Data.Colour.Matrix:determinant from colour-2.3.3, A

Percentage Accurate: 73.2% → 82.0%

Time: 18.5s

Alternatives: 22

Speedup: 0.5×

• 57.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

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) - (t * i)))) + (j * ((c * a) - (y * 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 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * 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 ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
}

Python

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

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(t * i)))) + Float64(j * Float64(Float64(c * a) - Float64(y * i))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
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[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 73.2% accurate, 1.0× speedup

Math

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

FPCore

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

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) - (t * i)))) + (j * ((c * a) - (y * 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 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * 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 ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
}

Python

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

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(t * i)))) + Float64(j * Float64(Float64(c * a) - Float64(y * i))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
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[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 82.0% accurate, 0.5× speedup

Math

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

FPCore

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

Python

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

Julia

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

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (j * ((a * c) - (y * i))) - ((x * ((t * a) - (y * z))) - (b * ((t * i) - (z * c))));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = (y * z) * (x - (i * (j / 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[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(y * z), $MachinePrecision] * N[(x - N[(i * N[(j / 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 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))) < +inf.0

   1. Initial program 92.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in t around inf 7.8%

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

      1. mul-1-neg 7.8%

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

      2. +-commutative 7.8%

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

      3. unsub-neg 7.8%

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

      4. associate-/l* 7.8%

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

      5. associate-/l* 7.8%

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

   5. Simplified 7.8%

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

   6. Taylor expanded in z around inf 23.8%

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

      1. +-commutative 23.8%

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

      2. mul-1-neg 23.8%

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

      3. unsub-neg 23.8%

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

      4. fma-define 27.8%

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

      5. associate-/l* 31.7%

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

      6. *-commutative 31.7%

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

      7. associate-/l* 33.6%

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

      8. +-commutative 33.6%

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

      9. mul-1-neg 33.6%

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

   8. Simplified 37.6%

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

   9. Taylor expanded in y around inf 53.3%

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

       1. associate-*r* 53.3%

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

       2. *-commutative 53.3%

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

       3. mul-1-neg 53.3%

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

       4. unsub-neg 53.3%

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

       5. associate-/l* 55.2%

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

   11. Simplified 55.2%

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

4. Final simplification 84.6%

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

Alternative 2: 29.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(b \cdot \left(-c\right)\right)\\ t_2 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -9.8 \cdot 10^{+273}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{+208}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+20}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-137}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-213}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-71}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+111}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* b (- c)))) (t_2 (* x (* y z))))
   (if (<= z -9.8e+273)
     t_2
     (if (<= z -1.16e+208)
       t_1
       (if (<= z -1.05e+20)
         t_2
         (if (<= z -2.05e-137)
           (* b (* t i))
           (if (<= z -1.55e-213)
             (* c (* a j))
             (if (<= z 2.2e-71)
               (* a (* x (- t)))
               (if (<= z 1.9e+111) (* 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 = z * (b * -c);
	double t_2 = x * (y * z);
	double tmp;
	if (z <= -9.8e+273) {
		tmp = t_2;
	} else if (z <= -1.16e+208) {
		tmp = t_1;
	} else if (z <= -1.05e+20) {
		tmp = t_2;
	} else if (z <= -2.05e-137) {
		tmp = b * (t * i);
	} else if (z <= -1.55e-213) {
		tmp = c * (a * j);
	} else if (z <= 2.2e-71) {
		tmp = a * (x * -t);
	} else if (z <= 1.9e+111) {
		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) :: t_2
    real(8) :: tmp
    t_1 = z * (b * -c)
    t_2 = x * (y * z)
    if (z <= (-9.8d+273)) then
        tmp = t_2
    else if (z <= (-1.16d+208)) then
        tmp = t_1
    else if (z <= (-1.05d+20)) then
        tmp = t_2
    else if (z <= (-2.05d-137)) then
        tmp = b * (t * i)
    else if (z <= (-1.55d-213)) then
        tmp = c * (a * j)
    else if (z <= 2.2d-71) then
        tmp = a * (x * -t)
    else if (z <= 1.9d+111) 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 = z * (b * -c);
	double t_2 = x * (y * z);
	double tmp;
	if (z <= -9.8e+273) {
		tmp = t_2;
	} else if (z <= -1.16e+208) {
		tmp = t_1;
	} else if (z <= -1.05e+20) {
		tmp = t_2;
	} else if (z <= -2.05e-137) {
		tmp = b * (t * i);
	} else if (z <= -1.55e-213) {
		tmp = c * (a * j);
	} else if (z <= 2.2e-71) {
		tmp = a * (x * -t);
	} else if (z <= 1.9e+111) {
		tmp = y * (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (b * -c)
	t_2 = x * (y * z)
	tmp = 0
	if z <= -9.8e+273:
		tmp = t_2
	elif z <= -1.16e+208:
		tmp = t_1
	elif z <= -1.05e+20:
		tmp = t_2
	elif z <= -2.05e-137:
		tmp = b * (t * i)
	elif z <= -1.55e-213:
		tmp = c * (a * j)
	elif z <= 2.2e-71:
		tmp = a * (x * -t)
	elif z <= 1.9e+111:
		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(z * Float64(b * Float64(-c)))
	t_2 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (z <= -9.8e+273)
		tmp = t_2;
	elseif (z <= -1.16e+208)
		tmp = t_1;
	elseif (z <= -1.05e+20)
		tmp = t_2;
	elseif (z <= -2.05e-137)
		tmp = Float64(b * Float64(t * i));
	elseif (z <= -1.55e-213)
		tmp = Float64(c * Float64(a * j));
	elseif (z <= 2.2e-71)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (z <= 1.9e+111)
		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 = z * (b * -c);
	t_2 = x * (y * z);
	tmp = 0.0;
	if (z <= -9.8e+273)
		tmp = t_2;
	elseif (z <= -1.16e+208)
		tmp = t_1;
	elseif (z <= -1.05e+20)
		tmp = t_2;
	elseif (z <= -2.05e-137)
		tmp = b * (t * i);
	elseif (z <= -1.55e-213)
		tmp = c * (a * j);
	elseif (z <= 2.2e-71)
		tmp = a * (x * -t);
	elseif (z <= 1.9e+111)
		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[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.8e+273], t$95$2, If[LessEqual[z, -1.16e+208], t$95$1, If[LessEqual[z, -1.05e+20], t$95$2, If[LessEqual[z, -2.05e-137], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.55e-213], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e-71], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e+111], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -9.80000000000000088e273 or -1.15999999999999999e208 < z < -1.05e20

   1. Initial program 53.6%

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

   3. Taylor expanded in x around inf 51.9%

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

      1. *-commutative 51.9%

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

   5. Simplified 51.9%

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

   6. Taylor expanded in z around inf 45.4%

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

      1. *-commutative 45.4%

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

   8. Simplified 45.4%

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

   if -9.80000000000000088e273 < z < -1.15999999999999999e208 or 1.89999999999999988e111 < z

   1. Initial program 66.1%

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

   3. Taylor expanded in t around inf 62.9%

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

      1. mul-1-neg 62.9%

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

      2. +-commutative 62.9%

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

      3. unsub-neg 62.9%

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

      4. associate-/l* 61.4%

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

      5. associate-/l* 56.7%

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

   5. Simplified 56.7%

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

   6. Taylor expanded in b around inf 66.4%

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

      1. mul-1-neg 66.4%

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

      2. associate-*r* 59.8%

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

      3. *-commutative 59.8%

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

      4. associate-*r/ 59.7%

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

      5. associate-*r* 68.0%

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

      6. distribute-lft-neg-out 68.0%

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

      7. *-commutative 68.0%

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

   8. Simplified 68.0%

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

   9. Taylor expanded in c around inf 56.4%

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

       1. mul-1-neg 56.4%

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

       2. associate-*r* 57.8%

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

       3. distribute-rgt-neg-in 57.8%

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

   11. Simplified 57.8%

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

   if -1.05e20 < z < -2.0499999999999999e-137

   1. Initial program 78.4%

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

   3. Taylor expanded in t around inf 56.8%

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

      1. distribute-lft-out-- 56.8%

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

   5. Simplified 56.8%

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

   6. Taylor expanded in a around 0 41.8%

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

   if -2.0499999999999999e-137 < z < -1.5499999999999999e-213

   1. Initial program 94.1%

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

   3. Taylor expanded in a around inf 60.0%

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

      1. +-commutative 60.0%

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

      2. mul-1-neg 60.0%

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

      3. unsub-neg 60.0%

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

   5. Simplified 60.0%

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

   6. Taylor expanded in c around inf 48.6%

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

      1. associate-*r* 48.0%

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

      2. *-commutative 48.0%

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

      3. associate-*l* 53.8%

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

   8. Simplified 53.8%

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

   if -1.5499999999999999e-213 < z < 2.19999999999999997e-71

   1. Initial program 86.2%

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

   3. Taylor expanded in a around inf 59.0%

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

      1. +-commutative 59.0%

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

      2. mul-1-neg 59.0%

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

      3. unsub-neg 59.0%

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

   5. Simplified 59.0%

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

   6. Taylor expanded in c around 0 45.8%

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

      1. associate-*r* 45.8%

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

      2. neg-mul-1 45.8%

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

   8. Simplified 45.8%

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

   if 2.19999999999999997e-71 < z < 1.89999999999999988e111

   1. Initial program 74.5%

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

   3. Taylor expanded in y around inf 53.1%

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

      1. +-commutative 53.1%

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

      2. mul-1-neg 53.1%

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

      3. unsub-neg 53.1%

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

      4. *-commutative 53.1%

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

   5. Simplified 53.1%

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

   6. Taylor expanded in z around inf 36.3%

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

      1. *-commutative 36.3%

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

   8. Simplified 36.3%

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

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+273}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{+208}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-137}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-213}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-71}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+111}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 29.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(z \cdot \left(-c\right)\right)\\ t_2 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+274}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{+210}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+20}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-138}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-212}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-70}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+108}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* z (- c)))) (t_2 (* x (* y z))))
   (if (<= z -1.1e+274)
     t_2
     (if (<= z -6.8e+210)
       t_1
       (if (<= z -1.05e+20)
         t_2
         (if (<= z -1.4e-138)
           (* b (* t i))
           (if (<= z -2.6e-212)
             (* c (* a j))
             (if (<= z 2e-70)
               (* a (* x (- t)))
               (if (<= z 7.8e+108) (* 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 = b * (z * -c);
	double t_2 = x * (y * z);
	double tmp;
	if (z <= -1.1e+274) {
		tmp = t_2;
	} else if (z <= -6.8e+210) {
		tmp = t_1;
	} else if (z <= -1.05e+20) {
		tmp = t_2;
	} else if (z <= -1.4e-138) {
		tmp = b * (t * i);
	} else if (z <= -2.6e-212) {
		tmp = c * (a * j);
	} else if (z <= 2e-70) {
		tmp = a * (x * -t);
	} else if (z <= 7.8e+108) {
		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) :: t_2
    real(8) :: tmp
    t_1 = b * (z * -c)
    t_2 = x * (y * z)
    if (z <= (-1.1d+274)) then
        tmp = t_2
    else if (z <= (-6.8d+210)) then
        tmp = t_1
    else if (z <= (-1.05d+20)) then
        tmp = t_2
    else if (z <= (-1.4d-138)) then
        tmp = b * (t * i)
    else if (z <= (-2.6d-212)) then
        tmp = c * (a * j)
    else if (z <= 2d-70) then
        tmp = a * (x * -t)
    else if (z <= 7.8d+108) 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 = b * (z * -c);
	double t_2 = x * (y * z);
	double tmp;
	if (z <= -1.1e+274) {
		tmp = t_2;
	} else if (z <= -6.8e+210) {
		tmp = t_1;
	} else if (z <= -1.05e+20) {
		tmp = t_2;
	} else if (z <= -1.4e-138) {
		tmp = b * (t * i);
	} else if (z <= -2.6e-212) {
		tmp = c * (a * j);
	} else if (z <= 2e-70) {
		tmp = a * (x * -t);
	} else if (z <= 7.8e+108) {
		tmp = y * (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (z * -c)
	t_2 = x * (y * z)
	tmp = 0
	if z <= -1.1e+274:
		tmp = t_2
	elif z <= -6.8e+210:
		tmp = t_1
	elif z <= -1.05e+20:
		tmp = t_2
	elif z <= -1.4e-138:
		tmp = b * (t * i)
	elif z <= -2.6e-212:
		tmp = c * (a * j)
	elif z <= 2e-70:
		tmp = a * (x * -t)
	elif z <= 7.8e+108:
		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(b * Float64(z * Float64(-c)))
	t_2 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (z <= -1.1e+274)
		tmp = t_2;
	elseif (z <= -6.8e+210)
		tmp = t_1;
	elseif (z <= -1.05e+20)
		tmp = t_2;
	elseif (z <= -1.4e-138)
		tmp = Float64(b * Float64(t * i));
	elseif (z <= -2.6e-212)
		tmp = Float64(c * Float64(a * j));
	elseif (z <= 2e-70)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (z <= 7.8e+108)
		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 = b * (z * -c);
	t_2 = x * (y * z);
	tmp = 0.0;
	if (z <= -1.1e+274)
		tmp = t_2;
	elseif (z <= -6.8e+210)
		tmp = t_1;
	elseif (z <= -1.05e+20)
		tmp = t_2;
	elseif (z <= -1.4e-138)
		tmp = b * (t * i);
	elseif (z <= -2.6e-212)
		tmp = c * (a * j);
	elseif (z <= 2e-70)
		tmp = a * (x * -t);
	elseif (z <= 7.8e+108)
		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[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.1e+274], t$95$2, If[LessEqual[z, -6.8e+210], t$95$1, If[LessEqual[z, -1.05e+20], t$95$2, If[LessEqual[z, -1.4e-138], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.6e-212], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e-70], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.8e+108], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.1e274 or -6.8000000000000005e210 < z < -1.05e20

   1. Initial program 53.6%

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

   3. Taylor expanded in x around inf 51.9%

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

      1. *-commutative 51.9%

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

   5. Simplified 51.9%

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

   6. Taylor expanded in z around inf 45.4%

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

      1. *-commutative 45.4%

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

   8. Simplified 45.4%

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

   if -1.1e274 < z < -6.8000000000000005e210 or 7.79999999999999969e108 < z

   1. Initial program 66.1%

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

   3. Taylor expanded in t around inf 62.9%

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

      1. mul-1-neg 62.9%

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

      2. +-commutative 62.9%

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

      3. unsub-neg 62.9%

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

      4. associate-/l* 61.4%

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

      5. associate-/l* 56.7%

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

   5. Simplified 56.7%

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

   6. Taylor expanded in b around inf 66.4%

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

      1. mul-1-neg 66.4%

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

      2. associate-*r* 59.8%

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

      3. *-commutative 59.8%

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

      4. associate-*r/ 59.7%

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

      5. associate-*r* 68.0%

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

      6. distribute-lft-neg-out 68.0%

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

      7. *-commutative 68.0%

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

   8. Simplified 68.0%

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

   9. Taylor expanded in c around inf 56.4%

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

       1. associate-*r* 56.4%

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

       2. neg-mul-1 56.4%

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

   11. Simplified 56.4%

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

   if -1.05e20 < z < -1.4e-138

   1. Initial program 78.4%

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

   3. Taylor expanded in t around inf 56.8%

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

      1. distribute-lft-out-- 56.8%

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

   5. Simplified 56.8%

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

   6. Taylor expanded in a around 0 41.8%

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

   if -1.4e-138 < z < -2.6e-212

   1. Initial program 94.1%

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

   3. Taylor expanded in a around inf 60.0%

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

      1. +-commutative 60.0%

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

      2. mul-1-neg 60.0%

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

      3. unsub-neg 60.0%

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

   5. Simplified 60.0%

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

   6. Taylor expanded in c around inf 48.6%

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

      1. associate-*r* 48.0%

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

      2. *-commutative 48.0%

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

      3. associate-*l* 53.8%

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

   8. Simplified 53.8%

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

   if -2.6e-212 < z < 1.99999999999999999e-70

   1. Initial program 86.2%

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

   3. Taylor expanded in a around inf 59.0%

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

      1. +-commutative 59.0%

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

      2. mul-1-neg 59.0%

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

      3. unsub-neg 59.0%

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

   5. Simplified 59.0%

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

   6. Taylor expanded in c around 0 45.8%

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

      1. associate-*r* 45.8%

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

      2. neg-mul-1 45.8%

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

   8. Simplified 45.8%

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

   if 1.99999999999999999e-70 < z < 7.79999999999999969e108

   1. Initial program 74.5%

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

   3. Taylor expanded in y around inf 53.1%

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

      1. +-commutative 53.1%

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

      2. mul-1-neg 53.1%

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

      3. unsub-neg 53.1%

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

      4. *-commutative 53.1%

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

   5. Simplified 53.1%

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

   6. Taylor expanded in z around inf 36.3%

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

      1. *-commutative 36.3%

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

   8. Simplified 36.3%

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

4. Final simplification 47.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+274}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{+210}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-138}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-212}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-70}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+108}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 64.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -6 \cdot 10^{+111}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-9}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;t \leq 1.14 \cdot 10^{+147}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* b i) (* x a)))))
   (if (<= t -6e+111)
     t_1
     (if (<= t 6.2e-9)
       (+ (* j (- (* a c) (* y i))) (* x (- (* y z) (* t a))))
       (if (<= t 1.14e+147)
         (+ (* a (- (* c j) (* x t))) (* b (- (* t i) (* z c))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -6e+111) {
		tmp = t_1;
	} else if (t <= 6.2e-9) {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else if (t <= 1.14e+147) {
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((b * i) - (x * a))
    if (t <= (-6d+111)) then
        tmp = t_1
    else if (t <= 6.2d-9) then
        tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
    else if (t <= 1.14d+147) then
        tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -6e+111) {
		tmp = t_1;
	} else if (t <= 6.2e-9) {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else if (t <= 1.14e+147) {
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((b * i) - (x * a))
	tmp = 0
	if t <= -6e+111:
		tmp = t_1
	elif t <= 6.2e-9:
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
	elif t <= 1.14e+147:
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	tmp = 0.0
	if (t <= -6e+111)
		tmp = t_1;
	elseif (t <= 6.2e-9)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	elseif (t <= 1.14e+147)
		tmp = Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -6e+111)
		tmp = t_1;
	elseif (t <= 6.2e-9)
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	elseif (t <= 1.14e+147)
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6e+111], t$95$1, If[LessEqual[t, 6.2e-9], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.14e+147], N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6e111 or 1.14e147 < t

   1. Initial program 56.1%

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

   3. Taylor expanded in t around inf 75.1%

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

      1. distribute-lft-out-- 75.1%

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

   5. Simplified 75.1%

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

   6. Taylor expanded in t around 0 75.1%

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

      1. mul-1-neg 75.1%

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

      2. *-commutative 75.1%

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

      3. distribute-rgt-neg-out 75.1%

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

      4. neg-mul-1 75.1%

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

      5. distribute-lft-out-- 75.1%

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

      6. *-commutative 75.1%

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

      7. neg-mul-1 75.1%

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

      8. sub-neg 75.1%

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

      9. remove-double-neg 75.1%

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

      10. +-commutative 75.1%

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

      11. mul-1-neg 75.1%

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

      12. *-commutative 75.1%

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

      13. unsub-neg 75.1%

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

      14. *-commutative 75.1%

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

   8. Simplified 75.1%

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

   if -6e111 < t < 6.2000000000000001e-9

   1. Initial program 80.2%

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

   3. Taylor expanded in b around 0 67.8%

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

   if 6.2000000000000001e-9 < t < 1.14e147

   1. Initial program 82.1%

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

   3. Taylor expanded in y around 0 75.4%

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

   5. Simplified 86.1%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+111}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-9}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;t \leq 1.14 \cdot 10^{+147}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 57.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -2.4 \cdot 10^{+73}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-112}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(x - i \cdot \frac{j}{z}\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+55}:\\ \;\;\;\;\left(a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* b i) (* x a)))))
   (if (<= t -2.4e+73)
     t_1
     (if (<= t -5.2e-112)
       (* (* y z) (- x (* i (/ j z))))
       (if (<= t 2.4e+55)
         (- (+ (* a (* c j)) (* x (* y z))) (* b (* z c)))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -2.4e+73) {
		tmp = t_1;
	} else if (t <= -5.2e-112) {
		tmp = (y * z) * (x - (i * (j / z)));
	} else if (t <= 2.4e+55) {
		tmp = ((a * (c * j)) + (x * (y * z))) - (b * (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((b * i) - (x * a))
    if (t <= (-2.4d+73)) then
        tmp = t_1
    else if (t <= (-5.2d-112)) then
        tmp = (y * z) * (x - (i * (j / z)))
    else if (t <= 2.4d+55) then
        tmp = ((a * (c * j)) + (x * (y * z))) - (b * (z * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -2.4e+73) {
		tmp = t_1;
	} else if (t <= -5.2e-112) {
		tmp = (y * z) * (x - (i * (j / z)));
	} else if (t <= 2.4e+55) {
		tmp = ((a * (c * j)) + (x * (y * z))) - (b * (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((b * i) - (x * a))
	tmp = 0
	if t <= -2.4e+73:
		tmp = t_1
	elif t <= -5.2e-112:
		tmp = (y * z) * (x - (i * (j / z)))
	elif t <= 2.4e+55:
		tmp = ((a * (c * j)) + (x * (y * z))) - (b * (z * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	tmp = 0.0
	if (t <= -2.4e+73)
		tmp = t_1;
	elseif (t <= -5.2e-112)
		tmp = Float64(Float64(y * z) * Float64(x - Float64(i * Float64(j / z))));
	elseif (t <= 2.4e+55)
		tmp = Float64(Float64(Float64(a * Float64(c * j)) + Float64(x * Float64(y * z))) - Float64(b * Float64(z * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -2.4e+73)
		tmp = t_1;
	elseif (t <= -5.2e-112)
		tmp = (y * z) * (x - (i * (j / z)));
	elseif (t <= 2.4e+55)
		tmp = ((a * (c * j)) + (x * (y * z))) - (b * (z * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.4e+73], t$95$1, If[LessEqual[t, -5.2e-112], N[(N[(y * z), $MachinePrecision] * N[(x - N[(i * N[(j / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.4e+55], N[(N[(N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.40000000000000002e73 or 2.3999999999999999e55 < t

   1. Initial program 62.9%

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

   3. Taylor expanded in t around inf 73.7%

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

      1. distribute-lft-out-- 73.7%

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

   5. Simplified 73.7%

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

   6. Taylor expanded in t around 0 73.7%

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

      1. mul-1-neg 73.7%

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

      2. *-commutative 73.7%

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

      3. distribute-rgt-neg-out 73.7%

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

      4. neg-mul-1 73.7%

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

      5. distribute-lft-out-- 73.7%

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

      6. *-commutative 73.7%

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

      7. neg-mul-1 73.7%

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

      8. sub-neg 73.7%

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

      9. remove-double-neg 73.7%

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

      10. +-commutative 73.7%

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

      11. mul-1-neg 73.7%

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

      12. *-commutative 73.7%

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

      13. unsub-neg 73.7%

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

      14. *-commutative 73.7%

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

   8. Simplified 73.7%

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

   if -2.40000000000000002e73 < t < -5.19999999999999983e-112

   1. Initial program 76.2%

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

   3. Taylor expanded in t around inf 72.8%

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

      1. mul-1-neg 72.8%

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

      2. +-commutative 72.8%

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

      3. unsub-neg 72.8%

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

      4. associate-/l* 69.6%

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

      5. associate-/l* 66.4%

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

   5. Simplified 66.4%

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

   6. Taylor expanded in z around inf 62.1%

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

      1. +-commutative 62.1%

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

      2. mul-1-neg 62.1%

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

      3. unsub-neg 62.1%

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

      4. fma-define 62.1%

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

      5. associate-/l* 58.6%

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

      6. *-commutative 58.6%

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

      7. associate-/l* 61.9%

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

      8. +-commutative 61.9%

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

      9. mul-1-neg 61.9%

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

   8. Simplified 65.3%

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

   9. Taylor expanded in y around inf 56.6%

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

       1. associate-*r* 53.6%

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

       2. *-commutative 53.6%

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

       3. mul-1-neg 53.6%

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

       4. unsub-neg 53.6%

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

       5. associate-/l* 57.1%

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

   11. Simplified 57.1%

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

   if -5.19999999999999983e-112 < t < 2.3999999999999999e55

   1. Initial program 80.9%

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

   3. Taylor expanded in i around 0 65.7%

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

   4. Taylor expanded in t around 0 57.7%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+73}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-112}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(x - i \cdot \frac{j}{z}\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+55}:\\ \;\;\;\;\left(a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.45 \cdot 10^{+142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -270000000:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-153}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{+46}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -1.45e+142)
     t_1
     (if (<= a -270000000.0)
       (* j (- (* a c) (* y i)))
       (if (<= a -4.8e-153)
         (* x (- (* y z) (* t a)))
         (if (<= a 4.4e+46) (* b (- (* t i) (* z c))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.45e+142) {
		tmp = t_1;
	} else if (a <= -270000000.0) {
		tmp = j * ((a * c) - (y * i));
	} else if (a <= -4.8e-153) {
		tmp = x * ((y * z) - (t * a));
	} else if (a <= 4.4e+46) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (a <= (-1.45d+142)) then
        tmp = t_1
    else if (a <= (-270000000.0d0)) then
        tmp = j * ((a * c) - (y * i))
    else if (a <= (-4.8d-153)) then
        tmp = x * ((y * z) - (t * a))
    else if (a <= 4.4d+46) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.45e+142) {
		tmp = t_1;
	} else if (a <= -270000000.0) {
		tmp = j * ((a * c) - (y * i));
	} else if (a <= -4.8e-153) {
		tmp = x * ((y * z) - (t * a));
	} else if (a <= 4.4e+46) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -1.45e+142:
		tmp = t_1
	elif a <= -270000000.0:
		tmp = j * ((a * c) - (y * i))
	elif a <= -4.8e-153:
		tmp = x * ((y * z) - (t * a))
	elif a <= 4.4e+46:
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -1.45e+142)
		tmp = t_1;
	elseif (a <= -270000000.0)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (a <= -4.8e-153)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (a <= 4.4e+46)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -1.45e+142)
		tmp = t_1;
	elseif (a <= -270000000.0)
		tmp = j * ((a * c) - (y * i));
	elseif (a <= -4.8e-153)
		tmp = x * ((y * z) - (t * a));
	elseif (a <= 4.4e+46)
		tmp = b * ((t * i) - (z * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.45e+142], t$95$1, If[LessEqual[a, -270000000.0], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.8e-153], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.4e+46], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.45000000000000007e142 or 4.4000000000000001e46 < a

   1. Initial program 61.2%

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

   3. Taylor expanded in a around inf 70.2%

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

      1. +-commutative 70.2%

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

      2. mul-1-neg 70.2%

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

      3. unsub-neg 70.2%

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

   5. Simplified 70.2%

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

   if -1.45000000000000007e142 < a < -2.7e8

   1. Initial program 73.0%

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

   3. Taylor expanded in j around inf 58.7%

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

   if -2.7e8 < a < -4.8000000000000004e-153

   1. Initial program 85.1%

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

   3. Taylor expanded in x around inf 48.0%

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

      1. *-commutative 48.0%

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

   5. Simplified 48.0%

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

   if -4.8000000000000004e-153 < a < 4.4000000000000001e46

   1. Initial program 82.3%

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

   3. Taylor expanded in b around inf 60.1%

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

      1. *-commutative 60.1%

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

   5. Simplified 60.1%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{+142}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -270000000:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-153}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{+46}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+19} \lor \neg \left(y \leq 2.7 \cdot 10^{+182}\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(x - i \cdot \frac{j}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= y -2.9e+19) (not (<= y 2.7e+182)))
   (* (* y z) (- x (* i (/ j z))))
   (+ (* a (- (* c j) (* x t))) (* b (- (* t i) (* z c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((y <= -2.9e+19) || !(y <= 2.7e+182)) {
		tmp = (y * z) * (x - (i * (j / z)));
	} else {
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((y <= (-2.9d+19)) .or. (.not. (y <= 2.7d+182))) then
        tmp = (y * z) * (x - (i * (j / z)))
    else
        tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((y <= -2.9e+19) || !(y <= 2.7e+182)) {
		tmp = (y * z) * (x - (i * (j / z)));
	} else {
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (y <= -2.9e+19) or not (y <= 2.7e+182):
		tmp = (y * z) * (x - (i * (j / z)))
	else:
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((y <= -2.9e+19) || !(y <= 2.7e+182))
		tmp = Float64(Float64(y * z) * Float64(x - Float64(i * Float64(j / z))));
	else
		tmp = Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((y <= -2.9e+19) || ~((y <= 2.7e+182)))
		tmp = (y * z) * (x - (i * (j / z)));
	else
		tmp = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[y, -2.9e+19], N[Not[LessEqual[y, 2.7e+182]], $MachinePrecision]], N[(N[(y * z), $MachinePrecision] * N[(x - N[(i * N[(j / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.9e19 or 2.7000000000000003e182 < y

   1. Initial program 53.8%

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

   3. Taylor expanded in t around inf 56.0%

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

      1. mul-1-neg 56.0%

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

      2. +-commutative 56.0%

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

      3. unsub-neg 56.0%

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

      4. associate-/l* 53.8%

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

      5. associate-/l* 53.7%

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

   5. Simplified 53.7%

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

   6. Taylor expanded in z around inf 53.7%

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

      1. +-commutative 53.7%

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

      2. mul-1-neg 53.7%

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

      3. unsub-neg 53.7%

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

      4. fma-define 58.2%

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

      5. associate-/l* 54.9%

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

      6. *-commutative 54.9%

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

      7. associate-/l* 54.9%

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

      8. +-commutative 54.9%

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

      9. mul-1-neg 54.9%

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

   8. Simplified 57.1%

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

   9. Taylor expanded in y around inf 64.7%

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

       1. associate-*r* 64.8%

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

       2. *-commutative 64.8%

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

       3. mul-1-neg 64.8%

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

       4. unsub-neg 64.8%

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

       5. associate-/l* 66.9%

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

   11. Simplified 66.9%

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

   if -2.9e19 < y < 2.7000000000000003e182

   1. Initial program 84.4%

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

   3. Taylor expanded in y around 0 66.7%

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

   5. Simplified 69.1%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+19} \lor \neg \left(y \leq 2.7 \cdot 10^{+182}\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(x - i \cdot \frac{j}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;t \leq -1.8 \cdot 10^{+116}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-179}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_1 + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= t -1.8e+116)
     (* t (- (* b i) (* x a)))
     (if (<= t 6.8e-179)
       (+ (* j (- (* a c) (* y i))) t_1)
       (+ t_1 (* b (- (* t i) (* z c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (t <= -1.8e+116) {
		tmp = t * ((b * i) - (x * a));
	} else if (t <= 6.8e-179) {
		tmp = (j * ((a * c) - (y * i))) + t_1;
	} else {
		tmp = t_1 + (b * ((t * i) - (z * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (t <= (-1.8d+116)) then
        tmp = t * ((b * i) - (x * a))
    else if (t <= 6.8d-179) then
        tmp = (j * ((a * c) - (y * i))) + t_1
    else
        tmp = t_1 + (b * ((t * i) - (z * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (t <= -1.8e+116) {
		tmp = t * ((b * i) - (x * a));
	} else if (t <= 6.8e-179) {
		tmp = (j * ((a * c) - (y * i))) + t_1;
	} else {
		tmp = t_1 + (b * ((t * i) - (z * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if t <= -1.8e+116:
		tmp = t * ((b * i) - (x * a))
	elif t <= 6.8e-179:
		tmp = (j * ((a * c) - (y * i))) + t_1
	else:
		tmp = t_1 + (b * ((t * i) - (z * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (t <= -1.8e+116)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (t <= 6.8e-179)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + t_1);
	else
		tmp = Float64(t_1 + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	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));
	tmp = 0.0;
	if (t <= -1.8e+116)
		tmp = t * ((b * i) - (x * a));
	elseif (t <= 6.8e-179)
		tmp = (j * ((a * c) - (y * i))) + t_1;
	else
		tmp = t_1 + (b * ((t * i) - (z * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.8e+116], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.8e-179], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(t$95$1 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.79999999999999985e116

   1. Initial program 54.1%

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

   3. Taylor expanded in t around inf 75.0%

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

      1. distribute-lft-out-- 75.0%

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

   5. Simplified 75.0%

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

   6. Taylor expanded in t around 0 75.0%

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

      1. mul-1-neg 75.0%

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

      2. *-commutative 75.0%

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

      3. distribute-rgt-neg-out 75.0%

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

      4. neg-mul-1 75.0%

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

      5. distribute-lft-out-- 75.0%

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

      6. *-commutative 75.0%

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

      7. neg-mul-1 75.0%

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

      8. sub-neg 75.0%

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

      9. remove-double-neg 75.0%

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

      10. +-commutative 75.0%

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

      11. mul-1-neg 75.0%

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

      12. *-commutative 75.0%

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

      13. unsub-neg 75.0%

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

      14. *-commutative 75.0%

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

   8. Simplified 75.0%

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

   if -1.79999999999999985e116 < t < 6.7999999999999995e-179

   1. Initial program 83.4%

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

   3. Taylor expanded in b around 0 71.3%

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

   if 6.7999999999999995e-179 < t

   1. Initial program 70.1%

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

   3. Taylor expanded in j around 0 69.9%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+116}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-179}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 30.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.1 \cdot 10^{+19}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-137}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{-213}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-72}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -7.1e+19)
   (* y (* x z))
   (if (<= z -1.9e-137)
     (* b (* t i))
     (if (<= z -4.9e-213)
       (* c (* a j))
       (if (<= z 1.3e-72) (* a (* x (- t))) (* x (* y z)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -7.1e+19) {
		tmp = y * (x * z);
	} else if (z <= -1.9e-137) {
		tmp = b * (t * i);
	} else if (z <= -4.9e-213) {
		tmp = c * (a * j);
	} else if (z <= 1.3e-72) {
		tmp = a * (x * -t);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-7.1d+19)) then
        tmp = y * (x * z)
    else if (z <= (-1.9d-137)) then
        tmp = b * (t * i)
    else if (z <= (-4.9d-213)) then
        tmp = c * (a * j)
    else if (z <= 1.3d-72) then
        tmp = a * (x * -t)
    else
        tmp = x * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -7.1e+19) {
		tmp = y * (x * z);
	} else if (z <= -1.9e-137) {
		tmp = b * (t * i);
	} else if (z <= -4.9e-213) {
		tmp = c * (a * j);
	} else if (z <= 1.3e-72) {
		tmp = a * (x * -t);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -7.1e+19:
		tmp = y * (x * z)
	elif z <= -1.9e-137:
		tmp = b * (t * i)
	elif z <= -4.9e-213:
		tmp = c * (a * j)
	elif z <= 1.3e-72:
		tmp = a * (x * -t)
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -7.1e+19)
		tmp = Float64(y * Float64(x * z));
	elseif (z <= -1.9e-137)
		tmp = Float64(b * Float64(t * i));
	elseif (z <= -4.9e-213)
		tmp = Float64(c * Float64(a * j));
	elseif (z <= 1.3e-72)
		tmp = Float64(a * Float64(x * Float64(-t)));
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -7.1e+19)
		tmp = y * (x * z);
	elseif (z <= -1.9e-137)
		tmp = b * (t * i);
	elseif (z <= -4.9e-213)
		tmp = c * (a * j);
	elseif (z <= 1.3e-72)
		tmp = a * (x * -t);
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -7.1e+19], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.9e-137], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.9e-213], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e-72], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -7.1e19

   1. Initial program 58.2%

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

   3. Taylor expanded in y around inf 43.8%

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

      1. +-commutative 43.8%

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

      2. mul-1-neg 43.8%

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

      3. unsub-neg 43.8%

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

      4. *-commutative 43.8%

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

   5. Simplified 43.8%

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

   6. Taylor expanded in z around inf 35.7%

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

      1. *-commutative 35.7%

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

   8. Simplified 35.7%

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

   if -7.1e19 < z < -1.89999999999999999e-137

   1. Initial program 78.4%

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

   3. Taylor expanded in t around inf 56.8%

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

      1. distribute-lft-out-- 56.8%

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

   5. Simplified 56.8%

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

   6. Taylor expanded in a around 0 41.8%

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

   if -1.89999999999999999e-137 < z < -4.8999999999999998e-213

   1. Initial program 94.1%

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

   3. Taylor expanded in a around inf 60.0%

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

      1. +-commutative 60.0%

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

      2. mul-1-neg 60.0%

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

      3. unsub-neg 60.0%

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

   5. Simplified 60.0%

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

   6. Taylor expanded in c around inf 48.6%

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

      1. associate-*r* 48.0%

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

      2. *-commutative 48.0%

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

      3. associate-*l* 53.8%

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

   8. Simplified 53.8%

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

   if -4.8999999999999998e-213 < z < 1.29999999999999998e-72

   1. Initial program 86.2%

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

   3. Taylor expanded in a around inf 59.0%

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

      1. +-commutative 59.0%

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

      2. mul-1-neg 59.0%

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

      3. unsub-neg 59.0%

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

   5. Simplified 59.0%

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

   6. Taylor expanded in c around 0 45.8%

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

      1. associate-*r* 45.8%

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

      2. neg-mul-1 45.8%

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

   8. Simplified 45.8%

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

   if 1.29999999999999998e-72 < z

   1. Initial program 69.2%

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

   3. Taylor expanded in x around inf 40.3%

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

      1. *-commutative 40.3%

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

   5. Simplified 40.3%

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

   6. Taylor expanded in z around inf 34.3%

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

      1. *-commutative 34.3%

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

   8. Simplified 34.3%

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

4. Final simplification 39.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.1 \cdot 10^{+19}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-137}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{-213}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-72}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 30.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+19}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-137}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-211}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-70}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -6.4e+19)
   (* y (* x z))
   (if (<= z -1.3e-137)
     (* b (* t i))
     (if (<= z -1.02e-211)
       (* c (* a j))
       (if (<= z 5e-70) (* x (* t (- a))) (* x (* y z)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -6.4e+19) {
		tmp = y * (x * z);
	} else if (z <= -1.3e-137) {
		tmp = b * (t * i);
	} else if (z <= -1.02e-211) {
		tmp = c * (a * j);
	} else if (z <= 5e-70) {
		tmp = x * (t * -a);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-6.4d+19)) then
        tmp = y * (x * z)
    else if (z <= (-1.3d-137)) then
        tmp = b * (t * i)
    else if (z <= (-1.02d-211)) then
        tmp = c * (a * j)
    else if (z <= 5d-70) then
        tmp = x * (t * -a)
    else
        tmp = x * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -6.4e+19) {
		tmp = y * (x * z);
	} else if (z <= -1.3e-137) {
		tmp = b * (t * i);
	} else if (z <= -1.02e-211) {
		tmp = c * (a * j);
	} else if (z <= 5e-70) {
		tmp = x * (t * -a);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -6.4e+19:
		tmp = y * (x * z)
	elif z <= -1.3e-137:
		tmp = b * (t * i)
	elif z <= -1.02e-211:
		tmp = c * (a * j)
	elif z <= 5e-70:
		tmp = x * (t * -a)
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -6.4e+19)
		tmp = Float64(y * Float64(x * z));
	elseif (z <= -1.3e-137)
		tmp = Float64(b * Float64(t * i));
	elseif (z <= -1.02e-211)
		tmp = Float64(c * Float64(a * j));
	elseif (z <= 5e-70)
		tmp = Float64(x * Float64(t * Float64(-a)));
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -6.4e+19)
		tmp = y * (x * z);
	elseif (z <= -1.3e-137)
		tmp = b * (t * i);
	elseif (z <= -1.02e-211)
		tmp = c * (a * j);
	elseif (z <= 5e-70)
		tmp = x * (t * -a);
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -6.4e+19], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.3e-137], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.02e-211], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e-70], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -6.4e19

   1. Initial program 58.2%

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

   3. Taylor expanded in y around inf 43.8%

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

      1. +-commutative 43.8%

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

      2. mul-1-neg 43.8%

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

      3. unsub-neg 43.8%

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

      4. *-commutative 43.8%

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

   5. Simplified 43.8%

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

   6. Taylor expanded in z around inf 35.7%

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

      1. *-commutative 35.7%

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

   8. Simplified 35.7%

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

   if -6.4e19 < z < -1.3e-137

   1. Initial program 78.4%

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

   3. Taylor expanded in t around inf 56.8%

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

      1. distribute-lft-out-- 56.8%

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

   5. Simplified 56.8%

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

   6. Taylor expanded in a around 0 41.8%

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

   if -1.3e-137 < z < -1.0199999999999999e-211

   1. Initial program 94.1%

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

   3. Taylor expanded in a around inf 60.0%

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

      1. +-commutative 60.0%

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

      2. mul-1-neg 60.0%

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

      3. unsub-neg 60.0%

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

   5. Simplified 60.0%

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

   6. Taylor expanded in c around inf 48.6%

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

      1. associate-*r* 48.0%

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

      2. *-commutative 48.0%

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

      3. associate-*l* 53.8%

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

   8. Simplified 53.8%

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

   if -1.0199999999999999e-211 < z < 4.9999999999999998e-70

   1. Initial program 86.2%

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

   3. Taylor expanded in x around inf 44.6%

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

      1. *-commutative 44.6%

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

   5. Simplified 44.6%

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

   6. Taylor expanded in z around 0 43.1%

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

      1. mul-1-neg 43.1%

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

      2. distribute-lft-neg-out 43.1%

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

      3. *-commutative 43.1%

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

   8. Simplified 43.1%

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

   if 4.9999999999999998e-70 < z

   1. Initial program 69.2%

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

   3. Taylor expanded in x around inf 40.3%

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

      1. *-commutative 40.3%

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

   5. Simplified 40.3%

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

   6. Taylor expanded in z around inf 34.3%

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

      1. *-commutative 34.3%

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

   8. Simplified 34.3%

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

4. Final simplification 39.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+19}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-137}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-211}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-70}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 29.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;t \leq -4.4 \cdot 10^{-60}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-149}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5400:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+55}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))))
   (if (<= t -4.4e-60)
     (* b (* t i))
     (if (<= t 2.3e-149)
       t_1
       (if (<= t 5400.0)
         (* z (* x y))
         (if (<= t 2.3e+55) t_1 (* t (* b i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double tmp;
	if (t <= -4.4e-60) {
		tmp = b * (t * i);
	} else if (t <= 2.3e-149) {
		tmp = t_1;
	} else if (t <= 5400.0) {
		tmp = z * (x * y);
	} else if (t <= 2.3e+55) {
		tmp = t_1;
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (c * j)
    if (t <= (-4.4d-60)) then
        tmp = b * (t * i)
    else if (t <= 2.3d-149) then
        tmp = t_1
    else if (t <= 5400.0d0) then
        tmp = z * (x * y)
    else if (t <= 2.3d+55) then
        tmp = t_1
    else
        tmp = t * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double tmp;
	if (t <= -4.4e-60) {
		tmp = b * (t * i);
	} else if (t <= 2.3e-149) {
		tmp = t_1;
	} else if (t <= 5400.0) {
		tmp = z * (x * y);
	} else if (t <= 2.3e+55) {
		tmp = t_1;
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	tmp = 0
	if t <= -4.4e-60:
		tmp = b * (t * i)
	elif t <= 2.3e-149:
		tmp = t_1
	elif t <= 5400.0:
		tmp = z * (x * y)
	elif t <= 2.3e+55:
		tmp = t_1
	else:
		tmp = t * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	tmp = 0.0
	if (t <= -4.4e-60)
		tmp = Float64(b * Float64(t * i));
	elseif (t <= 2.3e-149)
		tmp = t_1;
	elseif (t <= 5400.0)
		tmp = Float64(z * Float64(x * y));
	elseif (t <= 2.3e+55)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (c * j);
	tmp = 0.0;
	if (t <= -4.4e-60)
		tmp = b * (t * i);
	elseif (t <= 2.3e-149)
		tmp = t_1;
	elseif (t <= 5400.0)
		tmp = z * (x * y);
	elseif (t <= 2.3e+55)
		tmp = t_1;
	else
		tmp = t * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.4e-60], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.3e-149], t$95$1, If[LessEqual[t, 5400.0], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.3e+55], t$95$1, N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.3999999999999998e-60

   1. Initial program 63.0%

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

   3. Taylor expanded in t around inf 62.0%

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

      1. distribute-lft-out-- 62.0%

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

   5. Simplified 62.0%

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

   6. Taylor expanded in a around 0 37.7%

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

   if -4.3999999999999998e-60 < t < 2.3e-149 or 5400 < t < 2.29999999999999987e55

   1. Initial program 83.8%

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

   3. Taylor expanded in a around inf 45.6%

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

      1. +-commutative 45.6%

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

      2. mul-1-neg 45.6%

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

      3. unsub-neg 45.6%

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

   5. Simplified 45.6%

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

   6. Taylor expanded in c around inf 35.4%

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

   if 2.3e-149 < t < 5400

   1. Initial program 72.5%

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

   3. Taylor expanded in x around inf 46.1%

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

      1. *-commutative 46.1%

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

   5. Simplified 46.1%

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

   6. Taylor expanded in z around inf 38.1%

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

      1. associate-*r* 40.7%

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

   8. Simplified 40.7%

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

   if 2.29999999999999987e55 < t

   1. Initial program 67.7%

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

   3. Taylor expanded in t around inf 75.5%

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

      1. distribute-lft-out-- 75.5%

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

   5. Simplified 75.5%

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

   6. Taylor expanded in a around 0 48.2%

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

      1. associate-*r* 48.3%

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

   8. Simplified 48.3%

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

4. Final simplification 38.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{-60}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-149}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq 5400:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+55}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 29.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;t \leq -3.1 \cdot 10^{-59}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-149}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 800:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+56}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))))
   (if (<= t -3.1e-59)
     (* b (* t i))
     (if (<= t 1.9e-149)
       t_1
       (if (<= t 800.0)
         (* x (* y z))
         (if (<= t 6.2e+56) t_1 (* t (* b i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double tmp;
	if (t <= -3.1e-59) {
		tmp = b * (t * i);
	} else if (t <= 1.9e-149) {
		tmp = t_1;
	} else if (t <= 800.0) {
		tmp = x * (y * z);
	} else if (t <= 6.2e+56) {
		tmp = t_1;
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (c * j)
    if (t <= (-3.1d-59)) then
        tmp = b * (t * i)
    else if (t <= 1.9d-149) then
        tmp = t_1
    else if (t <= 800.0d0) then
        tmp = x * (y * z)
    else if (t <= 6.2d+56) then
        tmp = t_1
    else
        tmp = t * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double tmp;
	if (t <= -3.1e-59) {
		tmp = b * (t * i);
	} else if (t <= 1.9e-149) {
		tmp = t_1;
	} else if (t <= 800.0) {
		tmp = x * (y * z);
	} else if (t <= 6.2e+56) {
		tmp = t_1;
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	tmp = 0
	if t <= -3.1e-59:
		tmp = b * (t * i)
	elif t <= 1.9e-149:
		tmp = t_1
	elif t <= 800.0:
		tmp = x * (y * z)
	elif t <= 6.2e+56:
		tmp = t_1
	else:
		tmp = t * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	tmp = 0.0
	if (t <= -3.1e-59)
		tmp = Float64(b * Float64(t * i));
	elseif (t <= 1.9e-149)
		tmp = t_1;
	elseif (t <= 800.0)
		tmp = Float64(x * Float64(y * z));
	elseif (t <= 6.2e+56)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (c * j);
	tmp = 0.0;
	if (t <= -3.1e-59)
		tmp = b * (t * i);
	elseif (t <= 1.9e-149)
		tmp = t_1;
	elseif (t <= 800.0)
		tmp = x * (y * z);
	elseif (t <= 6.2e+56)
		tmp = t_1;
	else
		tmp = t * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.1e-59], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.9e-149], t$95$1, If[LessEqual[t, 800.0], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.2e+56], t$95$1, N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.09999999999999999e-59

   1. Initial program 63.0%

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

   3. Taylor expanded in t around inf 62.0%

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

      1. distribute-lft-out-- 62.0%

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

   5. Simplified 62.0%

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

   6. Taylor expanded in a around 0 37.7%

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

   if -3.09999999999999999e-59 < t < 1.90000000000000003e-149 or 800 < t < 6.20000000000000009e56

   1. Initial program 83.8%

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

   3. Taylor expanded in a around inf 45.6%

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

      1. +-commutative 45.6%

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

      2. mul-1-neg 45.6%

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

      3. unsub-neg 45.6%

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

   5. Simplified 45.6%

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

   6. Taylor expanded in c around inf 35.4%

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

   if 1.90000000000000003e-149 < t < 800

   1. Initial program 72.5%

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

   3. Taylor expanded in x around inf 46.1%

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

      1. *-commutative 46.1%

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

   5. Simplified 46.1%

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

   6. Taylor expanded in z around inf 38.1%

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

      1. *-commutative 38.1%

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

   8. Simplified 38.1%

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

   if 6.20000000000000009e56 < t

   1. Initial program 67.7%

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

   3. Taylor expanded in t around inf 75.5%

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

      1. distribute-lft-out-- 75.5%

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

   5. Simplified 75.5%

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

   6. Taylor expanded in a around 0 48.2%

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

      1. associate-*r* 48.3%

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

   8. Simplified 48.3%

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

4. Final simplification 38.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{-59}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-149}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq 800:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+56}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 30.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ t_2 := b \cdot \left(t \cdot i\right)\\ \mathbf{if}\;t \leq -1.05 \cdot 10^{-57}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-150}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 510:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+55}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))) (t_2 (* b (* t i))))
   (if (<= t -1.05e-57)
     t_2
     (if (<= t 3e-150)
       t_1
       (if (<= t 510.0) (* x (* y z)) (if (<= t 4.2e+55) 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 * (c * j);
	double t_2 = b * (t * i);
	double tmp;
	if (t <= -1.05e-57) {
		tmp = t_2;
	} else if (t <= 3e-150) {
		tmp = t_1;
	} else if (t <= 510.0) {
		tmp = x * (y * z);
	} else if (t <= 4.2e+55) {
		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 * (c * j)
    t_2 = b * (t * i)
    if (t <= (-1.05d-57)) then
        tmp = t_2
    else if (t <= 3d-150) then
        tmp = t_1
    else if (t <= 510.0d0) then
        tmp = x * (y * z)
    else if (t <= 4.2d+55) 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 * (c * j);
	double t_2 = b * (t * i);
	double tmp;
	if (t <= -1.05e-57) {
		tmp = t_2;
	} else if (t <= 3e-150) {
		tmp = t_1;
	} else if (t <= 510.0) {
		tmp = x * (y * z);
	} else if (t <= 4.2e+55) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	t_2 = b * (t * i)
	tmp = 0
	if t <= -1.05e-57:
		tmp = t_2
	elif t <= 3e-150:
		tmp = t_1
	elif t <= 510.0:
		tmp = x * (y * z)
	elif t <= 4.2e+55:
		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(c * j))
	t_2 = Float64(b * Float64(t * i))
	tmp = 0.0
	if (t <= -1.05e-57)
		tmp = t_2;
	elseif (t <= 3e-150)
		tmp = t_1;
	elseif (t <= 510.0)
		tmp = Float64(x * Float64(y * z));
	elseif (t <= 4.2e+55)
		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 * (c * j);
	t_2 = b * (t * i);
	tmp = 0.0;
	if (t <= -1.05e-57)
		tmp = t_2;
	elseif (t <= 3e-150)
		tmp = t_1;
	elseif (t <= 510.0)
		tmp = x * (y * z);
	elseif (t <= 4.2e+55)
		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[(c * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.05e-57], t$95$2, If[LessEqual[t, 3e-150], t$95$1, If[LessEqual[t, 510.0], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.2e+55], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.05e-57 or 4.2000000000000001e55 < t

   1. Initial program 64.7%

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

   3. Taylor expanded in t around inf 67.0%

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

      1. distribute-lft-out-- 67.0%

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

   5. Simplified 67.0%

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

   6. Taylor expanded in a around 0 41.6%

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

   if -1.05e-57 < t < 3.0000000000000002e-150 or 510 < t < 4.2000000000000001e55

   1. Initial program 83.8%

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

   3. Taylor expanded in a around inf 45.6%

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

      1. +-commutative 45.6%

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

      2. mul-1-neg 45.6%

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

      3. unsub-neg 45.6%

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

   5. Simplified 45.6%

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

   6. Taylor expanded in c around inf 35.4%

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

   if 3.0000000000000002e-150 < t < 510

   1. Initial program 72.5%

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

   3. Taylor expanded in x around inf 46.1%

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

      1. *-commutative 46.1%

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

   5. Simplified 46.1%

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

   6. Taylor expanded in z around inf 38.1%

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

      1. *-commutative 38.1%

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

   8. Simplified 38.1%

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

4. Final simplification 38.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-57}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-150}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq 510:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+55}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 50.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{+142}:\\ \;\;\;\;x \cdot \left(a \cdot \left(c \cdot \frac{j}{x} - t\right)\right)\\ \mathbf{elif}\;a \leq -7.8 \cdot 10^{-22}:\\ \;\;\;\;i \cdot \left(j \cdot \left(\frac{a \cdot c}{i} - y\right)\right)\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+46}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -1.45e+142)
   (* x (* a (- (* c (/ j x)) t)))
   (if (<= a -7.8e-22)
     (* i (* j (- (/ (* a c) i) y)))
     (if (<= a 3.2e+46) (* b (- (* t i) (* z c))) (* a (- (* c j) (* x t)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -1.45e+142) {
		tmp = x * (a * ((c * (j / x)) - t));
	} else if (a <= -7.8e-22) {
		tmp = i * (j * (((a * c) / i) - y));
	} else if (a <= 3.2e+46) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (a <= (-1.45d+142)) then
        tmp = x * (a * ((c * (j / x)) - t))
    else if (a <= (-7.8d-22)) then
        tmp = i * (j * (((a * c) / i) - y))
    else if (a <= 3.2d+46) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = a * ((c * j) - (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -1.45e+142) {
		tmp = x * (a * ((c * (j / x)) - t));
	} else if (a <= -7.8e-22) {
		tmp = i * (j * (((a * c) / i) - y));
	} else if (a <= 3.2e+46) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -1.45e+142:
		tmp = x * (a * ((c * (j / x)) - t))
	elif a <= -7.8e-22:
		tmp = i * (j * (((a * c) / i) - y))
	elif a <= 3.2e+46:
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = a * ((c * j) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -1.45e+142)
		tmp = Float64(x * Float64(a * Float64(Float64(c * Float64(j / x)) - t)));
	elseif (a <= -7.8e-22)
		tmp = Float64(i * Float64(j * Float64(Float64(Float64(a * c) / i) - y)));
	elseif (a <= 3.2e+46)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -1.45e+142)
		tmp = x * (a * ((c * (j / x)) - t));
	elseif (a <= -7.8e-22)
		tmp = i * (j * (((a * c) / i) - y));
	elseif (a <= 3.2e+46)
		tmp = b * ((t * i) - (z * c));
	else
		tmp = a * ((c * j) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -1.45e+142], N[(x * N[(a * N[(N[(c * N[(j / x), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -7.8e-22], N[(i * N[(j * N[(N[(N[(a * c), $MachinePrecision] / i), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.2e+46], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.45000000000000007e142

   1. Initial program 63.6%

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

   3. Taylor expanded in a around inf 75.6%

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

      1. +-commutative 75.6%

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

      2. mul-1-neg 75.6%

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

      3. unsub-neg 75.6%

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

   5. Simplified 75.6%

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

   6. Taylor expanded in x around inf 66.5%

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

      1. mul-1-neg 66.5%

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

      2. distribute-lft-neg-out 66.5%

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

      3. +-commutative 66.5%

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

      4. cancel-sign-sub-inv 66.5%

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

      5. associate-/l* 71.0%

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

      6. distribute-lft-out-- 75.6%

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

      7. associate-/l* 77.9%

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

   8. Simplified 77.9%

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

   if -1.45000000000000007e142 < a < -7.79999999999999996e-22

   1. Initial program 74.2%

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

   3. Taylor expanded in i around inf 64.4%

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

   5. Simplified 64.3%

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

   6. Taylor expanded in j around inf 54.5%

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

   if -7.79999999999999996e-22 < a < 3.1999999999999998e46

   1. Initial program 83.4%

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

   3. Taylor expanded in b around inf 55.2%

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

      1. *-commutative 55.2%

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

   5. Simplified 55.2%

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

   if 3.1999999999999998e46 < a

   1. Initial program 59.2%

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

   3. Taylor expanded in a around inf 65.7%

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

      1. +-commutative 65.7%

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

      2. mul-1-neg 65.7%

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

      3. unsub-neg 65.7%

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

   5. Simplified 65.7%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{+142}:\\ \;\;\;\;x \cdot \left(a \cdot \left(c \cdot \frac{j}{x} - t\right)\right)\\ \mathbf{elif}\;a \leq -7.8 \cdot 10^{-22}:\\ \;\;\;\;i \cdot \left(j \cdot \left(\frac{a \cdot c}{i} - y\right)\right)\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+46}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 51.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -4.5 \cdot 10^{+142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.42 \cdot 10^{-22}:\\ \;\;\;\;i \cdot \left(j \cdot \left(\frac{a \cdot c}{i} - y\right)\right)\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+47}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -4.5e+142)
     t_1
     (if (<= a -1.42e-22)
       (* i (* j (- (/ (* a c) i) y)))
       (if (<= a 1.8e+47) (* b (- (* t i) (* z c))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -4.5e+142) {
		tmp = t_1;
	} else if (a <= -1.42e-22) {
		tmp = i * (j * (((a * c) / i) - y));
	} else if (a <= 1.8e+47) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (a <= (-4.5d+142)) then
        tmp = t_1
    else if (a <= (-1.42d-22)) then
        tmp = i * (j * (((a * c) / i) - y))
    else if (a <= 1.8d+47) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -4.5e+142) {
		tmp = t_1;
	} else if (a <= -1.42e-22) {
		tmp = i * (j * (((a * c) / i) - y));
	} else if (a <= 1.8e+47) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -4.5e+142:
		tmp = t_1
	elif a <= -1.42e-22:
		tmp = i * (j * (((a * c) / i) - y))
	elif a <= 1.8e+47:
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -4.5e+142)
		tmp = t_1;
	elseif (a <= -1.42e-22)
		tmp = Float64(i * Float64(j * Float64(Float64(Float64(a * c) / i) - y)));
	elseif (a <= 1.8e+47)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -4.5e+142)
		tmp = t_1;
	elseif (a <= -1.42e-22)
		tmp = i * (j * (((a * c) / i) - y));
	elseif (a <= 1.8e+47)
		tmp = b * ((t * i) - (z * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.5e+142], t$95$1, If[LessEqual[a, -1.42e-22], N[(i * N[(j * N[(N[(N[(a * c), $MachinePrecision] / i), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.8e+47], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.4999999999999999e142 or 1.80000000000000004e47 < a

   1. Initial program 61.2%

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

   3. Taylor expanded in a around inf 70.2%

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

      1. +-commutative 70.2%

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

      2. mul-1-neg 70.2%

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

      3. unsub-neg 70.2%

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

   5. Simplified 70.2%

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

   if -4.4999999999999999e142 < a < -1.4200000000000001e-22

   1. Initial program 74.2%

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

   3. Taylor expanded in i around inf 64.4%

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

   5. Simplified 64.3%

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

   6. Taylor expanded in j around inf 54.5%

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

   if -1.4200000000000001e-22 < a < 1.80000000000000004e47

   1. Initial program 83.4%

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

   3. Taylor expanded in b around inf 55.2%

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

      1. *-commutative 55.2%

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

   5. Simplified 55.2%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+142}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.42 \cdot 10^{-22}:\\ \;\;\;\;i \cdot \left(j \cdot \left(\frac{a \cdot c}{i} - y\right)\right)\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+47}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 51.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.45 \cdot 10^{+142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-21}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+46}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -1.45e+142)
     t_1
     (if (<= a -2.3e-21)
       (* j (- (* a c) (* y i)))
       (if (<= a 2e+46) (* b (- (* t i) (* z c))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.45e+142) {
		tmp = t_1;
	} else if (a <= -2.3e-21) {
		tmp = j * ((a * c) - (y * i));
	} else if (a <= 2e+46) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (a <= (-1.45d+142)) then
        tmp = t_1
    else if (a <= (-2.3d-21)) then
        tmp = j * ((a * c) - (y * i))
    else if (a <= 2d+46) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.45e+142) {
		tmp = t_1;
	} else if (a <= -2.3e-21) {
		tmp = j * ((a * c) - (y * i));
	} else if (a <= 2e+46) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -1.45e+142:
		tmp = t_1
	elif a <= -2.3e-21:
		tmp = j * ((a * c) - (y * i))
	elif a <= 2e+46:
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -1.45e+142)
		tmp = t_1;
	elseif (a <= -2.3e-21)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (a <= 2e+46)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -1.45e+142)
		tmp = t_1;
	elseif (a <= -2.3e-21)
		tmp = j * ((a * c) - (y * i));
	elseif (a <= 2e+46)
		tmp = b * ((t * i) - (z * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.45e+142], t$95$1, If[LessEqual[a, -2.3e-21], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2e+46], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.45000000000000007e142 or 2e46 < a

   1. Initial program 61.2%

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

   3. Taylor expanded in a around inf 70.2%

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

      1. +-commutative 70.2%

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

      2. mul-1-neg 70.2%

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

      3. unsub-neg 70.2%

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

   5. Simplified 70.2%

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

   if -1.45000000000000007e142 < a < -2.29999999999999999e-21

   1. Initial program 74.2%

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

   3. Taylor expanded in j around inf 53.1%

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

   if -2.29999999999999999e-21 < a < 2e46

   1. Initial program 83.4%

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

   3. Taylor expanded in b around inf 55.2%

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

      1. *-commutative 55.2%

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

   5. Simplified 55.2%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{+142}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-21}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+46}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 50.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.7 \cdot 10^{+142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-41}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+46}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -1.7e+142)
     t_1
     (if (<= a -1.8e-41)
       (* i (- (* t b) (* y j)))
       (if (<= a 1.85e+46) (* b (- (* t i) (* z c))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.7e+142) {
		tmp = t_1;
	} else if (a <= -1.8e-41) {
		tmp = i * ((t * b) - (y * j));
	} else if (a <= 1.85e+46) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (a <= (-1.7d+142)) then
        tmp = t_1
    else if (a <= (-1.8d-41)) then
        tmp = i * ((t * b) - (y * j))
    else if (a <= 1.85d+46) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.7e+142) {
		tmp = t_1;
	} else if (a <= -1.8e-41) {
		tmp = i * ((t * b) - (y * j));
	} else if (a <= 1.85e+46) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -1.7e+142:
		tmp = t_1
	elif a <= -1.8e-41:
		tmp = i * ((t * b) - (y * j))
	elif a <= 1.85e+46:
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -1.7e+142)
		tmp = t_1;
	elseif (a <= -1.8e-41)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (a <= 1.85e+46)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -1.7e+142)
		tmp = t_1;
	elseif (a <= -1.8e-41)
		tmp = i * ((t * b) - (y * j));
	elseif (a <= 1.85e+46)
		tmp = b * ((t * i) - (z * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.7e+142], t$95$1, If[LessEqual[a, -1.8e-41], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.85e+46], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.6999999999999999e142 or 1.84999999999999995e46 < a

   1. Initial program 61.2%

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

   3. Taylor expanded in a around inf 70.2%

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

      1. +-commutative 70.2%

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

      2. mul-1-neg 70.2%

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

      3. unsub-neg 70.2%

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

   5. Simplified 70.2%

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

   if -1.6999999999999999e142 < a < -1.8e-41

   1. Initial program 74.8%

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

   3. Taylor expanded in i around inf 63.9%

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

   5. Simplified 63.8%

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

   6. Taylor expanded in i around inf 49.6%

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

   if -1.8e-41 < a < 1.84999999999999995e46

   1. Initial program 83.6%

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

   3. Taylor expanded in b around inf 55.2%

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

      1. *-commutative 55.2%

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

   5. Simplified 55.2%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+142}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-41}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+46}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 42.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -2.2 \cdot 10^{-141}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-254}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-27}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -2.2e-141)
     t_1
     (if (<= a 2.6e-254)
       (* b (* z (- c)))
       (if (<= a 2.9e-27) (* t (* b 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 * ((c * j) - (x * t));
	double tmp;
	if (a <= -2.2e-141) {
		tmp = t_1;
	} else if (a <= 2.6e-254) {
		tmp = b * (z * -c);
	} else if (a <= 2.9e-27) {
		tmp = t * (b * 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 * ((c * j) - (x * t))
    if (a <= (-2.2d-141)) then
        tmp = t_1
    else if (a <= 2.6d-254) then
        tmp = b * (z * -c)
    else if (a <= 2.9d-27) then
        tmp = t * (b * 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 * ((c * j) - (x * t));
	double tmp;
	if (a <= -2.2e-141) {
		tmp = t_1;
	} else if (a <= 2.6e-254) {
		tmp = b * (z * -c);
	} else if (a <= 2.9e-27) {
		tmp = t * (b * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -2.2e-141:
		tmp = t_1
	elif a <= 2.6e-254:
		tmp = b * (z * -c)
	elif a <= 2.9e-27:
		tmp = t * (b * 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(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -2.2e-141)
		tmp = t_1;
	elseif (a <= 2.6e-254)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (a <= 2.9e-27)
		tmp = Float64(t * Float64(b * 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 * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -2.2e-141)
		tmp = t_1;
	elseif (a <= 2.6e-254)
		tmp = b * (z * -c);
	elseif (a <= 2.9e-27)
		tmp = t * (b * 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[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.2e-141], t$95$1, If[LessEqual[a, 2.6e-254], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.9e-27], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.20000000000000009e-141 or 2.90000000000000004e-27 < a

   1. Initial program 67.8%

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

   3. Taylor expanded in a around inf 53.6%

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

      1. +-commutative 53.6%

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

      2. mul-1-neg 53.6%

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

      3. unsub-neg 53.6%

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

   5. Simplified 53.6%

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

   if -2.20000000000000009e-141 < a < 2.6e-254

   1. Initial program 84.3%

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

   3. Taylor expanded in t around inf 82.6%

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

      1. mul-1-neg 82.6%

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

      2. +-commutative 82.6%

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

      3. unsub-neg 82.6%

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

      4. associate-/l* 78.9%

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

      5. associate-/l* 77.1%

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

   5. Simplified 77.1%

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

   6. Taylor expanded in b around inf 68.7%

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

      1. mul-1-neg 68.7%

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

      2. associate-*r* 61.9%

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

      3. *-commutative 61.9%

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

      4. associate-*r/ 60.1%

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

      5. associate-*r* 63.3%

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

      6. distribute-lft-neg-out 63.3%

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

      7. *-commutative 63.3%

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

   8. Simplified 63.3%

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

   9. Taylor expanded in c around inf 43.5%

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

       1. associate-*r* 43.5%

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

       2. neg-mul-1 43.5%

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

   11. Simplified 43.5%

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

   if 2.6e-254 < a < 2.90000000000000004e-27

   1. Initial program 84.7%

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

   3. Taylor expanded in t around inf 50.1%

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

      1. distribute-lft-out-- 50.1%

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

   5. Simplified 50.1%

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

   6. Taylor expanded in a around 0 38.0%

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

      1. associate-*r* 42.8%

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

   8. Simplified 42.8%

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

4. Final simplification 50.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{-141}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-254}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-27}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 51.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+65} \lor \neg \left(t \leq 66000000\right):\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(x - i \cdot \frac{j}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -2.5e+65) (not (<= t 66000000.0)))
   (* t (- (* b i) (* x a)))
   (* (* y z) (- x (* i (/ j 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 ((t <= -2.5e+65) || !(t <= 66000000.0)) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = (y * z) * (x - (i * (j / 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 ((t <= (-2.5d+65)) .or. (.not. (t <= 66000000.0d0))) then
        tmp = t * ((b * i) - (x * a))
    else
        tmp = (y * z) * (x - (i * (j / 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 ((t <= -2.5e+65) || !(t <= 66000000.0)) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = (y * z) * (x - (i * (j / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -2.5e+65) or not (t <= 66000000.0):
		tmp = t * ((b * i) - (x * a))
	else:
		tmp = (y * z) * (x - (i * (j / z)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -2.5e+65) || !(t <= 66000000.0))
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	else
		tmp = Float64(Float64(y * z) * Float64(x - Float64(i * Float64(j / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -2.5e+65) || ~((t <= 66000000.0)))
		tmp = t * ((b * i) - (x * a));
	else
		tmp = (y * z) * (x - (i * (j / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -2.5e+65], N[Not[LessEqual[t, 66000000.0]], $MachinePrecision]], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * z), $MachinePrecision] * N[(x - N[(i * N[(j / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.49999999999999986e65 or 6.6e7 < t

   1. Initial program 64.1%

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

   3. Taylor expanded in t around inf 70.4%

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

      1. distribute-lft-out-- 70.4%

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

   5. Simplified 70.4%

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

   6. Taylor expanded in t around 0 70.4%

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

      1. mul-1-neg 70.4%

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

      2. *-commutative 70.4%

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

      3. distribute-rgt-neg-out 70.4%

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

      4. neg-mul-1 70.4%

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

      5. distribute-lft-out-- 70.4%

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

      6. *-commutative 70.4%

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

      7. neg-mul-1 70.4%

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

      8. sub-neg 70.4%

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

      9. remove-double-neg 70.4%

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

      10. +-commutative 70.4%

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

      11. mul-1-neg 70.4%

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

      12. *-commutative 70.4%

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

      13. unsub-neg 70.4%

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

      14. *-commutative 70.4%

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

   8. Simplified 70.4%

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

   if -2.49999999999999986e65 < t < 6.6e7

   1. Initial program 80.2%

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

   3. Taylor expanded in t around inf 73.2%

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

      1. mul-1-neg 73.2%

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

      2. +-commutative 73.2%

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

      3. unsub-neg 73.2%

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

      4. associate-/l* 70.7%

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

      5. associate-/l* 66.9%

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

   5. Simplified 66.9%

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

   6. Taylor expanded in z around inf 72.1%

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

      1. +-commutative 72.1%

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

      2. mul-1-neg 72.1%

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

      3. unsub-neg 72.1%

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

      4. fma-define 73.4%

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

      5. associate-/l* 68.8%

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

      6. *-commutative 68.8%

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

      7. associate-/l* 70.1%

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

      8. +-commutative 70.1%

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

      9. mul-1-neg 70.1%

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

   8. Simplified 70.7%

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

   9. Taylor expanded in y around inf 50.2%

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

       1. associate-*r* 51.2%

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

       2. *-commutative 51.2%

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

       3. mul-1-neg 51.2%

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

       4. unsub-neg 51.2%

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

       5. associate-/l* 53.1%

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

   11. Simplified 53.1%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+65} \lor \neg \left(t \leq 66000000\right):\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(x - i \cdot \frac{j}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 51.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{+50} \lor \neg \left(a \leq 1.15 \cdot 10^{+48}\right):\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -1.65e+50) (not (<= a 1.15e+48)))
   (* a (- (* c j) (* x t)))
   (* b (- (* t i) (* z c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -1.65e+50) || !(a <= 1.15e+48)) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = b * ((t * i) - (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((a <= (-1.65d+50)) .or. (.not. (a <= 1.15d+48))) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = b * ((t * i) - (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -1.65e+50) || !(a <= 1.15e+48)) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = b * ((t * i) - (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (a <= -1.65e+50) or not (a <= 1.15e+48):
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = b * ((t * i) - (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -1.65e+50) || !(a <= 1.15e+48))
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((a <= -1.65e+50) || ~((a <= 1.15e+48)))
		tmp = a * ((c * j) - (x * t));
	else
		tmp = b * ((t * i) - (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -1.65e+50], N[Not[LessEqual[a, 1.15e+48]], $MachinePrecision]], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.65e50 or 1.15e48 < a

   1. Initial program 63.8%

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

   3. Taylor expanded in a around inf 65.3%

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

      1. +-commutative 65.3%

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

      2. mul-1-neg 65.3%

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

      3. unsub-neg 65.3%

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

   5. Simplified 65.3%

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

   if -1.65e50 < a < 1.15e48

   1. Initial program 81.7%

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

   3. Taylor expanded in b around inf 50.6%

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

      1. *-commutative 50.6%

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

   5. Simplified 50.6%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{+50} \lor \neg \left(a \leq 1.15 \cdot 10^{+48}\right):\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 30.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-60} \lor \neg \left(t \leq 1.95 \cdot 10^{+56}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -1.45e-60) (not (<= t 1.95e+56))) (* b (* t i)) (* a (* c 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 ((t <= -1.45e-60) || !(t <= 1.95e+56)) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((t <= (-1.45d-60)) .or. (.not. (t <= 1.95d+56))) then
        tmp = b * (t * i)
    else
        tmp = a * (c * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -1.45e-60) || !(t <= 1.95e+56)) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -1.45e-60) or not (t <= 1.95e+56):
		tmp = b * (t * i)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -1.45e-60) || !(t <= 1.95e+56))
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(a * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -1.45e-60) || ~((t <= 1.95e+56)))
		tmp = b * (t * i);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -1.45e-60], N[Not[LessEqual[t, 1.95e+56]], $MachinePrecision]], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.45e-60 or 1.94999999999999997e56 < t

   1. Initial program 64.7%

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

   3. Taylor expanded in t around inf 67.0%

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

      1. distribute-lft-out-- 67.0%

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

   5. Simplified 67.0%

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

   6. Taylor expanded in a around 0 41.6%

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

   if -1.45e-60 < t < 1.94999999999999997e56

   1. Initial program 80.9%

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

   3. Taylor expanded in a around inf 40.1%

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

      1. +-commutative 40.1%

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

      2. mul-1-neg 40.1%

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

      3. unsub-neg 40.1%

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

   5. Simplified 40.1%

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

   6. Taylor expanded in c around inf 29.8%

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

4. Final simplification 35.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-60} \lor \neg \left(t \leq 1.95 \cdot 10^{+56}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 22.1% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(c \cdot j\right) \end{array} \]

FPCore

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

C

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

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 * (c * j)
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 * (c * j);
}

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 73.6%

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

3. Taylor expanded in a around inf 39.4%

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

   1. +-commutative 39.4%

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

   2. mul-1-neg 39.4%

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

   3. unsub-neg 39.4%

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

5. Simplified 39.4%

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

6. Taylor expanded in c around inf 21.5%

   \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
7. Add Preprocessing

Developer Target 1: 59.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right)\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + t\_1\\ \mathbf{if}\;x < -1.469694296777705 \cdot 10^{-64}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x < 3.2113527362226803 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* c a) (* y i))))
        (t_2
         (+
          (-
           (* x (- (* y z) (* t a)))
           (/
            (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0)))
            (+ (* c z) (* t i))))
          t_1)))
   (if (< x -1.469694296777705e-64)
     t_2
     (if (< x 3.2113527362226803e-147)
       (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) 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 * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (pow((c * z), 2.0) - pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - 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 * ((c * a) - (y * i))
    t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ** 2.0d0) - ((t * i) ** 2.0d0))) / ((c * z) + (t * i)))) + t_1
    if (x < (-1.469694296777705d-64)) then
        tmp = t_2
    else if (x < 3.2113527362226803d-147) then
        tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - 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 * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (Math.pow((c * z), 2.0) - Math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((c * a) - (y * i))
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (math.pow((c * z), 2.0) - math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1
	tmp = 0
	if x < -1.469694296777705e-64:
		tmp = t_2
	elif x < 3.2113527362226803e-147:
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(c * a) - Float64(y * i)))
	t_2 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(Float64(b * Float64((Float64(c * z) ^ 2.0) - (Float64(t * i) ^ 2.0))) / Float64(Float64(c * z) + Float64(t * i)))) + t_1)
	tmp = 0.0
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = Float64(Float64(Float64(Float64(b * i) - Float64(x * a)) * t) - Float64(Float64(z * Float64(c * b)) - 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 * ((c * a) - (y * i));
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ^ 2.0) - ((t * i) ^ 2.0))) / ((c * z) + (t * i)))) + t_1;
	tmp = 0.0;
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[Power[N[(c * z), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(t * i), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * z), $MachinePrecision] + N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[Less[x, -1.469694296777705e-64], t$95$2, If[Less[x, 3.2113527362226803e-147], N[(N[(N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] - N[(N[(z * N[(c * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024165 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< x -293938859355541/2000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2) (pow (* t i) 2))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 32113527362226803/10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2) (pow (* t i) 2))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i)))))