = y * ((x * z) - (i * j))
    else if (y <= (-5.2d-85)) then
        tmp = a * ((b * i) - (x * t))
    else if (y <= (-1.3d-116)) then
        tmp = t * ((c * j) - (x * a))
    else if (y <= 2.5d-229) then
        tmp = b * (z * ((a * (i / z)) - c))
    else if (y <= 1.2d-164) then
        tmp = x * ((y * z) - (t * a))
    else if (y <= 2.4d-164) then
        tmp = c * (t * j)
    else if (y <= 1.55d+118) then
        tmp = i * (y * ((b * (a / y)) - j))
    else if (y <= 1.96d+145) then
        tmp = z * ((x * y) - (b * c))
    else
        tmp = (y * j) * ((x * (z / j)) - i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -1.22e-35) {
		tmp = y * ((x * z) - (i * j));
	} else if (y <= -5.2e-85) {
		tmp = a * ((b * i) - (x * t));
	} else if (y <= -1.3e-116) {
		tmp = t * ((c * j) - (x * a));
	} else if (y <= 2.5e-229) {
		tmp = b * (z * ((a * (i / z)) - c));
	} else if (y <= 1.2e-164) {
		tmp = x * ((y * z) - (t * a));
	} else if (y <= 2.4e-164) {
		tmp = c * (t * j);
	} else if (y <= 1.55e+118) {
		tmp = i * (y * ((b * (a / y)) - j));
	} else if (y <= 1.96e+145) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = (y * j) * ((x * (z / j)) - i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -1.22e-35:
		tmp = y * ((x * z) - (i * j))
	elif y <= -5.2e-85:
		tmp = a * ((b * i) - (x * t))
	elif y <= -1.3e-116:
		tmp = t * ((c * j) - (x * a))
	elif y <= 2.5e-229:
		tmp = b * (z * ((a * (i / z)) - c))
	elif y <= 1.2e-164:
		tmp = x * ((y * z) - (t * a))
	elif y <= 2.4e-164:
		tmp = c * (t * j)
	elif y <= 1.55e+118:
		tmp = i * (y * ((b * (a / y)) - j))
	elif y <= 1.96e+145:
		tmp = z * ((x * y) - (b * c))
	else:
		tmp = (y * j) * ((x * (z / j)) - i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -1.22e-35)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (y <= -5.2e-85)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (y <= -1.3e-116)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (y <= 2.5e-229)
		tmp = Float64(b * Float64(z * Float64(Float64(a * Float64(i / z)) - c)));
	elseif (y <= 1.2e-164)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (y <= 2.4e-164)
		tmp = Float64(c * Float64(t * j));
	elseif (y <= 1.55e+118)
		tmp = Float64(i * Float64(y * Float64(Float64(b * Float64(a / y)) - j)));
	elseif (y <= 1.96e+145)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	else
		tmp = Float64(Float64(y * j) * Float64(Float64(x * Float64(z / j)) - i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -1.22e-35)
		tmp = y * ((x * z) - (i * j));
	elseif (y <= -5.2e-85)
		tmp = a * ((b * i) - (x * t));
	elseif (y <= -1.3e-116)
		tmp = t * ((c * j) - (x * a));
	elseif (y <= 2.5e-229)
		tmp = b * (z * ((a * (i / z)) - c));
	elseif (y <= 1.2e-164)
		tmp = x * ((y * z) - (t * a));
	elseif (y <= 2.4e-164)
		tmp = c * (t * j);
	elseif (y <= 1.55e+118)
		tmp = i * (y * ((b * (a / y)) - j));
	elseif (y <= 1.96e+145)
		tmp = z * ((x * y) - (b * c));
	else
		tmp = (y * j) * ((x * (z / j)) - i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -1.22e-35], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.2e-85], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.3e-116], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e-229], N[(b * N[(z * N[(N[(a * N[(i / z), $MachinePrecision]), $MachinePrecision] - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e-164], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.4e-164], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.55e+118], N[(i * N[(y * N[(N[(b * N[(a / y), $MachinePrecision]), $MachinePrecision] - j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.96e+145], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * j), $MachinePrecision] * N[(N[(x * N[(z / j), $MachinePrecision]), $MachinePrecision] - i), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y < -1.22e-35

   1. Initial program 67.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 68.9%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 68.9%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 68.9%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 68.9%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 68.9%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   5. Simplified 68.9%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   if -1.22e-35 < y < -5.20000000000000023e-85

   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 a around inf 70.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 70.2%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x - b \cdot i\right)\right)} \]

   5. Simplified 70.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x - b \cdot i\right)\right)} \]

   6. Taylor expanded in t around 0 70.2%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(b \cdot i\right)} \]
   7. Step-by-step derivation

      1. +-commutative 70.2%

         \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 70.2%

         \[\leadsto a \cdot \left(b \cdot i\right) + \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} \]

      3. distribute-rgt-neg-in 70.2%

         \[\leadsto a \cdot \left(b \cdot i\right) + \color{blue}{a \cdot \left(-t \cdot x\right)} \]

      4. distribute-lft-out 70.2%

         \[\leadsto \color{blue}{a \cdot \left(b \cdot i + \left(-t \cdot x\right)\right)} \]

      5. unsub-neg 70.2%

         \[\leadsto a \cdot \color{blue}{\left(b \cdot i - t \cdot x\right)} \]

   8. Simplified 70.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   if -5.20000000000000023e-85 < y < -1.3e-116

   1. Initial program 99.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 61.4%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 61.4%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 61.4%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 61.4%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   5. Simplified 61.4%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   if -1.3e-116 < y < 2.50000000000000008e-229

   1. Initial program 81.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 59.3%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]

   4. Taylor expanded in z around inf 59.5%

      \[\leadsto b \cdot \color{blue}{\left(z \cdot \left(\frac{a \cdot i}{z} - c\right)\right)} \]
   5. Step-by-step derivation

      1. associate-/l* 61.1%

         \[\leadsto b \cdot \left(z \cdot \left(\color{blue}{a \cdot \frac{i}{z}} - c\right)\right) \]

   6. Simplified 61.1%

      \[\leadsto b \cdot \color{blue}{\left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)} \]

   if 2.50000000000000008e-229 < y < 1.19999999999999992e-164

   1. Initial program 99.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 80.4%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   4. Step-by-step derivation

      1. *-commutative 80.4%

         \[\leadsto x \cdot \left(\color{blue}{z \cdot y} - a \cdot t\right) \]

   5. Simplified 80.4%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y - a \cdot t\right)} \]

   if 1.19999999999999992e-164 < y < 2.39999999999999983e-164

   1. Initial program 100.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 100.0%

      \[\leadsto \color{blue}{j \cdot \left(\left(c \cdot t + \frac{x \cdot \left(y \cdot z - a \cdot t\right)}{j}\right) - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 100.0%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t + \left(\frac{x \cdot \left(y \cdot z - a \cdot t\right)}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right)} \]

      2. sub-neg 100.0%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \color{blue}{\left(y \cdot z + \left(-a \cdot t\right)\right)}}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right) \]

      3. mul-1-neg 100.0%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \left(y \cdot z + \color{blue}{-1 \cdot \left(a \cdot t\right)}\right)}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right) \]

      4. +-commutative 100.0%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \color{blue}{\left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)}}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right) \]

      5. +-commutative 100.0%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)}{j} - \color{blue}{\left(\frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j} + i \cdot y\right)}\right)\right) \]

      6. associate--r+ 100.0%

         \[\leadsto j \cdot \left(c \cdot t + \color{blue}{\left(\left(\frac{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)}{j} - \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right) - i \cdot y\right)}\right) \]

   5. Simplified 100.0%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t + \left(\frac{x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(c \cdot z - a \cdot i\right)}{j} - i \cdot y\right)\right)} \]

   6. Taylor expanded in i around inf 100.0%

      \[\leadsto j \cdot \left(c \cdot t + \left(\color{blue}{\frac{a \cdot \left(b \cdot i\right)}{j}} - i \cdot y\right)\right) \]
   7. Step-by-step derivation

      1. associate-*r* 100.0%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{\color{blue}{\left(a \cdot b\right) \cdot i}}{j} - i \cdot y\right)\right) \]

   8. Simplified 100.0%

      \[\leadsto j \cdot \left(c \cdot t + \left(\color{blue}{\frac{\left(a \cdot b\right) \cdot i}{j}} - i \cdot y\right)\right) \]

   9. Taylor expanded in c around inf 100.0%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]

   if 2.39999999999999983e-164 < y < 1.54999999999999993e118

   1. Initial program 74.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 49.8%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 49.8%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. *-commutative 49.8%

         \[\leadsto i \cdot \left(-1 \cdot \left(j \cdot y - \color{blue}{b \cdot a}\right)\right) \]

   5. Simplified 49.8%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - b \cdot a\right)\right)} \]

   6. Taylor expanded in b around inf 41.7%

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \frac{i \cdot \left(j \cdot y\right)}{b} + a \cdot i\right)} \]
   7. Step-by-step derivation

      1. +-commutative 41.7%

         \[\leadsto b \cdot \color{blue}{\left(a \cdot i + -1 \cdot \frac{i \cdot \left(j \cdot y\right)}{b}\right)} \]

      2. *-commutative 41.7%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} + -1 \cdot \frac{i \cdot \left(j \cdot y\right)}{b}\right) \]

      3. mul-1-neg 41.7%

         \[\leadsto b \cdot \left(i \cdot a + \color{blue}{\left(-\frac{i \cdot \left(j \cdot y\right)}{b}\right)}\right) \]

      4. unsub-neg 41.7%

         \[\leadsto b \cdot \color{blue}{\left(i \cdot a - \frac{i \cdot \left(j \cdot y\right)}{b}\right)} \]

      5. *-commutative 41.7%

         \[\leadsto b \cdot \left(\color{blue}{a \cdot i} - \frac{i \cdot \left(j \cdot y\right)}{b}\right) \]

      6. associate-/l* 45.7%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{i \cdot \frac{j \cdot y}{b}}\right) \]

      7. *-commutative 45.7%

         \[\leadsto b \cdot \left(a \cdot i - i \cdot \frac{\color{blue}{y \cdot j}}{b}\right) \]

   8. Simplified 45.7%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - i \cdot \frac{y \cdot j}{b}\right)} \]

   9. Taylor expanded in b around inf 41.7%

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \frac{i \cdot \left(j \cdot y\right)}{b} + a \cdot i\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 41.7%

          \[\leadsto b \cdot \left(\color{blue}{\left(-\frac{i \cdot \left(j \cdot y\right)}{b}\right)} + a \cdot i\right) \]

       2. distribute-frac-neg 41.7%

          \[\leadsto b \cdot \left(\color{blue}{\frac{-i \cdot \left(j \cdot y\right)}{b}} + a \cdot i\right) \]

       3. distribute-lft-neg-in 41.7%

          \[\leadsto b \cdot \left(\frac{\color{blue}{\left(-i\right) \cdot \left(j \cdot y\right)}}{b} + a \cdot i\right) \]

       4. associate-*r/ 45.7%

          \[\leadsto b \cdot \left(\color{blue}{\left(-i\right) \cdot \frac{j \cdot y}{b}} + a \cdot i\right) \]

       5. *-commutative 45.7%

          \[\leadsto b \cdot \left(\left(-i\right) \cdot \frac{\color{blue}{y \cdot j}}{b} + a \cdot i\right) \]

       6. associate-*r/ 45.7%

          \[\leadsto b \cdot \left(\left(-i\right) \cdot \color{blue}{\left(y \cdot \frac{j}{b}\right)} + a \cdot i\right) \]

       7. distribute-lft-neg-in 45.7%

          \[\leadsto b \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot \frac{j}{b}\right)\right)} + a \cdot i\right) \]

       8. +-commutative 45.7%

          \[\leadsto b \cdot \color{blue}{\left(a \cdot i + \left(-i \cdot \left(y \cdot \frac{j}{b}\right)\right)\right)} \]

       9. distribute-lft-in 41.7%

          \[\leadsto \color{blue}{b \cdot \left(a \cdot i\right) + b \cdot \left(-i \cdot \left(y \cdot \frac{j}{b}\right)\right)} \]

       10. *-commutative 41.7%

           \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} + b \cdot \left(-i \cdot \left(y \cdot \frac{j}{b}\right)\right) \]

       11. associate-*r* 42.0%

           \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot a} + b \cdot \left(-i \cdot \left(y \cdot \frac{j}{b}\right)\right) \]

       12. distribute-rgt-neg-in 42.0%

           \[\leadsto \left(b \cdot i\right) \cdot a + b \cdot \color{blue}{\left(i \cdot \left(-y \cdot \frac{j}{b}\right)\right)} \]

       13. associate-*r* 39.9%

           \[\leadsto \left(b \cdot i\right) \cdot a + \color{blue}{\left(b \cdot i\right) \cdot \left(-y \cdot \frac{j}{b}\right)} \]

       14. distribute-lft-in 47.9%

           \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot \left(a + \left(-y \cdot \frac{j}{b}\right)\right)} \]

       15. associate-*r/ 48.0%

           \[\leadsto \left(b \cdot i\right) \cdot \left(a + \left(-\color{blue}{\frac{y \cdot j}{b}}\right)\right) \]

       16. *-commutative 48.0%

           \[\leadsto \left(b \cdot i\right) \cdot \left(a + \left(-\frac{\color{blue}{j \cdot y}}{b}\right)\right) \]

   11. Simplified 47.9%

       \[\leadsto \color{blue}{i \cdot \left(b \cdot \left(a - j \cdot \frac{y}{b}\right)\right)} \]

   12. Taylor expanded in y around inf 49.8%

       \[\leadsto i \cdot \color{blue}{\left(y \cdot \left(-1 \cdot j + \frac{a \cdot b}{y}\right)\right)} \]
   13. Step-by-step derivation

       1. neg-mul-1 49.8%

          \[\leadsto i \cdot \left(y \cdot \left(\color{blue}{\left(-j\right)} + \frac{a \cdot b}{y}\right)\right) \]

       2. +-commutative 49.8%

          \[\leadsto i \cdot \left(y \cdot \color{blue}{\left(\frac{a \cdot b}{y} + \left(-j\right)\right)}\right) \]

       3. unsub-neg 49.8%

          \[\leadsto i \cdot \left(y \cdot \color{blue}{\left(\frac{a \cdot b}{y} - j\right)}\right) \]

       4. *-commutative 49.8%

          \[\leadsto i \cdot \left(y \cdot \left(\frac{\color{blue}{b \cdot a}}{y} - j\right)\right) \]

       5. associate-/l* 55.5%

          \[\leadsto i \cdot \left(y \cdot \left(\color{blue}{b \cdot \frac{a}{y}} - j\right)\right) \]

   14. Simplified 55.5%

       \[\leadsto i \cdot \color{blue}{\left(y \cdot \left(b \cdot \frac{a}{y} - j\right)\right)} \]

   if 1.54999999999999993e118 < y < 1.96e145

   1. Initial program 67.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 84.2%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 84.2%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

   5. Simplified 84.2%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - b \cdot c\right)} \]

   if 1.96e145 < y

   1. Initial program 56.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 56.6%

      \[\leadsto \color{blue}{j \cdot \left(\left(c \cdot t + \frac{x \cdot \left(y \cdot z - a \cdot t\right)}{j}\right) - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 56.6%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t + \left(\frac{x \cdot \left(y \cdot z - a \cdot t\right)}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right)} \]

      2. sub-neg 56.6%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \color{blue}{\left(y \cdot z + \left(-a \cdot t\right)\right)}}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right) \]

      3. mul-1-neg 56.6%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \left(y \cdot z + \color{blue}{-1 \cdot \left(a \cdot t\right)}\right)}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right) \]

      4. +-commutative 56.6%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \color{blue}{\left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)}}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right) \]

      5. +-commutative 56.6%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)}{j} - \color{blue}{\left(\frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j} + i \cdot y\right)}\right)\right) \]

      6. associate--r+ 56.6%

         \[\leadsto j \cdot \left(c \cdot t + \color{blue}{\left(\left(\frac{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)}{j} - \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right) - i \cdot y\right)}\right) \]

   5. Simplified 56.6%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t + \left(\frac{x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(c \cdot z - a \cdot i\right)}{j} - i \cdot y\right)\right)} \]

   6. Taylor expanded in y around inf 73.8%

      \[\leadsto \color{blue}{j \cdot \left(y \cdot \left(\frac{x \cdot z}{j} - i\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 73.7%

         \[\leadsto \color{blue}{\left(j \cdot y\right) \cdot \left(\frac{x \cdot z}{j} - i\right)} \]

      2. *-commutative 73.7%

         \[\leadsto \color{blue}{\left(y \cdot j\right)} \cdot \left(\frac{x \cdot z}{j} - i\right) \]

      3. associate-/l* 73.7%

         \[\leadsto \left(y \cdot j\right) \cdot \left(\color{blue}{x \cdot \frac{z}{j}} - i\right) \]

   8. Simplified 73.7%

      \[\leadsto \color{blue}{\left(y \cdot j\right) \cdot \left(x \cdot \frac{z}{j} - i\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{-35}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-85}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-116}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-229}:\\ \;\;\;\;b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-164}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-164}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+118}:\\ \;\;\;\;i \cdot \left(y \cdot \left(b \cdot \frac{a}{y} - j\right)\right)\\ \mathbf{elif}\;y \leq 1.96 \cdot 10^{+145}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(x \cdot \frac{z}{j} - i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 58.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c + i \cdot \left(a \cdot \frac{b}{j} - y\right)\right)\\ t_2 := x \cdot y - b \cdot c\\ t_3 := z \cdot t\_2\\ \mathbf{if}\;z \leq -2.85 \cdot 10^{+171}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+131}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-14}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+142}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+156}:\\ \;\;\;\;j \cdot \left(\frac{b \cdot \left(z \cdot c\right)}{-j} - y \cdot i\right)\\ \mathbf{elif}\;z \leq 9.4 \cdot 10^{+275}:\\ \;\;\;\;\left(z \cdot j\right) \cdot \frac{t\_2}{j}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+280}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (+ (* t c) (* i (- (* a (/ b j)) y)))))
        (t_2 (- (* x y) (* b c)))
        (t_3 (* z t_2)))
   (if (<= z -2.85e+171)
     t_3
     (if (<= z -3.8e+131)
       t_1
       (if (<= z -1.12e-14)
         (* c (- (* t j) (* z b)))
         (if (<= z 2.7e+25)
           t_1
           (if (<= z 1.6e+142)
             t_3
             (if (<= z 3.5e+156)
               (* j (- (/ (* b (* z c)) (- j)) (* y i)))
               (if (<= z 9.4e+275)
                 (* (* z j) (/ t_2 j))
                 (if (<= z 1.9e+280) (* b (* a i)) t_3))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) + (i * ((a * (b / j)) - y)));
	double t_2 = (x * y) - (b * c);
	double t_3 = z * t_2;
	double tmp;
	if (z <= -2.85e+171) {
		tmp = t_3;
	} else if (z <= -3.8e+131) {
		tmp = t_1;
	} else if (z <= -1.12e-14) {
		tmp = c * ((t * j) - (z * b));
	} else if (z <= 2.7e+25) {
		tmp = t_1;
	} else if (z <= 1.6e+142) {
		tmp = t_3;
	} else if (z <= 3.5e+156) {
		tmp = j * (((b * (z * c)) / -j) - (y * i));
	} else if (z <= 9.4e+275) {
		tmp = (z * j) * (t_2 / j);
	} else if (z <= 1.9e+280) {
		tmp = b * (a * i);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * ((t * c) + (i * ((a * (b / j)) - y)))
    t_2 = (x * y) - (b * c)
    t_3 = z * t_2
    if (z <= (-2.85d+171)) then
        tmp = t_3
    else if (z <= (-3.8d+131)) then
        tmp = t_1
    else if (z <= (-1.12d-14)) then
        tmp = c * ((t * j) - (z * b))
    else if (z <= 2.7d+25) then
        tmp = t_1
    else if (z <= 1.6d+142) then
        tmp = t_3
    else if (z <= 3.5d+156) then
        tmp = j * (((b * (z * c)) / -j) - (y * i))
    else if (z <= 9.4d+275) then
        tmp = (z * j) * (t_2 / j)
    else if (z <= 1.9d+280) then
        tmp = b * (a * i)
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) + (i * ((a * (b / j)) - y)));
	double t_2 = (x * y) - (b * c);
	double t_3 = z * t_2;
	double tmp;
	if (z <= -2.85e+171) {
		tmp = t_3;
	} else if (z <= -3.8e+131) {
		tmp = t_1;
	} else if (z <= -1.12e-14) {
		tmp = c * ((t * j) - (z * b));
	} else if (z <= 2.7e+25) {
		tmp = t_1;
	} else if (z <= 1.6e+142) {
		tmp = t_3;
	} else if (z <= 3.5e+156) {
		tmp = j * (((b * (z * c)) / -j) - (y * i));
	} else if (z <= 9.4e+275) {
		tmp = (z * j) * (t_2 / j);
	} else if (z <= 1.9e+280) {
		tmp = b * (a * i);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) + (i * ((a * (b / j)) - y)))
	t_2 = (x * y) - (b * c)
	t_3 = z * t_2
	tmp = 0
	if z <= -2.85e+171:
		tmp = t_3
	elif z <= -3.8e+131:
		tmp = t_1
	elif z <= -1.12e-14:
		tmp = c * ((t * j) - (z * b))
	elif z <= 2.7e+25:
		tmp = t_1
	elif z <= 1.6e+142:
		tmp = t_3
	elif z <= 3.5e+156:
		tmp = j * (((b * (z * c)) / -j) - (y * i))
	elif z <= 9.4e+275:
		tmp = (z * j) * (t_2 / j)
	elif z <= 1.9e+280:
		tmp = b * (a * i)
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) + Float64(i * Float64(Float64(a * Float64(b / j)) - y))))
	t_2 = Float64(Float64(x * y) - Float64(b * c))
	t_3 = Float64(z * t_2)
	tmp = 0.0
	if (z <= -2.85e+171)
		tmp = t_3;
	elseif (z <= -3.8e+131)
		tmp = t_1;
	elseif (z <= -1.12e-14)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (z <= 2.7e+25)
		tmp = t_1;
	elseif (z <= 1.6e+142)
		tmp = t_3;
	elseif (z <= 3.5e+156)
		tmp = Float64(j * Float64(Float64(Float64(b * Float64(z * c)) / Float64(-j)) - Float64(y * i)));
	elseif (z <= 9.4e+275)
		tmp = Float64(Float64(z * j) * Float64(t_2 / j));
	elseif (z <= 1.9e+280)
		tmp = Float64(b * Float64(a * i));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) + (i * ((a * (b / j)) - y)));
	t_2 = (x * y) - (b * c);
	t_3 = z * t_2;
	tmp = 0.0;
	if (z <= -2.85e+171)
		tmp = t_3;
	elseif (z <= -3.8e+131)
		tmp = t_1;
	elseif (z <= -1.12e-14)
		tmp = c * ((t * j) - (z * b));
	elseif (z <= 2.7e+25)
		tmp = t_1;
	elseif (z <= 1.6e+142)
		tmp = t_3;
	elseif (z <= 3.5e+156)
		tmp = j * (((b * (z * c)) / -j) - (y * i));
	elseif (z <= 9.4e+275)
		tmp = (z * j) * (t_2 / j);
	elseif (z <= 1.9e+280)
		tmp = b * (a * i);
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] + N[(i * N[(N[(a * N[(b / j), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * t$95$2), $MachinePrecision]}, If[LessEqual[z, -2.85e+171], t$95$3, If[LessEqual[z, -3.8e+131], t$95$1, If[LessEqual[z, -1.12e-14], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.7e+25], t$95$1, If[LessEqual[z, 1.6e+142], t$95$3, If[LessEqual[z, 3.5e+156], N[(j * N[(N[(N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision] / (-j)), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.4e+275], N[(N[(z * j), $MachinePrecision] * N[(t$95$2 / j), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e+280], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -2.85e171 or 2.7e25 < z < 1.60000000000000003e142 or 1.89999999999999982e280 < z

   1. Initial program 67.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 75.6%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 75.6%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

   5. Simplified 75.6%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - b \cdot c\right)} \]

   if -2.85e171 < z < -3.8000000000000004e131 or -1.12000000000000006e-14 < z < 2.7e25

   1. Initial program 85.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 77.9%

      \[\leadsto \color{blue}{j \cdot \left(\left(c \cdot t + \frac{x \cdot \left(y \cdot z - a \cdot t\right)}{j}\right) - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 77.9%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t + \left(\frac{x \cdot \left(y \cdot z - a \cdot t\right)}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right)} \]

      2. sub-neg 77.9%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \color{blue}{\left(y \cdot z + \left(-a \cdot t\right)\right)}}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right) \]

      3. mul-1-neg 77.9%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \left(y \cdot z + \color{blue}{-1 \cdot \left(a \cdot t\right)}\right)}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right) \]

      4. +-commutative 77.9%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \color{blue}{\left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)}}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right) \]

      5. +-commutative 77.9%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)}{j} - \color{blue}{\left(\frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j} + i \cdot y\right)}\right)\right) \]

      6. associate--r+ 77.9%

         \[\leadsto j \cdot \left(c \cdot t + \color{blue}{\left(\left(\frac{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)}{j} - \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right) - i \cdot y\right)}\right) \]

   5. Simplified 79.5%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t + \left(\frac{x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(c \cdot z - a \cdot i\right)}{j} - i \cdot y\right)\right)} \]

   6. Taylor expanded in i around inf 63.9%

      \[\leadsto j \cdot \left(c \cdot t + \left(\color{blue}{\frac{a \cdot \left(b \cdot i\right)}{j}} - i \cdot y\right)\right) \]
   7. Step-by-step derivation

      1. associate-*r* 65.0%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{\color{blue}{\left(a \cdot b\right) \cdot i}}{j} - i \cdot y\right)\right) \]

   8. Simplified 65.0%

      \[\leadsto j \cdot \left(c \cdot t + \left(\color{blue}{\frac{\left(a \cdot b\right) \cdot i}{j}} - i \cdot y\right)\right) \]

   9. Taylor expanded in a around 0 63.9%

      \[\leadsto j \cdot \left(c \cdot t + \color{blue}{\left(\frac{a \cdot \left(b \cdot i\right)}{j} - i \cdot y\right)}\right) \]
   10. Step-by-step derivation

       1. sub-neg 63.9%

          \[\leadsto j \cdot \left(c \cdot t + \color{blue}{\left(\frac{a \cdot \left(b \cdot i\right)}{j} + \left(-i \cdot y\right)\right)}\right) \]

       2. *-commutative 63.9%

          \[\leadsto j \cdot \left(c \cdot t + \left(\frac{a \cdot \color{blue}{\left(i \cdot b\right)}}{j} + \left(-i \cdot y\right)\right)\right) \]

       3. associate-*r* 66.2%

          \[\leadsto j \cdot \left(c \cdot t + \left(\frac{\color{blue}{\left(a \cdot i\right) \cdot b}}{j} + \left(-i \cdot y\right)\right)\right) \]

       4. *-commutative 66.2%

          \[\leadsto j \cdot \left(c \cdot t + \left(\frac{\color{blue}{\left(i \cdot a\right)} \cdot b}{j} + \left(-i \cdot y\right)\right)\right) \]

       5. associate-*r* 65.0%

          \[\leadsto j \cdot \left(c \cdot t + \left(\frac{\color{blue}{i \cdot \left(a \cdot b\right)}}{j} + \left(-i \cdot y\right)\right)\right) \]

       6. associate-*r/ 67.2%

          \[\leadsto j \cdot \left(c \cdot t + \left(\color{blue}{i \cdot \frac{a \cdot b}{j}} + \left(-i \cdot y\right)\right)\right) \]

       7. distribute-rgt-neg-in 67.2%

          \[\leadsto j \cdot \left(c \cdot t + \left(i \cdot \frac{a \cdot b}{j} + \color{blue}{i \cdot \left(-y\right)}\right)\right) \]

       8. distribute-lft-in 68.7%

          \[\leadsto j \cdot \left(c \cdot t + \color{blue}{i \cdot \left(\frac{a \cdot b}{j} + \left(-y\right)\right)}\right) \]

       9. sub-neg 68.7%

          \[\leadsto j \cdot \left(c \cdot t + i \cdot \color{blue}{\left(\frac{a \cdot b}{j} - y\right)}\right) \]

       10. associate-/l* 68.3%

           \[\leadsto j \cdot \left(c \cdot t + i \cdot \left(\color{blue}{a \cdot \frac{b}{j}} - y\right)\right) \]

   11. Simplified 68.3%

       \[\leadsto j \cdot \left(c \cdot t + \color{blue}{i \cdot \left(a \cdot \frac{b}{j} - y\right)}\right) \]

   if -3.8000000000000004e131 < z < -1.12000000000000006e-14

   1. Initial program 61.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 58.3%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

   if 1.60000000000000003e142 < z < 3.5000000000000003e156

   1. Initial program 52.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 26.9%

      \[\leadsto \color{blue}{j \cdot \left(\left(c \cdot t + \frac{x \cdot \left(y \cdot z - a \cdot t\right)}{j}\right) - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 26.9%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t + \left(\frac{x \cdot \left(y \cdot z - a \cdot t\right)}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right)} \]

      2. sub-neg 26.9%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \color{blue}{\left(y \cdot z + \left(-a \cdot t\right)\right)}}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right) \]

      3. mul-1-neg 26.9%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \left(y \cdot z + \color{blue}{-1 \cdot \left(a \cdot t\right)}\right)}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right) \]

      4. +-commutative 26.9%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \color{blue}{\left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)}}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right) \]

      5. +-commutative 26.9%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)}{j} - \color{blue}{\left(\frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j} + i \cdot y\right)}\right)\right) \]

      6. associate--r+ 26.9%

         \[\leadsto j \cdot \left(c \cdot t + \color{blue}{\left(\left(\frac{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)}{j} - \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right) - i \cdot y\right)}\right) \]

   5. Simplified 52.0%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t + \left(\frac{x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(c \cdot z - a \cdot i\right)}{j} - i \cdot y\right)\right)} \]

   6. Taylor expanded in c around inf 75.0%

      \[\leadsto j \cdot \left(c \cdot t + \left(\color{blue}{-1 \cdot \frac{b \cdot \left(c \cdot z\right)}{j}} - i \cdot y\right)\right) \]
   7. Step-by-step derivation

      1. associate-*r/ 75.0%

         \[\leadsto j \cdot \left(c \cdot t + \left(\color{blue}{\frac{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)}{j}} - i \cdot y\right)\right) \]

      2. associate-*r* 75.0%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{\color{blue}{\left(-1 \cdot b\right) \cdot \left(c \cdot z\right)}}{j} - i \cdot y\right)\right) \]

      3. neg-mul-1 75.0%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{\color{blue}{\left(-b\right)} \cdot \left(c \cdot z\right)}{j} - i \cdot y\right)\right) \]

      4. *-commutative 75.0%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{\left(-b\right) \cdot \color{blue}{\left(z \cdot c\right)}}{j} - i \cdot y\right)\right) \]

   8. Simplified 75.0%

      \[\leadsto j \cdot \left(c \cdot t + \left(\color{blue}{\frac{\left(-b\right) \cdot \left(z \cdot c\right)}{j}} - i \cdot y\right)\right) \]

   9. Taylor expanded in t around 0 75.0%

      \[\leadsto \color{blue}{j \cdot \left(-1 \cdot \frac{b \cdot \left(c \cdot z\right)}{j} - i \cdot y\right)} \]
   10. Step-by-step derivation

       1. associate-*r/ 75.0%

          \[\leadsto j \cdot \left(\color{blue}{\frac{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)}{j}} - i \cdot y\right) \]

       2. neg-mul-1 75.0%

          \[\leadsto j \cdot \left(\frac{\color{blue}{-b \cdot \left(c \cdot z\right)}}{j} - i \cdot y\right) \]

       3. distribute-lft-neg-in 75.0%

          \[\leadsto j \cdot \left(\frac{\color{blue}{\left(-b\right) \cdot \left(c \cdot z\right)}}{j} - i \cdot y\right) \]

   11. Simplified 75.0%

       \[\leadsto \color{blue}{j \cdot \left(\frac{\left(-b\right) \cdot \left(c \cdot z\right)}{j} - i \cdot y\right)} \]

   if 3.5000000000000003e156 < z < 9.4000000000000001e275

   1. Initial program 55.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 42.2%

      \[\leadsto \color{blue}{j \cdot \left(\left(c \cdot t + \frac{x \cdot \left(y \cdot z - a \cdot t\right)}{j}\right) - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 42.2%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t + \left(\frac{x \cdot \left(y \cdot z - a \cdot t\right)}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right)} \]

      2. sub-neg 42.2%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \color{blue}{\left(y \cdot z + \left(-a \cdot t\right)\right)}}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right) \]

      3. mul-1-neg 42.2%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \left(y \cdot z + \color{blue}{-1 \cdot \left(a \cdot t\right)}\right)}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right) \]

      4. +-commutative 42.2%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \color{blue}{\left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)}}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right) \]

      5. +-commutative 42.2%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)}{j} - \color{blue}{\left(\frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j} + i \cdot y\right)}\right)\right) \]

      6. associate--r+ 42.2%

         \[\leadsto j \cdot \left(c \cdot t + \color{blue}{\left(\left(\frac{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)}{j} - \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right) - i \cdot y\right)}\right) \]

   5. Simplified 49.3%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t + \left(\frac{x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(c \cdot z - a \cdot i\right)}{j} - i \cdot y\right)\right)} \]

   6. Taylor expanded in z around inf 59.6%

      \[\leadsto \color{blue}{j \cdot \left(z \cdot \left(\frac{x \cdot y}{j} - \frac{b \cdot c}{j}\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 68.9%

         \[\leadsto \color{blue}{\left(j \cdot z\right) \cdot \left(\frac{x \cdot y}{j} - \frac{b \cdot c}{j}\right)} \]

      2. *-commutative 68.9%

         \[\leadsto \color{blue}{\left(z \cdot j\right)} \cdot \left(\frac{x \cdot y}{j} - \frac{b \cdot c}{j}\right) \]

      3. div-sub 72.4%

         \[\leadsto \left(z \cdot j\right) \cdot \color{blue}{\frac{x \cdot y - b \cdot c}{j}} \]

      4. *-commutative 72.4%

         \[\leadsto \left(z \cdot j\right) \cdot \frac{x \cdot y - \color{blue}{c \cdot b}}{j} \]

   8. Simplified 72.4%

      \[\leadsto \color{blue}{\left(z \cdot j\right) \cdot \frac{x \cdot y - c \cdot b}{j}} \]

   if 9.4000000000000001e275 < z < 1.89999999999999982e280

   1. Initial program 50.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 100.0%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]

   4. Taylor expanded in a around inf 100.0%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{+171}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+131}:\\ \;\;\;\;j \cdot \left(t \cdot c + i \cdot \left(a \cdot \frac{b}{j} - y\right)\right)\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-14}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+25}:\\ \;\;\;\;j \cdot \left(t \cdot c + i \cdot \left(a \cdot \frac{b}{j} - y\right)\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+142}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+156}:\\ \;\;\;\;j \cdot \left(\frac{b \cdot \left(z \cdot c\right)}{-j} - y \cdot i\right)\\ \mathbf{elif}\;z \leq 9.4 \cdot 10^{+275}:\\ \;\;\;\;\left(z \cdot j\right) \cdot \frac{x \cdot y - b \cdot c}{j}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+280}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 48.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -1.24 \cdot 10^{-36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-85}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-118}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-238}:\\ \;\;\;\;b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-170}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-164}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+118}:\\ \;\;\;\;i \cdot \left(y \cdot \left(b \cdot \frac{a}{y} - j\right)\right)\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+144}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j)))))
   (if (<= y -1.24e-36)
     t_1
     (if (<= y -8e-85)
       (* a (- (* b i) (* x t)))
       (if (<= y -8.2e-118)
         (* t (- (* c j) (* x a)))
         (if (<= y 9.8e-238)
           (* b (* z (- (* a (/ i z)) c)))
           (if (<= y 8e-170)
             (* x (- (* y z) (* t a)))
             (if (<= y 2.6e-164)
               (* c (* t j))
               (if (<= y 1.6e+118)
                 (* i (* y (- (* b (/ a y)) j)))
                 (if (<= y 5.4e+144) (* z (- (* x y) (* b c))) t_1))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.24e-36) {
		tmp = t_1;
	} else if (y <= -8e-85) {
		tmp = a * ((b * i) - (x * t));
	} else if (y <= -8.2e-118) {
		tmp = t * ((c * j) - (x * a));
	} else if (y <= 9.8e-238) {
		tmp = b * (z * ((a * (i / z)) - c));
	} else if (y <= 8e-170) {
		tmp = x * ((y * z) - (t * a));
	} else if (y <= 2.6e-164) {
		tmp = c * (t * j);
	} else if (y <= 1.6e+118) {
		tmp = i * (y * ((b * (a / y)) - j));
	} else if (y <= 5.4e+144) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((x * z) - (i * j))
    if (y <= (-1.24d-36)) then
        tmp = t_1
    else if (y <= (-8d-85)) then
        tmp = a * ((b * i) - (x * t))
    else if (y <= (-8.2d-118)) then
        tmp = t * ((c * j) - (x * a))
    else if (y <= 9.8d-238) then
        tmp = b * (z * ((a * (i / z)) - c))
    else if (y <= 8d-170) then
        tmp = x * ((y * z) - (t * a))
    else if (y <= 2.6d-164) then
        tmp = c * (t * j)
    else if (y <= 1.6d+118) then
        tmp = i * (y * ((b * (a / y)) - j))
    else if (y <= 5.4d+144) then
        tmp = z * ((x * y) - (b * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.24e-36) {
		tmp = t_1;
	} else if (y <= -8e-85) {
		tmp = a * ((b * i) - (x * t));
	} else if (y <= -8.2e-118) {
		tmp = t * ((c * j) - (x * a));
	} else if (y <= 9.8e-238) {
		tmp = b * (z * ((a * (i / z)) - c));
	} else if (y <= 8e-170) {
		tmp = x * ((y * z) - (t * a));
	} else if (y <= 2.6e-164) {
		tmp = c * (t * j);
	} else if (y <= 1.6e+118) {
		tmp = i * (y * ((b * (a / y)) - j));
	} else if (y <= 5.4e+144) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -1.24e-36:
		tmp = t_1
	elif y <= -8e-85:
		tmp = a * ((b * i) - (x * t))
	elif y <= -8.2e-118:
		tmp = t * ((c * j) - (x * a))
	elif y <= 9.8e-238:
		tmp = b * (z * ((a * (i / z)) - c))
	elif y <= 8e-170:
		tmp = x * ((y * z) - (t * a))
	elif y <= 2.6e-164:
		tmp = c * (t * j)
	elif y <= 1.6e+118:
		tmp = i * (y * ((b * (a / y)) - j))
	elif y <= 5.4e+144:
		tmp = z * ((x * y) - (b * c))
	else:
		tmp = t_1
	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)))
	tmp = 0.0
	if (y <= -1.24e-36)
		tmp = t_1;
	elseif (y <= -8e-85)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (y <= -8.2e-118)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (y <= 9.8e-238)
		tmp = Float64(b * Float64(z * Float64(Float64(a * Float64(i / z)) - c)));
	elseif (y <= 8e-170)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (y <= 2.6e-164)
		tmp = Float64(c * Float64(t * j));
	elseif (y <= 1.6e+118)
		tmp = Float64(i * Float64(y * Float64(Float64(b * Float64(a / y)) - j)));
	elseif (y <= 5.4e+144)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -1.24e-36)
		tmp = t_1;
	elseif (y <= -8e-85)
		tmp = a * ((b * i) - (x * t));
	elseif (y <= -8.2e-118)
		tmp = t * ((c * j) - (x * a));
	elseif (y <= 9.8e-238)
		tmp = b * (z * ((a * (i / z)) - c));
	elseif (y <= 8e-170)
		tmp = x * ((y * z) - (t * a));
	elseif (y <= 2.6e-164)
		tmp = c * (t * j);
	elseif (y <= 1.6e+118)
		tmp = i * (y * ((b * (a / y)) - j));
	elseif (y <= 5.4e+144)
		tmp = z * ((x * y) - (b * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.24e-36], t$95$1, If[LessEqual[y, -8e-85], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8.2e-118], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.8e-238], N[(b * N[(z * N[(N[(a * N[(i / z), $MachinePrecision]), $MachinePrecision] - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8e-170], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.6e-164], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e+118], N[(i * N[(y * N[(N[(b * N[(a / y), $MachinePrecision]), $MachinePrecision] - j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.4e+144], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y < -1.23999999999999997e-36 or 5.4000000000000003e144 < y

   1. Initial program 63.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 69.6%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 69.6%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 69.6%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 69.6%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 69.6%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   5. Simplified 69.6%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   if -1.23999999999999997e-36 < y < -7.9999999999999998e-85

   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 a around inf 70.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 70.2%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x - b \cdot i\right)\right)} \]

   5. Simplified 70.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x - b \cdot i\right)\right)} \]

   6. Taylor expanded in t around 0 70.2%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(b \cdot i\right)} \]
   7. Step-by-step derivation

      1. +-commutative 70.2%

         \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 70.2%

         \[\leadsto a \cdot \left(b \cdot i\right) + \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} \]

      3. distribute-rgt-neg-in 70.2%

         \[\leadsto a \cdot \left(b \cdot i\right) + \color{blue}{a \cdot \left(-t \cdot x\right)} \]

      4. distribute-lft-out 70.2%

         \[\leadsto \color{blue}{a \cdot \left(b \cdot i + \left(-t \cdot x\right)\right)} \]

      5. unsub-neg 70.2%

         \[\leadsto a \cdot \color{blue}{\left(b \cdot i - t \cdot x\right)} \]

   8. Simplified 70.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   if -7.9999999999999998e-85 < y < -8.2000000000000006e-118

   1. Initial program 99.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 61.4%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 61.4%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 61.4%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 61.4%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   5. Simplified 61.4%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   if -8.2000000000000006e-118 < y < 9.7999999999999996e-238

   1. Initial program 81.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 59.3%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]

   4. Taylor expanded in z around inf 59.5%

      \[\leadsto b \cdot \color{blue}{\left(z \cdot \left(\frac{a \cdot i}{z} - c\right)\right)} \]
   5. Step-by-step derivation

      1. associate-/l* 61.1%

         \[\leadsto b \cdot \left(z \cdot \left(\color{blue}{a \cdot \frac{i}{z}} - c\right)\right) \]

   6. Simplified 61.1%

      \[\leadsto b \cdot \color{blue}{\left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)} \]

   if 9.7999999999999996e-238 < y < 7.99999999999999987e-170

   1. Initial program 99.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 80.4%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   4. Step-by-step derivation

      1. *-commutative 80.4%

         \[\leadsto x \cdot \left(\color{blue}{z \cdot y} - a \cdot t\right) \]

   5. Simplified 80.4%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y - a \cdot t\right)} \]

   if 7.99999999999999987e-170 < y < 2.6000000000000002e-164

   1. Initial program 100.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 100.0%

      \[\leadsto \color{blue}{j \cdot \left(\left(c \cdot t + \frac{x \cdot \left(y \cdot z - a \cdot t\right)}{j}\right) - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 100.0%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t + \left(\frac{x \cdot \left(y \cdot z - a \cdot t\right)}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right)} \]

      2. sub-neg 100.0%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \color{blue}{\left(y \cdot z + \left(-a \cdot t\right)\right)}}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right) \]

      3. mul-1-neg 100.0%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \left(y \cdot z + \color{blue}{-1 \cdot \left(a \cdot t\right)}\right)}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right) \]

      4. +-commutative 100.0%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \color{blue}{\left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)}}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right) \]

      5. +-commutative 100.0%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)}{j} - \color{blue}{\left(\frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j} + i \cdot y\right)}\right)\right) \]

      6. associate--r+ 100.0%

         \[\leadsto j \cdot \left(c \cdot t + \color{blue}{\left(\left(\frac{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)}{j} - \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right) - i \cdot y\right)}\right) \]

   5. Simplified 100.0%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t + \left(\frac{x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(c \cdot z - a \cdot i\right)}{j} - i \cdot y\right)\right)} \]

   6. Taylor expanded in i around inf 100.0%

      \[\leadsto j \cdot \left(c \cdot t + \left(\color{blue}{\frac{a \cdot \left(b \cdot i\right)}{j}} - i \cdot y\right)\right) \]
   7. Step-by-step derivation

      1. associate-*r* 100.0%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{\color{blue}{\left(a \cdot b\right) \cdot i}}{j} - i \cdot y\right)\right) \]

   8. Simplified 100.0%

      \[\leadsto j \cdot \left(c \cdot t + \left(\color{blue}{\frac{\left(a \cdot b\right) \cdot i}{j}} - i \cdot y\right)\right) \]

   9. Taylor expanded in c around inf 100.0%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]

   if 2.6000000000000002e-164 < y < 1.60000000000000008e118

   1. Initial program 74.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 49.8%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 49.8%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. *-commutative 49.8%

         \[\leadsto i \cdot \left(-1 \cdot \left(j \cdot y - \color{blue}{b \cdot a}\right)\right) \]

   5. Simplified 49.8%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - b \cdot a\right)\right)} \]

   6. Taylor expanded in b around inf 41.7%

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \frac{i \cdot \left(j \cdot y\right)}{b} + a \cdot i\right)} \]
   7. Step-by-step derivation

      1. +-commutative 41.7%

         \[\leadsto b \cdot \color{blue}{\left(a \cdot i + -1 \cdot \frac{i \cdot \left(j \cdot y\right)}{b}\right)} \]

      2. *-commutative 41.7%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} + -1 \cdot \frac{i \cdot \left(j \cdot y\right)}{b}\right) \]

      3. mul-1-neg 41.7%

         \[\leadsto b \cdot \left(i \cdot a + \color{blue}{\left(-\frac{i \cdot \left(j \cdot y\right)}{b}\right)}\right) \]

      4. unsub-neg 41.7%

         \[\leadsto b \cdot \color{blue}{\left(i \cdot a - \frac{i \cdot \left(j \cdot y\right)}{b}\right)} \]

      5. *-commutative 41.7%

         \[\leadsto b \cdot \left(\color{blue}{a \cdot i} - \frac{i \cdot \left(j \cdot y\right)}{b}\right) \]

      6. associate-/l* 45.7%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{i \cdot \frac{j \cdot y}{b}}\right) \]

      7. *-commutative 45.7%

         \[\leadsto b \cdot \left(a \cdot i - i \cdot \frac{\color{blue}{y \cdot j}}{b}\right) \]

   8. Simplified 45.7%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - i \cdot \frac{y \cdot j}{b}\right)} \]

   9. Taylor expanded in b around inf 41.7%

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \frac{i \cdot \left(j \cdot y\right)}{b} + a \cdot i\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 41.7%

          \[\leadsto b \cdot \left(\color{blue}{\left(-\frac{i \cdot \left(j \cdot y\right)}{b}\right)} + a \cdot i\right) \]

       2. distribute-frac-neg 41.7%

          \[\leadsto b \cdot \left(\color{blue}{\frac{-i \cdot \left(j \cdot y\right)}{b}} + a \cdot i\right) \]

       3. distribute-lft-neg-in 41.7%

          \[\leadsto b \cdot \left(\frac{\color{blue}{\left(-i\right) \cdot \left(j \cdot y\right)}}{b} + a \cdot i\right) \]

       4. associate-*r/ 45.7%

          \[\leadsto b \cdot \left(\color{blue}{\left(-i\right) \cdot \frac{j \cdot y}{b}} + a \cdot i\right) \]

       5. *-commutative 45.7%

          \[\leadsto b \cdot \left(\left(-i\right) \cdot \frac{\color{blue}{y \cdot j}}{b} + a \cdot i\right) \]

       6. associate-*r/ 45.7%

          \[\leadsto b \cdot \left(\left(-i\right) \cdot \color{blue}{\left(y \cdot \frac{j}{b}\right)} + a \cdot i\right) \]

       7. distribute-lft-neg-in 45.7%

          \[\leadsto b \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot \frac{j}{b}\right)\right)} + a \cdot i\right) \]

       8. +-commutative 45.7%

          \[\leadsto b \cdot \color{blue}{\left(a \cdot i + \left(-i \cdot \left(y \cdot \frac{j}{b}\right)\right)\right)} \]

       9. distribute-lft-in 41.7%

          \[\leadsto \color{blue}{b \cdot \left(a \cdot i\right) + b \cdot \left(-i \cdot \left(y \cdot \frac{j}{b}\right)\right)} \]

       10. *-commutative 41.7%

           \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} + b \cdot \left(-i \cdot \left(y \cdot \frac{j}{b}\right)\right) \]

       11. associate-*r* 42.0%

           \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot a} + b \cdot \left(-i \cdot \left(y \cdot \frac{j}{b}\right)\right) \]

       12. distribute-rgt-neg-in 42.0%

           \[\leadsto \left(b \cdot i\right) \cdot a + b \cdot \color{blue}{\left(i \cdot \left(-y \cdot \frac{j}{b}\right)\right)} \]

       13. associate-*r* 39.9%

           \[\leadsto \left(b \cdot i\right) \cdot a + \color{blue}{\left(b \cdot i\right) \cdot \left(-y \cdot \frac{j}{b}\right)} \]

       14. distribute-lft-in 47.9%

           \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot \left(a + \left(-y \cdot \frac{j}{b}\right)\right)} \]

       15. associate-*r/ 48.0%

           \[\leadsto \left(b \cdot i\right) \cdot \left(a + \left(-\color{blue}{\frac{y \cdot j}{b}}\right)\right) \]

       16. *-commutative 48.0%

           \[\leadsto \left(b \cdot i\right) \cdot \left(a + \left(-\frac{\color{blue}{j \cdot y}}{b}\right)\right) \]

   11. Simplified 47.9%

       \[\leadsto \color{blue}{i \cdot \left(b \cdot \left(a - j \cdot \frac{y}{b}\right)\right)} \]

   12. Taylor expanded in y around inf 49.8%

       \[\leadsto i \cdot \color{blue}{\left(y \cdot \left(-1 \cdot j + \frac{a \cdot b}{y}\right)\right)} \]
   13. Step-by-step derivation

       1. neg-mul-1 49.8%

          \[\leadsto i \cdot \left(y \cdot \left(\color{blue}{\left(-j\right)} + \frac{a \cdot b}{y}\right)\right) \]

       2. +-commutative 49.8%

          \[\leadsto i \cdot \left(y \cdot \color{blue}{\left(\frac{a \cdot b}{y} + \left(-j\right)\right)}\right) \]

       3. unsub-neg 49.8%

          \[\leadsto i \cdot \left(y \cdot \color{blue}{\left(\frac{a \cdot b}{y} - j\right)}\right) \]

       4. *-commutative 49.8%

          \[\leadsto i \cdot \left(y \cdot \left(\frac{\color{blue}{b \cdot a}}{y} - j\right)\right) \]

       5. associate-/l* 55.5%

          \[\leadsto i \cdot \left(y \cdot \left(\color{blue}{b \cdot \frac{a}{y}} - j\right)\right) \]

   14. Simplified 55.5%

       \[\leadsto i \cdot \color{blue}{\left(y \cdot \left(b \cdot \frac{a}{y} - j\right)\right)} \]

   if 1.60000000000000008e118 < y < 5.4000000000000003e144

   1. Initial program 67.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 84.2%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 84.2%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

   5. Simplified 84.2%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - b \cdot c\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.24 \cdot 10^{-36}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-85}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-118}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-238}:\\ \;\;\;\;b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-170}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-164}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+118}:\\ \;\;\;\;i \cdot \left(y \cdot \left(b \cdot \frac{a}{y} - j\right)\right)\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+144}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 43.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -5.2 \cdot 10^{+18}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-134}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-170}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.9 \cdot 10^{-213}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-275}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{-175}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-66}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-20}:\\ \;\;\;\;j \cdot \left(i \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (* c j))) (t_2 (* a (- (* b i) (* x t)))))
   (if (<= a -5.2e+18)
     t_2
     (if (<= a -2.6e-134)
       (* z (* b (- c)))
       (if (<= a -9.5e-170)
         t_1
         (if (<= a -3.9e-213)
           (* z (* x y))
           (if (<= a -2e-275)
             t_1
             (if (<= a 2.25e-175)
               (* i (* j (- y)))
               (if (<= a 2.2e-66)
                 (* j (* t c))
                 (if (<= a 2.4e-20) (* j (* i (- y))) t_2))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (c * j);
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -5.2e+18) {
		tmp = t_2;
	} else if (a <= -2.6e-134) {
		tmp = z * (b * -c);
	} else if (a <= -9.5e-170) {
		tmp = t_1;
	} else if (a <= -3.9e-213) {
		tmp = z * (x * y);
	} else if (a <= -2e-275) {
		tmp = t_1;
	} else if (a <= 2.25e-175) {
		tmp = i * (j * -y);
	} else if (a <= 2.2e-66) {
		tmp = j * (t * c);
	} else if (a <= 2.4e-20) {
		tmp = j * (i * -y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (c * j)
    t_2 = a * ((b * i) - (x * t))
    if (a <= (-5.2d+18)) then
        tmp = t_2
    else if (a <= (-2.6d-134)) then
        tmp = z * (b * -c)
    else if (a <= (-9.5d-170)) then
        tmp = t_1
    else if (a <= (-3.9d-213)) then
        tmp = z * (x * y)
    else if (a <= (-2d-275)) then
        tmp = t_1
    else if (a <= 2.25d-175) then
        tmp = i * (j * -y)
    else if (a <= 2.2d-66) then
        tmp = j * (t * c)
    else if (a <= 2.4d-20) then
        tmp = j * (i * -y)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (c * j);
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -5.2e+18) {
		tmp = t_2;
	} else if (a <= -2.6e-134) {
		tmp = z * (b * -c);
	} else if (a <= -9.5e-170) {
		tmp = t_1;
	} else if (a <= -3.9e-213) {
		tmp = z * (x * y);
	} else if (a <= -2e-275) {
		tmp = t_1;
	} else if (a <= 2.25e-175) {
		tmp = i * (j * -y);
	} else if (a <= 2.2e-66) {
		tmp = j * (t * c);
	} else if (a <= 2.4e-20) {
		tmp = j * (i * -y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * (c * j)
	t_2 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -5.2e+18:
		tmp = t_2
	elif a <= -2.6e-134:
		tmp = z * (b * -c)
	elif a <= -9.5e-170:
		tmp = t_1
	elif a <= -3.9e-213:
		tmp = z * (x * y)
	elif a <= -2e-275:
		tmp = t_1
	elif a <= 2.25e-175:
		tmp = i * (j * -y)
	elif a <= 2.2e-66:
		tmp = j * (t * c)
	elif a <= 2.4e-20:
		tmp = j * (i * -y)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(c * j))
	t_2 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -5.2e+18)
		tmp = t_2;
	elseif (a <= -2.6e-134)
		tmp = Float64(z * Float64(b * Float64(-c)));
	elseif (a <= -9.5e-170)
		tmp = t_1;
	elseif (a <= -3.9e-213)
		tmp = Float64(z * Float64(x * y));
	elseif (a <= -2e-275)
		tmp = t_1;
	elseif (a <= 2.25e-175)
		tmp = Float64(i * Float64(j * Float64(-y)));
	elseif (a <= 2.2e-66)
		tmp = Float64(j * Float64(t * c));
	elseif (a <= 2.4e-20)
		tmp = Float64(j * Float64(i * Float64(-y)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * (c * j);
	t_2 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -5.2e+18)
		tmp = t_2;
	elseif (a <= -2.6e-134)
		tmp = z * (b * -c);
	elseif (a <= -9.5e-170)
		tmp = t_1;
	elseif (a <= -3.9e-213)
		tmp = z * (x * y);
	elseif (a <= -2e-275)
		tmp = t_1;
	elseif (a <= 2.25e-175)
		tmp = i * (j * -y);
	elseif (a <= 2.2e-66)
		tmp = j * (t * c);
	elseif (a <= 2.4e-20)
		tmp = j * (i * -y);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.2e+18], t$95$2, If[LessEqual[a, -2.6e-134], N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -9.5e-170], t$95$1, If[LessEqual[a, -3.9e-213], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2e-275], t$95$1, If[LessEqual[a, 2.25e-175], N[(i * N[(j * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.2e-66], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.4e-20], N[(j * N[(i * (-y)), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if a < -5.2e18 or 2.39999999999999993e-20 < a

   1. Initial program 70.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 59.9%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 59.9%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x - b \cdot i\right)\right)} \]

   5. Simplified 59.9%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x - b \cdot i\right)\right)} \]

   6. Taylor expanded in t around 0 59.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(b \cdot i\right)} \]
   7. Step-by-step derivation

      1. +-commutative 59.9%

         \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 59.9%

         \[\leadsto a \cdot \left(b \cdot i\right) + \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} \]

      3. distribute-rgt-neg-in 59.9%

         \[\leadsto a \cdot \left(b \cdot i\right) + \color{blue}{a \cdot \left(-t \cdot x\right)} \]

      4. distribute-lft-out 59.9%

         \[\leadsto \color{blue}{a \cdot \left(b \cdot i + \left(-t \cdot x\right)\right)} \]

      5. unsub-neg 59.9%

         \[\leadsto a \cdot \color{blue}{\left(b \cdot i - t \cdot x\right)} \]

   8. Simplified 59.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   if -5.2e18 < a < -2.60000000000000023e-134

   1. Initial program 81.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 73.0%

      \[\leadsto \color{blue}{j \cdot \left(\left(c \cdot t + \frac{x \cdot \left(y \cdot z - a \cdot t\right)}{j}\right) - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 73.0%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t + \left(\frac{x \cdot \left(y \cdot z - a \cdot t\right)}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right)} \]

      2. sub-neg 73.0%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \color{blue}{\left(y \cdot z + \left(-a \cdot t\right)\right)}}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right) \]

      3. mul-1-neg 73.0%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \left(y \cdot z + \color{blue}{-1 \cdot \left(a \cdot t\right)}\right)}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right) \]

      4. +-commutative 73.0%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \color{blue}{\left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)}}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right) \]

      5. +-commutative 73.0%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)}{j} - \color{blue}{\left(\frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j} + i \cdot y\right)}\right)\right) \]

      6. associate--r+ 73.0%

         \[\leadsto j \cdot \left(c \cdot t + \color{blue}{\left(\left(\frac{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)}{j} - \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right) - i \cdot y\right)}\right) \]

   5. Simplified 78.7%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t + \left(\frac{x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(c \cdot z - a \cdot i\right)}{j} - i \cdot y\right)\right)} \]

   6. Taylor expanded in c around inf 70.6%

      \[\leadsto j \cdot \left(c \cdot t + \left(\color{blue}{-1 \cdot \frac{b \cdot \left(c \cdot z\right)}{j}} - i \cdot y\right)\right) \]
   7. Step-by-step derivation

      1. associate-*r/ 70.6%

         \[\leadsto j \cdot \left(c \cdot t + \left(\color{blue}{\frac{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)}{j}} - i \cdot y\right)\right) \]

      2. associate-*r* 70.6%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{\color{blue}{\left(-1 \cdot b\right) \cdot \left(c \cdot z\right)}}{j} - i \cdot y\right)\right) \]

      3. neg-mul-1 70.6%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{\color{blue}{\left(-b\right)} \cdot \left(c \cdot z\right)}{j} - i \cdot y\right)\right) \]

      4. *-commutative 70.6%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{\left(-b\right) \cdot \color{blue}{\left(z \cdot c\right)}}{j} - i \cdot y\right)\right) \]

   8. Simplified 70.6%

      \[\leadsto j \cdot \left(c \cdot t + \left(\color{blue}{\frac{\left(-b\right) \cdot \left(z \cdot c\right)}{j}} - i \cdot y\right)\right) \]

   9. Taylor expanded in j around 0 41.0%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. neg-mul-1 41.0%

          \[\leadsto \color{blue}{-b \cdot \left(c \cdot z\right)} \]

       2. *-commutative 41.0%

          \[\leadsto -b \cdot \color{blue}{\left(z \cdot c\right)} \]

       3. associate-*r* 43.5%

          \[\leadsto -\color{blue}{\left(b \cdot z\right) \cdot c} \]

       4. *-commutative 43.5%

          \[\leadsto -\color{blue}{\left(z \cdot b\right)} \cdot c \]

       5. associate-*r* 46.1%

          \[\leadsto -\color{blue}{z \cdot \left(b \cdot c\right)} \]

       6. distribute-rgt-neg-out 46.1%

          \[\leadsto \color{blue}{z \cdot \left(-b \cdot c\right)} \]

       7. distribute-rgt-neg-in 46.1%

          \[\leadsto z \cdot \color{blue}{\left(b \cdot \left(-c\right)\right)} \]

   11. Simplified 46.1%

       \[\leadsto \color{blue}{z \cdot \left(b \cdot \left(-c\right)\right)} \]

   if -2.60000000000000023e-134 < a < -9.5000000000000001e-170 or -3.89999999999999989e-213 < a < -1.99999999999999987e-275

   1. Initial program 89.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 62.4%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 62.4%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 62.4%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 62.4%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   5. Simplified 62.4%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   6. Taylor expanded in c around inf 62.1%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot j\right)} \]

   if -9.5000000000000001e-170 < a < -3.89999999999999989e-213

   1. Initial program 88.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 67.9%

      \[\leadsto \color{blue}{j \cdot \left(\left(c \cdot t + \frac{x \cdot \left(y \cdot z - a \cdot t\right)}{j}\right) - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 67.9%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t + \left(\frac{x \cdot \left(y \cdot z - a \cdot t\right)}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right)} \]

      2. sub-neg 67.9%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \color{blue}{\left(y \cdot z + \left(-a \cdot t\right)\right)}}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right) \]

      3. mul-1-neg 67.9%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \left(y \cdot z + \color{blue}{-1 \cdot \left(a \cdot t\right)}\right)}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right) \]

      4. +-commutative 67.9%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \color{blue}{\left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)}}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right) \]

      5. +-commutative 67.9%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)}{j} - \color{blue}{\left(\frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j} + i \cdot y\right)}\right)\right) \]

      6. associate--r+ 67.9%

         \[\leadsto j \cdot \left(c \cdot t + \color{blue}{\left(\left(\frac{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)}{j} - \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right) - i \cdot y\right)}\right) \]

   5. Simplified 68.5%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t + \left(\frac{x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(c \cdot z - a \cdot i\right)}{j} - i \cdot y\right)\right)} \]

   6. Taylor expanded in z around inf 47.2%

      \[\leadsto \color{blue}{j \cdot \left(z \cdot \left(\frac{x \cdot y}{j} - \frac{b \cdot c}{j}\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 57.8%

         \[\leadsto \color{blue}{\left(j \cdot z\right) \cdot \left(\frac{x \cdot y}{j} - \frac{b \cdot c}{j}\right)} \]

      2. *-commutative 57.8%

         \[\leadsto \color{blue}{\left(z \cdot j\right)} \cdot \left(\frac{x \cdot y}{j} - \frac{b \cdot c}{j}\right) \]

      3. div-sub 57.8%

         \[\leadsto \left(z \cdot j\right) \cdot \color{blue}{\frac{x \cdot y - b \cdot c}{j}} \]

      4. *-commutative 57.8%

         \[\leadsto \left(z \cdot j\right) \cdot \frac{x \cdot y - \color{blue}{c \cdot b}}{j} \]

   8. Simplified 57.8%

      \[\leadsto \color{blue}{\left(z \cdot j\right) \cdot \frac{x \cdot y - c \cdot b}{j}} \]

   9. Taylor expanded in x around inf 46.4%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   10. Step-by-step derivation

       1. *-commutative 46.4%

          \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

       2. *-commutative 46.4%

          \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot x \]

       3. associate-*l* 46.4%

          \[\leadsto \color{blue}{z \cdot \left(y \cdot x\right)} \]

   11. Simplified 46.4%

       \[\leadsto \color{blue}{z \cdot \left(y \cdot x\right)} \]

   if -1.99999999999999987e-275 < a < 2.24999999999999999e-175

   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 i around inf 47.0%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 47.0%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. *-commutative 47.0%

         \[\leadsto i \cdot \left(-1 \cdot \left(j \cdot y - \color{blue}{b \cdot a}\right)\right) \]

   5. Simplified 47.0%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - b \cdot a\right)\right)} \]

   6. Taylor expanded in j around inf 46.7%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 46.7%

         \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(j \cdot y\right)} \]

      2. mul-1-neg 46.7%

         \[\leadsto \color{blue}{\left(-i\right)} \cdot \left(j \cdot y\right) \]

      3. *-commutative 46.7%

         \[\leadsto \left(-i\right) \cdot \color{blue}{\left(y \cdot j\right)} \]

   8. Simplified 46.7%

      \[\leadsto \color{blue}{\left(-i\right) \cdot \left(y \cdot j\right)} \]

   if 2.24999999999999999e-175 < a < 2.2000000000000001e-66

   1. Initial program 85.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 78.5%

      \[\leadsto \color{blue}{j \cdot \left(\left(c \cdot t + \frac{x \cdot \left(y \cdot z - a \cdot t\right)}{j}\right) - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 78.5%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t + \left(\frac{x \cdot \left(y \cdot z - a \cdot t\right)}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right)} \]

      2. sub-neg 78.5%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \color{blue}{\left(y \cdot z + \left(-a \cdot t\right)\right)}}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right) \]

      3. mul-1-neg 78.5%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \left(y \cdot z + \color{blue}{-1 \cdot \left(a \cdot t\right)}\right)}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right) \]

      4. +-commutative 78.5%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \color{blue}{\left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)}}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right) \]

      5. +-commutative 78.5%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)}{j} - \color{blue}{\left(\frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j} + i \cdot y\right)}\right)\right) \]

      6. associate--r+ 78.5%

         \[\leadsto j \cdot \left(c \cdot t + \color{blue}{\left(\left(\frac{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)}{j} - \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right) - i \cdot y\right)}\right) \]

   5. Simplified 85.6%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t + \left(\frac{x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(c \cdot z - a \cdot i\right)}{j} - i \cdot y\right)\right)} \]

   6. Taylor expanded in i around inf 79.1%

      \[\leadsto j \cdot \left(c \cdot t + \left(\color{blue}{\frac{a \cdot \left(b \cdot i\right)}{j}} - i \cdot y\right)\right) \]
   7. Step-by-step derivation

      1. associate-*r* 79.1%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{\color{blue}{\left(a \cdot b\right) \cdot i}}{j} - i \cdot y\right)\right) \]

   8. Simplified 79.1%

      \[\leadsto j \cdot \left(c \cdot t + \left(\color{blue}{\frac{\left(a \cdot b\right) \cdot i}{j}} - i \cdot y\right)\right) \]

   9. Taylor expanded in c around inf 43.9%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 37.1%

          \[\leadsto \color{blue}{\left(c \cdot j\right) \cdot t} \]

       2. *-commutative 37.1%

          \[\leadsto \color{blue}{\left(j \cdot c\right)} \cdot t \]

       3. associate-*r* 50.5%

          \[\leadsto \color{blue}{j \cdot \left(c \cdot t\right)} \]

   11. Simplified 50.5%

       \[\leadsto \color{blue}{j \cdot \left(c \cdot t\right)} \]

   if 2.2000000000000001e-66 < a < 2.39999999999999993e-20

   1. Initial program 74.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 42.5%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 42.5%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. *-commutative 42.5%

         \[\leadsto i \cdot \left(-1 \cdot \left(j \cdot y - \color{blue}{b \cdot a}\right)\right) \]

   5. Simplified 42.5%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - b \cdot a\right)\right)} \]

   6. Taylor expanded in j around inf 42.3%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 42.3%

         \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(j \cdot y\right)} \]

      2. mul-1-neg 42.3%

         \[\leadsto \color{blue}{\left(-i\right)} \cdot \left(j \cdot y\right) \]

      3. *-commutative 42.3%

         \[\leadsto \left(-i\right) \cdot \color{blue}{\left(y \cdot j\right)} \]

   8. Simplified 42.3%

      \[\leadsto \color{blue}{\left(-i\right) \cdot \left(y \cdot j\right)} \]

   9. Taylor expanded in i around 0 42.3%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 42.3%

          \[\leadsto \color{blue}{-i \cdot \left(j \cdot y\right)} \]

       2. *-commutative 42.3%

          \[\leadsto -i \cdot \color{blue}{\left(y \cdot j\right)} \]

       3. associate-*l* 42.3%

          \[\leadsto -\color{blue}{\left(i \cdot y\right) \cdot j} \]

       4. distribute-rgt-neg-in 42.3%

          \[\leadsto \color{blue}{\left(i \cdot y\right) \cdot \left(-j\right)} \]

   11. Simplified 42.3%

       \[\leadsto \color{blue}{\left(i \cdot y\right) \cdot \left(-j\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{+18}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-134}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-170}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq -3.9 \cdot 10^{-213}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-275}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{-175}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-66}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-20}:\\ \;\;\;\;j \cdot \left(i \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 66.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right) + t\_1\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_4 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_5 := t\_4 + t\_3\\ \mathbf{if}\;x \leq -6.6 \cdot 10^{+34}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-45}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -1.26 \cdot 10^{-86}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+147}:\\ \;\;\;\;t\_4 + t\_1\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+230}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+261}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_5\\ \end{array} \end{array} \]

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 j) (* x a))) t_1))
        (t_3 (* x (- (* y z) (* t a))))
        (t_4 (* j (- (* t c) (* y i))))
        (t_5 (+ t_4 t_3)))
   (if (<= x -6.6e+34)
     t_5
     (if (<= x -1.5e-45)
       t_2
       (if (<= x -1.26e-86)
         (* i (- (* a b) (* y j)))
         (if (<= x 6e+147)
           (+ t_4 t_1)
           (if (<= x 4.8e+230) t_2 (if (<= x 1.9e+261) t_3 t_5))))))))

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 * j) - (x * a))) + t_1;
	double t_3 = x * ((y * z) - (t * a));
	double t_4 = j * ((t * c) - (y * i));
	double t_5 = t_4 + t_3;
	double tmp;
	if (x <= -6.6e+34) {
		tmp = t_5;
	} else if (x <= -1.5e-45) {
		tmp = t_2;
	} else if (x <= -1.26e-86) {
		tmp = i * ((a * b) - (y * j));
	} else if (x <= 6e+147) {
		tmp = t_4 + t_1;
	} else if (x <= 4.8e+230) {
		tmp = t_2;
	} else if (x <= 1.9e+261) {
		tmp = t_3;
	} else {
		tmp = t_5;
	}
	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) :: t_5
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = (t * ((c * j) - (x * a))) + t_1
    t_3 = x * ((y * z) - (t * a))
    t_4 = j * ((t * c) - (y * i))
    t_5 = t_4 + t_3
    if (x <= (-6.6d+34)) then
        tmp = t_5
    else if (x <= (-1.5d-45)) then
        tmp = t_2
    else if (x <= (-1.26d-86)) then
        tmp = i * ((a * b) - (y * j))
    else if (x <= 6d+147) then
        tmp = t_4 + t_1
    else if (x <= 4.8d+230) then
        tmp = t_2
    else if (x <= 1.9d+261) then
        tmp = t_3
    else
        tmp = t_5
    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 = (t * ((c * j) - (x * a))) + t_1;
	double t_3 = x * ((y * z) - (t * a));
	double t_4 = j * ((t * c) - (y * i));
	double t_5 = t_4 + t_3;
	double tmp;
	if (x <= -6.6e+34) {
		tmp = t_5;
	} else if (x <= -1.5e-45) {
		tmp = t_2;
	} else if (x <= -1.26e-86) {
		tmp = i * ((a * b) - (y * j));
	} else if (x <= 6e+147) {
		tmp = t_4 + t_1;
	} else if (x <= 4.8e+230) {
		tmp = t_2;
	} else if (x <= 1.9e+261) {
		tmp = t_3;
	} else {
		tmp = t_5;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = (t * ((c * j) - (x * a))) + t_1
	t_3 = x * ((y * z) - (t * a))
	t_4 = j * ((t * c) - (y * i))
	t_5 = t_4 + t_3
	tmp = 0
	if x <= -6.6e+34:
		tmp = t_5
	elif x <= -1.5e-45:
		tmp = t_2
	elif x <= -1.26e-86:
		tmp = i * ((a * b) - (y * j))
	elif x <= 6e+147:
		tmp = t_4 + t_1
	elif x <= 4.8e+230:
		tmp = t_2
	elif x <= 1.9e+261:
		tmp = t_3
	else:
		tmp = t_5
	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 * Float64(Float64(c * j) - Float64(x * a))) + t_1)
	t_3 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_4 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_5 = Float64(t_4 + t_3)
	tmp = 0.0
	if (x <= -6.6e+34)
		tmp = t_5;
	elseif (x <= -1.5e-45)
		tmp = t_2;
	elseif (x <= -1.26e-86)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (x <= 6e+147)
		tmp = Float64(t_4 + t_1);
	elseif (x <= 4.8e+230)
		tmp = t_2;
	elseif (x <= 1.9e+261)
		tmp = t_3;
	else
		tmp = t_5;
	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 = (t * ((c * j) - (x * a))) + t_1;
	t_3 = x * ((y * z) - (t * a));
	t_4 = j * ((t * c) - (y * i));
	t_5 = t_4 + t_3;
	tmp = 0.0;
	if (x <= -6.6e+34)
		tmp = t_5;
	elseif (x <= -1.5e-45)
		tmp = t_2;
	elseif (x <= -1.26e-86)
		tmp = i * ((a * b) - (y * j));
	elseif (x <= 6e+147)
		tmp = t_4 + t_1;
	elseif (x <= 4.8e+230)
		tmp = t_2;
	elseif (x <= 1.9e+261)
		tmp = t_3;
	else
		tmp = t_5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 + t$95$3), $MachinePrecision]}, If[LessEqual[x, -6.6e+34], t$95$5, If[LessEqual[x, -1.5e-45], t$95$2, If[LessEqual[x, -1.26e-86], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6e+147], N[(t$95$4 + t$95$1), $MachinePrecision], If[LessEqual[x, 4.8e+230], t$95$2, If[LessEqual[x, 1.9e+261], t$95$3, t$95$5]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -6.59999999999999976e34 or 1.9000000000000001e261 < x

   1. Initial program 65.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 71.0%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   if -6.59999999999999976e34 < x < -1.50000000000000005e-45 or 5.99999999999999987e147 < x < 4.79999999999999996e230

   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 y around 0 72.4%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 72.4%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x\right)} + c \cdot \left(j \cdot t\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. *-commutative 72.4%

         \[\leadsto \left(\left(-1 \cdot a\right) \cdot \color{blue}{\left(x \cdot t\right)} + c \cdot \left(j \cdot t\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. associate-*r* 77.9%

         \[\leadsto \left(\color{blue}{\left(\left(-1 \cdot a\right) \cdot x\right) \cdot t} + c \cdot \left(j \cdot t\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 77.9%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(a \cdot x\right)\right)} \cdot t + c \cdot \left(j \cdot t\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. associate-*r* 77.9%

         \[\leadsto \left(\left(-1 \cdot \left(a \cdot x\right)\right) \cdot t + \color{blue}{\left(c \cdot j\right) \cdot t}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. distribute-rgt-in 77.9%

         \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. +-commutative 77.9%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. mul-1-neg 77.9%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. unsub-neg 77.9%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

   5. Simplified 77.9%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]

   if -1.50000000000000005e-45 < x < -1.25999999999999995e-86

   1. Initial program 66.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 69.4%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 69.4%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. *-commutative 69.4%

         \[\leadsto i \cdot \left(-1 \cdot \left(j \cdot y - \color{blue}{b \cdot a}\right)\right) \]

   5. Simplified 69.4%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - b \cdot a\right)\right)} \]

   if -1.25999999999999995e-86 < x < 5.99999999999999987e147

   1. Initial program 77.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 74.9%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]

   if 4.79999999999999996e230 < x < 1.9000000000000001e261

   1. Initial program 50.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 100.0%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   4. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto x \cdot \left(\color{blue}{z \cdot y} - a \cdot t\right) \]

   5. Simplified 100.0%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y - a \cdot t\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{+34}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-45}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq -1.26 \cdot 10^{-86}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+147}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+230}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+261}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 56.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - \left(y \cdot i + \frac{b \cdot \left(z \cdot c\right)}{j}\right)\right)\\ \mathbf{if}\;a \leq -1.6 \cdot 10^{+165}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{+72}:\\ \;\;\;\;i \cdot \left(b \cdot \left(a - j \cdot \frac{y}{b}\right)\right)\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-272}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-225}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 620:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+44}:\\ \;\;\;\;b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c + i \cdot \left(a \cdot \frac{b}{j} - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (+ (* y i) (/ (* b (* z c)) j))))))
   (if (<= a -1.6e+165)
     (* a (- (* b i) (* x t)))
     (if (<= a -4.6e+72)
       (* i (* b (- a (* j (/ y b)))))
       (if (<= a -2.3e-272)
         t_1
         (if (<= a 7.5e-225)
           (* y (- (* x z) (* i j)))
           (if (<= a 620.0)
             t_1
             (if (<= a 5.5e+44)
               (* b (* z (- (* a (/ i z)) 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 t_1 = j * ((t * c) - ((y * i) + ((b * (z * c)) / j)));
	double tmp;
	if (a <= -1.6e+165) {
		tmp = a * ((b * i) - (x * t));
	} else if (a <= -4.6e+72) {
		tmp = i * (b * (a - (j * (y / b))));
	} else if (a <= -2.3e-272) {
		tmp = t_1;
	} else if (a <= 7.5e-225) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= 620.0) {
		tmp = t_1;
	} else if (a <= 5.5e+44) {
		tmp = b * (z * ((a * (i / z)) - 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) :: t_1
    real(8) :: tmp
    t_1 = j * ((t * c) - ((y * i) + ((b * (z * c)) / j)))
    if (a <= (-1.6d+165)) then
        tmp = a * ((b * i) - (x * t))
    else if (a <= (-4.6d+72)) then
        tmp = i * (b * (a - (j * (y / b))))
    else if (a <= (-2.3d-272)) then
        tmp = t_1
    else if (a <= 7.5d-225) then
        tmp = y * ((x * z) - (i * j))
    else if (a <= 620.0d0) then
        tmp = t_1
    else if (a <= 5.5d+44) then
        tmp = b * (z * ((a * (i / z)) - 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 t_1 = j * ((t * c) - ((y * i) + ((b * (z * c)) / j)));
	double tmp;
	if (a <= -1.6e+165) {
		tmp = a * ((b * i) - (x * t));
	} else if (a <= -4.6e+72) {
		tmp = i * (b * (a - (j * (y / b))));
	} else if (a <= -2.3e-272) {
		tmp = t_1;
	} else if (a <= 7.5e-225) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= 620.0) {
		tmp = t_1;
	} else if (a <= 5.5e+44) {
		tmp = b * (z * ((a * (i / z)) - 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):
	t_1 = j * ((t * c) - ((y * i) + ((b * (z * c)) / j)))
	tmp = 0
	if a <= -1.6e+165:
		tmp = a * ((b * i) - (x * t))
	elif a <= -4.6e+72:
		tmp = i * (b * (a - (j * (y / b))))
	elif a <= -2.3e-272:
		tmp = t_1
	elif a <= 7.5e-225:
		tmp = y * ((x * z) - (i * j))
	elif a <= 620.0:
		tmp = t_1
	elif a <= 5.5e+44:
		tmp = b * (z * ((a * (i / z)) - 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)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(Float64(y * i) + Float64(Float64(b * Float64(z * c)) / j))))
	tmp = 0.0
	if (a <= -1.6e+165)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (a <= -4.6e+72)
		tmp = Float64(i * Float64(b * Float64(a - Float64(j * Float64(y / b)))));
	elseif (a <= -2.3e-272)
		tmp = t_1;
	elseif (a <= 7.5e-225)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (a <= 620.0)
		tmp = t_1;
	elseif (a <= 5.5e+44)
		tmp = Float64(b * Float64(z * Float64(Float64(a * Float64(i / z)) - 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)
	t_1 = j * ((t * c) - ((y * i) + ((b * (z * c)) / j)));
	tmp = 0.0;
	if (a <= -1.6e+165)
		tmp = a * ((b * i) - (x * t));
	elseif (a <= -4.6e+72)
		tmp = i * (b * (a - (j * (y / b))));
	elseif (a <= -2.3e-272)
		tmp = t_1;
	elseif (a <= 7.5e-225)
		tmp = y * ((x * z) - (i * j));
	elseif (a <= 620.0)
		tmp = t_1;
	elseif (a <= 5.5e+44)
		tmp = b * (z * ((a * (i / z)) - 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_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(N[(y * i), $MachinePrecision] + N[(N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision] / j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.6e+165], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.6e+72], N[(i * N[(b * N[(a - N[(j * N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.3e-272], t$95$1, If[LessEqual[a, 7.5e-225], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 620.0], t$95$1, If[LessEqual[a, 5.5e+44], N[(b * N[(z * N[(N[(a * N[(i / z), $MachinePrecision]), $MachinePrecision] - 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 6 regimes

2. if a < -1.6e165

   1. Initial program 69.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 87.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 87.2%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x - b \cdot i\right)\right)} \]

   5. Simplified 87.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x - b \cdot i\right)\right)} \]

   6. Taylor expanded in t around 0 87.2%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(b \cdot i\right)} \]
   7. Step-by-step derivation

      1. +-commutative 87.2%

         \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 87.2%

         \[\leadsto a \cdot \left(b \cdot i\right) + \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} \]

      3. distribute-rgt-neg-in 87.2%

         \[\leadsto a \cdot \left(b \cdot i\right) + \color{blue}{a \cdot \left(-t \cdot x\right)} \]

      4. distribute-lft-out 87.2%

         \[\leadsto \color{blue}{a \cdot \left(b \cdot i + \left(-t \cdot x\right)\right)} \]

      5. unsub-neg 87.2%

         \[\leadsto a \cdot \color{blue}{\left(b \cdot i - t \cdot x\right)} \]

   8. Simplified 87.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   if -1.6e165 < a < -4.6e72

   1. Initial program 66.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 55.0%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 55.0%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. *-commutative 55.0%

         \[\leadsto i \cdot \left(-1 \cdot \left(j \cdot y - \color{blue}{b \cdot a}\right)\right) \]

   5. Simplified 55.0%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - b \cdot a\right)\right)} \]

   6. Taylor expanded in b around inf 54.9%

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \frac{i \cdot \left(j \cdot y\right)}{b} + a \cdot i\right)} \]
   7. Step-by-step derivation

      1. +-commutative 54.9%

         \[\leadsto b \cdot \color{blue}{\left(a \cdot i + -1 \cdot \frac{i \cdot \left(j \cdot y\right)}{b}\right)} \]

      2. *-commutative 54.9%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} + -1 \cdot \frac{i \cdot \left(j \cdot y\right)}{b}\right) \]

      3. mul-1-neg 54.9%

         \[\leadsto b \cdot \left(i \cdot a + \color{blue}{\left(-\frac{i \cdot \left(j \cdot y\right)}{b}\right)}\right) \]

      4. unsub-neg 54.9%

         \[\leadsto b \cdot \color{blue}{\left(i \cdot a - \frac{i \cdot \left(j \cdot y\right)}{b}\right)} \]

      5. *-commutative 54.9%

         \[\leadsto b \cdot \left(\color{blue}{a \cdot i} - \frac{i \cdot \left(j \cdot y\right)}{b}\right) \]

      6. associate-/l* 55.0%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{i \cdot \frac{j \cdot y}{b}}\right) \]

      7. *-commutative 55.0%

         \[\leadsto b \cdot \left(a \cdot i - i \cdot \frac{\color{blue}{y \cdot j}}{b}\right) \]

   8. Simplified 55.0%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - i \cdot \frac{y \cdot j}{b}\right)} \]

   9. Taylor expanded in b around inf 54.9%

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \frac{i \cdot \left(j \cdot y\right)}{b} + a \cdot i\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 54.9%

          \[\leadsto b \cdot \left(\color{blue}{\left(-\frac{i \cdot \left(j \cdot y\right)}{b}\right)} + a \cdot i\right) \]

       2. distribute-frac-neg 54.9%

          \[\leadsto b \cdot \left(\color{blue}{\frac{-i \cdot \left(j \cdot y\right)}{b}} + a \cdot i\right) \]

       3. distribute-lft-neg-in 54.9%

          \[\leadsto b \cdot \left(\frac{\color{blue}{\left(-i\right) \cdot \left(j \cdot y\right)}}{b} + a \cdot i\right) \]

       4. associate-*r/ 55.0%

          \[\leadsto b \cdot \left(\color{blue}{\left(-i\right) \cdot \frac{j \cdot y}{b}} + a \cdot i\right) \]

       5. *-commutative 55.0%

          \[\leadsto b \cdot \left(\left(-i\right) \cdot \frac{\color{blue}{y \cdot j}}{b} + a \cdot i\right) \]

       6. associate-*r/ 50.8%

          \[\leadsto b \cdot \left(\left(-i\right) \cdot \color{blue}{\left(y \cdot \frac{j}{b}\right)} + a \cdot i\right) \]

       7. distribute-lft-neg-in 50.8%

          \[\leadsto b \cdot \left(\color{blue}{\left(-i \cdot \left(y \cdot \frac{j}{b}\right)\right)} + a \cdot i\right) \]

       8. +-commutative 50.8%

          \[\leadsto b \cdot \color{blue}{\left(a \cdot i + \left(-i \cdot \left(y \cdot \frac{j}{b}\right)\right)\right)} \]

       9. distribute-lft-in 46.6%

          \[\leadsto \color{blue}{b \cdot \left(a \cdot i\right) + b \cdot \left(-i \cdot \left(y \cdot \frac{j}{b}\right)\right)} \]

       10. *-commutative 46.6%

           \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} + b \cdot \left(-i \cdot \left(y \cdot \frac{j}{b}\right)\right) \]

       11. associate-*r* 47.1%

           \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot a} + b \cdot \left(-i \cdot \left(y \cdot \frac{j}{b}\right)\right) \]

       12. distribute-rgt-neg-in 47.1%

           \[\leadsto \left(b \cdot i\right) \cdot a + b \cdot \color{blue}{\left(i \cdot \left(-y \cdot \frac{j}{b}\right)\right)} \]

       13. associate-*r* 34.5%

           \[\leadsto \left(b \cdot i\right) \cdot a + \color{blue}{\left(b \cdot i\right) \cdot \left(-y \cdot \frac{j}{b}\right)} \]

       14. distribute-lft-in 51.2%

           \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot \left(a + \left(-y \cdot \frac{j}{b}\right)\right)} \]

       15. associate-*r/ 59.2%

           \[\leadsto \left(b \cdot i\right) \cdot \left(a + \left(-\color{blue}{\frac{y \cdot j}{b}}\right)\right) \]

       16. *-commutative 59.2%

           \[\leadsto \left(b \cdot i\right) \cdot \left(a + \left(-\frac{\color{blue}{j \cdot y}}{b}\right)\right) \]

   11. Simplified 67.4%

       \[\leadsto \color{blue}{i \cdot \left(b \cdot \left(a - j \cdot \frac{y}{b}\right)\right)} \]

   if -4.6e72 < a < -2.29999999999999989e-272 or 7.49999999999999954e-225 < a < 620

   1. Initial program 83.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 74.6%

      \[\leadsto \color{blue}{j \cdot \left(\left(c \cdot t + \frac{x \cdot \left(y \cdot z - a \cdot t\right)}{j}\right) - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 74.6%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t + \left(\frac{x \cdot \left(y \cdot z - a \cdot t\right)}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right)} \]

      2. sub-neg 74.6%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \color{blue}{\left(y \cdot z + \left(-a \cdot t\right)\right)}}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right) \]

      3. mul-1-neg 74.6%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \left(y \cdot z + \color{blue}{-1 \cdot \left(a \cdot t\right)}\right)}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right) \]

      4. +-commutative 74.6%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \color{blue}{\left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)}}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right) \]

      5. +-commutative 74.6%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)}{j} - \color{blue}{\left(\frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j} + i \cdot y\right)}\right)\right) \]

      6. associate--r+ 74.6%

         \[\leadsto j \cdot \left(c \cdot t + \color{blue}{\left(\left(\frac{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)}{j} - \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right) - i \cdot y\right)}\right) \]

   5. Simplified 78.3%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t + \left(\frac{x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(c \cdot z - a \cdot i\right)}{j} - i \cdot y\right)\right)} \]

   6. Taylor expanded in c around inf 66.2%

      \[\leadsto j \cdot \left(c \cdot t + \left(\color{blue}{-1 \cdot \frac{b \cdot \left(c \cdot z\right)}{j}} - i \cdot y\right)\right) \]
   7. Step-by-step derivation

      1. associate-*r/ 66.2%

         \[\leadsto j \cdot \left(c \cdot t + \left(\color{blue}{\frac{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)}{j}} - i \cdot y\right)\right) \]

      2. associate-*r* 66.2%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{\color{blue}{\left(-1 \cdot b\right) \cdot \left(c \cdot z\right)}}{j} - i \cdot y\right)\right) \]

      3. neg-mul-1 66.2%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{\color{blue}{\left(-b\right)} \cdot \left(c \cdot z\right)}{j} - i \cdot y\right)\right) \]

      4. *-commutative 66.2%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{\left(-b\right) \cdot \color{blue}{\left(z \cdot c\right)}}{j} - i \cdot y\right)\right) \]

   8. Simplified 66.2%

      \[\leadsto j \cdot \left(c \cdot t + \left(\color{blue}{\frac{\left(-b\right) \cdot \left(z \cdot c\right)}{j}} - i \cdot y\right)\right) \]

   if -2.29999999999999989e-272 < a < 7.49999999999999954e-225

   1. Initial program 59.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 73.7%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 73.7%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 73.7%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 73.7%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 73.7%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   5. Simplified 73.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   if 620 < a < 5.5000000000000001e44

   1. Initial program 64.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 56.3%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]

   4. Taylor expanded in z around inf 64.7%

      \[\leadsto b \cdot \color{blue}{\left(z \cdot \left(\frac{a \cdot i}{z} - c\right)\right)} \]
   5. Step-by-step derivation

      1. associate-/l* 64.7%

         \[\leadsto b \cdot \left(z \cdot \left(\color{blue}{a \cdot \frac{i}{z}} - c\right)\right) \]

   6. Simplified 64.7%

      \[\leadsto b \cdot \color{blue}{\left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)} \]

   if 5.5000000000000001e44 < a

   1. Initial program 70.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 62.1%

      \[\leadsto \color{blue}{j \cdot \left(\left(c \cdot t + \frac{x \cdot \left(y \cdot z - a \cdot t\right)}{j}\right) - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 62.1%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t + \left(\frac{x \cdot \left(y \cdot z - a \cdot t\right)}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right)} \]

      2. sub-neg 62.1%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \color{blue}{\left(y \cdot z + \left(-a \cdot t\right)\right)}}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right) \]

      3. mul-1-neg 62.1%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \left(y \cdot z + \color{blue}{-1 \cdot \left(a \cdot t\right)}\right)}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right) \]

      4. +-commutative 62.1%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \color{blue}{\left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)}}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right) \]

      5. +-commutative 62.1%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)}{j} - \color{blue}{\left(\frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j} + i \cdot y\right)}\right)\right) \]

      6. associate--r+ 62.1%

         \[\leadsto j \cdot \left(c \cdot t + \color{blue}{\left(\left(\frac{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)}{j} - \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right) - i \cdot y\right)}\right) \]

   5. Simplified 67.5%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t + \left(\frac{x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(c \cdot z - a \cdot i\right)}{j} - i \cdot y\right)\right)} \]

   6. Taylor expanded in i around inf 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* 58.8%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{\color{blue}{\left(a \cdot b\right) \cdot i}}{j} - i \cdot y\right)\right) \]

   8. Simplified 58.8%

      \[\leadsto j \cdot \left(c \cdot t + \left(\color{blue}{\frac{\left(a \cdot b\right) \cdot i}{j}} - i \cdot y\right)\right) \]

   9. Taylor expanded in a around 0 58.8%

      \[\leadsto j \cdot \left(c \cdot t + \color{blue}{\left(\frac{a \cdot \left(b \cdot i\right)}{j} - i \cdot y\right)}\right) \]
   10. Step-by-step derivation

       1. sub-neg 58.8%

          \[\leadsto j \cdot \left(c \cdot t + \color{blue}{\left(\frac{a \cdot \left(b \cdot i\right)}{j} + \left(-i \cdot y\right)\right)}\right) \]

       2. *-commutative 58.8%

          \[\leadsto j \cdot \left(c \cdot t + \left(\frac{a \cdot \color{blue}{\left(i \cdot b\right)}}{j} + \left(-i \cdot y\right)\right)\right) \]

       3. associate-*r* 55.1%

          \[\leadsto j \cdot \left(c \cdot t + \left(\frac{\color{blue}{\left(a \cdot i\right) \cdot b}}{j} + \left(-i \cdot y\right)\right)\right) \]

       4. *-commutative 55.1%

          \[\leadsto j \cdot \left(c \cdot t + \left(\frac{\color{blue}{\left(i \cdot a\right)} \cdot b}{j} + \left(-i \cdot y\right)\right)\right) \]

       5. associate-*r* 58.8%

          \[\leadsto j \cdot \left(c \cdot t + \left(\frac{\color{blue}{i \cdot \left(a \cdot b\right)}}{j} + \left(-i \cdot y\right)\right)\right) \]

       6. associate-*r/ 60.6%

          \[\leadsto j \cdot \left(c \cdot t + \left(\color{blue}{i \cdot \frac{a \cdot b}{j}} + \left(-i \cdot y\right)\right)\right) \]

       7. distribute-rgt-neg-in 60.6%

          \[\leadsto j \cdot \left(c \cdot t + \left(i \cdot \frac{a \cdot b}{j} + \color{blue}{i \cdot \left(-y\right)}\right)\right) \]

       8. distribute-lft-in 64.2%

          \[\leadsto j \cdot \left(c \cdot t + \color{blue}{i \cdot \left(\frac{a \cdot b}{j} + \left(-y\right)\right)}\right) \]

       9. sub-neg 64.2%

          \[\leadsto j \cdot \left(c \cdot t + i \cdot \color{blue}{\left(\frac{a \cdot b}{j} - y\right)}\right) \]

       10. associate-/l* 64.3%

           \[\leadsto j \cdot \left(c \cdot t + i \cdot \left(\color{blue}{a \cdot \frac{b}{j}} - y\right)\right) \]

   11. Simplified 64.3%

       \[\leadsto j \cdot \left(c \cdot t + \color{blue}{i \cdot \left(a \cdot \frac{b}{j} - y\right)}\right) \]
3. Recombined 6 regimes into one program.

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+165}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{+72}:\\ \;\;\;\;i \cdot \left(b \cdot \left(a - j \cdot \frac{y}{b}\right)\right)\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-272}:\\ \;\;\;\;j \cdot \left(t \cdot c - \left(y \cdot i + \frac{b \cdot \left(z \cdot c\right)}{j}\right)\right)\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-225}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 620:\\ \;\;\;\;j \cdot \left(t \cdot c - \left(y \cdot i + \frac{b \cdot \left(z \cdot c\right)}{j}\right)\right)\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+44}:\\ \;\;\;\;b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c + i \cdot \left(a \cdot \frac{b}{j} - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 50.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -1.22 \cdot 10^{-35}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.08 \cdot 10^{-85}:\\ \;\;\;\;b \cdot \left(a \cdot i - a \cdot \left(t \cdot \frac{x}{b}\right)\right)\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-120}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-259}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-189}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* z (- (* a (/ i z)) c)))) (t_2 (* y (- (* x z) (* i j)))))
   (if (<= y -1.22e-35)
     t_2
     (if (<= y -1.08e-85)
       (* b (- (* a i) (* a (* t (/ x b)))))
       (if (<= y -5.2e-120)
         (* t (- (* c j) (* x a)))
         (if (<= y 4e-259)
           t_1
           (if (<= y 1.35e-189)
             (* x (- (* y z) (* t a)))
             (if (<= y 4.1e+45) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (z * ((a * (i / z)) - c));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.22e-35) {
		tmp = t_2;
	} else if (y <= -1.08e-85) {
		tmp = b * ((a * i) - (a * (t * (x / b))));
	} else if (y <= -5.2e-120) {
		tmp = t * ((c * j) - (x * a));
	} else if (y <= 4e-259) {
		tmp = t_1;
	} else if (y <= 1.35e-189) {
		tmp = x * ((y * z) - (t * a));
	} else if (y <= 4.1e+45) {
		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 = b * (z * ((a * (i / z)) - c))
    t_2 = y * ((x * z) - (i * j))
    if (y <= (-1.22d-35)) then
        tmp = t_2
    else if (y <= (-1.08d-85)) then
        tmp = b * ((a * i) - (a * (t * (x / b))))
    else if (y <= (-5.2d-120)) then
        tmp = t * ((c * j) - (x * a))
    else if (y <= 4d-259) then
        tmp = t_1
    else if (y <= 1.35d-189) then
        tmp = x * ((y * z) - (t * a))
    else if (y <= 4.1d+45) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (z * ((a * (i / z)) - c));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.22e-35) {
		tmp = t_2;
	} else if (y <= -1.08e-85) {
		tmp = b * ((a * i) - (a * (t * (x / b))));
	} else if (y <= -5.2e-120) {
		tmp = t * ((c * j) - (x * a));
	} else if (y <= 4e-259) {
		tmp = t_1;
	} else if (y <= 1.35e-189) {
		tmp = x * ((y * z) - (t * a));
	} else if (y <= 4.1e+45) {
		tmp = t_1;
	} 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 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -1.22e-35:
		tmp = t_2
	elif y <= -1.08e-85:
		tmp = b * ((a * i) - (a * (t * (x / b))))
	elif y <= -5.2e-120:
		tmp = t * ((c * j) - (x * a))
	elif y <= 4e-259:
		tmp = t_1
	elif y <= 1.35e-189:
		tmp = x * ((y * z) - (t * a))
	elif y <= 4.1e+45:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(z * Float64(Float64(a * Float64(i / z)) - c)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -1.22e-35)
		tmp = t_2;
	elseif (y <= -1.08e-85)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(a * Float64(t * Float64(x / b)))));
	elseif (y <= -5.2e-120)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (y <= 4e-259)
		tmp = t_1;
	elseif (y <= 1.35e-189)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (y <= 4.1e+45)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (z * ((a * (i / z)) - c));
	t_2 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -1.22e-35)
		tmp = t_2;
	elseif (y <= -1.08e-85)
		tmp = b * ((a * i) - (a * (t * (x / b))));
	elseif (y <= -5.2e-120)
		tmp = t * ((c * j) - (x * a));
	elseif (y <= 4e-259)
		tmp = t_1;
	elseif (y <= 1.35e-189)
		tmp = x * ((y * z) - (t * a));
	elseif (y <= 4.1e+45)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(z * N[(N[(a * N[(i / z), $MachinePrecision]), $MachinePrecision] - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.22e-35], t$95$2, If[LessEqual[y, -1.08e-85], N[(b * N[(N[(a * i), $MachinePrecision] - N[(a * N[(t * N[(x / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.2e-120], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e-259], t$95$1, If[LessEqual[y, 1.35e-189], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.1e+45], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.22e-35 or 4.10000000000000012e45 < y

   1. Initial program 64.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 68.0%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 68.0%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 68.0%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 68.0%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 68.0%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   5. Simplified 68.0%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   if -1.22e-35 < y < -1.07999999999999997e-85

   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 a around inf 70.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 70.2%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x - b \cdot i\right)\right)} \]

   5. Simplified 70.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x - b \cdot i\right)\right)} \]

   6. Taylor expanded in b around inf 71.8%

      \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \frac{a \cdot \left(t \cdot x\right)}{b} + a \cdot i\right)} \]
   7. Step-by-step derivation

      1. +-commutative 71.8%

         \[\leadsto b \cdot \color{blue}{\left(a \cdot i + -1 \cdot \frac{a \cdot \left(t \cdot x\right)}{b}\right)} \]

      2. mul-1-neg 71.8%

         \[\leadsto b \cdot \left(a \cdot i + \color{blue}{\left(-\frac{a \cdot \left(t \cdot x\right)}{b}\right)}\right) \]

      3. unsub-neg 71.8%

         \[\leadsto b \cdot \color{blue}{\left(a \cdot i - \frac{a \cdot \left(t \cdot x\right)}{b}\right)} \]

      4. *-commutative 71.8%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - \frac{a \cdot \left(t \cdot x\right)}{b}\right) \]

      5. associate-/l* 71.8%

         \[\leadsto b \cdot \left(i \cdot a - \color{blue}{a \cdot \frac{t \cdot x}{b}}\right) \]

      6. associate-/l* 71.8%

         \[\leadsto b \cdot \left(i \cdot a - a \cdot \color{blue}{\left(t \cdot \frac{x}{b}\right)}\right) \]

   8. Simplified 71.8%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a - a \cdot \left(t \cdot \frac{x}{b}\right)\right)} \]

   if -1.07999999999999997e-85 < y < -5.2000000000000002e-120

   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 t around inf 64.9%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 64.9%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 64.9%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 64.9%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   5. Simplified 64.9%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   if -5.2000000000000002e-120 < y < 4.0000000000000003e-259 or 1.35e-189 < y < 4.10000000000000012e45

   1. Initial program 80.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 54.9%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]

   4. Taylor expanded in z around inf 57.8%

      \[\leadsto b \cdot \color{blue}{\left(z \cdot \left(\frac{a \cdot i}{z} - c\right)\right)} \]
   5. Step-by-step derivation

      1. associate-/l* 59.7%

         \[\leadsto b \cdot \left(z \cdot \left(\color{blue}{a \cdot \frac{i}{z}} - c\right)\right) \]

   6. Simplified 59.7%

      \[\leadsto b \cdot \color{blue}{\left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)} \]

   if 4.0000000000000003e-259 < y < 1.35e-189

   1. Initial program 89.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 75.6%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   4. Step-by-step derivation

      1. *-commutative 75.6%

         \[\leadsto x \cdot \left(\color{blue}{z \cdot y} - a \cdot t\right) \]

   5. Simplified 75.6%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y - a \cdot t\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{-35}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -1.08 \cdot 10^{-85}:\\ \;\;\;\;b \cdot \left(a \cdot i - a \cdot \left(t \cdot \frac{x}{b}\right)\right)\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-120}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-259}:\\ \;\;\;\;b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-189}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+45}:\\ \;\;\;\;b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 51.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -2.6 \cdot 10^{-36}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-85}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq -1.66 \cdot 10^{-116}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-229}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{-170}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* z (- (* a (/ i z)) c)))) (t_2 (* y (- (* x z) (* i j)))))
   (if (<= y -2.6e-36)
     t_2
     (if (<= y -8e-85)
       (* a (- (* b i) (* x t)))
       (if (<= y -1.66e-116)
         (* t (- (* c j) (* x a)))
         (if (<= y 2.5e-229)
           t_1
           (if (<= y 9.6e-170)
             (* x (- (* y z) (* t a)))
             (if (<= y 5.4e+44) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (z * ((a * (i / z)) - c));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -2.6e-36) {
		tmp = t_2;
	} else if (y <= -8e-85) {
		tmp = a * ((b * i) - (x * t));
	} else if (y <= -1.66e-116) {
		tmp = t * ((c * j) - (x * a));
	} else if (y <= 2.5e-229) {
		tmp = t_1;
	} else if (y <= 9.6e-170) {
		tmp = x * ((y * z) - (t * a));
	} else if (y <= 5.4e+44) {
		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 = b * (z * ((a * (i / z)) - c))
    t_2 = y * ((x * z) - (i * j))
    if (y <= (-2.6d-36)) then
        tmp = t_2
    else if (y <= (-8d-85)) then
        tmp = a * ((b * i) - (x * t))
    else if (y <= (-1.66d-116)) then
        tmp = t * ((c * j) - (x * a))
    else if (y <= 2.5d-229) then
        tmp = t_1
    else if (y <= 9.6d-170) then
        tmp = x * ((y * z) - (t * a))
    else if (y <= 5.4d+44) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (z * ((a * (i / z)) - c));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -2.6e-36) {
		tmp = t_2;
	} else if (y <= -8e-85) {
		tmp = a * ((b * i) - (x * t));
	} else if (y <= -1.66e-116) {
		tmp = t * ((c * j) - (x * a));
	} else if (y <= 2.5e-229) {
		tmp = t_1;
	} else if (y <= 9.6e-170) {
		tmp = x * ((y * z) - (t * a));
	} else if (y <= 5.4e+44) {
		tmp = t_1;
	} 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 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -2.6e-36:
		tmp = t_2
	elif y <= -8e-85:
		tmp = a * ((b * i) - (x * t))
	elif y <= -1.66e-116:
		tmp = t * ((c * j) - (x * a))
	elif y <= 2.5e-229:
		tmp = t_1
	elif y <= 9.6e-170:
		tmp = x * ((y * z) - (t * a))
	elif y <= 5.4e+44:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(z * Float64(Float64(a * Float64(i / z)) - c)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -2.6e-36)
		tmp = t_2;
	elseif (y <= -8e-85)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (y <= -1.66e-116)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (y <= 2.5e-229)
		tmp = t_1;
	elseif (y <= 9.6e-170)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (y <= 5.4e+44)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (z * ((a * (i / z)) - c));
	t_2 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -2.6e-36)
		tmp = t_2;
	elseif (y <= -8e-85)
		tmp = a * ((b * i) - (x * t));
	elseif (y <= -1.66e-116)
		tmp = t * ((c * j) - (x * a));
	elseif (y <= 2.5e-229)
		tmp = t_1;
	elseif (y <= 9.6e-170)
		tmp = x * ((y * z) - (t * a));
	elseif (y <= 5.4e+44)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(z * N[(N[(a * N[(i / z), $MachinePrecision]), $MachinePrecision] - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.6e-36], t$95$2, If[LessEqual[y, -8e-85], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.66e-116], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e-229], t$95$1, If[LessEqual[y, 9.6e-170], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.4e+44], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.6e-36 or 5.4e44 < y

   1. Initial program 64.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 68.0%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 68.0%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 68.0%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 68.0%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 68.0%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   5. Simplified 68.0%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   if -2.6e-36 < y < -7.9999999999999998e-85

   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 a around inf 70.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 70.2%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x - b \cdot i\right)\right)} \]

   5. Simplified 70.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x - b \cdot i\right)\right)} \]

   6. Taylor expanded in t around 0 70.2%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(b \cdot i\right)} \]
   7. Step-by-step derivation

      1. +-commutative 70.2%

         \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 70.2%

         \[\leadsto a \cdot \left(b \cdot i\right) + \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} \]

      3. distribute-rgt-neg-in 70.2%

         \[\leadsto a \cdot \left(b \cdot i\right) + \color{blue}{a \cdot \left(-t \cdot x\right)} \]

      4. distribute-lft-out 70.2%

         \[\leadsto \color{blue}{a \cdot \left(b \cdot i + \left(-t \cdot x\right)\right)} \]

      5. unsub-neg 70.2%

         \[\leadsto a \cdot \color{blue}{\left(b \cdot i - t \cdot x\right)} \]

   8. Simplified 70.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   if -7.9999999999999998e-85 < y < -1.65999999999999988e-116

   1. Initial program 99.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 61.4%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 61.4%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 61.4%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 61.4%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   5. Simplified 61.4%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   if -1.65999999999999988e-116 < y < 2.50000000000000008e-229 or 9.5999999999999998e-170 < y < 5.4e44

   1. Initial program 78.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 54.6%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]

   4. Taylor expanded in z around inf 56.6%

      \[\leadsto b \cdot \color{blue}{\left(z \cdot \left(\frac{a \cdot i}{z} - c\right)\right)} \]
   5. Step-by-step derivation

      1. associate-/l* 58.5%

         \[\leadsto b \cdot \left(z \cdot \left(\color{blue}{a \cdot \frac{i}{z}} - c\right)\right) \]

   6. Simplified 58.5%

      \[\leadsto b \cdot \color{blue}{\left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)} \]

   if 2.50000000000000008e-229 < y < 9.5999999999999998e-170

   1. Initial program 99.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 80.4%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   4. Step-by-step derivation

      1. *-commutative 80.4%

         \[\leadsto x \cdot \left(\color{blue}{z \cdot y} - a \cdot t\right) \]

   5. Simplified 80.4%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y - a \cdot t\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-36}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-85}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq -1.66 \cdot 10^{-116}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-229}:\\ \;\;\;\;b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{-170}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+44}:\\ \;\;\;\;b \cdot \left(z \cdot \left(a \cdot \frac{i}{z} - c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 68.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := t\_1 + b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := t\_1 + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -6.6 \cdot 10^{+34}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-54}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-86}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-57}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i))))
        (t_2 (+ t_1 (* b (- (* a i) (* z c)))))
        (t_3 (+ t_1 (* x (- (* y z) (* t a))))))
   (if (<= x -6.6e+34)
     t_3
     (if (<= x -1.55e-54)
       t_2
       (if (<= x -3.2e-86)
         (* a (- (* b i) (* x t)))
         (if (<= x 8.2e-57) t_2 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = t_1 + (b * ((a * i) - (z * c)));
	double t_3 = t_1 + (x * ((y * z) - (t * a)));
	double tmp;
	if (x <= -6.6e+34) {
		tmp = t_3;
	} else if (x <= -1.55e-54) {
		tmp = t_2;
	} else if (x <= -3.2e-86) {
		tmp = a * ((b * i) - (x * t));
	} else if (x <= 8.2e-57) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = t_1 + (b * ((a * i) - (z * c)))
    t_3 = t_1 + (x * ((y * z) - (t * a)))
    if (x <= (-6.6d+34)) then
        tmp = t_3
    else if (x <= (-1.55d-54)) then
        tmp = t_2
    else if (x <= (-3.2d-86)) then
        tmp = a * ((b * i) - (x * t))
    else if (x <= 8.2d-57) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = t_1 + (b * ((a * i) - (z * c)));
	double t_3 = t_1 + (x * ((y * z) - (t * a)));
	double tmp;
	if (x <= -6.6e+34) {
		tmp = t_3;
	} else if (x <= -1.55e-54) {
		tmp = t_2;
	} else if (x <= -3.2e-86) {
		tmp = a * ((b * i) - (x * t));
	} else if (x <= 8.2e-57) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = t_1 + (b * ((a * i) - (z * c)))
	t_3 = t_1 + (x * ((y * z) - (t * a)))
	tmp = 0
	if x <= -6.6e+34:
		tmp = t_3
	elif x <= -1.55e-54:
		tmp = t_2
	elif x <= -3.2e-86:
		tmp = a * ((b * i) - (x * t))
	elif x <= 8.2e-57:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(t_1 + Float64(b * Float64(Float64(a * i) - Float64(z * c))))
	t_3 = Float64(t_1 + Float64(x * Float64(Float64(y * z) - Float64(t * a))))
	tmp = 0.0
	if (x <= -6.6e+34)
		tmp = t_3;
	elseif (x <= -1.55e-54)
		tmp = t_2;
	elseif (x <= -3.2e-86)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (x <= 8.2e-57)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = t_1 + (b * ((a * i) - (z * c)));
	t_3 = t_1 + (x * ((y * z) - (t * a)));
	tmp = 0.0;
	if (x <= -6.6e+34)
		tmp = t_3;
	elseif (x <= -1.55e-54)
		tmp = t_2;
	elseif (x <= -3.2e-86)
		tmp = a * ((b * i) - (x * t));
	elseif (x <= 8.2e-57)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.6e+34], t$95$3, If[LessEqual[x, -1.55e-54], t$95$2, If[LessEqual[x, -3.2e-86], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.2e-57], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.59999999999999976e34 or 8.2000000000000003e-57 < x

   1. Initial program 72.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 69.6%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   if -6.59999999999999976e34 < x < -1.55000000000000002e-54 or -3.20000000000000006e-86 < x < 8.2000000000000003e-57

   1. Initial program 76.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 76.7%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]

   if -1.55000000000000002e-54 < x < -3.20000000000000006e-86

   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 a around inf 75.6%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 75.6%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x - b \cdot i\right)\right)} \]

   5. Simplified 75.6%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x - b \cdot i\right)\right)} \]

   6. Taylor expanded in t around 0 75.6%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(b \cdot i\right)} \]
   7. Step-by-step derivation

      1. +-commutative 75.6%

         \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 75.6%

         \[\leadsto a \cdot \left(b \cdot i\right) + \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} \]

      3. distribute-rgt-neg-in 75.6%

         \[\leadsto a \cdot \left(b \cdot i\right) + \color{blue}{a \cdot \left(-t \cdot x\right)} \]

      4. distribute-lft-out 75.6%

         \[\leadsto \color{blue}{a \cdot \left(b \cdot i + \left(-t \cdot x\right)\right)} \]

      5. unsub-neg 75.6%

         \[\leadsto a \cdot \color{blue}{\left(b \cdot i - t \cdot x\right)} \]

   8. Simplified 75.6%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{+34}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-54}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-86}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-57}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 29.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i\right)\\ t_2 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq -1.85 \cdot 10^{-22}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-121}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+157}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+209}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+305}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* a i))) (t_2 (* z (* x y))))
   (if (<= y -1.85e-22)
     t_2
     (if (<= y -2.1e-121)
       (* j (* t c))
       (if (<= y 1.25e+44)
         t_1
         (if (<= y 5.5e+157)
           t_2
           (if (<= y 8.5e+209) t_1 (if (<= y 5e+305) t_2 (* a (* b i))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (a * i);
	double t_2 = z * (x * y);
	double tmp;
	if (y <= -1.85e-22) {
		tmp = t_2;
	} else if (y <= -2.1e-121) {
		tmp = j * (t * c);
	} else if (y <= 1.25e+44) {
		tmp = t_1;
	} else if (y <= 5.5e+157) {
		tmp = t_2;
	} else if (y <= 8.5e+209) {
		tmp = t_1;
	} else if (y <= 5e+305) {
		tmp = t_2;
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (a * i)
    t_2 = z * (x * y)
    if (y <= (-1.85d-22)) then
        tmp = t_2
    else if (y <= (-2.1d-121)) then
        tmp = j * (t * c)
    else if (y <= 1.25d+44) then
        tmp = t_1
    else if (y <= 5.5d+157) then
        tmp = t_2
    else if (y <= 8.5d+209) then
        tmp = t_1
    else if (y <= 5d+305) then
        tmp = t_2
    else
        tmp = a * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (a * i);
	double t_2 = z * (x * y);
	double tmp;
	if (y <= -1.85e-22) {
		tmp = t_2;
	} else if (y <= -2.1e-121) {
		tmp = j * (t * c);
	} else if (y <= 1.25e+44) {
		tmp = t_1;
	} else if (y <= 5.5e+157) {
		tmp = t_2;
	} else if (y <= 8.5e+209) {
		tmp = t_1;
	} else if (y <= 5e+305) {
		tmp = t_2;
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (a * i)
	t_2 = z * (x * y)
	tmp = 0
	if y <= -1.85e-22:
		tmp = t_2
	elif y <= -2.1e-121:
		tmp = j * (t * c)
	elif y <= 1.25e+44:
		tmp = t_1
	elif y <= 5.5e+157:
		tmp = t_2
	elif y <= 8.5e+209:
		tmp = t_1
	elif y <= 5e+305:
		tmp = t_2
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(a * i))
	t_2 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (y <= -1.85e-22)
		tmp = t_2;
	elseif (y <= -2.1e-121)
		tmp = Float64(j * Float64(t * c));
	elseif (y <= 1.25e+44)
		tmp = t_1;
	elseif (y <= 5.5e+157)
		tmp = t_2;
	elseif (y <= 8.5e+209)
		tmp = t_1;
	elseif (y <= 5e+305)
		tmp = t_2;
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (a * i);
	t_2 = z * (x * y);
	tmp = 0.0;
	if (y <= -1.85e-22)
		tmp = t_2;
	elseif (y <= -2.1e-121)
		tmp = j * (t * c);
	elseif (y <= 1.25e+44)
		tmp = t_1;
	elseif (y <= 5.5e+157)
		tmp = t_2;
	elseif (y <= 8.5e+209)
		tmp = t_1;
	elseif (y <= 5e+305)
		tmp = t_2;
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.85e-22], t$95$2, If[LessEqual[y, -2.1e-121], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.25e+44], t$95$1, If[LessEqual[y, 5.5e+157], t$95$2, If[LessEqual[y, 8.5e+209], t$95$1, If[LessEqual[y, 5e+305], t$95$2, N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.85e-22 or 1.2499999999999999e44 < y < 5.5000000000000003e157 or 8.50000000000000062e209 < y < 5.00000000000000009e305

   1. Initial program 67.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 60.3%

      \[\leadsto \color{blue}{j \cdot \left(\left(c \cdot t + \frac{x \cdot \left(y \cdot z - a \cdot t\right)}{j}\right) - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 60.3%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t + \left(\frac{x \cdot \left(y \cdot z - a \cdot t\right)}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right)} \]

      2. sub-neg 60.3%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \color{blue}{\left(y \cdot z + \left(-a \cdot t\right)\right)}}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right) \]

      3. mul-1-neg 60.3%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \left(y \cdot z + \color{blue}{-1 \cdot \left(a \cdot t\right)}\right)}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right) \]

      4. +-commutative 60.3%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \color{blue}{\left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)}}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right) \]

      5. +-commutative 60.3%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)}{j} - \color{blue}{\left(\frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j} + i \cdot y\right)}\right)\right) \]

      6. associate--r+ 60.3%

         \[\leadsto j \cdot \left(c \cdot t + \color{blue}{\left(\left(\frac{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)}{j} - \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right) - i \cdot y\right)}\right) \]

   5. Simplified 65.7%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t + \left(\frac{x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(c \cdot z - a \cdot i\right)}{j} - i \cdot y\right)\right)} \]

   6. Taylor expanded in z around inf 38.9%

      \[\leadsto \color{blue}{j \cdot \left(z \cdot \left(\frac{x \cdot y}{j} - \frac{b \cdot c}{j}\right)\right)} \]
   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 42.9%

         \[\leadsto \left(z \cdot j\right) \cdot \color{blue}{\frac{x \cdot y - b \cdot c}{j}} \]

      4. *-commutative 42.9%

         \[\leadsto \left(z \cdot j\right) \cdot \frac{x \cdot y - \color{blue}{c \cdot b}}{j} \]

   8. Simplified 42.9%

      \[\leadsto \color{blue}{\left(z \cdot j\right) \cdot \frac{x \cdot y - c \cdot b}{j}} \]

   9. Taylor expanded in x around inf 35.0%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   10. Step-by-step derivation

       1. *-commutative 35.0%

          \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

       2. *-commutative 35.0%

          \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot x \]

       3. associate-*l* 38.8%

          \[\leadsto \color{blue}{z \cdot \left(y \cdot x\right)} \]

   11. Simplified 38.8%

       \[\leadsto \color{blue}{z \cdot \left(y \cdot x\right)} \]

   if -1.85e-22 < y < -2.0999999999999999e-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 -2.0999999999999999e-121 < y < 1.2499999999999999e44 or 5.5000000000000003e157 < y < 8.50000000000000062e209

   1. Initial program 76.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 52.6%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]

   4. Taylor expanded in a around inf 33.7%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]

   if 5.00000000000000009e305 < y

   1. Initial program 100.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 100.0%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]

   4. Taylor expanded in a around inf 100.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 36.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{-22}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-121}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+44}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+157}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+209}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+305}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 28.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i\right)\\ \mathbf{if}\;y \leq -1.15 \cdot 10^{-23}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-121}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-238}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-308}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+51}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+196}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* b i))))
   (if (<= y -1.15e-23)
     (* y (* x z))
     (if (<= y -1e-121)
       (* j (* t c))
       (if (<= y -2.4e-238)
         t_1
         (if (<= y -3.4e-308)
           (* t (* c j))
           (if (<= y 2.1e+51)
             (* b (* a i))
             (if (<= y 8.5e+196) (* x (* y z)) 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);
	double tmp;
	if (y <= -1.15e-23) {
		tmp = y * (x * z);
	} else if (y <= -1e-121) {
		tmp = j * (t * c);
	} else if (y <= -2.4e-238) {
		tmp = t_1;
	} else if (y <= -3.4e-308) {
		tmp = t * (c * j);
	} else if (y <= 2.1e+51) {
		tmp = b * (a * i);
	} else if (y <= 8.5e+196) {
		tmp = x * (y * z);
	} 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)
    if (y <= (-1.15d-23)) then
        tmp = y * (x * z)
    else if (y <= (-1d-121)) then
        tmp = j * (t * c)
    else if (y <= (-2.4d-238)) then
        tmp = t_1
    else if (y <= (-3.4d-308)) then
        tmp = t * (c * j)
    else if (y <= 2.1d+51) then
        tmp = b * (a * i)
    else if (y <= 8.5d+196) then
        tmp = x * (y * z)
    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);
	double tmp;
	if (y <= -1.15e-23) {
		tmp = y * (x * z);
	} else if (y <= -1e-121) {
		tmp = j * (t * c);
	} else if (y <= -2.4e-238) {
		tmp = t_1;
	} else if (y <= -3.4e-308) {
		tmp = t * (c * j);
	} else if (y <= 2.1e+51) {
		tmp = b * (a * i);
	} else if (y <= 8.5e+196) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (b * i)
	tmp = 0
	if y <= -1.15e-23:
		tmp = y * (x * z)
	elif y <= -1e-121:
		tmp = j * (t * c)
	elif y <= -2.4e-238:
		tmp = t_1
	elif y <= -3.4e-308:
		tmp = t * (c * j)
	elif y <= 2.1e+51:
		tmp = b * (a * i)
	elif y <= 8.5e+196:
		tmp = x * (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(b * i))
	tmp = 0.0
	if (y <= -1.15e-23)
		tmp = Float64(y * Float64(x * z));
	elseif (y <= -1e-121)
		tmp = Float64(j * Float64(t * c));
	elseif (y <= -2.4e-238)
		tmp = t_1;
	elseif (y <= -3.4e-308)
		tmp = Float64(t * Float64(c * j));
	elseif (y <= 2.1e+51)
		tmp = Float64(b * Float64(a * i));
	elseif (y <= 8.5e+196)
		tmp = Float64(x * Float64(y * z));
	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);
	tmp = 0.0;
	if (y <= -1.15e-23)
		tmp = y * (x * z);
	elseif (y <= -1e-121)
		tmp = j * (t * c);
	elseif (y <= -2.4e-238)
		tmp = t_1;
	elseif (y <= -3.4e-308)
		tmp = t * (c * j);
	elseif (y <= 2.1e+51)
		tmp = b * (a * i);
	elseif (y <= 8.5e+196)
		tmp = x * (y * z);
	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[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.15e-23], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1e-121], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.4e-238], t$95$1, If[LessEqual[y, -3.4e-308], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.1e+51], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.5e+196], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -1.15000000000000005e-23

   1. Initial program 66.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 68.5%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 68.5%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 68.5%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 68.5%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 68.5%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   5. Simplified 68.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   6. Taylor expanded in z around inf 34.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-commutative 34.3%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

      2. associate-*l* 35.5%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   8. Simplified 35.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if -1.15000000000000005e-23 < y < -9.9999999999999998e-122

   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 -9.9999999999999998e-122 < y < -2.3999999999999998e-238 or 8.50000000000000041e196 < y

   1. Initial program 72.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 50.4%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]

   4. Taylor expanded in a around inf 37.3%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

   if -2.3999999999999998e-238 < y < -3.39999999999999999e-308

   1. Initial program 78.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 65.4%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 65.4%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 65.4%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 65.4%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   5. Simplified 65.4%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   6. Taylor expanded in c around inf 51.5%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot j\right)} \]

   if -3.39999999999999999e-308 < y < 2.1000000000000001e51

   1. Initial program 79.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 47.1%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]

   4. Taylor expanded in a around inf 35.0%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]

   if 2.1000000000000001e51 < y < 8.50000000000000041e196

   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 x around inf 47.5%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   4. Step-by-step derivation

      1. *-commutative 47.5%

         \[\leadsto x \cdot \left(\color{blue}{z \cdot y} - a \cdot t\right) \]

   5. Simplified 47.5%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y - a \cdot t\right)} \]

   6. Taylor expanded in z around inf 32.4%

      \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 36.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-23}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-121}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-238}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-308}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+51}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+196}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 28.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i\right)\\ t_2 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{-22}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-118}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{-236}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-305}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+60}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+198}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* b i))) (t_2 (* x (* y z))))
   (if (<= y -3.8e-22)
     t_2
     (if (<= y -5e-118)
       (* j (* t c))
       (if (<= y -1.12e-236)
         t_1
         (if (<= y -2e-305)
           (* t (* c j))
           (if (<= y 5e+60) (* b (* a i)) (if (<= y 7.5e+198) t_2 t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (b * i);
	double t_2 = x * (y * z);
	double tmp;
	if (y <= -3.8e-22) {
		tmp = t_2;
	} else if (y <= -5e-118) {
		tmp = j * (t * c);
	} else if (y <= -1.12e-236) {
		tmp = t_1;
	} else if (y <= -2e-305) {
		tmp = t * (c * j);
	} else if (y <= 5e+60) {
		tmp = b * (a * i);
	} else if (y <= 7.5e+198) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (b * i)
    t_2 = x * (y * z)
    if (y <= (-3.8d-22)) then
        tmp = t_2
    else if (y <= (-5d-118)) then
        tmp = j * (t * c)
    else if (y <= (-1.12d-236)) then
        tmp = t_1
    else if (y <= (-2d-305)) then
        tmp = t * (c * j)
    else if (y <= 5d+60) then
        tmp = b * (a * i)
    else if (y <= 7.5d+198) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (b * i);
	double t_2 = x * (y * z);
	double tmp;
	if (y <= -3.8e-22) {
		tmp = t_2;
	} else if (y <= -5e-118) {
		tmp = j * (t * c);
	} else if (y <= -1.12e-236) {
		tmp = t_1;
	} else if (y <= -2e-305) {
		tmp = t * (c * j);
	} else if (y <= 5e+60) {
		tmp = b * (a * i);
	} else if (y <= 7.5e+198) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (b * i)
	t_2 = x * (y * z)
	tmp = 0
	if y <= -3.8e-22:
		tmp = t_2
	elif y <= -5e-118:
		tmp = j * (t * c)
	elif y <= -1.12e-236:
		tmp = t_1
	elif y <= -2e-305:
		tmp = t * (c * j)
	elif y <= 5e+60:
		tmp = b * (a * i)
	elif y <= 7.5e+198:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(b * i))
	t_2 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (y <= -3.8e-22)
		tmp = t_2;
	elseif (y <= -5e-118)
		tmp = Float64(j * Float64(t * c));
	elseif (y <= -1.12e-236)
		tmp = t_1;
	elseif (y <= -2e-305)
		tmp = Float64(t * Float64(c * j));
	elseif (y <= 5e+60)
		tmp = Float64(b * Float64(a * i));
	elseif (y <= 7.5e+198)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (b * i);
	t_2 = x * (y * z);
	tmp = 0.0;
	if (y <= -3.8e-22)
		tmp = t_2;
	elseif (y <= -5e-118)
		tmp = j * (t * c);
	elseif (y <= -1.12e-236)
		tmp = t_1;
	elseif (y <= -2e-305)
		tmp = t * (c * j);
	elseif (y <= 5e+60)
		tmp = b * (a * i);
	elseif (y <= 7.5e+198)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.8e-22], t$95$2, If[LessEqual[y, -5e-118], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.12e-236], t$95$1, If[LessEqual[y, -2e-305], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5e+60], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.5e+198], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.80000000000000023e-22 or 4.99999999999999975e60 < y < 7.5000000000000002e198

   1. Initial program 65.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 41.7%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   4. Step-by-step derivation

      1. *-commutative 41.7%

         \[\leadsto x \cdot \left(\color{blue}{z \cdot y} - a \cdot t\right) \]

   5. Simplified 41.7%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y - a \cdot t\right)} \]

   6. Taylor expanded in z around inf 33.8%

      \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]

   if -3.80000000000000023e-22 < y < -5.00000000000000015e-118

   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 -5.00000000000000015e-118 < y < -1.11999999999999999e-236 or 7.5000000000000002e198 < y

   1. Initial program 72.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 50.4%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]

   4. Taylor expanded in a around inf 37.3%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

   if -1.11999999999999999e-236 < y < -1.99999999999999999e-305

   1. Initial program 78.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 65.4%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 65.4%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 65.4%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 65.4%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   5. Simplified 65.4%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   6. Taylor expanded in c around inf 51.5%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot j\right)} \]

   if -1.99999999999999999e-305 < y < 4.99999999999999975e60

   1. Initial program 79.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 47.1%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]

   4. Taylor expanded in a around inf 35.0%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 36.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-22}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-118}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{-236}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-305}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+60}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+198}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 43.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -4.4 \cdot 10^{+251}:\\ \;\;\;\;j \cdot \left(i \cdot \left(-y\right)\right)\\ \mathbf{elif}\;i \leq -8 \cdot 10^{+172} \lor \neg \left(i \leq 5.2 \cdot 10^{-44}\right) \land \left(i \leq 1.02 \cdot 10^{-11} \lor \neg \left(i \leq 1.9 \cdot 10^{+132}\right)\right):\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -4.4e+251)
   (* j (* i (- y)))
   (if (or (<= i -8e+172)
           (and (not (<= i 5.2e-44))
                (or (<= i 1.02e-11) (not (<= i 1.9e+132)))))
     (* 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 (i <= -4.4e+251) {
		tmp = j * (i * -y);
	} else if ((i <= -8e+172) || (!(i <= 5.2e-44) && ((i <= 1.02e-11) || !(i <= 1.9e+132)))) {
		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 (i <= (-4.4d+251)) then
        tmp = j * (i * -y)
    else if ((i <= (-8d+172)) .or. (.not. (i <= 5.2d-44)) .and. (i <= 1.02d-11) .or. (.not. (i <= 1.9d+132))) 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 (i <= -4.4e+251) {
		tmp = j * (i * -y);
	} else if ((i <= -8e+172) || (!(i <= 5.2e-44) && ((i <= 1.02e-11) || !(i <= 1.9e+132)))) {
		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 i <= -4.4e+251:
		tmp = j * (i * -y)
	elif (i <= -8e+172) or (not (i <= 5.2e-44) and ((i <= 1.02e-11) or not (i <= 1.9e+132))):
		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 (i <= -4.4e+251)
		tmp = Float64(j * Float64(i * Float64(-y)));
	elseif ((i <= -8e+172) || (!(i <= 5.2e-44) && ((i <= 1.02e-11) || !(i <= 1.9e+132))))
		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 (i <= -4.4e+251)
		tmp = j * (i * -y);
	elseif ((i <= -8e+172) || (~((i <= 5.2e-44)) && ((i <= 1.02e-11) || ~((i <= 1.9e+132)))))
		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[LessEqual[i, -4.4e+251], N[(j * N[(i * (-y)), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[i, -8e+172], And[N[Not[LessEqual[i, 5.2e-44]], $MachinePrecision], Or[LessEqual[i, 1.02e-11], N[Not[LessEqual[i, 1.9e+132]], $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 3 regimes

2. if i < -4.3999999999999999e251

   1. Initial program 66.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 75.0%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 75.0%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. *-commutative 75.0%

         \[\leadsto i \cdot \left(-1 \cdot \left(j \cdot y - \color{blue}{b \cdot a}\right)\right) \]

   5. Simplified 75.0%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - b \cdot a\right)\right)} \]

   6. Taylor expanded in j around inf 59.0%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 59.0%

         \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(j \cdot y\right)} \]

      2. mul-1-neg 59.0%

         \[\leadsto \color{blue}{\left(-i\right)} \cdot \left(j \cdot y\right) \]

      3. *-commutative 59.0%

         \[\leadsto \left(-i\right) \cdot \color{blue}{\left(y \cdot j\right)} \]

   8. Simplified 59.0%

      \[\leadsto \color{blue}{\left(-i\right) \cdot \left(y \cdot j\right)} \]

   9. Taylor expanded in i around 0 59.0%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 59.0%

          \[\leadsto \color{blue}{-i \cdot \left(j \cdot y\right)} \]

       2. *-commutative 59.0%

          \[\leadsto -i \cdot \color{blue}{\left(y \cdot j\right)} \]

       3. associate-*l* 66.8%

          \[\leadsto -\color{blue}{\left(i \cdot y\right) \cdot j} \]

       4. distribute-rgt-neg-in 66.8%

          \[\leadsto \color{blue}{\left(i \cdot y\right) \cdot \left(-j\right)} \]

   11. Simplified 66.8%

       \[\leadsto \color{blue}{\left(i \cdot y\right) \cdot \left(-j\right)} \]

   if -4.3999999999999999e251 < i < -8.0000000000000007e172 or 5.1999999999999996e-44 < i < 1.01999999999999994e-11 or 1.90000000000000003e132 < i

   1. Initial program 62.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 57.4%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 57.4%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x - b \cdot i\right)\right)} \]

   5. Simplified 57.4%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x - b \cdot i\right)\right)} \]

   6. Taylor expanded in t around 0 57.4%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(b \cdot i\right)} \]
   7. Step-by-step derivation

      1. +-commutative 57.4%

         \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 57.4%

         \[\leadsto a \cdot \left(b \cdot i\right) + \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} \]

      3. distribute-rgt-neg-in 57.4%

         \[\leadsto a \cdot \left(b \cdot i\right) + \color{blue}{a \cdot \left(-t \cdot x\right)} \]

      4. distribute-lft-out 57.4%

         \[\leadsto \color{blue}{a \cdot \left(b \cdot i + \left(-t \cdot x\right)\right)} \]

      5. unsub-neg 57.4%

         \[\leadsto a \cdot \color{blue}{\left(b \cdot i - t \cdot x\right)} \]

   8. Simplified 57.4%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   if -8.0000000000000007e172 < i < 5.1999999999999996e-44 or 1.01999999999999994e-11 < i < 1.90000000000000003e132

   1. Initial program 80.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 48.0%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4.4 \cdot 10^{+251}:\\ \;\;\;\;j \cdot \left(i \cdot \left(-y\right)\right)\\ \mathbf{elif}\;i \leq -8 \cdot 10^{+172} \lor \neg \left(i \leq 5.2 \cdot 10^{-44}\right) \land \left(i \leq 1.02 \cdot 10^{-11} \lor \neg \left(i \leq 1.9 \cdot 10^{+132}\right)\right):\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 31: 28.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i\right)\\ t_2 := c \cdot \left(t \cdot j\right)\\ \mathbf{if}\;t \leq -3.1 \cdot 10^{+113}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+112}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+183}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+301}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* b i))) (t_2 (* c (* t j))))
   (if (<= t -3.1e+113)
     t_2
     (if (<= t 1.8e-24)
       t_1
       (if (<= t 2.2e+112)
         t_2
         (if (<= t 1.2e+183) (* b (* a i)) (if (<= t 2.6e+301) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (b * i);
	double t_2 = c * (t * j);
	double tmp;
	if (t <= -3.1e+113) {
		tmp = t_2;
	} else if (t <= 1.8e-24) {
		tmp = t_1;
	} else if (t <= 2.2e+112) {
		tmp = t_2;
	} else if (t <= 1.2e+183) {
		tmp = b * (a * i);
	} else if (t <= 2.6e+301) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (b * i)
    t_2 = c * (t * j)
    if (t <= (-3.1d+113)) then
        tmp = t_2
    else if (t <= 1.8d-24) then
        tmp = t_1
    else if (t <= 2.2d+112) then
        tmp = t_2
    else if (t <= 1.2d+183) then
        tmp = b * (a * i)
    else if (t <= 2.6d+301) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (b * i);
	double t_2 = c * (t * j);
	double tmp;
	if (t <= -3.1e+113) {
		tmp = t_2;
	} else if (t <= 1.8e-24) {
		tmp = t_1;
	} else if (t <= 2.2e+112) {
		tmp = t_2;
	} else if (t <= 1.2e+183) {
		tmp = b * (a * i);
	} else if (t <= 2.6e+301) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (b * i)
	t_2 = c * (t * j)
	tmp = 0
	if t <= -3.1e+113:
		tmp = t_2
	elif t <= 1.8e-24:
		tmp = t_1
	elif t <= 2.2e+112:
		tmp = t_2
	elif t <= 1.2e+183:
		tmp = b * (a * i)
	elif t <= 2.6e+301:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(b * i))
	t_2 = Float64(c * Float64(t * j))
	tmp = 0.0
	if (t <= -3.1e+113)
		tmp = t_2;
	elseif (t <= 1.8e-24)
		tmp = t_1;
	elseif (t <= 2.2e+112)
		tmp = t_2;
	elseif (t <= 1.2e+183)
		tmp = Float64(b * Float64(a * i));
	elseif (t <= 2.6e+301)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (b * i);
	t_2 = c * (t * j);
	tmp = 0.0;
	if (t <= -3.1e+113)
		tmp = t_2;
	elseif (t <= 1.8e-24)
		tmp = t_1;
	elseif (t <= 2.2e+112)
		tmp = t_2;
	elseif (t <= 1.2e+183)
		tmp = b * (a * i);
	elseif (t <= 2.6e+301)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.1e+113], t$95$2, If[LessEqual[t, 1.8e-24], t$95$1, If[LessEqual[t, 2.2e+112], t$95$2, If[LessEqual[t, 1.2e+183], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.6e+301], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.09999999999999991e113 or 1.8e-24 < t < 2.1999999999999999e112 or 1.2000000000000001e183 < t < 2.5999999999999998e301

   1. Initial program 69.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 59.0%

      \[\leadsto \color{blue}{j \cdot \left(\left(c \cdot t + \frac{x \cdot \left(y \cdot z - a \cdot t\right)}{j}\right) - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 59.0%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t + \left(\frac{x \cdot \left(y \cdot z - a \cdot t\right)}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right)} \]

      2. sub-neg 59.0%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \color{blue}{\left(y \cdot z + \left(-a \cdot t\right)\right)}}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right) \]

      3. mul-1-neg 59.0%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \left(y \cdot z + \color{blue}{-1 \cdot \left(a \cdot t\right)}\right)}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right) \]

      4. +-commutative 59.0%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \color{blue}{\left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)}}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right) \]

      5. +-commutative 59.0%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)}{j} - \color{blue}{\left(\frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j} + i \cdot y\right)}\right)\right) \]

      6. associate--r+ 59.0%

         \[\leadsto j \cdot \left(c \cdot t + \color{blue}{\left(\left(\frac{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)}{j} - \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right) - i \cdot y\right)}\right) \]

   5. Simplified 64.7%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t + \left(\frac{x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(c \cdot z - a \cdot i\right)}{j} - i \cdot y\right)\right)} \]

   6. Taylor expanded in i around inf 49.4%

      \[\leadsto j \cdot \left(c \cdot t + \left(\color{blue}{\frac{a \cdot \left(b \cdot i\right)}{j}} - i \cdot y\right)\right) \]
   7. Step-by-step derivation

      1. associate-*r* 49.3%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{\color{blue}{\left(a \cdot b\right) \cdot i}}{j} - i \cdot y\right)\right) \]

   8. Simplified 49.3%

      \[\leadsto j \cdot \left(c \cdot t + \left(\color{blue}{\frac{\left(a \cdot b\right) \cdot i}{j}} - i \cdot y\right)\right) \]

   9. Taylor expanded in c around inf 43.0%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]

   if -3.09999999999999991e113 < t < 1.8e-24 or 2.5999999999999998e301 < t

   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 b around inf 46.6%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]

   4. Taylor expanded in a around inf 33.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

   if 2.1999999999999999e112 < t < 1.2000000000000001e183

   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 b around inf 44.4%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]

   4. Taylor expanded in a around inf 26.4%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 36.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+113}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-24}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+112}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+183}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+301}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 32: 28.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+103}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-26}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-91}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -8.5e+103)
   (* c (* t j))
   (if (<= t -1e-26)
     (* b (* a i))
     (if (<= t 9.2e-91) (* a (* b i)) (* j (* t c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -8.5e+103) {
		tmp = c * (t * j);
	} else if (t <= -1e-26) {
		tmp = b * (a * i);
	} else if (t <= 9.2e-91) {
		tmp = a * (b * i);
	} else {
		tmp = j * (t * c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (t <= (-8.5d+103)) then
        tmp = c * (t * j)
    else if (t <= (-1d-26)) then
        tmp = b * (a * i)
    else if (t <= 9.2d-91) then
        tmp = a * (b * i)
    else
        tmp = j * (t * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -8.5e+103) {
		tmp = c * (t * j);
	} else if (t <= -1e-26) {
		tmp = b * (a * i);
	} else if (t <= 9.2e-91) {
		tmp = a * (b * i);
	} else {
		tmp = j * (t * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -8.5e+103:
		tmp = c * (t * j)
	elif t <= -1e-26:
		tmp = b * (a * i)
	elif t <= 9.2e-91:
		tmp = a * (b * i)
	else:
		tmp = j * (t * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -8.5e+103)
		tmp = Float64(c * Float64(t * j));
	elseif (t <= -1e-26)
		tmp = Float64(b * Float64(a * i));
	elseif (t <= 9.2e-91)
		tmp = Float64(a * Float64(b * i));
	else
		tmp = Float64(j * Float64(t * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -8.5e+103)
		tmp = c * (t * j);
	elseif (t <= -1e-26)
		tmp = b * (a * i);
	elseif (t <= 9.2e-91)
		tmp = a * (b * i);
	else
		tmp = j * (t * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -8.5e+103], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1e-26], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.2e-91], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.4999999999999992e103

   1. Initial program 66.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 59.5%

      \[\leadsto \color{blue}{j \cdot \left(\left(c \cdot t + \frac{x \cdot \left(y \cdot z - a \cdot t\right)}{j}\right) - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 59.5%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t + \left(\frac{x \cdot \left(y \cdot z - a \cdot t\right)}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right)} \]

      2. sub-neg 59.5%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \color{blue}{\left(y \cdot z + \left(-a \cdot t\right)\right)}}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right) \]

      3. mul-1-neg 59.5%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \left(y \cdot z + \color{blue}{-1 \cdot \left(a \cdot t\right)}\right)}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right) \]

      4. +-commutative 59.5%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \color{blue}{\left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)}}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right) \]

      5. +-commutative 59.5%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)}{j} - \color{blue}{\left(\frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j} + i \cdot y\right)}\right)\right) \]

      6. associate--r+ 59.5%

         \[\leadsto j \cdot \left(c \cdot t + \color{blue}{\left(\left(\frac{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)}{j} - \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right) - i \cdot y\right)}\right) \]

   5. Simplified 64.4%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t + \left(\frac{x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(c \cdot z - a \cdot i\right)}{j} - i \cdot y\right)\right)} \]

   6. Taylor expanded in i around inf 52.4%

      \[\leadsto j \cdot \left(c \cdot t + \left(\color{blue}{\frac{a \cdot \left(b \cdot i\right)}{j}} - i \cdot y\right)\right) \]
   7. Step-by-step derivation

      1. associate-*r* 52.2%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{\color{blue}{\left(a \cdot b\right) \cdot i}}{j} - i \cdot y\right)\right) \]

   8. Simplified 52.2%

      \[\leadsto j \cdot \left(c \cdot t + \left(\color{blue}{\frac{\left(a \cdot b\right) \cdot i}{j}} - i \cdot y\right)\right) \]

   9. Taylor expanded in c around inf 54.7%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]

   if -8.4999999999999992e103 < t < -1e-26

   1. Initial program 74.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 42.2%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]

   4. Taylor expanded in a around inf 28.0%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]

   if -1e-26 < t < 9.19999999999999982e-91

   1. Initial program 82.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 49.2%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]

   4. Taylor expanded in a around inf 34.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

   if 9.19999999999999982e-91 < t

   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 j around inf 59.6%

      \[\leadsto \color{blue}{j \cdot \left(\left(c \cdot t + \frac{x \cdot \left(y \cdot z - a \cdot t\right)}{j}\right) - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 59.6%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t + \left(\frac{x \cdot \left(y \cdot z - a \cdot t\right)}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right)} \]

      2. sub-neg 59.6%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \color{blue}{\left(y \cdot z + \left(-a \cdot t\right)\right)}}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right) \]

      3. mul-1-neg 59.6%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \left(y \cdot z + \color{blue}{-1 \cdot \left(a \cdot t\right)}\right)}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right) \]

      4. +-commutative 59.6%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \color{blue}{\left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)}}{j} - \left(i \cdot y + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right)\right)\right) \]

      5. +-commutative 59.6%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)}{j} - \color{blue}{\left(\frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j} + i \cdot y\right)}\right)\right) \]

      6. associate--r+ 59.6%

         \[\leadsto j \cdot \left(c \cdot t + \color{blue}{\left(\left(\frac{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)}{j} - \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{j}\right) - i \cdot y\right)}\right) \]

   5. Simplified 66.1%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t + \left(\frac{x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(c \cdot z - a \cdot i\right)}{j} - i \cdot y\right)\right)} \]

   6. Taylor expanded in i around inf 48.9%

      \[\leadsto j \cdot \left(c \cdot t + \left(\color{blue}{\frac{a \cdot \left(b \cdot i\right)}{j}} - i \cdot y\right)\right) \]
   7. Step-by-step derivation

      1. associate-*r* 50.2%

         \[\leadsto j \cdot \left(c \cdot t + \left(\frac{\color{blue}{\left(a \cdot b\right) \cdot i}}{j} - i \cdot y\right)\right) \]

   8. Simplified 50.2%

      \[\leadsto j \cdot \left(c \cdot t + \left(\color{blue}{\frac{\left(a \cdot b\right) \cdot i}{j}} - i \cdot y\right)\right) \]

   9. Taylor expanded in c around inf 24.6%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 24.6%

          \[\leadsto \color{blue}{\left(c \cdot j\right) \cdot t} \]

       2. *-commutative 24.6%

          \[\leadsto \color{blue}{\left(j \cdot c\right)} \cdot t \]

       3. associate-*r* 29.4%

          \[\leadsto \color{blue}{j \cdot \left(c \cdot t\right)} \]

   11. Simplified 29.4%

       \[\leadsto \color{blue}{j \cdot \left(c \cdot t\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 35.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+103}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-26}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-91}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 33: 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)))))