Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 72.8% → 84.4%

Time: 27.1s

Alternatives: 28

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: 72.8% 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: 84.4% accurate, 0.1× speedup

Math

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

FPCore

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

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(j * t$95$2), $MachinePrecision] - N[(t$95$1 + N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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[(x * N[(z * N[(N[(y + N[(a * N[(b * N[(i / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t / z), $MachinePrecision] + N[(c * N[(b / x), $MachinePrecision]), $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 89.6%

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

      1. +-commutative 89.6%

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

      2. fma-define 89.6%

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

      3. *-commutative 89.6%

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

      4. *-commutative 89.6%

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

      5. cancel-sign-sub-inv 89.6%

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

      6. cancel-sign-sub 89.6%

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

      7. sub-neg 89.6%

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

      8. sub-neg 89.6%

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

      9. *-commutative 89.6%

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

      10. fma-neg 89.6%

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

      11. *-commutative 89.6%

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

      12. distribute-rgt-neg-out 89.6%

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

      13. remove-double-neg 89.6%

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

      14. *-commutative 89.6%

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

      15. *-commutative 89.6%

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

   3. Simplified 89.6%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in j around 0 28.9%

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

      1. *-commutative 28.9%

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

   5. Simplified 28.9%

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

   6. Taylor expanded in x around inf 40.0%

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

      1. +-commutative 40.0%

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

      2. mul-1-neg 40.0%

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

      3. unsub-neg 40.0%

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

      4. associate-/l* 48.9%

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

      5. *-commutative 48.9%

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

   8. Simplified 48.9%

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

   9. Taylor expanded in z around -inf 46.7%

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

       1. mul-1-neg 46.7%

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

       2. distribute-rgt-neg-in 46.7%

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

       3. associate-+r+ 46.7%

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

       4. associate--l+ 46.7%

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

   11. Simplified 62.2%

       \[\leadsto x \cdot \color{blue}{\left(z \cdot \left(-\left(\left(\left(-y\right) - a \cdot \left(b \cdot \frac{i}{z \cdot x}\right)\right) + \mathsf{fma}\left(a, \frac{t}{z}, c \cdot \frac{b}{x}\right)\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.8%

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

Alternative 2: 84.4% accurate, 0.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(x * N[(z * N[(N[(y + N[(a * N[(b * N[(i / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t / z), $MachinePrecision] + N[(c * N[(b / x), $MachinePrecision]), $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 89.6%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in j around 0 28.9%

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

      1. *-commutative 28.9%

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

   5. Simplified 28.9%

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

   6. Taylor expanded in x around inf 40.0%

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

      1. +-commutative 40.0%

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

      2. mul-1-neg 40.0%

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

      3. unsub-neg 40.0%

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

      4. associate-/l* 48.9%

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

      5. *-commutative 48.9%

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

   8. Simplified 48.9%

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

   9. Taylor expanded in z around -inf 46.7%

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

       1. mul-1-neg 46.7%

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

       2. distribute-rgt-neg-in 46.7%

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

       3. associate-+r+ 46.7%

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

       4. associate--l+ 46.7%

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

   11. Simplified 62.2%

       \[\leadsto x \cdot \color{blue}{\left(z \cdot \left(-\left(\left(\left(-y\right) - a \cdot \left(b \cdot \frac{i}{z \cdot x}\right)\right) + \mathsf{fma}\left(a, \frac{t}{z}, c \cdot \frac{b}{x}\right)\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.7%

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

Alternative 3: 82.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(z * N[(N[(x * N[(y - N[(b * N[(c / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(N[(a * N[(b * N[(i / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision] / z), $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 89.6%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in j around 0 28.9%

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

      1. *-commutative 28.9%

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

   5. Simplified 28.9%

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

   6. Taylor expanded in x around inf 40.0%

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

      1. +-commutative 40.0%

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

      2. mul-1-neg 40.0%

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

      3. unsub-neg 40.0%

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

      4. associate-/l* 48.9%

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

      5. *-commutative 48.9%

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

   8. Simplified 48.9%

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

   9. Taylor expanded in z around inf 42.2%

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

       1. +-commutative 42.2%

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

       2. mul-1-neg 42.2%

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

       3. unsub-neg 42.2%

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

       4. associate-/l* 42.2%

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

       5. associate-/l* 48.9%

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

       6. +-commutative 48.9%

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

       7. mul-1-neg 48.9%

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

       8. unsub-neg 48.9%

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

       9. associate-/l* 55.6%

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

       10. associate-/l* 57.8%

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

   11. Simplified 57.8%

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

4. Final simplification 84.0%

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

Alternative 4: 53.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i\right)\\ t_2 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -2.6 \cdot 10^{+64}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -1.26 \cdot 10^{-79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 6 \cdot 10^{-253}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;i \leq 4 \cdot 10^{-161}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 6 \cdot 10^{-28}:\\ \;\;\;\;x \cdot \left(c \cdot \frac{t \cdot j}{x} - t \cdot a\right)\\ \mathbf{elif}\;i \leq 5.8 \cdot 10^{+34}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;i \leq 5.8 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* j (- (* t c) (* y i))) (* a (* b i))))
        (t_2 (* i (- (* a b) (* y j)))))
   (if (<= i -2.6e+64)
     t_2
     (if (<= i -1.26e-79)
       t_1
       (if (<= i 6e-253)
         (* t (- (* c j) (* x a)))
         (if (<= i 4e-161)
           (* z (- (* x y) (* b c)))
           (if (<= i 6e-28)
             (* x (- (* c (/ (* t j) x)) (* t a)))
             (if (<= i 5.8e+34)
               (* y (- (* x z) (* i j)))
               (if (<= i 5.8e+98) 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))) + (a * (b * i));
	double t_2 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -2.6e+64) {
		tmp = t_2;
	} else if (i <= -1.26e-79) {
		tmp = t_1;
	} else if (i <= 6e-253) {
		tmp = t * ((c * j) - (x * a));
	} else if (i <= 4e-161) {
		tmp = z * ((x * y) - (b * c));
	} else if (i <= 6e-28) {
		tmp = x * ((c * ((t * j) / x)) - (t * a));
	} else if (i <= 5.8e+34) {
		tmp = y * ((x * z) - (i * j));
	} else if (i <= 5.8e+98) {
		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))) + (a * (b * i))
    t_2 = i * ((a * b) - (y * j))
    if (i <= (-2.6d+64)) then
        tmp = t_2
    else if (i <= (-1.26d-79)) then
        tmp = t_1
    else if (i <= 6d-253) then
        tmp = t * ((c * j) - (x * a))
    else if (i <= 4d-161) then
        tmp = z * ((x * y) - (b * c))
    else if (i <= 6d-28) then
        tmp = x * ((c * ((t * j) / x)) - (t * a))
    else if (i <= 5.8d+34) then
        tmp = y * ((x * z) - (i * j))
    else if (i <= 5.8d+98) 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))) + (a * (b * i));
	double t_2 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -2.6e+64) {
		tmp = t_2;
	} else if (i <= -1.26e-79) {
		tmp = t_1;
	} else if (i <= 6e-253) {
		tmp = t * ((c * j) - (x * a));
	} else if (i <= 4e-161) {
		tmp = z * ((x * y) - (b * c));
	} else if (i <= 6e-28) {
		tmp = x * ((c * ((t * j) / x)) - (t * a));
	} else if (i <= 5.8e+34) {
		tmp = y * ((x * z) - (i * j));
	} else if (i <= 5.8e+98) {
		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))) + (a * (b * i))
	t_2 = i * ((a * b) - (y * j))
	tmp = 0
	if i <= -2.6e+64:
		tmp = t_2
	elif i <= -1.26e-79:
		tmp = t_1
	elif i <= 6e-253:
		tmp = t * ((c * j) - (x * a))
	elif i <= 4e-161:
		tmp = z * ((x * y) - (b * c))
	elif i <= 6e-28:
		tmp = x * ((c * ((t * j) / x)) - (t * a))
	elif i <= 5.8e+34:
		tmp = y * ((x * z) - (i * j))
	elif i <= 5.8e+98:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(a * Float64(b * i)))
	t_2 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -2.6e+64)
		tmp = t_2;
	elseif (i <= -1.26e-79)
		tmp = t_1;
	elseif (i <= 6e-253)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (i <= 4e-161)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (i <= 6e-28)
		tmp = Float64(x * Float64(Float64(c * Float64(Float64(t * j) / x)) - Float64(t * a)));
	elseif (i <= 5.8e+34)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (i <= 5.8e+98)
		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))) + (a * (b * i));
	t_2 = i * ((a * b) - (y * j));
	tmp = 0.0;
	if (i <= -2.6e+64)
		tmp = t_2;
	elseif (i <= -1.26e-79)
		tmp = t_1;
	elseif (i <= 6e-253)
		tmp = t * ((c * j) - (x * a));
	elseif (i <= 4e-161)
		tmp = z * ((x * y) - (b * c));
	elseif (i <= 6e-28)
		tmp = x * ((c * ((t * j) / x)) - (t * a));
	elseif (i <= 5.8e+34)
		tmp = y * ((x * z) - (i * j));
	elseif (i <= 5.8e+98)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.6e+64], t$95$2, If[LessEqual[i, -1.26e-79], t$95$1, If[LessEqual[i, 6e-253], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4e-161], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 6e-28], N[(x * N[(N[(c * N[(N[(t * j), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5.8e+34], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5.8e+98], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -2.59999999999999997e64 or 5.8000000000000002e98 < i

   1. Initial program 63.5%

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

   3. Taylor expanded in x around inf 61.1%

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

      1. +-commutative 61.1%

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

      2. mul-1-neg 61.1%

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

      3. unsub-neg 61.1%

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

      4. associate-/l* 61.1%

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

      5. *-commutative 61.1%

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

   5. Simplified 61.1%

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

   6. Taylor expanded in i around inf 77.0%

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

      1. +-commutative 77.0%

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

      2. mul-1-neg 77.0%

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

      3. unsub-neg 77.0%

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

      4. *-commutative 77.0%

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

      5. *-commutative 77.0%

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

   8. Simplified 77.0%

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

   if -2.59999999999999997e64 < i < -1.25999999999999993e-79 or 5.8000000000000003e34 < i < 5.8000000000000002e98

   1. Initial program 72.0%

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

   3. Taylor expanded in i around inf 71.7%

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

      1. *-commutative 71.7%

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

   5. Simplified 71.7%

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

   if -1.25999999999999993e-79 < i < 6.0000000000000004e-253

   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 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%

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

      4. *-commutative 59.0%

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

      5. *-commutative 59.0%

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

   5. Simplified 59.0%

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

   if 6.0000000000000004e-253 < i < 4.00000000000000011e-161

   1. Initial program 73.3%

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

   3. Taylor expanded in z around inf 69.7%

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

      1. *-commutative 69.7%

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

   5. Simplified 69.7%

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

   if 4.00000000000000011e-161 < i < 6.00000000000000005e-28

   1. Initial program 88.4%

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

   3. Taylor expanded in t around -inf 57.3%

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

      1. mul-1-neg 57.3%

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

      2. distribute-rgt-neg-in 57.3%

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

      3. +-commutative 57.3%

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

      4. *-commutative 57.3%

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

      5. fma-define 57.3%

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

      6. mul-1-neg 57.3%

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

      7. distribute-rgt-neg-in 57.3%

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

   5. Simplified 57.3%

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

   6. Taylor expanded in x around inf 57.6%

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

      1. mul-1-neg 57.6%

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

      2. +-commutative 57.6%

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

      3. unsub-neg 57.6%

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

      4. associate-/l* 57.6%

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

      5. *-commutative 57.6%

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

   8. Simplified 57.6%

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

   if 6.00000000000000005e-28 < i < 5.8000000000000003e34

   1. Initial program 63.0%

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

   3. Taylor expanded in y around inf 63.3%

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

      1. +-commutative 63.3%

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

      2. mul-1-neg 63.3%

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

      3. unsub-neg 63.3%

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

      4. *-commutative 63.3%

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

   5. Simplified 63.3%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.6 \cdot 10^{+64}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -1.26 \cdot 10^{-79}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 6 \cdot 10^{-253}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;i \leq 4 \cdot 10^{-161}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 6 \cdot 10^{-28}:\\ \;\;\;\;x \cdot \left(c \cdot \frac{t \cdot j}{x} - t \cdot a\right)\\ \mathbf{elif}\;i \leq 5.8 \cdot 10^{+34}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;i \leq 5.8 \cdot 10^{+98}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 56.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := t\_1 - b \cdot \left(z \cdot c\right)\\ t_3 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.12 \cdot 10^{+120}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq -2800000000:\\ \;\;\;\;t\_1 + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{-60}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-274}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-159}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 6200000:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

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 (* z c))))
        (t_3 (* a (- (* b i) (* x t)))))
   (if (<= a -1.12e+120)
     t_3
     (if (<= a -2800000000.0)
       (+ t_1 (* a (* b i)))
       (if (<= a -5.8e-60)
         (* i (- (* a b) (* y j)))
         (if (<= a 1.8e-274)
           t_2
           (if (<= a 1.15e-159)
             (* y (- (* x z) (* i j)))
             (if (<= a 6200000.0) 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 * (z * c));
	double t_3 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -1.12e+120) {
		tmp = t_3;
	} else if (a <= -2800000000.0) {
		tmp = t_1 + (a * (b * i));
	} else if (a <= -5.8e-60) {
		tmp = i * ((a * b) - (y * j));
	} else if (a <= 1.8e-274) {
		tmp = t_2;
	} else if (a <= 1.15e-159) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= 6200000.0) {
		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 * (z * c))
    t_3 = a * ((b * i) - (x * t))
    if (a <= (-1.12d+120)) then
        tmp = t_3
    else if (a <= (-2800000000.0d0)) then
        tmp = t_1 + (a * (b * i))
    else if (a <= (-5.8d-60)) then
        tmp = i * ((a * b) - (y * j))
    else if (a <= 1.8d-274) then
        tmp = t_2
    else if (a <= 1.15d-159) then
        tmp = y * ((x * z) - (i * j))
    else if (a <= 6200000.0d0) 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 * (z * c));
	double t_3 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -1.12e+120) {
		tmp = t_3;
	} else if (a <= -2800000000.0) {
		tmp = t_1 + (a * (b * i));
	} else if (a <= -5.8e-60) {
		tmp = i * ((a * b) - (y * j));
	} else if (a <= 1.8e-274) {
		tmp = t_2;
	} else if (a <= 1.15e-159) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= 6200000.0) {
		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 * (z * c))
	t_3 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -1.12e+120:
		tmp = t_3
	elif a <= -2800000000.0:
		tmp = t_1 + (a * (b * i))
	elif a <= -5.8e-60:
		tmp = i * ((a * b) - (y * j))
	elif a <= 1.8e-274:
		tmp = t_2
	elif a <= 1.15e-159:
		tmp = y * ((x * z) - (i * j))
	elif a <= 6200000.0:
		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(z * c)))
	t_3 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -1.12e+120)
		tmp = t_3;
	elseif (a <= -2800000000.0)
		tmp = Float64(t_1 + Float64(a * Float64(b * i)));
	elseif (a <= -5.8e-60)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (a <= 1.8e-274)
		tmp = t_2;
	elseif (a <= 1.15e-159)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (a <= 6200000.0)
		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 * (z * c));
	t_3 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -1.12e+120)
		tmp = t_3;
	elseif (a <= -2800000000.0)
		tmp = t_1 + (a * (b * i));
	elseif (a <= -5.8e-60)
		tmp = i * ((a * b) - (y * j));
	elseif (a <= 1.8e-274)
		tmp = t_2;
	elseif (a <= 1.15e-159)
		tmp = y * ((x * z) - (i * j));
	elseif (a <= 6200000.0)
		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[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.12e+120], t$95$3, If[LessEqual[a, -2800000000.0], N[(t$95$1 + N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5.8e-60], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.8e-274], t$95$2, If[LessEqual[a, 1.15e-159], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6200000.0], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.12000000000000005e120 or 6.2e6 < a

   1. Initial program 69.9%

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

   3. Taylor expanded in j around 0 71.1%

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

      1. *-commutative 71.1%

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

   5. Simplified 71.1%

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

   6. Taylor expanded in z around 0 60.7%

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

      1. associate-*r* 60.7%

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

      2. neg-mul-1 60.7%

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

      3. *-commutative 60.7%

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

      4. associate-*r* 60.7%

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

      5. neg-mul-1 60.7%

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

      6. distribute-lft-out-- 65.5%

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

      7. distribute-lft-neg-in 65.5%

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

      8. distribute-rgt-neg-out 65.5%

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

      9. neg-sub0 65.5%

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

      10. sub-neg 65.5%

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

      11. +-commutative 65.5%

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

      12. associate--r+ 65.5%

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

      13. neg-sub0 65.5%

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

      14. remove-double-neg 65.5%

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

      15. *-commutative 65.5%

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

   8. Simplified 65.5%

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

   if -1.12000000000000005e120 < a < -2.8e9

   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 i around inf 60.0%

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

      1. *-commutative 60.0%

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

   5. Simplified 60.0%

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

   if -2.8e9 < a < -5.7999999999999999e-60

   1. Initial program 74.5%

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

   3. Taylor expanded in x around inf 68.2%

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

      1. +-commutative 68.2%

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

      2. mul-1-neg 68.2%

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

      3. unsub-neg 68.2%

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

      4. associate-/l* 67.7%

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

      5. *-commutative 67.7%

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

   5. Simplified 67.7%

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

   6. Taylor expanded in i around inf 61.2%

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

      1. +-commutative 61.2%

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

      2. mul-1-neg 61.2%

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

      3. unsub-neg 61.2%

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

      4. *-commutative 61.2%

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

      5. *-commutative 61.2%

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

   8. Simplified 61.2%

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

   if -5.7999999999999999e-60 < a < 1.79999999999999991e-274 or 1.14999999999999989e-159 < a < 6.2e6

   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 c around inf 71.0%

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

      1. associate-*r* 71.0%

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

      2. neg-mul-1 71.0%

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

      3. *-commutative 71.0%

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

   5. Simplified 71.0%

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

   if 1.79999999999999991e-274 < a < 1.14999999999999989e-159

   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 y around inf 78.0%

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

      1. +-commutative 78.0%

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

      2. mul-1-neg 78.0%

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

      3. unsub-neg 78.0%

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

      4. *-commutative 78.0%

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

   5. Simplified 78.0%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.12 \cdot 10^{+120}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -2800000000:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{-60}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-274}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-159}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 6200000:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 56.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -7.5 \cdot 10^{+118}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -2.5:\\ \;\;\;\;a \cdot \left(b \cdot i\right) - j \cdot \left(i \cdot \left(y - c \cdot \frac{t}{i}\right)\right)\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{-60}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{-274}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-159}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 2700000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* j (- (* t c) (* y i))) (* b (* z c))))
        (t_2 (* a (- (* b i) (* x t)))))
   (if (<= a -7.5e+118)
     t_2
     (if (<= a -2.5)
       (- (* a (* b i)) (* j (* i (- y (* c (/ t i))))))
       (if (<= a -1.95e-60)
         t_2
         (if (<= a 1.12e-274)
           t_1
           (if (<= a 1.3e-159)
             (* y (- (* x z) (* i j)))
             (if (<= a 2700000.0) 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))) - (b * (z * c));
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -7.5e+118) {
		tmp = t_2;
	} else if (a <= -2.5) {
		tmp = (a * (b * i)) - (j * (i * (y - (c * (t / i)))));
	} else if (a <= -1.95e-60) {
		tmp = t_2;
	} else if (a <= 1.12e-274) {
		tmp = t_1;
	} else if (a <= 1.3e-159) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= 2700000.0) {
		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))) - (b * (z * c))
    t_2 = a * ((b * i) - (x * t))
    if (a <= (-7.5d+118)) then
        tmp = t_2
    else if (a <= (-2.5d0)) then
        tmp = (a * (b * i)) - (j * (i * (y - (c * (t / i)))))
    else if (a <= (-1.95d-60)) then
        tmp = t_2
    else if (a <= 1.12d-274) then
        tmp = t_1
    else if (a <= 1.3d-159) then
        tmp = y * ((x * z) - (i * j))
    else if (a <= 2700000.0d0) 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))) - (b * (z * c));
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -7.5e+118) {
		tmp = t_2;
	} else if (a <= -2.5) {
		tmp = (a * (b * i)) - (j * (i * (y - (c * (t / i)))));
	} else if (a <= -1.95e-60) {
		tmp = t_2;
	} else if (a <= 1.12e-274) {
		tmp = t_1;
	} else if (a <= 1.3e-159) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= 2700000.0) {
		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))) - (b * (z * c))
	t_2 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -7.5e+118:
		tmp = t_2
	elif a <= -2.5:
		tmp = (a * (b * i)) - (j * (i * (y - (c * (t / i)))))
	elif a <= -1.95e-60:
		tmp = t_2
	elif a <= 1.12e-274:
		tmp = t_1
	elif a <= 1.3e-159:
		tmp = y * ((x * z) - (i * j))
	elif a <= 2700000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) - Float64(b * Float64(z * c)))
	t_2 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -7.5e+118)
		tmp = t_2;
	elseif (a <= -2.5)
		tmp = Float64(Float64(a * Float64(b * i)) - Float64(j * Float64(i * Float64(y - Float64(c * Float64(t / i))))));
	elseif (a <= -1.95e-60)
		tmp = t_2;
	elseif (a <= 1.12e-274)
		tmp = t_1;
	elseif (a <= 1.3e-159)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (a <= 2700000.0)
		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))) - (b * (z * c));
	t_2 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -7.5e+118)
		tmp = t_2;
	elseif (a <= -2.5)
		tmp = (a * (b * i)) - (j * (i * (y - (c * (t / i)))));
	elseif (a <= -1.95e-60)
		tmp = t_2;
	elseif (a <= 1.12e-274)
		tmp = t_1;
	elseif (a <= 1.3e-159)
		tmp = y * ((x * z) - (i * j));
	elseif (a <= 2700000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * 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, -7.5e+118], t$95$2, If[LessEqual[a, -2.5], N[(N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision] - N[(j * N[(i * N[(y - N[(c * N[(t / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.95e-60], t$95$2, If[LessEqual[a, 1.12e-274], t$95$1, If[LessEqual[a, 1.3e-159], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2700000.0], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -7.50000000000000003e118 or -2.5 < a < -1.9500000000000001e-60 or 2.7e6 < a

   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 j around 0 72.4%

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

      1. *-commutative 72.4%

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

   5. Simplified 72.4%

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

   6. Taylor expanded in z around 0 61.4%

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

      1. associate-*r* 61.4%

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

      2. neg-mul-1 61.4%

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

      3. *-commutative 61.4%

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

      4. associate-*r* 61.4%

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

      5. neg-mul-1 61.4%

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

      6. distribute-lft-out-- 65.7%

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

      7. distribute-lft-neg-in 65.7%

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

      8. distribute-rgt-neg-out 65.7%

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

      9. neg-sub0 65.7%

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

      10. sub-neg 65.7%

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

      11. +-commutative 65.7%

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

      12. associate--r+ 65.7%

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

      13. neg-sub0 65.7%

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

      14. remove-double-neg 65.7%

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

      15. *-commutative 65.7%

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

   8. Simplified 65.7%

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

   if -7.50000000000000003e118 < a < -2.5

   1. Initial program 73.1%

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

   3. Taylor expanded in i around inf 56.5%

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

      1. *-commutative 56.5%

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

   5. Simplified 56.5%

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

   6. Taylor expanded in i around inf 56.5%

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

      1. associate-/l* 61.0%

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

   8. Simplified 61.0%

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

   if -1.9500000000000001e-60 < a < 1.11999999999999998e-274 or 1.2999999999999999e-159 < a < 2.7e6

   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 c around inf 71.0%

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

      1. associate-*r* 71.0%

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

      2. neg-mul-1 71.0%

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

      3. *-commutative 71.0%

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

   5. Simplified 71.0%

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

   if 1.11999999999999998e-274 < a < 1.2999999999999999e-159

   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 y around inf 78.0%

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

      1. +-commutative 78.0%

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

      2. mul-1-neg 78.0%

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

      3. unsub-neg 78.0%

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

      4. *-commutative 78.0%

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

   5. Simplified 78.0%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{+118}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -2.5:\\ \;\;\;\;a \cdot \left(b \cdot i\right) - j \cdot \left(i \cdot \left(y - c \cdot \frac{t}{i}\right)\right)\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{-60}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{-274}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-159}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 2700000:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_3 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -8 \cdot 10^{-24}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;i \leq -1.95 \cdot 10^{-125}:\\ \;\;\;\;t \cdot \left(j \cdot \left(c - a \cdot \frac{x}{j}\right)\right)\\ \mathbf{elif}\;i \leq -1.15 \cdot 10^{-207}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 2.7 \cdot 10^{-251}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq 2.4 \cdot 10^{-149}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 1.95 \cdot 10^{-29}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq 5.2 \cdot 10^{+89}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c))))
        (t_2 (* t (- (* c j) (* x a))))
        (t_3 (* i (- (* a b) (* y j)))))
   (if (<= i -8e-24)
     t_3
     (if (<= i -1.95e-125)
       (* t (* j (- c (* a (/ x j)))))
       (if (<= i -1.15e-207)
         t_1
         (if (<= i 2.7e-251)
           t_2
           (if (<= i 2.4e-149)
             t_1
             (if (<= i 1.95e-29)
               t_2
               (if (<= i 5.2e+89) (* y (- (* x z) (* i j))) 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 = z * ((x * y) - (b * c));
	double t_2 = t * ((c * j) - (x * a));
	double t_3 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -8e-24) {
		tmp = t_3;
	} else if (i <= -1.95e-125) {
		tmp = t * (j * (c - (a * (x / j))));
	} else if (i <= -1.15e-207) {
		tmp = t_1;
	} else if (i <= 2.7e-251) {
		tmp = t_2;
	} else if (i <= 2.4e-149) {
		tmp = t_1;
	} else if (i <= 1.95e-29) {
		tmp = t_2;
	} else if (i <= 5.2e+89) {
		tmp = y * ((x * z) - (i * j));
	} 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 = z * ((x * y) - (b * c))
    t_2 = t * ((c * j) - (x * a))
    t_3 = i * ((a * b) - (y * j))
    if (i <= (-8d-24)) then
        tmp = t_3
    else if (i <= (-1.95d-125)) then
        tmp = t * (j * (c - (a * (x / j))))
    else if (i <= (-1.15d-207)) then
        tmp = t_1
    else if (i <= 2.7d-251) then
        tmp = t_2
    else if (i <= 2.4d-149) then
        tmp = t_1
    else if (i <= 1.95d-29) then
        tmp = t_2
    else if (i <= 5.2d+89) then
        tmp = y * ((x * z) - (i * j))
    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 = z * ((x * y) - (b * c));
	double t_2 = t * ((c * j) - (x * a));
	double t_3 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -8e-24) {
		tmp = t_3;
	} else if (i <= -1.95e-125) {
		tmp = t * (j * (c - (a * (x / j))));
	} else if (i <= -1.15e-207) {
		tmp = t_1;
	} else if (i <= 2.7e-251) {
		tmp = t_2;
	} else if (i <= 2.4e-149) {
		tmp = t_1;
	} else if (i <= 1.95e-29) {
		tmp = t_2;
	} else if (i <= 5.2e+89) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * ((x * y) - (b * c))
	t_2 = t * ((c * j) - (x * a))
	t_3 = i * ((a * b) - (y * j))
	tmp = 0
	if i <= -8e-24:
		tmp = t_3
	elif i <= -1.95e-125:
		tmp = t * (j * (c - (a * (x / j))))
	elif i <= -1.15e-207:
		tmp = t_1
	elif i <= 2.7e-251:
		tmp = t_2
	elif i <= 2.4e-149:
		tmp = t_1
	elif i <= 1.95e-29:
		tmp = t_2
	elif i <= 5.2e+89:
		tmp = y * ((x * z) - (i * j))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	t_2 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_3 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -8e-24)
		tmp = t_3;
	elseif (i <= -1.95e-125)
		tmp = Float64(t * Float64(j * Float64(c - Float64(a * Float64(x / j)))));
	elseif (i <= -1.15e-207)
		tmp = t_1;
	elseif (i <= 2.7e-251)
		tmp = t_2;
	elseif (i <= 2.4e-149)
		tmp = t_1;
	elseif (i <= 1.95e-29)
		tmp = t_2;
	elseif (i <= 5.2e+89)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * ((x * y) - (b * c));
	t_2 = t * ((c * j) - (x * a));
	t_3 = i * ((a * b) - (y * j));
	tmp = 0.0;
	if (i <= -8e-24)
		tmp = t_3;
	elseif (i <= -1.95e-125)
		tmp = t * (j * (c - (a * (x / j))));
	elseif (i <= -1.15e-207)
		tmp = t_1;
	elseif (i <= 2.7e-251)
		tmp = t_2;
	elseif (i <= 2.4e-149)
		tmp = t_1;
	elseif (i <= 1.95e-29)
		tmp = t_2;
	elseif (i <= 5.2e+89)
		tmp = y * ((x * z) - (i * j));
	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[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -8e-24], t$95$3, If[LessEqual[i, -1.95e-125], N[(t * N[(j * N[(c - N[(a * N[(x / j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.15e-207], t$95$1, If[LessEqual[i, 2.7e-251], t$95$2, If[LessEqual[i, 2.4e-149], t$95$1, If[LessEqual[i, 1.95e-29], t$95$2, If[LessEqual[i, 5.2e+89], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -7.99999999999999939e-24 or 5.2000000000000001e89 < i

   1. Initial program 63.1%

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

   3. Taylor expanded in x around inf 59.3%

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

      1. +-commutative 59.3%

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

      2. mul-1-neg 59.3%

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

      3. unsub-neg 59.3%

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

      4. associate-/l* 58.3%

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

      5. *-commutative 58.3%

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

   5. Simplified 58.3%

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

   6. Taylor expanded in i around inf 73.0%

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

      1. +-commutative 73.0%

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

      2. mul-1-neg 73.0%

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

      3. unsub-neg 73.0%

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

      4. *-commutative 73.0%

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

      5. *-commutative 73.0%

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

   8. Simplified 73.0%

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

   if -7.99999999999999939e-24 < i < -1.94999999999999991e-125

   1. Initial program 75.2%

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

   3. Taylor expanded in t around -inf 59.7%

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

      1. mul-1-neg 59.7%

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

      2. distribute-rgt-neg-in 59.7%

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

      3. +-commutative 59.7%

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

      4. *-commutative 59.7%

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

      5. fma-define 59.7%

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

      6. mul-1-neg 59.7%

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

      7. distribute-rgt-neg-in 59.7%

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

   5. Simplified 59.7%

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

   6. Taylor expanded in j around inf 63.8%

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

      1. +-commutative 63.8%

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

      2. neg-mul-1 63.8%

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

      3. unsub-neg 63.8%

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

      4. associate-/l* 63.8%

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

   8. Simplified 63.8%

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

   if -1.94999999999999991e-125 < i < -1.15e-207 or 2.7000000000000001e-251 < i < 2.4000000000000001e-149

   1. Initial program 78.6%

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

   3. Taylor expanded in z around inf 64.1%

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

      1. *-commutative 64.1%

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

   5. Simplified 64.1%

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

   if -1.15e-207 < i < 2.7000000000000001e-251 or 2.4000000000000001e-149 < i < 1.9499999999999999e-29

   1. Initial program 87.5%

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

   3. Taylor expanded in t around inf 64.0%

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

      1. +-commutative 64.0%

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

      2. mul-1-neg 64.0%

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

      3. unsub-neg 64.0%

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

      4. *-commutative 64.0%

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

      5. *-commutative 64.0%

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

   5. Simplified 64.0%

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

   if 1.9499999999999999e-29 < i < 5.2000000000000001e89

   1. Initial program 70.5%

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

   3. Taylor expanded in y around inf 64.1%

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

      1. +-commutative 64.1%

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

      2. mul-1-neg 64.1%

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

      3. unsub-neg 64.1%

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

      4. *-commutative 64.1%

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

   5. Simplified 64.1%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -8 \cdot 10^{-24}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -1.95 \cdot 10^{-125}:\\ \;\;\;\;t \cdot \left(j \cdot \left(c - a \cdot \frac{x}{j}\right)\right)\\ \mathbf{elif}\;i \leq -1.15 \cdot 10^{-207}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 2.7 \cdot 10^{-251}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;i \leq 2.4 \cdot 10^{-149}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 1.95 \cdot 10^{-29}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;i \leq 5.2 \cdot 10^{+89}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -2.6 \cdot 10^{-24}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -3.2 \cdot 10^{-124}:\\ \;\;\;\;t \cdot \left(j \cdot \left(c - a \cdot \frac{x}{j}\right)\right)\\ \mathbf{elif}\;i \leq -5.6 \cdot 10^{-207}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 7.2 \cdot 10^{-254}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;i \leq 9.2 \cdot 10^{-160}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 3.5 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \left(c \cdot \frac{t \cdot j}{x} - t \cdot a\right)\\ \mathbf{elif}\;i \leq 9.2 \cdot 10^{+89}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c)))) (t_2 (* i (- (* a b) (* y j)))))
   (if (<= i -2.6e-24)
     t_2
     (if (<= i -3.2e-124)
       (* t (* j (- c (* a (/ x j)))))
       (if (<= i -5.6e-207)
         t_1
         (if (<= i 7.2e-254)
           (* t (- (* c j) (* x a)))
           (if (<= i 9.2e-160)
             t_1
             (if (<= i 3.5e-26)
               (* x (- (* c (/ (* t j) x)) (* t a)))
               (if (<= i 9.2e+89) (* y (- (* x z) (* i j))) t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double t_2 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -2.6e-24) {
		tmp = t_2;
	} else if (i <= -3.2e-124) {
		tmp = t * (j * (c - (a * (x / j))));
	} else if (i <= -5.6e-207) {
		tmp = t_1;
	} else if (i <= 7.2e-254) {
		tmp = t * ((c * j) - (x * a));
	} else if (i <= 9.2e-160) {
		tmp = t_1;
	} else if (i <= 3.5e-26) {
		tmp = x * ((c * ((t * j) / x)) - (t * a));
	} else if (i <= 9.2e+89) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * ((x * y) - (b * c))
    t_2 = i * ((a * b) - (y * j))
    if (i <= (-2.6d-24)) then
        tmp = t_2
    else if (i <= (-3.2d-124)) then
        tmp = t * (j * (c - (a * (x / j))))
    else if (i <= (-5.6d-207)) then
        tmp = t_1
    else if (i <= 7.2d-254) then
        tmp = t * ((c * j) - (x * a))
    else if (i <= 9.2d-160) then
        tmp = t_1
    else if (i <= 3.5d-26) then
        tmp = x * ((c * ((t * j) / x)) - (t * a))
    else if (i <= 9.2d+89) then
        tmp = y * ((x * z) - (i * j))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double t_2 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -2.6e-24) {
		tmp = t_2;
	} else if (i <= -3.2e-124) {
		tmp = t * (j * (c - (a * (x / j))));
	} else if (i <= -5.6e-207) {
		tmp = t_1;
	} else if (i <= 7.2e-254) {
		tmp = t * ((c * j) - (x * a));
	} else if (i <= 9.2e-160) {
		tmp = t_1;
	} else if (i <= 3.5e-26) {
		tmp = x * ((c * ((t * j) / x)) - (t * a));
	} else if (i <= 9.2e+89) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * ((x * y) - (b * c))
	t_2 = i * ((a * b) - (y * j))
	tmp = 0
	if i <= -2.6e-24:
		tmp = t_2
	elif i <= -3.2e-124:
		tmp = t * (j * (c - (a * (x / j))))
	elif i <= -5.6e-207:
		tmp = t_1
	elif i <= 7.2e-254:
		tmp = t * ((c * j) - (x * a))
	elif i <= 9.2e-160:
		tmp = t_1
	elif i <= 3.5e-26:
		tmp = x * ((c * ((t * j) / x)) - (t * a))
	elif i <= 9.2e+89:
		tmp = y * ((x * z) - (i * j))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	t_2 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -2.6e-24)
		tmp = t_2;
	elseif (i <= -3.2e-124)
		tmp = Float64(t * Float64(j * Float64(c - Float64(a * Float64(x / j)))));
	elseif (i <= -5.6e-207)
		tmp = t_1;
	elseif (i <= 7.2e-254)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (i <= 9.2e-160)
		tmp = t_1;
	elseif (i <= 3.5e-26)
		tmp = Float64(x * Float64(Float64(c * Float64(Float64(t * j) / x)) - Float64(t * a)));
	elseif (i <= 9.2e+89)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * ((x * y) - (b * c));
	t_2 = i * ((a * b) - (y * j));
	tmp = 0.0;
	if (i <= -2.6e-24)
		tmp = t_2;
	elseif (i <= -3.2e-124)
		tmp = t * (j * (c - (a * (x / j))));
	elseif (i <= -5.6e-207)
		tmp = t_1;
	elseif (i <= 7.2e-254)
		tmp = t * ((c * j) - (x * a));
	elseif (i <= 9.2e-160)
		tmp = t_1;
	elseif (i <= 3.5e-26)
		tmp = x * ((c * ((t * j) / x)) - (t * a));
	elseif (i <= 9.2e+89)
		tmp = y * ((x * z) - (i * j));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.6e-24], t$95$2, If[LessEqual[i, -3.2e-124], N[(t * N[(j * N[(c - N[(a * N[(x / j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -5.6e-207], t$95$1, If[LessEqual[i, 7.2e-254], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 9.2e-160], t$95$1, If[LessEqual[i, 3.5e-26], N[(x * N[(N[(c * N[(N[(t * j), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 9.2e+89], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -2.6e-24 or 9.1999999999999996e89 < i

   1. Initial program 63.1%

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

   3. Taylor expanded in x around inf 59.3%

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

      1. +-commutative 59.3%

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

      2. mul-1-neg 59.3%

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

      3. unsub-neg 59.3%

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

      4. associate-/l* 58.3%

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

      5. *-commutative 58.3%

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

   5. Simplified 58.3%

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

   6. Taylor expanded in i around inf 73.0%

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

      1. +-commutative 73.0%

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

      2. mul-1-neg 73.0%

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

      3. unsub-neg 73.0%

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

      4. *-commutative 73.0%

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

      5. *-commutative 73.0%

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

   8. Simplified 73.0%

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

   if -2.6e-24 < i < -3.20000000000000004e-124

   1. Initial program 75.2%

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

   3. Taylor expanded in t around -inf 59.7%

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

      1. mul-1-neg 59.7%

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

      2. distribute-rgt-neg-in 59.7%

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

      3. +-commutative 59.7%

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

      4. *-commutative 59.7%

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

      5. fma-define 59.7%

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

      6. mul-1-neg 59.7%

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

      7. distribute-rgt-neg-in 59.7%

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

   5. Simplified 59.7%

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

   6. Taylor expanded in j around inf 63.8%

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

      1. +-commutative 63.8%

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

      2. neg-mul-1 63.8%

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

      3. unsub-neg 63.8%

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

      4. associate-/l* 63.8%

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

   8. Simplified 63.8%

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

   if -3.20000000000000004e-124 < i < -5.59999999999999986e-207 or 7.19999999999999967e-254 < i < 9.19999999999999939e-160

   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 z around inf 66.0%

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

      1. *-commutative 66.0%

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

   5. Simplified 66.0%

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

   if -5.59999999999999986e-207 < i < 7.19999999999999967e-254

   1. Initial program 85.4%

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

   3. Taylor expanded in t around inf 66.1%

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

      1. +-commutative 66.1%

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

      2. mul-1-neg 66.1%

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

      3. unsub-neg 66.1%

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

      4. *-commutative 66.1%

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

      5. *-commutative 66.1%

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

   5. Simplified 66.1%

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

   if 9.19999999999999939e-160 < i < 3.49999999999999985e-26

   1. Initial program 88.4%

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

   3. Taylor expanded in t around -inf 57.3%

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

      1. mul-1-neg 57.3%

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

      2. distribute-rgt-neg-in 57.3%

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

      3. +-commutative 57.3%

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

      4. *-commutative 57.3%

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

      5. fma-define 57.3%

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

      6. mul-1-neg 57.3%

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

      7. distribute-rgt-neg-in 57.3%

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

   5. Simplified 57.3%

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

   6. Taylor expanded in x around inf 57.6%

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

      1. mul-1-neg 57.6%

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

      2. +-commutative 57.6%

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

      3. unsub-neg 57.6%

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

      4. associate-/l* 57.6%

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

      5. *-commutative 57.6%

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

   8. Simplified 57.6%

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

   if 3.49999999999999985e-26 < i < 9.1999999999999996e89

   1. Initial program 70.5%

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

   3. Taylor expanded in y around inf 64.1%

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

      1. +-commutative 64.1%

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

      2. mul-1-neg 64.1%

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

      3. unsub-neg 64.1%

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

      4. *-commutative 64.1%

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

   5. Simplified 64.1%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.6 \cdot 10^{-24}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -3.2 \cdot 10^{-124}:\\ \;\;\;\;t \cdot \left(j \cdot \left(c - a \cdot \frac{x}{j}\right)\right)\\ \mathbf{elif}\;i \leq -5.6 \cdot 10^{-207}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 7.2 \cdot 10^{-254}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;i \leq 9.2 \cdot 10^{-160}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 3.5 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \left(c \cdot \frac{t \cdot j}{x} - t \cdot a\right)\\ \mathbf{elif}\;i \leq 9.2 \cdot 10^{+89}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 68.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.65 \cdot 10^{+219}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.18 \cdot 10^{+64}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + t\_1\\ \mathbf{elif}\;b \leq -45:\\ \;\;\;\;z \cdot \left(x \cdot \left(y - b \cdot \frac{c}{x}\right) + x \cdot \frac{a \cdot \left(b \cdot \frac{i}{x}\right) - t \cdot a}{z}\right)\\ \mathbf{elif}\;b \leq 1.28 \cdot 10^{-101}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(y \cdot z - b \cdot \frac{z \cdot c - a \cdot i}{x}\right) - t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= b -1.65e+219)
     t_1
     (if (<= b -1.18e+64)
       (+ (* x (- (* y z) (* t a))) t_1)
       (if (<= b -45.0)
         (*
          z
          (+
           (* x (- y (* b (/ c x))))
           (* x (/ (- (* a (* b (/ i x))) (* t a)) z))))
         (if (<= b 1.28e-101)
           (- (* j (- (* t c) (* y i))) (* x (- (* t a) (* y z))))
           (* x (- (- (* y z) (* b (/ (- (* z c) (* a i)) x))) (* t a)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.65e+219) {
		tmp = t_1;
	} else if (b <= -1.18e+64) {
		tmp = (x * ((y * z) - (t * a))) + t_1;
	} else if (b <= -45.0) {
		tmp = z * ((x * (y - (b * (c / x)))) + (x * (((a * (b * (i / x))) - (t * a)) / z)));
	} else if (b <= 1.28e-101) {
		tmp = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)));
	} else {
		tmp = x * (((y * z) - (b * (((z * c) - (a * i)) / x))) - (t * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    if (b <= (-1.65d+219)) then
        tmp = t_1
    else if (b <= (-1.18d+64)) then
        tmp = (x * ((y * z) - (t * a))) + t_1
    else if (b <= (-45.0d0)) then
        tmp = z * ((x * (y - (b * (c / x)))) + (x * (((a * (b * (i / x))) - (t * a)) / z)))
    else if (b <= 1.28d-101) then
        tmp = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)))
    else
        tmp = x * (((y * z) - (b * (((z * c) - (a * i)) / x))) - (t * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.65e+219) {
		tmp = t_1;
	} else if (b <= -1.18e+64) {
		tmp = (x * ((y * z) - (t * a))) + t_1;
	} else if (b <= -45.0) {
		tmp = z * ((x * (y - (b * (c / x)))) + (x * (((a * (b * (i / x))) - (t * a)) / z)));
	} else if (b <= 1.28e-101) {
		tmp = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)));
	} else {
		tmp = x * (((y * z) - (b * (((z * c) - (a * i)) / x))) - (t * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -1.65e+219:
		tmp = t_1
	elif b <= -1.18e+64:
		tmp = (x * ((y * z) - (t * a))) + t_1
	elif b <= -45.0:
		tmp = z * ((x * (y - (b * (c / x)))) + (x * (((a * (b * (i / x))) - (t * a)) / z)))
	elif b <= 1.28e-101:
		tmp = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)))
	else:
		tmp = x * (((y * z) - (b * (((z * c) - (a * i)) / x))) - (t * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -1.65e+219)
		tmp = t_1;
	elseif (b <= -1.18e+64)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_1);
	elseif (b <= -45.0)
		tmp = Float64(z * Float64(Float64(x * Float64(y - Float64(b * Float64(c / x)))) + Float64(x * Float64(Float64(Float64(a * Float64(b * Float64(i / x))) - Float64(t * a)) / z))));
	elseif (b <= 1.28e-101)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) - Float64(x * Float64(Float64(t * a) - Float64(y * z))));
	else
		tmp = Float64(x * Float64(Float64(Float64(y * z) - Float64(b * Float64(Float64(Float64(z * c) - Float64(a * i)) / x))) - Float64(t * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -1.65e+219)
		tmp = t_1;
	elseif (b <= -1.18e+64)
		tmp = (x * ((y * z) - (t * a))) + t_1;
	elseif (b <= -45.0)
		tmp = z * ((x * (y - (b * (c / x)))) + (x * (((a * (b * (i / x))) - (t * a)) / z)));
	elseif (b <= 1.28e-101)
		tmp = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)));
	else
		tmp = x * (((y * z) - (b * (((z * c) - (a * i)) / x))) - (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.65e+219], t$95$1, If[LessEqual[b, -1.18e+64], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[b, -45.0], N[(z * N[(N[(x * N[(y - N[(b * N[(c / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(N[(a * N[(b * N[(i / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.28e-101], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(N[(y * z), $MachinePrecision] - N[(b * N[(N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.6500000000000001e219

   1. Initial program 62.4%

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

   3. Taylor expanded in b around inf 87.7%

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

      1. *-commutative 87.7%

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

   5. Simplified 87.7%

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

   if -1.6500000000000001e219 < b < -1.18000000000000006e64

   1. Initial program 79.8%

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

   3. Taylor expanded in j around 0 82.3%

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

      1. *-commutative 82.3%

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

   5. Simplified 82.3%

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

   if -1.18000000000000006e64 < b < -45

   1. Initial program 59.5%

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

   3. Taylor expanded in j around 0 43.3%

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

      1. *-commutative 43.3%

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

   5. Simplified 43.3%

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

   6. Taylor expanded in x around inf 51.7%

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

      1. +-commutative 51.7%

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

      2. mul-1-neg 51.7%

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

      3. unsub-neg 51.7%

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

      4. associate-/l* 59.9%

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

      5. *-commutative 59.9%

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

   8. Simplified 59.9%

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

   9. Taylor expanded in z around inf 75.8%

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

       1. +-commutative 75.8%

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

       2. mul-1-neg 75.8%

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

       3. unsub-neg 75.8%

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

       4. associate-/l* 75.8%

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

       5. associate-/l* 75.9%

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

       6. +-commutative 75.9%

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

       7. mul-1-neg 75.9%

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

       8. unsub-neg 75.9%

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

       9. associate-/l* 75.8%

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

       10. associate-/l* 75.8%

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

   11. Simplified 75.8%

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

   if -45 < b < 1.27999999999999995e-101

   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 0 75.5%

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

   if 1.27999999999999995e-101 < b

   1. Initial program 69.9%

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

   3. Taylor expanded in j around 0 63.0%

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

      1. *-commutative 63.0%

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

   5. Simplified 63.0%

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

   6. Taylor expanded in x around inf 62.0%

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

      1. +-commutative 62.0%

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

      2. mul-1-neg 62.0%

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

      3. unsub-neg 62.0%

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

      4. associate-/l* 63.3%

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

      5. *-commutative 63.3%

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

   8. Simplified 63.3%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.65 \cdot 10^{+219}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.18 \cdot 10^{+64}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -45:\\ \;\;\;\;z \cdot \left(x \cdot \left(y - b \cdot \frac{c}{x}\right) + x \cdot \frac{a \cdot \left(b \cdot \frac{i}{x}\right) - t \cdot a}{z}\right)\\ \mathbf{elif}\;b \leq 1.28 \cdot 10^{-101}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(y \cdot z - b \cdot \frac{z \cdot c - a \cdot i}{x}\right) - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -9 \cdot 10^{+150}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{+122}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-35}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-294}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-180}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 620000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))) (t_2 (* y (- (* x z) (* i j)))))
   (if (<= y -9e+150)
     t_2
     (if (<= y -3.5e+122)
       t_1
       (if (<= y -4e-35)
         t_2
         (if (<= y -3.2e-294)
           t_1
           (if (<= y 2.4e-180)
             (* c (- (* t j) (* z b)))
             (if (<= y 620000000.0) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -9e+150) {
		tmp = t_2;
	} else if (y <= -3.5e+122) {
		tmp = t_1;
	} else if (y <= -4e-35) {
		tmp = t_2;
	} else if (y <= -3.2e-294) {
		tmp = t_1;
	} else if (y <= 2.4e-180) {
		tmp = c * ((t * j) - (z * b));
	} else if (y <= 620000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((b * i) - (x * t))
    t_2 = y * ((x * z) - (i * j))
    if (y <= (-9d+150)) then
        tmp = t_2
    else if (y <= (-3.5d+122)) then
        tmp = t_1
    else if (y <= (-4d-35)) then
        tmp = t_2
    else if (y <= (-3.2d-294)) then
        tmp = t_1
    else if (y <= 2.4d-180) then
        tmp = c * ((t * j) - (z * b))
    else if (y <= 620000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -9e+150) {
		tmp = t_2;
	} else if (y <= -3.5e+122) {
		tmp = t_1;
	} else if (y <= -4e-35) {
		tmp = t_2;
	} else if (y <= -3.2e-294) {
		tmp = t_1;
	} else if (y <= 2.4e-180) {
		tmp = c * ((t * j) - (z * b));
	} else if (y <= 620000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	t_2 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -9e+150:
		tmp = t_2
	elif y <= -3.5e+122:
		tmp = t_1
	elif y <= -4e-35:
		tmp = t_2
	elif y <= -3.2e-294:
		tmp = t_1
	elif y <= 2.4e-180:
		tmp = c * ((t * j) - (z * b))
	elif y <= 620000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -9e+150)
		tmp = t_2;
	elseif (y <= -3.5e+122)
		tmp = t_1;
	elseif (y <= -4e-35)
		tmp = t_2;
	elseif (y <= -3.2e-294)
		tmp = t_1;
	elseif (y <= 2.4e-180)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (y <= 620000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((b * i) - (x * t));
	t_2 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -9e+150)
		tmp = t_2;
	elseif (y <= -3.5e+122)
		tmp = t_1;
	elseif (y <= -4e-35)
		tmp = t_2;
	elseif (y <= -3.2e-294)
		tmp = t_1;
	elseif (y <= 2.4e-180)
		tmp = c * ((t * j) - (z * b));
	elseif (y <= 620000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9e+150], t$95$2, If[LessEqual[y, -3.5e+122], t$95$1, If[LessEqual[y, -4e-35], t$95$2, If[LessEqual[y, -3.2e-294], t$95$1, If[LessEqual[y, 2.4e-180], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 620000000.0], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.00000000000000001e150 or -3.50000000000000014e122 < y < -4.00000000000000003e-35 or 6.2e8 < y

   1. Initial program 64.8%

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

   3. Taylor expanded in y around inf 63.7%

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

      1. +-commutative 63.7%

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

      2. mul-1-neg 63.7%

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

      3. unsub-neg 63.7%

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

      4. *-commutative 63.7%

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

   5. Simplified 63.7%

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

   if -9.00000000000000001e150 < y < -3.50000000000000014e122 or -4.00000000000000003e-35 < y < -3.20000000000000019e-294 or 2.39999999999999979e-180 < y < 6.2e8

   1. Initial program 82.6%

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

   3. Taylor expanded in j around 0 73.9%

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

      1. *-commutative 73.9%

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

   5. Simplified 73.9%

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

   6. Taylor expanded in z around 0 63.1%

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

      1. associate-*r* 63.1%

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

      2. neg-mul-1 63.1%

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

      3. *-commutative 63.1%

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

      4. associate-*r* 63.1%

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

      5. neg-mul-1 63.1%

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

      6. distribute-lft-out-- 67.5%

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

      7. distribute-lft-neg-in 67.5%

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

      8. distribute-rgt-neg-out 67.5%

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

      9. neg-sub0 67.5%

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

      10. sub-neg 67.5%

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

      11. +-commutative 67.5%

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

      12. associate--r+ 67.5%

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

      13. neg-sub0 67.5%

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

      14. remove-double-neg 67.5%

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

      15. *-commutative 67.5%

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

   8. Simplified 67.5%

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

   if -3.20000000000000019e-294 < y < 2.39999999999999979e-180

   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 c around inf 58.9%

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

      1. *-commutative 58.9%

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

      2. *-commutative 58.9%

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

   5. Simplified 58.9%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+150}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{+122}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-35}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-294}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-180}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 620000000:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 61.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ t_2 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -2.6:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq 1.8 \cdot 10^{-249}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 8.2 \cdot 10^{-150}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 2.6 \cdot 10^{+90}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* j (- (* t c) (* y i))) (* x (- (* t a) (* y z)))))
        (t_2 (* i (- (* a b) (* y j)))))
   (if (<= i -2.6)
     t_2
     (if (<= i 1.8e-249)
       t_1
       (if (<= i 8.2e-150)
         (* z (- (* x y) (* b c)))
         (if (<= i 2.6e+90) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)));
	double t_2 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -2.6) {
		tmp = t_2;
	} else if (i <= 1.8e-249) {
		tmp = t_1;
	} else if (i <= 8.2e-150) {
		tmp = z * ((x * y) - (b * c));
	} else if (i <= 2.6e+90) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)))
    t_2 = i * ((a * b) - (y * j))
    if (i <= (-2.6d0)) then
        tmp = t_2
    else if (i <= 1.8d-249) then
        tmp = t_1
    else if (i <= 8.2d-150) then
        tmp = z * ((x * y) - (b * c))
    else if (i <= 2.6d+90) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)));
	double t_2 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -2.6) {
		tmp = t_2;
	} else if (i <= 1.8e-249) {
		tmp = t_1;
	} else if (i <= 8.2e-150) {
		tmp = z * ((x * y) - (b * c));
	} else if (i <= 2.6e+90) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)))
	t_2 = i * ((a * b) - (y * j))
	tmp = 0
	if i <= -2.6:
		tmp = t_2
	elif i <= 1.8e-249:
		tmp = t_1
	elif i <= 8.2e-150:
		tmp = z * ((x * y) - (b * c))
	elif i <= 2.6e+90:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) - Float64(x * Float64(Float64(t * a) - Float64(y * z))))
	t_2 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -2.6)
		tmp = t_2;
	elseif (i <= 1.8e-249)
		tmp = t_1;
	elseif (i <= 8.2e-150)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (i <= 2.6e+90)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)));
	t_2 = i * ((a * b) - (y * j));
	tmp = 0.0;
	if (i <= -2.6)
		tmp = t_2;
	elseif (i <= 1.8e-249)
		tmp = t_1;
	elseif (i <= 8.2e-150)
		tmp = z * ((x * y) - (b * c));
	elseif (i <= 2.6e+90)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.6], t$95$2, If[LessEqual[i, 1.8e-249], t$95$1, If[LessEqual[i, 8.2e-150], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.6e+90], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -2.60000000000000009 or 2.5999999999999998e90 < i

   1. Initial program 61.9%

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

   3. Taylor expanded in x around inf 60.0%

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

      1. +-commutative 60.0%

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

      2. mul-1-neg 60.0%

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

      3. unsub-neg 60.0%

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

      4. associate-/l* 59.0%

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

      5. *-commutative 59.0%

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

   5. Simplified 59.0%

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

   6. Taylor expanded in i around inf 74.2%

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

      1. +-commutative 74.2%

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

      2. mul-1-neg 74.2%

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

      3. unsub-neg 74.2%

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

      4. *-commutative 74.2%

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

      5. *-commutative 74.2%

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

   8. Simplified 74.2%

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

   if -2.60000000000000009 < i < 1.79999999999999997e-249 or 8.1999999999999997e-150 < i < 2.5999999999999998e90

   1. Initial program 81.8%

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

   3. Taylor expanded in 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 1.79999999999999997e-249 < i < 8.1999999999999997e-150

   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 z around inf 65.8%

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

      1. *-commutative 65.8%

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

   5. Simplified 65.8%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.6:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq 1.8 \cdot 10^{-249}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;i \leq 8.2 \cdot 10^{-150}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 2.6 \cdot 10^{+90}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -2.45 \cdot 10^{+125}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -4.5 \cdot 10^{-137}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;c \leq -2.3 \cdot 10^{-191}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 4 \cdot 10^{-217}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 2.8 \cdot 10^{+80}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* a b) (* y j)))) (t_2 (* c (- (* t j) (* z b)))))
   (if (<= c -2.45e+125)
     t_2
     (if (<= c -4.5e-137)
       (* t (- (* c j) (* x a)))
       (if (<= c -2.3e-191)
         t_1
         (if (<= c 4e-217)
           (* a (- (* b i) (* x t)))
           (if (<= c 2.8e+80) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -2.45e+125) {
		tmp = t_2;
	} else if (c <= -4.5e-137) {
		tmp = t * ((c * j) - (x * a));
	} else if (c <= -2.3e-191) {
		tmp = t_1;
	} else if (c <= 4e-217) {
		tmp = a * ((b * i) - (x * t));
	} else if (c <= 2.8e+80) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i * ((a * b) - (y * j))
    t_2 = c * ((t * j) - (z * b))
    if (c <= (-2.45d+125)) then
        tmp = t_2
    else if (c <= (-4.5d-137)) then
        tmp = t * ((c * j) - (x * a))
    else if (c <= (-2.3d-191)) then
        tmp = t_1
    else if (c <= 4d-217) then
        tmp = a * ((b * i) - (x * t))
    else if (c <= 2.8d+80) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -2.45e+125) {
		tmp = t_2;
	} else if (c <= -4.5e-137) {
		tmp = t * ((c * j) - (x * a));
	} else if (c <= -2.3e-191) {
		tmp = t_1;
	} else if (c <= 4e-217) {
		tmp = a * ((b * i) - (x * t));
	} else if (c <= 2.8e+80) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((a * b) - (y * j))
	t_2 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -2.45e+125:
		tmp = t_2
	elif c <= -4.5e-137:
		tmp = t * ((c * j) - (x * a))
	elif c <= -2.3e-191:
		tmp = t_1
	elif c <= 4e-217:
		tmp = a * ((b * i) - (x * t))
	elif c <= 2.8e+80:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -2.45e+125)
		tmp = t_2;
	elseif (c <= -4.5e-137)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (c <= -2.3e-191)
		tmp = t_1;
	elseif (c <= 4e-217)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (c <= 2.8e+80)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((a * b) - (y * j));
	t_2 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -2.45e+125)
		tmp = t_2;
	elseif (c <= -4.5e-137)
		tmp = t * ((c * j) - (x * a));
	elseif (c <= -2.3e-191)
		tmp = t_1;
	elseif (c <= 4e-217)
		tmp = a * ((b * i) - (x * t));
	elseif (c <= 2.8e+80)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.45e+125], t$95$2, If[LessEqual[c, -4.5e-137], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.3e-191], t$95$1, If[LessEqual[c, 4e-217], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.8e+80], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -2.45000000000000008e125 or 2.79999999999999984e80 < c

   1. Initial program 61.9%

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

   3. Taylor expanded in c around inf 71.2%

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

      1. *-commutative 71.2%

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

      2. *-commutative 71.2%

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

   5. Simplified 71.2%

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

   if -2.45000000000000008e125 < c < -4.4999999999999997e-137

   1. Initial program 79.2%

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

   3. Taylor expanded in t around inf 54.2%

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

      1. +-commutative 54.2%

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

      2. mul-1-neg 54.2%

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

      3. unsub-neg 54.2%

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

      4. *-commutative 54.2%

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

      5. *-commutative 54.2%

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

   5. Simplified 54.2%

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

   if -4.4999999999999997e-137 < c < -2.30000000000000011e-191 or 4.00000000000000033e-217 < c < 2.79999999999999984e80

   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 x around inf 78.4%

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

      1. +-commutative 78.4%

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

      2. mul-1-neg 78.4%

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

      3. unsub-neg 78.4%

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

      4. associate-/l* 76.8%

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

      5. *-commutative 76.8%

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

   5. Simplified 76.8%

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

   6. Taylor expanded in i around inf 57.9%

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

      1. +-commutative 57.9%

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

      2. mul-1-neg 57.9%

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

      3. unsub-neg 57.9%

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

      4. *-commutative 57.9%

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

      5. *-commutative 57.9%

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

   8. Simplified 57.9%

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

   if -2.30000000000000011e-191 < c < 4.00000000000000033e-217

   1. Initial program 75.8%

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

   3. Taylor expanded in j around 0 74.5%

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

      1. *-commutative 74.5%

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

   5. Simplified 74.5%

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

   6. Taylor expanded in z around 0 55.4%

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

      1. associate-*r* 55.4%

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

      2. neg-mul-1 55.4%

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

      3. *-commutative 55.4%

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

      4. associate-*r* 55.4%

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

      5. neg-mul-1 55.4%

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

      6. distribute-lft-out-- 57.0%

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

      7. distribute-lft-neg-in 57.0%

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

      8. distribute-rgt-neg-out 57.0%

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

      9. neg-sub0 57.0%

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

      10. sub-neg 57.0%

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

      11. +-commutative 57.0%

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

      12. associate--r+ 57.0%

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

      13. neg-sub0 57.0%

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

      14. remove-double-neg 57.0%

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

      15. *-commutative 57.0%

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

   8. Simplified 57.0%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.45 \cdot 10^{+125}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -4.5 \cdot 10^{-137}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;c \leq -2.3 \cdot 10^{-191}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 4 \cdot 10^{-217}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 2.8 \cdot 10^{+80}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -7.8 \cdot 10^{-24}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq 8.8 \cdot 10^{-254}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 3.9 \cdot 10^{-147}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 6.2 \cdot 10^{-27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 9.5 \cdot 10^{+89}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a)))) (t_2 (* i (- (* a b) (* y j)))))
   (if (<= i -7.8e-24)
     t_2
     (if (<= i 8.8e-254)
       t_1
       (if (<= i 3.9e-147)
         (* z (- (* x y) (* b c)))
         (if (<= i 6.2e-27)
           t_1
           (if (<= i 9.5e+89) (* y (- (* x z) (* i j))) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double t_2 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -7.8e-24) {
		tmp = t_2;
	} else if (i <= 8.8e-254) {
		tmp = t_1;
	} else if (i <= 3.9e-147) {
		tmp = z * ((x * y) - (b * c));
	} else if (i <= 6.2e-27) {
		tmp = t_1;
	} else if (i <= 9.5e+89) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((c * j) - (x * a))
    t_2 = i * ((a * b) - (y * j))
    if (i <= (-7.8d-24)) then
        tmp = t_2
    else if (i <= 8.8d-254) then
        tmp = t_1
    else if (i <= 3.9d-147) then
        tmp = z * ((x * y) - (b * c))
    else if (i <= 6.2d-27) then
        tmp = t_1
    else if (i <= 9.5d+89) then
        tmp = y * ((x * z) - (i * j))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double t_2 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -7.8e-24) {
		tmp = t_2;
	} else if (i <= 8.8e-254) {
		tmp = t_1;
	} else if (i <= 3.9e-147) {
		tmp = z * ((x * y) - (b * c));
	} else if (i <= 6.2e-27) {
		tmp = t_1;
	} else if (i <= 9.5e+89) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	t_2 = i * ((a * b) - (y * j))
	tmp = 0
	if i <= -7.8e-24:
		tmp = t_2
	elif i <= 8.8e-254:
		tmp = t_1
	elif i <= 3.9e-147:
		tmp = z * ((x * y) - (b * c))
	elif i <= 6.2e-27:
		tmp = t_1
	elif i <= 9.5e+89:
		tmp = y * ((x * z) - (i * j))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_2 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -7.8e-24)
		tmp = t_2;
	elseif (i <= 8.8e-254)
		tmp = t_1;
	elseif (i <= 3.9e-147)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (i <= 6.2e-27)
		tmp = t_1;
	elseif (i <= 9.5e+89)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((c * j) - (x * a));
	t_2 = i * ((a * b) - (y * j));
	tmp = 0.0;
	if (i <= -7.8e-24)
		tmp = t_2;
	elseif (i <= 8.8e-254)
		tmp = t_1;
	elseif (i <= 3.9e-147)
		tmp = z * ((x * y) - (b * c));
	elseif (i <= 6.2e-27)
		tmp = t_1;
	elseif (i <= 9.5e+89)
		tmp = y * ((x * z) - (i * j));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -7.8e-24], t$95$2, If[LessEqual[i, 8.8e-254], t$95$1, If[LessEqual[i, 3.9e-147], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 6.2e-27], t$95$1, If[LessEqual[i, 9.5e+89], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -7.8e-24 or 9.5000000000000003e89 < i

   1. Initial program 63.1%

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

   3. Taylor expanded in x around inf 59.3%

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

      1. +-commutative 59.3%

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

      2. mul-1-neg 59.3%

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

      3. unsub-neg 59.3%

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

      4. associate-/l* 58.3%

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

      5. *-commutative 58.3%

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

   5. Simplified 58.3%

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

   6. Taylor expanded in i around inf 73.0%

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

      1. +-commutative 73.0%

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

      2. mul-1-neg 73.0%

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

      3. unsub-neg 73.0%

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

      4. *-commutative 73.0%

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

      5. *-commutative 73.0%

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

   8. Simplified 73.0%

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

   if -7.8e-24 < i < 8.8000000000000004e-254 or 3.8999999999999998e-147 < i < 6.1999999999999997e-27

   1. Initial program 84.4%

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

   3. Taylor expanded in t around inf 58.4%

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

      1. +-commutative 58.4%

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

      2. mul-1-neg 58.4%

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

      3. unsub-neg 58.4%

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

      4. *-commutative 58.4%

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

      5. *-commutative 58.4%

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

   5. Simplified 58.4%

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

   if 8.8000000000000004e-254 < i < 3.8999999999999998e-147

   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 z around inf 65.8%

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

      1. *-commutative 65.8%

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

   5. Simplified 65.8%

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

   if 6.1999999999999997e-27 < i < 9.5000000000000003e89

   1. Initial program 70.5%

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

   3. Taylor expanded in y around inf 64.1%

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

      1. +-commutative 64.1%

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

      2. mul-1-neg 64.1%

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

      3. unsub-neg 64.1%

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

      4. *-commutative 64.1%

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

   5. Simplified 64.1%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -7.8 \cdot 10^{-24}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq 8.8 \cdot 10^{-254}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;i \leq 3.9 \cdot 10^{-147}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 6.2 \cdot 10^{-27}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;i \leq 9.5 \cdot 10^{+89}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 65.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -1.5 \cdot 10^{+156}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 0.25:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+155}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j)))))
   (if (<= y -1.5e+156)
     t_1
     (if (<= y 0.25)
       (+ (* x (- (* y z) (* t a))) (* b (- (* a i) (* z c))))
       (if (<= y 7.8e+155)
         (- (* j (- (* t c) (* y i))) (* x (- (* t a) (* 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 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.5e+156) {
		tmp = t_1;
	} else if (y <= 0.25) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	} else if (y <= 7.8e+155) {
		tmp = (j * ((t * c) - (y * i))) - (x * ((t * a) - (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 = y * ((x * z) - (i * j))
    if (y <= (-1.5d+156)) then
        tmp = t_1
    else if (y <= 0.25d0) then
        tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))
    else if (y <= 7.8d+155) then
        tmp = (j * ((t * c) - (y * i))) - (x * ((t * a) - (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 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.5e+156) {
		tmp = t_1;
	} else if (y <= 0.25) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	} else if (y <= 7.8e+155) {
		tmp = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)));
	} 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 <= -1.5e+156:
		tmp = t_1
	elif y <= 0.25:
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))
	elif y <= 7.8e+155:
		tmp = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)))
	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 <= -1.5e+156)
		tmp = t_1;
	elseif (y <= 0.25)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (y <= 7.8e+155)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) - Float64(x * Float64(Float64(t * a) - 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 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -1.5e+156)
		tmp = t_1;
	elseif (y <= 0.25)
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	elseif (y <= 7.8e+155)
		tmp = (j * ((t * c) - (y * i))) - (x * ((t * a) - (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[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.5e+156], t$95$1, If[LessEqual[y, 0.25], 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], If[LessEqual[y, 7.8e+155], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.5e156 or 7.7999999999999996e155 < y

   1. Initial program 45.6%

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

   3. Taylor expanded in y around inf 71.4%

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

      1. +-commutative 71.4%

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

      2. mul-1-neg 71.4%

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

      3. unsub-neg 71.4%

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

      4. *-commutative 71.4%

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

   5. Simplified 71.4%

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

   if -1.5e156 < y < 0.25

   1. Initial program 84.8%

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

   3. Taylor expanded in j around 0 71.5%

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

      1. *-commutative 71.5%

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

   5. Simplified 71.5%

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

   if 0.25 < y < 7.7999999999999996e155

   1. Initial program 77.2%

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

   3. Taylor expanded in b around 0 74.7%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+156}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq 0.25:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+155}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 44.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -2.2 \cdot 10^{-97}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-296}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-153}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 -2.2e-97)
     t_2
     (if (<= a -1.05e-296)
       t_1
       (if (<= a 2.9e-153) (* y (* x z)) (if (<= a 4.7e-10) 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 <= -2.2e-97) {
		tmp = t_2;
	} else if (a <= -1.05e-296) {
		tmp = t_1;
	} else if (a <= 2.9e-153) {
		tmp = y * (x * z);
	} else if (a <= 4.7e-10) {
		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 <= (-2.2d-97)) then
        tmp = t_2
    else if (a <= (-1.05d-296)) then
        tmp = t_1
    else if (a <= 2.9d-153) then
        tmp = y * (x * z)
    else if (a <= 4.7d-10) 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 <= -2.2e-97) {
		tmp = t_2;
	} else if (a <= -1.05e-296) {
		tmp = t_1;
	} else if (a <= 2.9e-153) {
		tmp = y * (x * z);
	} else if (a <= 4.7e-10) {
		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 <= -2.2e-97:
		tmp = t_2
	elif a <= -1.05e-296:
		tmp = t_1
	elif a <= 2.9e-153:
		tmp = y * (x * z)
	elif a <= 4.7e-10:
		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 <= -2.2e-97)
		tmp = t_2;
	elseif (a <= -1.05e-296)
		tmp = t_1;
	elseif (a <= 2.9e-153)
		tmp = Float64(y * Float64(x * z));
	elseif (a <= 4.7e-10)
		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 <= -2.2e-97)
		tmp = t_2;
	elseif (a <= -1.05e-296)
		tmp = t_1;
	elseif (a <= 2.9e-153)
		tmp = y * (x * z);
	elseif (a <= 4.7e-10)
		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, -2.2e-97], t$95$2, If[LessEqual[a, -1.05e-296], t$95$1, If[LessEqual[a, 2.9e-153], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.7e-10], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.1999999999999999e-97 or 4.7000000000000003e-10 < a

   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 j around 0 67.5%

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

      1. *-commutative 67.5%

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

   5. Simplified 67.5%

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

   6. Taylor expanded in z around 0 55.4%

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

      1. associate-*r* 55.4%

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

      2. neg-mul-1 55.4%

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

      3. *-commutative 55.4%

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

      4. associate-*r* 55.4%

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

      5. neg-mul-1 55.4%

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

      6. distribute-lft-out-- 59.5%

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

      7. distribute-lft-neg-in 59.5%

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

      8. distribute-rgt-neg-out 59.5%

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

      9. neg-sub0 59.5%

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

      10. sub-neg 59.5%

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

      11. +-commutative 59.5%

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

      12. associate--r+ 59.5%

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

      13. neg-sub0 59.5%

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

      14. remove-double-neg 59.5%

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

      15. *-commutative 59.5%

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

   8. Simplified 59.5%

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

   if -2.1999999999999999e-97 < a < -1.05e-296 or 2.90000000000000002e-153 < a < 4.7000000000000003e-10

   1. Initial program 79.0%

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

   3. Taylor expanded in b around inf 50.6%

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

      1. *-commutative 50.6%

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

   5. Simplified 50.6%

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

   if -1.05e-296 < a < 2.90000000000000002e-153

   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 y around inf 69.9%

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

      1. +-commutative 69.9%

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

      2. mul-1-neg 69.9%

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

      3. unsub-neg 69.9%

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

      4. *-commutative 69.9%

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

   5. Simplified 69.9%

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

   6. Taylor expanded in x around inf 48.7%

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

      1. *-commutative 48.7%

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

   8. Simplified 48.7%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{-97}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-296}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-153}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{-10}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 47.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -1 \cdot 10^{-58}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-299}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-159}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-33}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))) (t_2 (* a (- (* b i) (* x t)))))
   (if (<= a -1e-58)
     t_2
     (if (<= a -1.75e-299)
       t_1
       (if (<= a 1.15e-159) (* y (* x z)) (if (<= a 9.5e-33) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -1e-58) {
		tmp = t_2;
	} else if (a <= -1.75e-299) {
		tmp = t_1;
	} else if (a <= 1.15e-159) {
		tmp = y * (x * z);
	} else if (a <= 9.5e-33) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * ((t * j) - (z * b))
    t_2 = a * ((b * i) - (x * t))
    if (a <= (-1d-58)) then
        tmp = t_2
    else if (a <= (-1.75d-299)) then
        tmp = t_1
    else if (a <= 1.15d-159) then
        tmp = y * (x * z)
    else if (a <= 9.5d-33) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -1e-58) {
		tmp = t_2;
	} else if (a <= -1.75e-299) {
		tmp = t_1;
	} else if (a <= 1.15e-159) {
		tmp = y * (x * z);
	} else if (a <= 9.5e-33) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	t_2 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -1e-58:
		tmp = t_2
	elif a <= -1.75e-299:
		tmp = t_1
	elif a <= 1.15e-159:
		tmp = y * (x * z)
	elif a <= 9.5e-33:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	t_2 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -1e-58)
		tmp = t_2;
	elseif (a <= -1.75e-299)
		tmp = t_1;
	elseif (a <= 1.15e-159)
		tmp = Float64(y * Float64(x * z));
	elseif (a <= 9.5e-33)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((t * j) - (z * b));
	t_2 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -1e-58)
		tmp = t_2;
	elseif (a <= -1.75e-299)
		tmp = t_1;
	elseif (a <= 1.15e-159)
		tmp = y * (x * z);
	elseif (a <= 9.5e-33)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1e-58], t$95$2, If[LessEqual[a, -1.75e-299], t$95$1, If[LessEqual[a, 1.15e-159], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.5e-33], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1e-58 or 9.50000000000000019e-33 < a

   1. Initial program 71.1%

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

   3. Taylor expanded in j around 0 67.2%

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

      1. *-commutative 67.2%

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

   5. Simplified 67.2%

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

   6. Taylor expanded in z around 0 55.1%

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

      1. associate-*r* 55.1%

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

      2. neg-mul-1 55.1%

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

      3. *-commutative 55.1%

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

      4. associate-*r* 55.1%

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

      5. neg-mul-1 55.1%

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

      6. distribute-lft-out-- 59.2%

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

      7. distribute-lft-neg-in 59.2%

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

      8. distribute-rgt-neg-out 59.2%

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

      9. neg-sub0 59.2%

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

      10. sub-neg 59.2%

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

      11. +-commutative 59.2%

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

      12. associate--r+ 59.2%

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

      13. neg-sub0 59.2%

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

      14. remove-double-neg 59.2%

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

      15. *-commutative 59.2%

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

   8. Simplified 59.2%

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

   if -1e-58 < a < -1.74999999999999995e-299 or 1.14999999999999989e-159 < a < 9.50000000000000019e-33

   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 c around inf 56.9%

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

      1. *-commutative 56.9%

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

      2. *-commutative 56.9%

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

   5. Simplified 56.9%

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

   if -1.74999999999999995e-299 < a < 1.14999999999999989e-159

   1. Initial program 73.4%

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

   3. Taylor expanded in y around inf 73.6%

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

      1. +-commutative 73.6%

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

      2. mul-1-neg 73.6%

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

      3. unsub-neg 73.6%

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

      4. *-commutative 73.6%

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

   5. Simplified 73.6%

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

   6. Taylor expanded in x around inf 54.7%

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

      1. *-commutative 54.7%

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

   8. Simplified 54.7%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{-58}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-299}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-159}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-33}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 49.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_2 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -2.6 \cdot 10^{-45}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -3.5 \cdot 10^{-229}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 1.45 \cdot 10^{-257}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;i \leq 4.5 \cdot 10^{-16}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))) (t_2 (* i (- (* a b) (* y j)))))
   (if (<= i -2.6e-45)
     t_2
     (if (<= i -3.5e-229)
       t_1
       (if (<= i 1.45e-257) (* t (* x (- a))) (if (<= i 4.5e-16) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double t_2 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -2.6e-45) {
		tmp = t_2;
	} else if (i <= -3.5e-229) {
		tmp = t_1;
	} else if (i <= 1.45e-257) {
		tmp = t * (x * -a);
	} else if (i <= 4.5e-16) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * ((t * j) - (z * b))
    t_2 = i * ((a * b) - (y * j))
    if (i <= (-2.6d-45)) then
        tmp = t_2
    else if (i <= (-3.5d-229)) then
        tmp = t_1
    else if (i <= 1.45d-257) then
        tmp = t * (x * -a)
    else if (i <= 4.5d-16) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double t_2 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -2.6e-45) {
		tmp = t_2;
	} else if (i <= -3.5e-229) {
		tmp = t_1;
	} else if (i <= 1.45e-257) {
		tmp = t * (x * -a);
	} else if (i <= 4.5e-16) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	t_2 = i * ((a * b) - (y * j))
	tmp = 0
	if i <= -2.6e-45:
		tmp = t_2
	elif i <= -3.5e-229:
		tmp = t_1
	elif i <= 1.45e-257:
		tmp = t * (x * -a)
	elif i <= 4.5e-16:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	t_2 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -2.6e-45)
		tmp = t_2;
	elseif (i <= -3.5e-229)
		tmp = t_1;
	elseif (i <= 1.45e-257)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (i <= 4.5e-16)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((t * j) - (z * b));
	t_2 = i * ((a * b) - (y * j));
	tmp = 0.0;
	if (i <= -2.6e-45)
		tmp = t_2;
	elseif (i <= -3.5e-229)
		tmp = t_1;
	elseif (i <= 1.45e-257)
		tmp = t * (x * -a);
	elseif (i <= 4.5e-16)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.6e-45], t$95$2, If[LessEqual[i, -3.5e-229], t$95$1, If[LessEqual[i, 1.45e-257], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4.5e-16], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -2.59999999999999987e-45 or 4.5000000000000002e-16 < i

   1. Initial program 65.5%

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

   3. Taylor expanded in x around inf 62.6%

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

      1. +-commutative 62.6%

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

      2. mul-1-neg 62.6%

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

      3. unsub-neg 62.6%

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

      4. associate-/l* 61.1%

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

      5. *-commutative 61.1%

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

   5. Simplified 61.1%

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

   6. Taylor expanded in i around inf 67.4%

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

      1. +-commutative 67.4%

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

      2. mul-1-neg 67.4%

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

      3. unsub-neg 67.4%

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

      4. *-commutative 67.4%

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

      5. *-commutative 67.4%

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

   8. Simplified 67.4%

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

   if -2.59999999999999987e-45 < i < -3.5000000000000003e-229 or 1.4500000000000001e-257 < i < 4.5000000000000002e-16

   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 c around inf 50.3%

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

      1. *-commutative 50.3%

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

      2. *-commutative 50.3%

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

   5. Simplified 50.3%

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

   if -3.5000000000000003e-229 < i < 1.4500000000000001e-257

   1. Initial program 84.5%

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

   3. Taylor expanded in t around -inf 64.9%

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

      1. mul-1-neg 64.9%

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

      2. distribute-rgt-neg-in 64.9%

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

      3. +-commutative 64.9%

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

      4. *-commutative 64.9%

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

      5. fma-define 65.0%

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

      6. mul-1-neg 65.0%

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

      7. distribute-rgt-neg-in 65.0%

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

   5. Simplified 65.0%

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

   6. Taylor expanded in x around inf 46.2%

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

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.6 \cdot 10^{-45}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -3.5 \cdot 10^{-229}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 1.45 \cdot 10^{-257}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;i \leq 4.5 \cdot 10^{-16}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 48.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -8 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-299}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-159}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 38000000000:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))))
   (if (<= a -8e-59)
     t_1
     (if (<= a -1.5e-299)
       (* c (- (* t j) (* z b)))
       (if (<= a 1.6e-159)
         (* y (* x z))
         (if (<= a 38000000000.0) (* j (- (* t c) (* y i))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -8e-59) {
		tmp = t_1;
	} else if (a <= -1.5e-299) {
		tmp = c * ((t * j) - (z * b));
	} else if (a <= 1.6e-159) {
		tmp = y * (x * z);
	} else if (a <= 38000000000.0) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((b * i) - (x * t))
    if (a <= (-8d-59)) then
        tmp = t_1
    else if (a <= (-1.5d-299)) then
        tmp = c * ((t * j) - (z * b))
    else if (a <= 1.6d-159) then
        tmp = y * (x * z)
    else if (a <= 38000000000.0d0) then
        tmp = j * ((t * c) - (y * i))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -8e-59) {
		tmp = t_1;
	} else if (a <= -1.5e-299) {
		tmp = c * ((t * j) - (z * b));
	} else if (a <= 1.6e-159) {
		tmp = y * (x * z);
	} else if (a <= 38000000000.0) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -8e-59:
		tmp = t_1
	elif a <= -1.5e-299:
		tmp = c * ((t * j) - (z * b))
	elif a <= 1.6e-159:
		tmp = y * (x * z)
	elif a <= 38000000000.0:
		tmp = j * ((t * c) - (y * i))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -8e-59)
		tmp = t_1;
	elseif (a <= -1.5e-299)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (a <= 1.6e-159)
		tmp = Float64(y * Float64(x * z));
	elseif (a <= 38000000000.0)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -8e-59)
		tmp = t_1;
	elseif (a <= -1.5e-299)
		tmp = c * ((t * j) - (z * b));
	elseif (a <= 1.6e-159)
		tmp = y * (x * z);
	elseif (a <= 38000000000.0)
		tmp = j * ((t * c) - (y * i));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8e-59], t$95$1, If[LessEqual[a, -1.5e-299], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.6e-159], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 38000000000.0], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -8.0000000000000002e-59 or 3.8e10 < a

   1. Initial program 71.9%

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

   3. Taylor expanded in j around 0 69.2%

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

      1. *-commutative 69.2%

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

   5. Simplified 69.2%

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

   6. Taylor expanded in z around 0 56.9%

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

      1. associate-*r* 56.9%

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

      2. neg-mul-1 56.9%

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

      3. *-commutative 56.9%

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

      4. associate-*r* 56.9%

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

      5. neg-mul-1 56.9%

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

      6. distribute-lft-out-- 61.3%

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

      7. distribute-lft-neg-in 61.3%

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

      8. distribute-rgt-neg-out 61.3%

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

      9. neg-sub0 61.3%

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

      10. sub-neg 61.3%

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

      11. +-commutative 61.3%

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

      12. associate--r+ 61.3%

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

      13. neg-sub0 61.3%

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

      14. remove-double-neg 61.3%

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

      15. *-commutative 61.3%

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

   8. Simplified 61.3%

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

   if -8.0000000000000002e-59 < a < -1.49999999999999992e-299

   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 c around inf 57.7%

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

      1. *-commutative 57.7%

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

      2. *-commutative 57.7%

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

   5. Simplified 57.7%

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

   if -1.49999999999999992e-299 < a < 1.6e-159

   1. Initial program 73.4%

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

   3. Taylor expanded in y around inf 73.6%

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

      1. +-commutative 73.6%

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

      2. mul-1-neg 73.6%

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

      3. unsub-neg 73.6%

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

      4. *-commutative 73.6%

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

   5. Simplified 73.6%

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

   6. Taylor expanded in x around inf 54.7%

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

      1. *-commutative 54.7%

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

   8. Simplified 54.7%

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

   if 1.6e-159 < a < 3.8e10

   1. Initial program 75.1%

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

   3. Taylor expanded in j around inf 48.9%

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

      1. *-commutative 48.9%

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

      2. *-commutative 48.9%

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

   5. Simplified 48.9%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{-59}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-299}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-159}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 38000000000:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 29.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1650000000000:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-210}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-255}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;z \leq 12200000:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -1650000000000.0)
   (* b (* z (- c)))
   (if (<= z -2.2e-210)
     (* i (* a b))
     (if (<= z 1.15e-255)
       (* a (* x (- t)))
       (if (<= z 12200000.0) (* a (* b i)) (* y (* x z)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -1650000000000.0) {
		tmp = b * (z * -c);
	} else if (z <= -2.2e-210) {
		tmp = i * (a * b);
	} else if (z <= 1.15e-255) {
		tmp = a * (x * -t);
	} else if (z <= 12200000.0) {
		tmp = a * (b * i);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-1650000000000.0d0)) then
        tmp = b * (z * -c)
    else if (z <= (-2.2d-210)) then
        tmp = i * (a * b)
    else if (z <= 1.15d-255) then
        tmp = a * (x * -t)
    else if (z <= 12200000.0d0) then
        tmp = a * (b * i)
    else
        tmp = y * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -1650000000000.0) {
		tmp = b * (z * -c);
	} else if (z <= -2.2e-210) {
		tmp = i * (a * b);
	} else if (z <= 1.15e-255) {
		tmp = a * (x * -t);
	} else if (z <= 12200000.0) {
		tmp = a * (b * i);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -1650000000000.0:
		tmp = b * (z * -c)
	elif z <= -2.2e-210:
		tmp = i * (a * b)
	elif z <= 1.15e-255:
		tmp = a * (x * -t)
	elif z <= 12200000.0:
		tmp = a * (b * i)
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -1650000000000.0)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (z <= -2.2e-210)
		tmp = Float64(i * Float64(a * b));
	elseif (z <= 1.15e-255)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (z <= 12200000.0)
		tmp = Float64(a * Float64(b * i));
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -1650000000000.0)
		tmp = b * (z * -c);
	elseif (z <= -2.2e-210)
		tmp = i * (a * b);
	elseif (z <= 1.15e-255)
		tmp = a * (x * -t);
	elseif (z <= 12200000.0)
		tmp = a * (b * i);
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -1650000000000.0], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.2e-210], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e-255], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 12200000.0], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.65e12

   1. Initial program 66.0%

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

   3. Taylor expanded in b around inf 46.7%

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

      1. *-commutative 46.7%

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

   5. Simplified 46.7%

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

   6. Taylor expanded in a around 0 45.1%

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

      1. mul-1-neg 45.1%

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

      2. *-commutative 45.1%

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

      3. distribute-rgt-neg-in 45.1%

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

   8. Simplified 45.1%

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

   if -1.65e12 < z < -2.19999999999999989e-210

   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 j around 0 55.5%

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

      1. *-commutative 55.5%

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

   5. Simplified 55.5%

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

   6. Taylor expanded in i around inf 30.5%

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

      1. *-commutative 30.5%

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

      2. *-commutative 30.5%

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

      3. associate-*r* 34.1%

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

      4. *-commutative 34.1%

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

   8. Simplified 34.1%

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

   if -2.19999999999999989e-210 < z < 1.1499999999999999e-255

   1. Initial program 76.9%

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

   3. Taylor expanded in j around 0 59.7%

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

      1. *-commutative 59.7%

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

   5. Simplified 59.7%

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

   6. Taylor expanded in x around inf 62.5%

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

      1. +-commutative 62.5%

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

      2. mul-1-neg 62.5%

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

      3. unsub-neg 62.5%

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

      4. associate-/l* 65.4%

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

      5. *-commutative 65.4%

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

   8. Simplified 65.4%

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

   9. Taylor expanded in t around inf 54.1%

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

       1. associate-*r* 54.1%

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

       2. mul-1-neg 54.1%

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

       3. *-commutative 54.1%

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

   11. Simplified 54.1%

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

   if 1.1499999999999999e-255 < z < 1.22e7

   1. Initial program 86.0%

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

   3. Taylor expanded in j around 0 60.2%

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

      1. *-commutative 60.2%

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

   5. Simplified 60.2%

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

   6. Taylor expanded in i around inf 36.6%

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

   if 1.22e7 < z

   1. Initial program 69.2%

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

   3. Taylor expanded in y around inf 51.3%

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

      1. +-commutative 51.3%

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

      2. mul-1-neg 51.3%

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

      3. unsub-neg 51.3%

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

      4. *-commutative 51.3%

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

   5. Simplified 51.3%

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

   6. Taylor expanded in x around inf 43.0%

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

      1. *-commutative 43.0%

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

   8. Simplified 43.0%

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

4. Final simplification 41.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1650000000000:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-210}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-255}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;z \leq 12200000:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 42.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -2.05 \cdot 10^{-97}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.05 \cdot 10^{-299}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-80}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))))
   (if (<= a -2.05e-97)
     t_1
     (if (<= a -2.05e-299)
       (* z (* b (- c)))
       (if (<= a 2.7e-80) (* y (* x 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) - (x * t));
	double tmp;
	if (a <= -2.05e-97) {
		tmp = t_1;
	} else if (a <= -2.05e-299) {
		tmp = z * (b * -c);
	} else if (a <= 2.7e-80) {
		tmp = y * (x * 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) - (x * t))
    if (a <= (-2.05d-97)) then
        tmp = t_1
    else if (a <= (-2.05d-299)) then
        tmp = z * (b * -c)
    else if (a <= 2.7d-80) then
        tmp = y * (x * 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) - (x * t));
	double tmp;
	if (a <= -2.05e-97) {
		tmp = t_1;
	} else if (a <= -2.05e-299) {
		tmp = z * (b * -c);
	} else if (a <= 2.7e-80) {
		tmp = y * (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -2.05e-97:
		tmp = t_1
	elif a <= -2.05e-299:
		tmp = z * (b * -c)
	elif a <= 2.7e-80:
		tmp = y * (x * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -2.05e-97)
		tmp = t_1;
	elseif (a <= -2.05e-299)
		tmp = Float64(z * Float64(b * Float64(-c)));
	elseif (a <= 2.7e-80)
		tmp = Float64(y * Float64(x * 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) - (x * t));
	tmp = 0.0;
	if (a <= -2.05e-97)
		tmp = t_1;
	elseif (a <= -2.05e-299)
		tmp = z * (b * -c);
	elseif (a <= 2.7e-80)
		tmp = y * (x * 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[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.05e-97], t$95$1, If[LessEqual[a, -2.05e-299], N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.7e-80], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.04999999999999996e-97 or 2.7000000000000002e-80 < a

   1. Initial program 72.8%

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

   3. Taylor expanded in j around 0 67.1%

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

      1. *-commutative 67.1%

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

   5. Simplified 67.1%

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

   6. Taylor expanded in z around 0 52.3%

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

      1. associate-*r* 52.3%

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

      2. neg-mul-1 52.3%

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

      3. *-commutative 52.3%

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

      4. associate-*r* 52.3%

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

      5. neg-mul-1 52.3%

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

      6. distribute-lft-out-- 55.9%

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

      7. distribute-lft-neg-in 55.9%

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

      8. distribute-rgt-neg-out 55.9%

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

      9. neg-sub0 55.9%

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

      10. sub-neg 55.9%

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

      11. +-commutative 55.9%

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

      12. associate--r+ 55.9%

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

      13. neg-sub0 55.9%

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

      14. remove-double-neg 55.9%

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

      15. *-commutative 55.9%

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

   8. Simplified 55.9%

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

   if -2.04999999999999996e-97 < a < -2.05e-299

   1. Initial program 82.1%

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

   3. Taylor expanded in j around 0 55.4%

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

      1. *-commutative 55.4%

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

   5. Simplified 55.4%

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

   6. Taylor expanded in c around inf 42.7%

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

      1. associate-*r* 42.7%

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

      2. neg-mul-1 42.7%

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

      3. *-commutative 42.7%

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

      4. *-commutative 42.7%

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

      5. associate-*l* 47.6%

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

   8. Simplified 47.6%

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

   if -2.05e-299 < a < 2.7000000000000002e-80

   1. Initial program 71.0%

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

   3. Taylor expanded in y around inf 67.7%

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

      1. +-commutative 67.7%

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

      2. mul-1-neg 67.7%

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

      3. unsub-neg 67.7%

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

      4. *-commutative 67.7%

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

   5. Simplified 67.7%

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

   6. Taylor expanded in x around inf 44.3%

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

      1. *-commutative 44.3%

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

   8. Simplified 44.3%

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

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.05 \cdot 10^{-97}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -2.05 \cdot 10^{-299}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-80}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 29.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.15 \cdot 10^{+94}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq -1.55 \cdot 10^{-105}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 1.1 \cdot 10^{+100}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -1.15e+94)
   (* t (* c j))
   (if (<= j -1.55e-105)
     (* x (* y z))
     (if (<= j 1.1e+100) (* b (* a i)) (* c (* t j))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -1.15e+94) {
		tmp = t * (c * j);
	} else if (j <= -1.55e-105) {
		tmp = x * (y * z);
	} else if (j <= 1.1e+100) {
		tmp = b * (a * i);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (j <= (-1.15d+94)) then
        tmp = t * (c * j)
    else if (j <= (-1.55d-105)) then
        tmp = x * (y * z)
    else if (j <= 1.1d+100) then
        tmp = b * (a * i)
    else
        tmp = c * (t * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -1.15e+94) {
		tmp = t * (c * j);
	} else if (j <= -1.55e-105) {
		tmp = x * (y * z);
	} else if (j <= 1.1e+100) {
		tmp = b * (a * i);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -1.15e+94:
		tmp = t * (c * j)
	elif j <= -1.55e-105:
		tmp = x * (y * z)
	elif j <= 1.1e+100:
		tmp = b * (a * i)
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -1.15e+94)
		tmp = Float64(t * Float64(c * j));
	elseif (j <= -1.55e-105)
		tmp = Float64(x * Float64(y * z));
	elseif (j <= 1.1e+100)
		tmp = Float64(b * Float64(a * i));
	else
		tmp = Float64(c * Float64(t * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -1.15e+94)
		tmp = t * (c * j);
	elseif (j <= -1.55e-105)
		tmp = x * (y * z);
	elseif (j <= 1.1e+100)
		tmp = b * (a * i);
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -1.15e+94], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.55e-105], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.1e+100], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.15e94

   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 t around -inf 38.4%

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

      1. mul-1-neg 38.4%

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

      2. distribute-rgt-neg-in 38.4%

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

      3. +-commutative 38.4%

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

      4. *-commutative 38.4%

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

      5. fma-define 41.3%

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

      6. mul-1-neg 41.3%

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

      7. distribute-rgt-neg-in 41.3%

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

   5. Simplified 41.3%

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

   6. Taylor expanded in x around 0 41.1%

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

      1. mul-1-neg 41.1%

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

      2. distribute-rgt-neg-out 41.1%

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

   8. Simplified 41.1%

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

   9. Taylor expanded in t around 0 38.6%

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

       1. *-commutative 38.6%

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

       2. associate-*r* 41.2%

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

       3. *-commutative 41.2%

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

       4. associate-*r* 41.1%

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

   11. Simplified 41.1%

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

   if -1.15e94 < j < -1.55000000000000007e-105

   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 j around 0 58.9%

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

      1. *-commutative 58.9%

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

   5. Simplified 58.9%

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

   6. Taylor expanded in x around inf 60.9%

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

      1. +-commutative 60.9%

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

      2. mul-1-neg 60.9%

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

      3. unsub-neg 60.9%

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

      4. associate-/l* 63.0%

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

      5. *-commutative 63.0%

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

   8. Simplified 63.0%

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

   9. Taylor expanded in y around inf 36.9%

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

       1. *-commutative 36.9%

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

   11. Simplified 36.9%

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

   if -1.55000000000000007e-105 < j < 1.1e100

   1. Initial program 75.9%

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

   3. Taylor expanded in b around inf 43.8%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 43.8%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   5. Simplified 43.8%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   6. Taylor expanded in a around inf 32.5%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]

   if 1.1e100 < j

   1. Initial program 75.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around -inf 60.4%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-1 \cdot \left(c \cdot j\right) + a \cdot x\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 60.4%

         \[\leadsto \color{blue}{-t \cdot \left(-1 \cdot \left(c \cdot j\right) + a \cdot x\right)} \]

      2. distribute-rgt-neg-in 60.4%

         \[\leadsto \color{blue}{t \cdot \left(-\left(-1 \cdot \left(c \cdot j\right) + a \cdot x\right)\right)} \]

      3. +-commutative 60.4%

         \[\leadsto t \cdot \left(-\color{blue}{\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right)}\right) \]

      4. *-commutative 60.4%

         \[\leadsto t \cdot \left(-\left(\color{blue}{x \cdot a} + -1 \cdot \left(c \cdot j\right)\right)\right) \]

      5. fma-define 62.7%

         \[\leadsto t \cdot \left(-\color{blue}{\mathsf{fma}\left(x, a, -1 \cdot \left(c \cdot j\right)\right)}\right) \]

      6. mul-1-neg 62.7%

         \[\leadsto t \cdot \left(-\mathsf{fma}\left(x, a, \color{blue}{-c \cdot j}\right)\right) \]

      7. distribute-rgt-neg-in 62.7%

         \[\leadsto t \cdot \left(-\mathsf{fma}\left(x, a, \color{blue}{c \cdot \left(-j\right)}\right)\right) \]

   5. Simplified 62.7%

      \[\leadsto \color{blue}{t \cdot \left(-\mathsf{fma}\left(x, a, c \cdot \left(-j\right)\right)\right)} \]

   6. Taylor expanded in x around 0 33.4%

      \[\leadsto t \cdot \left(-\color{blue}{-1 \cdot \left(c \cdot j\right)}\right) \]
   7. Step-by-step derivation

      1. mul-1-neg 33.4%

         \[\leadsto t \cdot \left(-\color{blue}{\left(-c \cdot j\right)}\right) \]

      2. distribute-rgt-neg-out 33.4%

         \[\leadsto t \cdot \left(-\color{blue}{c \cdot \left(-j\right)}\right) \]

   8. Simplified 33.4%

      \[\leadsto t \cdot \left(-\color{blue}{c \cdot \left(-j\right)}\right) \]

   9. Taylor expanded in t around 0 39.3%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   10. Step-by-step derivation

       1. *-commutative 39.3%

          \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

   11. Simplified 39.3%

       \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 35.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.15 \cdot 10^{+94}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq -1.55 \cdot 10^{-105}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 1.1 \cdot 10^{+100}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 29.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+60}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-252}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;z \leq 2200:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -1.25e+60)
   (* b (* z (- c)))
   (if (<= z 6.8e-252)
     (* t (* x (- a)))
     (if (<= z 2200.0) (* a (* b i)) (* y (* x z))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -1.25e+60) {
		tmp = b * (z * -c);
	} else if (z <= 6.8e-252) {
		tmp = t * (x * -a);
	} else if (z <= 2200.0) {
		tmp = a * (b * i);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-1.25d+60)) then
        tmp = b * (z * -c)
    else if (z <= 6.8d-252) then
        tmp = t * (x * -a)
    else if (z <= 2200.0d0) then
        tmp = a * (b * i)
    else
        tmp = y * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -1.25e+60) {
		tmp = b * (z * -c);
	} else if (z <= 6.8e-252) {
		tmp = t * (x * -a);
	} else if (z <= 2200.0) {
		tmp = a * (b * i);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -1.25e+60:
		tmp = b * (z * -c)
	elif z <= 6.8e-252:
		tmp = t * (x * -a)
	elif z <= 2200.0:
		tmp = a * (b * i)
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -1.25e+60)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (z <= 6.8e-252)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (z <= 2200.0)
		tmp = Float64(a * Float64(b * i));
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -1.25e+60)
		tmp = b * (z * -c);
	elseif (z <= 6.8e-252)
		tmp = t * (x * -a);
	elseif (z <= 2200.0)
		tmp = a * (b * i);
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -1.25e+60], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e-252], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2200.0], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.24999999999999994e60

   1. Initial program 60.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 52.2%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 52.2%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   5. Simplified 52.2%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   6. Taylor expanded in a around 0 50.3%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(c \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 50.3%

         \[\leadsto b \cdot \color{blue}{\left(-c \cdot z\right)} \]

      2. *-commutative 50.3%

         \[\leadsto b \cdot \left(-\color{blue}{z \cdot c}\right) \]

      3. distribute-rgt-neg-in 50.3%

         \[\leadsto b \cdot \color{blue}{\left(z \cdot \left(-c\right)\right)} \]

   8. Simplified 50.3%

      \[\leadsto b \cdot \color{blue}{\left(z \cdot \left(-c\right)\right)} \]

   if -1.24999999999999994e60 < z < 6.7999999999999999e-252

   1. Initial program 77.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around -inf 49.3%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-1 \cdot \left(c \cdot j\right) + a \cdot x\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 49.3%

         \[\leadsto \color{blue}{-t \cdot \left(-1 \cdot \left(c \cdot j\right) + a \cdot x\right)} \]

      2. distribute-rgt-neg-in 49.3%

         \[\leadsto \color{blue}{t \cdot \left(-\left(-1 \cdot \left(c \cdot j\right) + a \cdot x\right)\right)} \]

      3. +-commutative 49.3%

         \[\leadsto t \cdot \left(-\color{blue}{\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right)}\right) \]

      4. *-commutative 49.3%

         \[\leadsto t \cdot \left(-\left(\color{blue}{x \cdot a} + -1 \cdot \left(c \cdot j\right)\right)\right) \]

      5. fma-define 51.4%

         \[\leadsto t \cdot \left(-\color{blue}{\mathsf{fma}\left(x, a, -1 \cdot \left(c \cdot j\right)\right)}\right) \]

      6. mul-1-neg 51.4%

         \[\leadsto t \cdot \left(-\mathsf{fma}\left(x, a, \color{blue}{-c \cdot j}\right)\right) \]

      7. distribute-rgt-neg-in 51.4%

         \[\leadsto t \cdot \left(-\mathsf{fma}\left(x, a, \color{blue}{c \cdot \left(-j\right)}\right)\right) \]

   5. Simplified 51.4%

      \[\leadsto \color{blue}{t \cdot \left(-\mathsf{fma}\left(x, a, c \cdot \left(-j\right)\right)\right)} \]

   6. Taylor expanded in x around inf 34.8%

      \[\leadsto t \cdot \left(-\color{blue}{a \cdot x}\right) \]

   if 6.7999999999999999e-252 < z < 2200

   1. Initial program 86.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around 0 60.2%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. *-commutative 60.2%

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right) \]

   5. Simplified 60.2%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(z \cdot c - a \cdot i\right)} \]

   6. Taylor expanded in i around inf 36.6%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

   if 2200 < z

   1. Initial program 69.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 51.3%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 51.3%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 51.3%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 51.3%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 51.3%

         \[\leadsto y \cdot \left(x \cdot z - \color{blue}{j \cdot i}\right) \]

   5. Simplified 51.3%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z - j \cdot i\right)} \]

   6. Taylor expanded in x around inf 43.0%

      \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-commutative 43.0%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} \]

   8. Simplified 43.0%

      \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 40.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+60}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-252}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;z \leq 2200:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 27.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -7.2 \cdot 10^{-107} \lor \neg \left(c \leq 2.5 \cdot 10^{+132}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -7.2e-107) (not (<= c 2.5e+132))) (* c (* t j)) (* b (* a i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -7.2e-107) || !(c <= 2.5e+132)) {
		tmp = c * (t * j);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((c <= (-7.2d-107)) .or. (.not. (c <= 2.5d+132))) then
        tmp = c * (t * j)
    else
        tmp = b * (a * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -7.2e-107) || !(c <= 2.5e+132)) {
		tmp = c * (t * j);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -7.2e-107) or not (c <= 2.5e+132):
		tmp = c * (t * j)
	else:
		tmp = b * (a * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -7.2e-107) || !(c <= 2.5e+132))
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(b * Float64(a * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -7.2e-107) || ~((c <= 2.5e+132)))
		tmp = c * (t * j);
	else
		tmp = b * (a * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -7.2e-107], N[Not[LessEqual[c, 2.5e+132]], $MachinePrecision]], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -7.19999999999999953e-107 or 2.5000000000000001e132 < c

   1. Initial program 68.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around -inf 41.8%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-1 \cdot \left(c \cdot j\right) + a \cdot x\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 41.8%

         \[\leadsto \color{blue}{-t \cdot \left(-1 \cdot \left(c \cdot j\right) + a \cdot x\right)} \]

      2. distribute-rgt-neg-in 41.8%

         \[\leadsto \color{blue}{t \cdot \left(-\left(-1 \cdot \left(c \cdot j\right) + a \cdot x\right)\right)} \]

      3. +-commutative 41.8%

         \[\leadsto t \cdot \left(-\color{blue}{\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right)}\right) \]

      4. *-commutative 41.8%

         \[\leadsto t \cdot \left(-\left(\color{blue}{x \cdot a} + -1 \cdot \left(c \cdot j\right)\right)\right) \]

      5. fma-define 43.6%

         \[\leadsto t \cdot \left(-\color{blue}{\mathsf{fma}\left(x, a, -1 \cdot \left(c \cdot j\right)\right)}\right) \]

      6. mul-1-neg 43.6%

         \[\leadsto t \cdot \left(-\mathsf{fma}\left(x, a, \color{blue}{-c \cdot j}\right)\right) \]

      7. distribute-rgt-neg-in 43.6%

         \[\leadsto t \cdot \left(-\mathsf{fma}\left(x, a, \color{blue}{c \cdot \left(-j\right)}\right)\right) \]

   5. Simplified 43.6%

      \[\leadsto \color{blue}{t \cdot \left(-\mathsf{fma}\left(x, a, c \cdot \left(-j\right)\right)\right)} \]

   6. Taylor expanded in x around 0 32.7%

      \[\leadsto t \cdot \left(-\color{blue}{-1 \cdot \left(c \cdot j\right)}\right) \]
   7. Step-by-step derivation

      1. mul-1-neg 32.7%

         \[\leadsto t \cdot \left(-\color{blue}{\left(-c \cdot j\right)}\right) \]

      2. distribute-rgt-neg-out 32.7%

         \[\leadsto t \cdot \left(-\color{blue}{c \cdot \left(-j\right)}\right) \]

   8. Simplified 32.7%

      \[\leadsto t \cdot \left(-\color{blue}{c \cdot \left(-j\right)}\right) \]

   9. Taylor expanded in t around 0 33.2%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   10. Step-by-step derivation

       1. *-commutative 33.2%

          \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

   11. Simplified 33.2%

       \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if -7.19999999999999953e-107 < c < 2.5000000000000001e132

   1. Initial program 77.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 39.1%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 39.1%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   5. Simplified 39.1%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   6. Taylor expanded in a around inf 32.5%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 32.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -7.2 \cdot 10^{-107} \lor \neg \left(c \leq 2.5 \cdot 10^{+132}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 29.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+14} \lor \neg \left(z \leq 105000000\right):\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= z -8.2e+14) (not (<= z 105000000.0)))
   (* y (* x z))
   (* i (* a b))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((z <= -8.2e+14) || !(z <= 105000000.0)) {
		tmp = y * (x * z);
	} else {
		tmp = i * (a * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((z <= (-8.2d+14)) .or. (.not. (z <= 105000000.0d0))) then
        tmp = y * (x * z)
    else
        tmp = i * (a * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((z <= -8.2e+14) || !(z <= 105000000.0)) {
		tmp = y * (x * z);
	} else {
		tmp = i * (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (z <= -8.2e+14) or not (z <= 105000000.0):
		tmp = y * (x * z)
	else:
		tmp = i * (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((z <= -8.2e+14) || !(z <= 105000000.0))
		tmp = Float64(y * Float64(x * z));
	else
		tmp = Float64(i * Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((z <= -8.2e+14) || ~((z <= 105000000.0)))
		tmp = y * (x * z);
	else
		tmp = i * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[z, -8.2e+14], N[Not[LessEqual[z, 105000000.0]], $MachinePrecision]], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.2e14 or 1.05e8 < z

   1. Initial program 67.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 52.8%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 52.8%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 52.8%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 52.8%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 52.8%

         \[\leadsto y \cdot \left(x \cdot z - \color{blue}{j \cdot i}\right) \]

   5. Simplified 52.8%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z - j \cdot i\right)} \]

   6. Taylor expanded in x around inf 41.7%

      \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-commutative 41.7%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} \]

   8. Simplified 41.7%

      \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} \]

   if -8.2e14 < z < 1.05e8

   1. Initial program 79.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around 0 58.5%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. *-commutative 58.5%

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right) \]

   5. Simplified 58.5%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(z \cdot c - a \cdot i\right)} \]

   6. Taylor expanded in i around inf 28.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   7. Step-by-step derivation

      1. *-commutative 28.9%

         \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot a} \]

      2. *-commutative 28.9%

         \[\leadsto \color{blue}{\left(i \cdot b\right)} \cdot a \]

      3. associate-*r* 29.8%

         \[\leadsto \color{blue}{i \cdot \left(b \cdot a\right)} \]

      4. *-commutative 29.8%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b\right)} \]

   8. Simplified 29.8%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 35.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+14} \lor \neg \left(z \leq 105000000\right):\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 28.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -2.6 \cdot 10^{-20}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq 7.5 \cdot 10^{+97}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -2.6e-20)
   (* t (* c j))
   (if (<= j 7.5e+97) (* b (* a i)) (* c (* t j)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -2.6e-20) {
		tmp = t * (c * j);
	} else if (j <= 7.5e+97) {
		tmp = b * (a * i);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (j <= (-2.6d-20)) then
        tmp = t * (c * j)
    else if (j <= 7.5d+97) then
        tmp = b * (a * i)
    else
        tmp = c * (t * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -2.6e-20) {
		tmp = t * (c * j);
	} else if (j <= 7.5e+97) {
		tmp = b * (a * i);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -2.6e-20:
		tmp = t * (c * j)
	elif j <= 7.5e+97:
		tmp = b * (a * i)
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -2.6e-20)
		tmp = Float64(t * Float64(c * j));
	elseif (j <= 7.5e+97)
		tmp = Float64(b * Float64(a * i));
	else
		tmp = Float64(c * Float64(t * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -2.6e-20)
		tmp = t * (c * j);
	elseif (j <= 7.5e+97)
		tmp = b * (a * i);
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -2.6e-20], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7.5e+97], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -2.59999999999999995e-20

   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 t around -inf 40.6%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-1 \cdot \left(c \cdot j\right) + a \cdot x\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 40.6%

         \[\leadsto \color{blue}{-t \cdot \left(-1 \cdot \left(c \cdot j\right) + a \cdot x\right)} \]

      2. distribute-rgt-neg-in 40.6%

         \[\leadsto \color{blue}{t \cdot \left(-\left(-1 \cdot \left(c \cdot j\right) + a \cdot x\right)\right)} \]

      3. +-commutative 40.6%

         \[\leadsto t \cdot \left(-\color{blue}{\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right)}\right) \]

      4. *-commutative 40.6%

         \[\leadsto t \cdot \left(-\left(\color{blue}{x \cdot a} + -1 \cdot \left(c \cdot j\right)\right)\right) \]

      5. fma-define 42.1%

         \[\leadsto t \cdot \left(-\color{blue}{\mathsf{fma}\left(x, a, -1 \cdot \left(c \cdot j\right)\right)}\right) \]

      6. mul-1-neg 42.1%

         \[\leadsto t \cdot \left(-\mathsf{fma}\left(x, a, \color{blue}{-c \cdot j}\right)\right) \]

      7. distribute-rgt-neg-in 42.1%

         \[\leadsto t \cdot \left(-\mathsf{fma}\left(x, a, \color{blue}{c \cdot \left(-j\right)}\right)\right) \]

   5. Simplified 42.1%

      \[\leadsto \color{blue}{t \cdot \left(-\mathsf{fma}\left(x, a, c \cdot \left(-j\right)\right)\right)} \]

   6. Taylor expanded in x around 0 34.8%

      \[\leadsto t \cdot \left(-\color{blue}{-1 \cdot \left(c \cdot j\right)}\right) \]
   7. Step-by-step derivation

      1. mul-1-neg 34.8%

         \[\leadsto t \cdot \left(-\color{blue}{\left(-c \cdot j\right)}\right) \]

      2. distribute-rgt-neg-out 34.8%

         \[\leadsto t \cdot \left(-\color{blue}{c \cdot \left(-j\right)}\right) \]

   8. Simplified 34.8%

      \[\leadsto t \cdot \left(-\color{blue}{c \cdot \left(-j\right)}\right) \]

   9. Taylor expanded in t around 0 32.0%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   10. Step-by-step derivation

       1. *-commutative 32.0%

          \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

       2. associate-*r* 33.4%

          \[\leadsto \color{blue}{\left(c \cdot t\right) \cdot j} \]

       3. *-commutative 33.4%

          \[\leadsto \color{blue}{\left(t \cdot c\right)} \cdot j \]

       4. associate-*r* 34.8%

          \[\leadsto \color{blue}{t \cdot \left(c \cdot j\right)} \]

   11. Simplified 34.8%

       \[\leadsto \color{blue}{t \cdot \left(c \cdot j\right)} \]

   if -2.59999999999999995e-20 < j < 7.5000000000000004e97

   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 42.6%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 42.6%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   5. Simplified 42.6%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   6. Taylor expanded in a around inf 30.4%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]

   if 7.5000000000000004e97 < j

   1. Initial program 75.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around -inf 60.4%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-1 \cdot \left(c \cdot j\right) + a \cdot x\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 60.4%

         \[\leadsto \color{blue}{-t \cdot \left(-1 \cdot \left(c \cdot j\right) + a \cdot x\right)} \]

      2. distribute-rgt-neg-in 60.4%

         \[\leadsto \color{blue}{t \cdot \left(-\left(-1 \cdot \left(c \cdot j\right) + a \cdot x\right)\right)} \]

      3. +-commutative 60.4%

         \[\leadsto t \cdot \left(-\color{blue}{\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right)}\right) \]

      4. *-commutative 60.4%

         \[\leadsto t \cdot \left(-\left(\color{blue}{x \cdot a} + -1 \cdot \left(c \cdot j\right)\right)\right) \]

      5. fma-define 62.7%

         \[\leadsto t \cdot \left(-\color{blue}{\mathsf{fma}\left(x, a, -1 \cdot \left(c \cdot j\right)\right)}\right) \]

      6. mul-1-neg 62.7%

         \[\leadsto t \cdot \left(-\mathsf{fma}\left(x, a, \color{blue}{-c \cdot j}\right)\right) \]

      7. distribute-rgt-neg-in 62.7%

         \[\leadsto t \cdot \left(-\mathsf{fma}\left(x, a, \color{blue}{c \cdot \left(-j\right)}\right)\right) \]

   5. Simplified 62.7%

      \[\leadsto \color{blue}{t \cdot \left(-\mathsf{fma}\left(x, a, c \cdot \left(-j\right)\right)\right)} \]

   6. Taylor expanded in x around 0 33.4%

      \[\leadsto t \cdot \left(-\color{blue}{-1 \cdot \left(c \cdot j\right)}\right) \]
   7. Step-by-step derivation

      1. mul-1-neg 33.4%

         \[\leadsto t \cdot \left(-\color{blue}{\left(-c \cdot j\right)}\right) \]

      2. distribute-rgt-neg-out 33.4%

         \[\leadsto t \cdot \left(-\color{blue}{c \cdot \left(-j\right)}\right) \]

   8. Simplified 33.4%

      \[\leadsto t \cdot \left(-\color{blue}{c \cdot \left(-j\right)}\right) \]

   9. Taylor expanded in t around 0 39.3%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   10. Step-by-step derivation

       1. *-commutative 39.3%

          \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

   11. Simplified 39.3%

       \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 33.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.6 \cdot 10^{-20}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq 7.5 \cdot 10^{+97}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 29.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6500000000000:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;z \leq 10000000:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -6500000000000.0)
   (* b (* z (- c)))
   (if (<= z 10000000.0) (* i (* a b)) (* y (* x z)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -6500000000000.0) {
		tmp = b * (z * -c);
	} else if (z <= 10000000.0) {
		tmp = i * (a * b);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-6500000000000.0d0)) then
        tmp = b * (z * -c)
    else if (z <= 10000000.0d0) then
        tmp = i * (a * b)
    else
        tmp = y * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -6500000000000.0) {
		tmp = b * (z * -c);
	} else if (z <= 10000000.0) {
		tmp = i * (a * b);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -6500000000000.0:
		tmp = b * (z * -c)
	elif z <= 10000000.0:
		tmp = i * (a * b)
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -6500000000000.0)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (z <= 10000000.0)
		tmp = Float64(i * Float64(a * b));
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -6500000000000.0)
		tmp = b * (z * -c);
	elseif (z <= 10000000.0)
		tmp = i * (a * b);
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -6500000000000.0], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 10000000.0], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.5e12

   1. Initial program 66.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 46.7%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 46.7%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   5. Simplified 46.7%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   6. Taylor expanded in a around 0 45.1%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(c \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 45.1%

         \[\leadsto b \cdot \color{blue}{\left(-c \cdot z\right)} \]

      2. *-commutative 45.1%

         \[\leadsto b \cdot \left(-\color{blue}{z \cdot c}\right) \]

      3. distribute-rgt-neg-in 45.1%

         \[\leadsto b \cdot \color{blue}{\left(z \cdot \left(-c\right)\right)} \]

   8. Simplified 45.1%

      \[\leadsto b \cdot \color{blue}{\left(z \cdot \left(-c\right)\right)} \]

   if -6.5e12 < z < 1e7

   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 j around 0 58.2%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. *-commutative 58.2%

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right) \]

   5. Simplified 58.2%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(z \cdot c - a \cdot i\right)} \]

   6. Taylor expanded in i around inf 29.1%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   7. Step-by-step derivation

      1. *-commutative 29.1%

         \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot a} \]

      2. *-commutative 29.1%

         \[\leadsto \color{blue}{\left(i \cdot b\right)} \cdot a \]

      3. associate-*r* 30.0%

         \[\leadsto \color{blue}{i \cdot \left(b \cdot a\right)} \]

      4. *-commutative 30.0%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b\right)} \]

   8. Simplified 30.0%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]

   if 1e7 < z

   1. Initial program 69.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 51.3%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 51.3%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 51.3%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 51.3%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 51.3%

         \[\leadsto y \cdot \left(x \cdot z - \color{blue}{j \cdot i}\right) \]

   5. Simplified 51.3%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z - j \cdot i\right)} \]

   6. Taylor expanded in x around inf 43.0%

      \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-commutative 43.0%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} \]

   8. Simplified 43.0%

      \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 36.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6500000000000:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;z \leq 10000000:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 21.8% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(b \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* b i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (b * i);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = a * (b * i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (b * i);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (b * i)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(b * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (b * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 73.8%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
2. Add Preprocessing

3. Taylor expanded in j around 0 62.0%

   \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
4. Step-by-step derivation

   1. *-commutative 62.0%

      \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right) \]

5. Simplified 62.0%

   \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(z \cdot c - a \cdot i\right)} \]

6. Taylor expanded in i around inf 22.3%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

7. Final simplification 22.3%

   \[\leadsto a \cdot \left(b \cdot i\right) \]
8. Add Preprocessing

Alternative 28: 21.9% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ b \cdot \left(a \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* b (* a i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return b * (a * i);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = b * (a * i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return b * (a * i);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return b * (a * i)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(b * Float64(a * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = b * (a * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 73.8%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
2. Add Preprocessing

3. Taylor expanded in b around inf 39.6%

   \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
4. Step-by-step derivation

   1. *-commutative 39.6%

      \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

5. Simplified 39.6%

   \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

6. Taylor expanded in a around inf 23.1%

   \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]

7. Final simplification 23.1%

   \[\leadsto b \cdot \left(a \cdot i\right) \]
8. Add Preprocessing

Developer target: 68.0% 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 2024073 
(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)))))