Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.5% → 83.5%

Time: 33.0s

Alternatives: 29

Speedup: 0.5×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 83.5% accurate, 0.5× speedup

Math

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

FPCore

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 90.2%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in t around -inf 27.3%

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

   5. Simplified 35.9%

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

   6. Taylor expanded in c around inf 49.3%

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

      1. associate-*r/ 49.3%

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

      2. associate-*r* 49.3%

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

      3. neg-mul-1 49.3%

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

   8. Simplified 49.3%

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

   9. Taylor expanded in z around inf 51.0%

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

       1. mul-1-neg 51.0%

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

       2. associate-/l* 52.7%

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

       3. +-commutative 52.7%

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

       4. unsub-neg 52.7%

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

       5. associate-/l* 56.0%

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

       6. associate-/l* 61.1%

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

   11. Simplified 61.1%

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

4. Final simplification 83.5%

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

Alternative 2: 56.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(z \cdot c\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_3 := t\_2 + a \cdot \left(b \cdot i\right)\\ t_4 := x \cdot \left(y \cdot z - t \cdot a\right) - t\_1\\ \mathbf{if}\;x \leq -5.3 \cdot 10^{-30}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-251}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-152}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-28}:\\ \;\;\;\;t\_2 - t\_1\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-6}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{+25}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+60}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* z c)))
        (t_2 (* j (- (* t c) (* y i))))
        (t_3 (+ t_2 (* a (* b i))))
        (t_4 (- (* x (- (* y z) (* t a))) t_1)))
   (if (<= x -5.3e-30)
     t_4
     (if (<= x 1.55e-251)
       (+ (* c (* t j)) (* b (- (* a i) (* z c))))
       (if (<= x 1.05e-152)
         t_3
         (if (<= x 1.15e-28)
           (- t_2 t_1)
           (if (<= x 1.7e-6)
             (* i (- (* a b) (* y j)))
             (if (<= x 9.6e+25)
               t_4
               (if (<= x 3.5e+60) t_3 (* z (- (* x y) (* b 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 = b * (z * c);
	double t_2 = j * ((t * c) - (y * i));
	double t_3 = t_2 + (a * (b * i));
	double t_4 = (x * ((y * z) - (t * a))) - t_1;
	double tmp;
	if (x <= -5.3e-30) {
		tmp = t_4;
	} else if (x <= 1.55e-251) {
		tmp = (c * (t * j)) + (b * ((a * i) - (z * c)));
	} else if (x <= 1.05e-152) {
		tmp = t_3;
	} else if (x <= 1.15e-28) {
		tmp = t_2 - t_1;
	} else if (x <= 1.7e-6) {
		tmp = i * ((a * b) - (y * j));
	} else if (x <= 9.6e+25) {
		tmp = t_4;
	} else if (x <= 3.5e+60) {
		tmp = t_3;
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = b * (z * c)
    t_2 = j * ((t * c) - (y * i))
    t_3 = t_2 + (a * (b * i))
    t_4 = (x * ((y * z) - (t * a))) - t_1
    if (x <= (-5.3d-30)) then
        tmp = t_4
    else if (x <= 1.55d-251) then
        tmp = (c * (t * j)) + (b * ((a * i) - (z * c)))
    else if (x <= 1.05d-152) then
        tmp = t_3
    else if (x <= 1.15d-28) then
        tmp = t_2 - t_1
    else if (x <= 1.7d-6) then
        tmp = i * ((a * b) - (y * j))
    else if (x <= 9.6d+25) then
        tmp = t_4
    else if (x <= 3.5d+60) then
        tmp = t_3
    else
        tmp = z * ((x * y) - (b * 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 = b * (z * c);
	double t_2 = j * ((t * c) - (y * i));
	double t_3 = t_2 + (a * (b * i));
	double t_4 = (x * ((y * z) - (t * a))) - t_1;
	double tmp;
	if (x <= -5.3e-30) {
		tmp = t_4;
	} else if (x <= 1.55e-251) {
		tmp = (c * (t * j)) + (b * ((a * i) - (z * c)));
	} else if (x <= 1.05e-152) {
		tmp = t_3;
	} else if (x <= 1.15e-28) {
		tmp = t_2 - t_1;
	} else if (x <= 1.7e-6) {
		tmp = i * ((a * b) - (y * j));
	} else if (x <= 9.6e+25) {
		tmp = t_4;
	} else if (x <= 3.5e+60) {
		tmp = t_3;
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (z * c)
	t_2 = j * ((t * c) - (y * i))
	t_3 = t_2 + (a * (b * i))
	t_4 = (x * ((y * z) - (t * a))) - t_1
	tmp = 0
	if x <= -5.3e-30:
		tmp = t_4
	elif x <= 1.55e-251:
		tmp = (c * (t * j)) + (b * ((a * i) - (z * c)))
	elif x <= 1.05e-152:
		tmp = t_3
	elif x <= 1.15e-28:
		tmp = t_2 - t_1
	elif x <= 1.7e-6:
		tmp = i * ((a * b) - (y * j))
	elif x <= 9.6e+25:
		tmp = t_4
	elif x <= 3.5e+60:
		tmp = t_3
	else:
		tmp = z * ((x * y) - (b * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(z * c))
	t_2 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_3 = Float64(t_2 + Float64(a * Float64(b * i)))
	t_4 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - t_1)
	tmp = 0.0
	if (x <= -5.3e-30)
		tmp = t_4;
	elseif (x <= 1.55e-251)
		tmp = Float64(Float64(c * Float64(t * j)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (x <= 1.05e-152)
		tmp = t_3;
	elseif (x <= 1.15e-28)
		tmp = Float64(t_2 - t_1);
	elseif (x <= 1.7e-6)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (x <= 9.6e+25)
		tmp = t_4;
	elseif (x <= 3.5e+60)
		tmp = t_3;
	else
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	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 = j * ((t * c) - (y * i));
	t_3 = t_2 + (a * (b * i));
	t_4 = (x * ((y * z) - (t * a))) - t_1;
	tmp = 0.0;
	if (x <= -5.3e-30)
		tmp = t_4;
	elseif (x <= 1.55e-251)
		tmp = (c * (t * j)) + (b * ((a * i) - (z * c)));
	elseif (x <= 1.05e-152)
		tmp = t_3;
	elseif (x <= 1.15e-28)
		tmp = t_2 - t_1;
	elseif (x <= 1.7e-6)
		tmp = i * ((a * b) - (y * j));
	elseif (x <= 9.6e+25)
		tmp = t_4;
	elseif (x <= 3.5e+60)
		tmp = t_3;
	else
		tmp = z * ((x * y) - (b * c));
	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[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, If[LessEqual[x, -5.3e-30], t$95$4, If[LessEqual[x, 1.55e-251], N[(N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.05e-152], t$95$3, If[LessEqual[x, 1.15e-28], N[(t$95$2 - t$95$1), $MachinePrecision], If[LessEqual[x, 1.7e-6], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.6e+25], t$95$4, If[LessEqual[x, 3.5e+60], t$95$3, N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -5.29999999999999974e-30 or 1.70000000000000003e-6 < x < 9.59999999999999984e25

   1. Initial program 79.0%

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

   3. Taylor expanded in j around 0 75.6%

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

   4. Taylor expanded in c around inf 69.4%

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

      1. *-commutative 69.4%

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

   6. Simplified 69.4%

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

   if -5.29999999999999974e-30 < x < 1.55000000000000001e-251

   1. Initial program 66.0%

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

   3. Taylor expanded in z around inf 75.9%

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

   4. Taylor expanded in x around 0 68.7%

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

      1. *-commutative 68.7%

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

      2. *-commutative 68.7%

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

      3. *-commutative 68.7%

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

   6. Simplified 68.7%

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

   7. Taylor expanded in t around inf 67.4%

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

      1. *-commutative 67.4%

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

   9. Simplified 67.4%

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

   if 1.55000000000000001e-251 < x < 1.04999999999999999e-152 or 9.59999999999999984e25 < x < 3.5000000000000002e60

   1. Initial program 73.9%

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

   3. Taylor expanded in z around inf 74.1%

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

   4. Taylor expanded in x around 0 72.1%

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

      1. *-commutative 72.1%

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

      2. *-commutative 72.1%

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

      3. *-commutative 72.1%

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

   6. Simplified 72.1%

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

   7. Taylor expanded in z around 0 75.9%

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

      1. associate-*r* 75.9%

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

      2. neg-mul-1 75.9%

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

   9. Simplified 75.9%

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

   if 1.04999999999999999e-152 < x < 1.14999999999999993e-28

   1. Initial program 61.7%

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

   3. Taylor expanded in z around inf 77.1%

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

   4. Taylor expanded in x around 0 84.8%

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

      1. *-commutative 84.8%

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

      2. *-commutative 84.8%

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

      3. *-commutative 84.8%

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

   6. Simplified 84.8%

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

   7. Taylor expanded in z around inf 76.9%

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

   if 1.14999999999999993e-28 < x < 1.70000000000000003e-6

   1. Initial program 59.7%

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

   3. Taylor expanded in i around inf 96.6%

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

      1. distribute-lft-out-- 96.6%

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

   5. Simplified 96.6%

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

   if 3.5000000000000002e60 < x

   1. Initial program 58.4%

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

   3. Taylor expanded in z around inf 63.0%

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

      1. *-commutative 63.0%

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

      2. *-commutative 63.0%

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

   5. Simplified 63.0%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.3 \cdot 10^{-30}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-251}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-152}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-28}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-6}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{+25}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+60}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 53.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(x \cdot \left(y \cdot \frac{z}{t} - a\right)\right)\\ t_2 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;x \leq -4 \cdot 10^{+113}:\\ \;\;\;\;a \cdot \left(\frac{x \cdot \left(y \cdot z\right)}{a} - x \cdot t\right)\\ \mathbf{elif}\;x \leq -5 \cdot 10^{+27}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(b \cdot \frac{i}{t} - x\right)\\ \mathbf{elif}\;x \leq -29000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-28}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 3.15 \cdot 10^{-6}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 70000000000:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+80}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (* x (- (* y (/ z t)) a)))) (t_2 (* i (- (* a b) (* y j)))))
   (if (<= x -4e+113)
     (* a (- (/ (* x (* y z)) a) (* x t)))
     (if (<= x -5e+27)
       (* (* t a) (- (* b (/ i t)) x))
       (if (<= x -29000000000.0)
         t_1
         (if (<= x 1.45e-28)
           (+ (* c (* t j)) (* b (- (* a i) (* z c))))
           (if (<= x 3.15e-6)
             t_2
             (if (<= x 70000000000.0)
               (* t (- (* c j) (* x a)))
               (if (<= x 1.55e+23)
                 t_1
                 (if (<= x 7.8e+80) t_2 (* z (- (* x y) (* b 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 = t * (x * ((y * (z / t)) - a));
	double t_2 = i * ((a * b) - (y * j));
	double tmp;
	if (x <= -4e+113) {
		tmp = a * (((x * (y * z)) / a) - (x * t));
	} else if (x <= -5e+27) {
		tmp = (t * a) * ((b * (i / t)) - x);
	} else if (x <= -29000000000.0) {
		tmp = t_1;
	} else if (x <= 1.45e-28) {
		tmp = (c * (t * j)) + (b * ((a * i) - (z * c)));
	} else if (x <= 3.15e-6) {
		tmp = t_2;
	} else if (x <= 70000000000.0) {
		tmp = t * ((c * j) - (x * a));
	} else if (x <= 1.55e+23) {
		tmp = t_1;
	} else if (x <= 7.8e+80) {
		tmp = t_2;
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (x * ((y * (z / t)) - a))
    t_2 = i * ((a * b) - (y * j))
    if (x <= (-4d+113)) then
        tmp = a * (((x * (y * z)) / a) - (x * t))
    else if (x <= (-5d+27)) then
        tmp = (t * a) * ((b * (i / t)) - x)
    else if (x <= (-29000000000.0d0)) then
        tmp = t_1
    else if (x <= 1.45d-28) then
        tmp = (c * (t * j)) + (b * ((a * i) - (z * c)))
    else if (x <= 3.15d-6) then
        tmp = t_2
    else if (x <= 70000000000.0d0) then
        tmp = t * ((c * j) - (x * a))
    else if (x <= 1.55d+23) then
        tmp = t_1
    else if (x <= 7.8d+80) then
        tmp = t_2
    else
        tmp = z * ((x * y) - (b * 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 = t * (x * ((y * (z / t)) - a));
	double t_2 = i * ((a * b) - (y * j));
	double tmp;
	if (x <= -4e+113) {
		tmp = a * (((x * (y * z)) / a) - (x * t));
	} else if (x <= -5e+27) {
		tmp = (t * a) * ((b * (i / t)) - x);
	} else if (x <= -29000000000.0) {
		tmp = t_1;
	} else if (x <= 1.45e-28) {
		tmp = (c * (t * j)) + (b * ((a * i) - (z * c)));
	} else if (x <= 3.15e-6) {
		tmp = t_2;
	} else if (x <= 70000000000.0) {
		tmp = t * ((c * j) - (x * a));
	} else if (x <= 1.55e+23) {
		tmp = t_1;
	} else if (x <= 7.8e+80) {
		tmp = t_2;
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * (x * ((y * (z / t)) - a))
	t_2 = i * ((a * b) - (y * j))
	tmp = 0
	if x <= -4e+113:
		tmp = a * (((x * (y * z)) / a) - (x * t))
	elif x <= -5e+27:
		tmp = (t * a) * ((b * (i / t)) - x)
	elif x <= -29000000000.0:
		tmp = t_1
	elif x <= 1.45e-28:
		tmp = (c * (t * j)) + (b * ((a * i) - (z * c)))
	elif x <= 3.15e-6:
		tmp = t_2
	elif x <= 70000000000.0:
		tmp = t * ((c * j) - (x * a))
	elif x <= 1.55e+23:
		tmp = t_1
	elif x <= 7.8e+80:
		tmp = t_2
	else:
		tmp = z * ((x * y) - (b * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(x * Float64(Float64(y * Float64(z / t)) - a)))
	t_2 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	tmp = 0.0
	if (x <= -4e+113)
		tmp = Float64(a * Float64(Float64(Float64(x * Float64(y * z)) / a) - Float64(x * t)));
	elseif (x <= -5e+27)
		tmp = Float64(Float64(t * a) * Float64(Float64(b * Float64(i / t)) - x));
	elseif (x <= -29000000000.0)
		tmp = t_1;
	elseif (x <= 1.45e-28)
		tmp = Float64(Float64(c * Float64(t * j)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (x <= 3.15e-6)
		tmp = t_2;
	elseif (x <= 70000000000.0)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (x <= 1.55e+23)
		tmp = t_1;
	elseif (x <= 7.8e+80)
		tmp = t_2;
	else
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * (x * ((y * (z / t)) - a));
	t_2 = i * ((a * b) - (y * j));
	tmp = 0.0;
	if (x <= -4e+113)
		tmp = a * (((x * (y * z)) / a) - (x * t));
	elseif (x <= -5e+27)
		tmp = (t * a) * ((b * (i / t)) - x);
	elseif (x <= -29000000000.0)
		tmp = t_1;
	elseif (x <= 1.45e-28)
		tmp = (c * (t * j)) + (b * ((a * i) - (z * c)));
	elseif (x <= 3.15e-6)
		tmp = t_2;
	elseif (x <= 70000000000.0)
		tmp = t * ((c * j) - (x * a));
	elseif (x <= 1.55e+23)
		tmp = t_1;
	elseif (x <= 7.8e+80)
		tmp = t_2;
	else
		tmp = z * ((x * y) - (b * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(x * N[(N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4e+113], N[(a * N[(N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5e+27], N[(N[(t * a), $MachinePrecision] * N[(N[(b * N[(i / t), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -29000000000.0], t$95$1, If[LessEqual[x, 1.45e-28], N[(N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.15e-6], t$95$2, If[LessEqual[x, 70000000000.0], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.55e+23], t$95$1, If[LessEqual[x, 7.8e+80], t$95$2, N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if x < -4e113

   1. Initial program 72.4%

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

   3. Taylor expanded in j around 0 66.6%

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

   4. Taylor expanded in a around -inf 71.8%

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

      1. mul-1-neg 71.8%

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

      2. *-commutative 71.8%

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

      3. distribute-rgt-neg-in 71.8%

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

   6. Simplified 72.0%

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

   7. Taylor expanded in b around 0 74.5%

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

   if -4e113 < x < -4.99999999999999979e27

   1. Initial program 86.8%

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

   3. Taylor expanded in t around -inf 78.7%

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

   5. Simplified 70.0%

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

   6. Taylor expanded in a around -inf 56.6%

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

      1. associate-*r* 60.7%

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

      2. *-commutative 60.7%

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

      3. +-commutative 60.7%

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

      4. mul-1-neg 60.7%

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

      5. unsub-neg 60.7%

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

      6. associate-/l* 64.8%

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

   8. Simplified 64.8%

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

   if -4.99999999999999979e27 < x < -2.9e10 or 7e10 < x < 1.54999999999999985e23

   1. Initial program 77.6%

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

   3. Taylor expanded in t around -inf 77.3%

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

   5. Simplified 78.5%

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

   6. Taylor expanded in x around inf 80.2%

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

      1. associate-*r* 80.2%

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

      2. neg-mul-1 80.2%

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

      3. associate-/l* 91.1%

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

   8. Simplified 91.1%

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

   if -2.9e10 < x < 1.45000000000000006e-28

   1. Initial program 67.8%

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

   3. Taylor expanded in z around inf 78.5%

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

   4. Taylor expanded in x around 0 72.1%

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

      1. *-commutative 72.1%

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

      2. *-commutative 72.1%

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

      3. *-commutative 72.1%

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

   6. Simplified 72.1%

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

   7. Taylor expanded in t around inf 64.7%

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

      1. *-commutative 64.7%

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

   9. Simplified 64.7%

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

   if 1.45000000000000006e-28 < x < 3.14999999999999991e-6 or 1.54999999999999985e23 < x < 7.79999999999999998e80

   1. Initial program 65.2%

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

   3. Taylor expanded in i around inf 70.3%

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

      1. distribute-lft-out-- 70.3%

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

   5. Simplified 70.3%

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

   if 3.14999999999999991e-6 < x < 7e10

   1. Initial program 99.6%

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

   3. Taylor expanded in z around inf 77.9%

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

   4. Taylor expanded in t around inf 99.2%

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

      1. +-commutative 99.2%

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

      2. mul-1-neg 99.2%

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

      3. unsub-neg 99.2%

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

      4. *-commutative 99.2%

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

   6. Simplified 99.2%

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

   if 7.79999999999999998e80 < x

   1. Initial program 58.6%

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

   3. Taylor expanded in z around inf 63.4%

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

      1. *-commutative 63.4%

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

      2. *-commutative 63.4%

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

   5. Simplified 63.4%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+113}:\\ \;\;\;\;a \cdot \left(\frac{x \cdot \left(y \cdot z\right)}{a} - x \cdot t\right)\\ \mathbf{elif}\;x \leq -5 \cdot 10^{+27}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(b \cdot \frac{i}{t} - x\right)\\ \mathbf{elif}\;x \leq -29000000000:\\ \;\;\;\;t \cdot \left(x \cdot \left(y \cdot \frac{z}{t} - a\right)\right)\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-28}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 3.15 \cdot 10^{-6}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 70000000000:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+23}:\\ \;\;\;\;t \cdot \left(x \cdot \left(y \cdot \frac{z}{t} - a\right)\right)\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+80}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 49.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;b \leq -5.5 \cdot 10^{+220}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{+209}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{+27}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq -8.2 \cdot 10^{-97}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-170}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 8.6 \cdot 10^{-40}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(c \cdot \left(\frac{a \cdot i}{c} - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j)))) (t_2 (* t (- (* c j) (* x a)))))
   (if (<= b -5.5e+220)
     (* b (- (* a i) (* z c)))
     (if (<= b -1.5e+209)
       t_2
       (if (<= b -3.6e+27)
         (* z (- (* x y) (* b c)))
         (if (<= b -8.2e-97)
           (* a (- (* b i) (* x t)))
           (if (<= b -2.5e-170)
             t_1
             (if (<= b 8.6e-40)
               t_2
               (if (<= b 2e+43) t_1 (* b (* c (- (/ (* a i) c) 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 = y * ((x * z) - (i * j));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (b <= -5.5e+220) {
		tmp = b * ((a * i) - (z * c));
	} else if (b <= -1.5e+209) {
		tmp = t_2;
	} else if (b <= -3.6e+27) {
		tmp = z * ((x * y) - (b * c));
	} else if (b <= -8.2e-97) {
		tmp = a * ((b * i) - (x * t));
	} else if (b <= -2.5e-170) {
		tmp = t_1;
	} else if (b <= 8.6e-40) {
		tmp = t_2;
	} else if (b <= 2e+43) {
		tmp = t_1;
	} else {
		tmp = b * (c * (((a * i) / c) - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((x * z) - (i * j))
    t_2 = t * ((c * j) - (x * a))
    if (b <= (-5.5d+220)) then
        tmp = b * ((a * i) - (z * c))
    else if (b <= (-1.5d+209)) then
        tmp = t_2
    else if (b <= (-3.6d+27)) then
        tmp = z * ((x * y) - (b * c))
    else if (b <= (-8.2d-97)) then
        tmp = a * ((b * i) - (x * t))
    else if (b <= (-2.5d-170)) then
        tmp = t_1
    else if (b <= 8.6d-40) then
        tmp = t_2
    else if (b <= 2d+43) then
        tmp = t_1
    else
        tmp = b * (c * (((a * i) / c) - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (b <= -5.5e+220) {
		tmp = b * ((a * i) - (z * c));
	} else if (b <= -1.5e+209) {
		tmp = t_2;
	} else if (b <= -3.6e+27) {
		tmp = z * ((x * y) - (b * c));
	} else if (b <= -8.2e-97) {
		tmp = a * ((b * i) - (x * t));
	} else if (b <= -2.5e-170) {
		tmp = t_1;
	} else if (b <= 8.6e-40) {
		tmp = t_2;
	} else if (b <= 2e+43) {
		tmp = t_1;
	} else {
		tmp = b * (c * (((a * i) / c) - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	t_2 = t * ((c * j) - (x * a))
	tmp = 0
	if b <= -5.5e+220:
		tmp = b * ((a * i) - (z * c))
	elif b <= -1.5e+209:
		tmp = t_2
	elif b <= -3.6e+27:
		tmp = z * ((x * y) - (b * c))
	elif b <= -8.2e-97:
		tmp = a * ((b * i) - (x * t))
	elif b <= -2.5e-170:
		tmp = t_1
	elif b <= 8.6e-40:
		tmp = t_2
	elif b <= 2e+43:
		tmp = t_1
	else:
		tmp = b * (c * (((a * i) / c) - z))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_2 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (b <= -5.5e+220)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (b <= -1.5e+209)
		tmp = t_2;
	elseif (b <= -3.6e+27)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (b <= -8.2e-97)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (b <= -2.5e-170)
		tmp = t_1;
	elseif (b <= 8.6e-40)
		tmp = t_2;
	elseif (b <= 2e+43)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(c * Float64(Float64(Float64(a * i) / c) - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((x * z) - (i * j));
	t_2 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (b <= -5.5e+220)
		tmp = b * ((a * i) - (z * c));
	elseif (b <= -1.5e+209)
		tmp = t_2;
	elseif (b <= -3.6e+27)
		tmp = z * ((x * y) - (b * c));
	elseif (b <= -8.2e-97)
		tmp = a * ((b * i) - (x * t));
	elseif (b <= -2.5e-170)
		tmp = t_1;
	elseif (b <= 8.6e-40)
		tmp = t_2;
	elseif (b <= 2e+43)
		tmp = t_1;
	else
		tmp = b * (c * (((a * i) / c) - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.5e+220], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.5e+209], t$95$2, If[LessEqual[b, -3.6e+27], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -8.2e-97], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.5e-170], t$95$1, If[LessEqual[b, 8.6e-40], t$95$2, If[LessEqual[b, 2e+43], t$95$1, N[(b * N[(c * N[(N[(N[(a * i), $MachinePrecision] / c), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -5.4999999999999999e220

   1. Initial program 57.6%

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

   3. Taylor expanded in b around inf 81.5%

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

      1. *-commutative 81.5%

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

   5. Simplified 81.5%

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

   if -5.4999999999999999e220 < b < -1.49999999999999993e209 or -2.50000000000000005e-170 < b < 8.6000000000000005e-40

   1. Initial program 70.1%

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

   3. Taylor expanded in z around inf 68.3%

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

   4. Taylor expanded in t around inf 59.7%

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

      1. +-commutative 59.7%

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

      2. mul-1-neg 59.7%

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

      3. unsub-neg 59.7%

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

      4. *-commutative 59.7%

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

   6. Simplified 59.7%

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

   if -1.49999999999999993e209 < b < -3.59999999999999983e27

   1. Initial program 68.8%

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

   3. Taylor expanded in z around inf 66.4%

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

      1. *-commutative 66.4%

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

      2. *-commutative 66.4%

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

   5. Simplified 66.4%

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

   if -3.59999999999999983e27 < b < -8.19999999999999986e-97

   1. Initial program 70.0%

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

   3. Taylor expanded in a around inf 50.1%

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

      1. distribute-lft-out-- 50.1%

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

      2. *-commutative 50.1%

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

   5. Simplified 50.1%

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

   if -8.19999999999999986e-97 < b < -2.50000000000000005e-170 or 8.6000000000000005e-40 < b < 2.00000000000000003e43

   1. Initial program 70.7%

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

   3. Taylor expanded in y around inf 50.2%

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

      1. +-commutative 50.2%

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

      2. mul-1-neg 50.2%

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

      3. unsub-neg 50.2%

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

   5. Simplified 50.2%

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

   if 2.00000000000000003e43 < b

   1. Initial program 72.3%

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

   3. Taylor expanded in b around inf 75.3%

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

      1. *-commutative 75.3%

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

   5. Simplified 75.3%

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

   6. Taylor expanded in c around inf 77.2%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{+220}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{+209}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{+27}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq -8.2 \cdot 10^{-97}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-170}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 8.6 \cdot 10^{-40}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+43}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(c \cdot \left(\frac{a \cdot i}{c} - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;b \leq -2.2 \cdot 10^{+227}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -9.2 \cdot 10^{+151}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -5 \cdot 10^{+27}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-94}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3.8 \cdot 10^{-168}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{-35}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+36}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(c \cdot \left(\frac{a \cdot i}{c} - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* a b) (* y j)))))
   (if (<= b -2.2e+227)
     (* b (- (* a i) (* z c)))
     (if (<= b -9.2e+151)
       t_1
       (if (<= b -5e+27)
         (* z (- (* x y) (* b c)))
         (if (<= b -2.3e-94)
           t_1
           (if (<= b -3.8e-168)
             (* y (- (* x z) (* i j)))
             (if (<= b 1.1e-35)
               (* t (- (* c j) (* x a)))
               (if (<= b 8.5e+36) t_1 (* b (* c (- (/ (* a i) c) 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 = i * ((a * b) - (y * j));
	double tmp;
	if (b <= -2.2e+227) {
		tmp = b * ((a * i) - (z * c));
	} else if (b <= -9.2e+151) {
		tmp = t_1;
	} else if (b <= -5e+27) {
		tmp = z * ((x * y) - (b * c));
	} else if (b <= -2.3e-94) {
		tmp = t_1;
	} else if (b <= -3.8e-168) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 1.1e-35) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= 8.5e+36) {
		tmp = t_1;
	} else {
		tmp = b * (c * (((a * i) / c) - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * ((a * b) - (y * j))
    if (b <= (-2.2d+227)) then
        tmp = b * ((a * i) - (z * c))
    else if (b <= (-9.2d+151)) then
        tmp = t_1
    else if (b <= (-5d+27)) then
        tmp = z * ((x * y) - (b * c))
    else if (b <= (-2.3d-94)) then
        tmp = t_1
    else if (b <= (-3.8d-168)) then
        tmp = y * ((x * z) - (i * j))
    else if (b <= 1.1d-35) then
        tmp = t * ((c * j) - (x * a))
    else if (b <= 8.5d+36) then
        tmp = t_1
    else
        tmp = b * (c * (((a * i) / c) - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double tmp;
	if (b <= -2.2e+227) {
		tmp = b * ((a * i) - (z * c));
	} else if (b <= -9.2e+151) {
		tmp = t_1;
	} else if (b <= -5e+27) {
		tmp = z * ((x * y) - (b * c));
	} else if (b <= -2.3e-94) {
		tmp = t_1;
	} else if (b <= -3.8e-168) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 1.1e-35) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= 8.5e+36) {
		tmp = t_1;
	} else {
		tmp = b * (c * (((a * i) / c) - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((a * b) - (y * j))
	tmp = 0
	if b <= -2.2e+227:
		tmp = b * ((a * i) - (z * c))
	elif b <= -9.2e+151:
		tmp = t_1
	elif b <= -5e+27:
		tmp = z * ((x * y) - (b * c))
	elif b <= -2.3e-94:
		tmp = t_1
	elif b <= -3.8e-168:
		tmp = y * ((x * z) - (i * j))
	elif b <= 1.1e-35:
		tmp = t * ((c * j) - (x * a))
	elif b <= 8.5e+36:
		tmp = t_1
	else:
		tmp = b * (c * (((a * i) / c) - z))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	tmp = 0.0
	if (b <= -2.2e+227)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (b <= -9.2e+151)
		tmp = t_1;
	elseif (b <= -5e+27)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (b <= -2.3e-94)
		tmp = t_1;
	elseif (b <= -3.8e-168)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (b <= 1.1e-35)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (b <= 8.5e+36)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(c * Float64(Float64(Float64(a * i) / c) - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((a * b) - (y * j));
	tmp = 0.0;
	if (b <= -2.2e+227)
		tmp = b * ((a * i) - (z * c));
	elseif (b <= -9.2e+151)
		tmp = t_1;
	elseif (b <= -5e+27)
		tmp = z * ((x * y) - (b * c));
	elseif (b <= -2.3e-94)
		tmp = t_1;
	elseif (b <= -3.8e-168)
		tmp = y * ((x * z) - (i * j));
	elseif (b <= 1.1e-35)
		tmp = t * ((c * j) - (x * a));
	elseif (b <= 8.5e+36)
		tmp = t_1;
	else
		tmp = b * (c * (((a * i) / c) - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.2e+227], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -9.2e+151], t$95$1, If[LessEqual[b, -5e+27], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.3e-94], t$95$1, If[LessEqual[b, -3.8e-168], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.1e-35], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.5e+36], t$95$1, N[(b * N[(c * N[(N[(N[(a * i), $MachinePrecision] / c), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -2.2000000000000002e227

   1. Initial program 61.7%

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

   3. Taylor expanded in b around inf 84.0%

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

      1. *-commutative 84.0%

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

   5. Simplified 84.0%

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

   if -2.2000000000000002e227 < b < -9.2000000000000003e151 or -4.99999999999999979e27 < b < -2.2999999999999999e-94 or 1.09999999999999997e-35 < b < 8.50000000000000014e36

   1. Initial program 64.3%

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

   3. Taylor expanded in i around inf 57.3%

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

      1. distribute-lft-out-- 57.3%

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

   5. Simplified 57.3%

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

   if -9.2000000000000003e151 < b < -4.99999999999999979e27

   1. Initial program 66.7%

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

   3. Taylor expanded in z around inf 75.5%

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

      1. *-commutative 75.5%

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

      2. *-commutative 75.5%

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

   5. Simplified 75.5%

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

   if -2.2999999999999999e-94 < b < -3.8e-168

   1. Initial program 75.2%

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

   3. Taylor expanded in y around inf 53.3%

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

      1. +-commutative 53.3%

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

      2. mul-1-neg 53.3%

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

      3. unsub-neg 53.3%

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

   5. Simplified 53.3%

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

   if -3.8e-168 < b < 1.09999999999999997e-35

   1. Initial program 72.5%

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

   3. Taylor expanded in z around inf 70.7%

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

   4. Taylor expanded in t around inf 58.1%

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

      1. +-commutative 58.1%

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

      2. mul-1-neg 58.1%

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

      3. unsub-neg 58.1%

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

      4. *-commutative 58.1%

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

   6. Simplified 58.1%

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

   if 8.50000000000000014e36 < b

   1. Initial program 72.3%

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

   3. Taylor expanded in b around inf 75.3%

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

      1. *-commutative 75.3%

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

   5. Simplified 75.3%

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

   6. Taylor expanded in c around inf 77.2%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.2 \cdot 10^{+227}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -9.2 \cdot 10^{+151}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq -5 \cdot 10^{+27}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-94}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq -3.8 \cdot 10^{-168}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{-35}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+36}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(c \cdot \left(\frac{a \cdot i}{c} - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 49.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;b \leq -2.2 \cdot 10^{+227}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -9.5 \cdot 10^{+151}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3.9 \cdot 10^{+27}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-94}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3.8 \cdot 10^{-171}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{-45}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+44}:\\ \;\;\;\;t \cdot \left(x \cdot \left(y \cdot \frac{z}{t} - a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(c \cdot \left(\frac{a \cdot i}{c} - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* a b) (* y j)))))
   (if (<= b -2.2e+227)
     (* b (- (* a i) (* z c)))
     (if (<= b -9.5e+151)
       t_1
       (if (<= b -3.9e+27)
         (* z (- (* x y) (* b c)))
         (if (<= b -2.5e-94)
           t_1
           (if (<= b -3.8e-171)
             (* y (- (* x z) (* i j)))
             (if (<= b 2.05e-45)
               (* t (- (* c j) (* x a)))
               (if (<= b 9.5e+44)
                 (* t (* x (- (* y (/ z t)) a)))
                 (* b (* c (- (/ (* a i) c) 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 = i * ((a * b) - (y * j));
	double tmp;
	if (b <= -2.2e+227) {
		tmp = b * ((a * i) - (z * c));
	} else if (b <= -9.5e+151) {
		tmp = t_1;
	} else if (b <= -3.9e+27) {
		tmp = z * ((x * y) - (b * c));
	} else if (b <= -2.5e-94) {
		tmp = t_1;
	} else if (b <= -3.8e-171) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 2.05e-45) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= 9.5e+44) {
		tmp = t * (x * ((y * (z / t)) - a));
	} else {
		tmp = b * (c * (((a * i) / c) - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * ((a * b) - (y * j))
    if (b <= (-2.2d+227)) then
        tmp = b * ((a * i) - (z * c))
    else if (b <= (-9.5d+151)) then
        tmp = t_1
    else if (b <= (-3.9d+27)) then
        tmp = z * ((x * y) - (b * c))
    else if (b <= (-2.5d-94)) then
        tmp = t_1
    else if (b <= (-3.8d-171)) then
        tmp = y * ((x * z) - (i * j))
    else if (b <= 2.05d-45) then
        tmp = t * ((c * j) - (x * a))
    else if (b <= 9.5d+44) then
        tmp = t * (x * ((y * (z / t)) - a))
    else
        tmp = b * (c * (((a * i) / c) - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double tmp;
	if (b <= -2.2e+227) {
		tmp = b * ((a * i) - (z * c));
	} else if (b <= -9.5e+151) {
		tmp = t_1;
	} else if (b <= -3.9e+27) {
		tmp = z * ((x * y) - (b * c));
	} else if (b <= -2.5e-94) {
		tmp = t_1;
	} else if (b <= -3.8e-171) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 2.05e-45) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= 9.5e+44) {
		tmp = t * (x * ((y * (z / t)) - a));
	} else {
		tmp = b * (c * (((a * i) / c) - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((a * b) - (y * j))
	tmp = 0
	if b <= -2.2e+227:
		tmp = b * ((a * i) - (z * c))
	elif b <= -9.5e+151:
		tmp = t_1
	elif b <= -3.9e+27:
		tmp = z * ((x * y) - (b * c))
	elif b <= -2.5e-94:
		tmp = t_1
	elif b <= -3.8e-171:
		tmp = y * ((x * z) - (i * j))
	elif b <= 2.05e-45:
		tmp = t * ((c * j) - (x * a))
	elif b <= 9.5e+44:
		tmp = t * (x * ((y * (z / t)) - a))
	else:
		tmp = b * (c * (((a * i) / c) - z))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	tmp = 0.0
	if (b <= -2.2e+227)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (b <= -9.5e+151)
		tmp = t_1;
	elseif (b <= -3.9e+27)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (b <= -2.5e-94)
		tmp = t_1;
	elseif (b <= -3.8e-171)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (b <= 2.05e-45)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (b <= 9.5e+44)
		tmp = Float64(t * Float64(x * Float64(Float64(y * Float64(z / t)) - a)));
	else
		tmp = Float64(b * Float64(c * Float64(Float64(Float64(a * i) / c) - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((a * b) - (y * j));
	tmp = 0.0;
	if (b <= -2.2e+227)
		tmp = b * ((a * i) - (z * c));
	elseif (b <= -9.5e+151)
		tmp = t_1;
	elseif (b <= -3.9e+27)
		tmp = z * ((x * y) - (b * c));
	elseif (b <= -2.5e-94)
		tmp = t_1;
	elseif (b <= -3.8e-171)
		tmp = y * ((x * z) - (i * j));
	elseif (b <= 2.05e-45)
		tmp = t * ((c * j) - (x * a));
	elseif (b <= 9.5e+44)
		tmp = t * (x * ((y * (z / t)) - a));
	else
		tmp = b * (c * (((a * i) / c) - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.2e+227], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -9.5e+151], t$95$1, If[LessEqual[b, -3.9e+27], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.5e-94], t$95$1, If[LessEqual[b, -3.8e-171], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.05e-45], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.5e+44], N[(t * N[(x * N[(N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(c * N[(N[(N[(a * i), $MachinePrecision] / c), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -2.2000000000000002e227

   1. Initial program 61.7%

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

   3. Taylor expanded in b around inf 84.0%

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

      1. *-commutative 84.0%

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

   5. Simplified 84.0%

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

   if -2.2000000000000002e227 < b < -9.5000000000000001e151 or -3.8999999999999999e27 < b < -2.4999999999999998e-94

   1. Initial program 61.8%

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

   3. Taylor expanded in i around inf 60.6%

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

      1. distribute-lft-out-- 60.6%

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

   5. Simplified 60.6%

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

   if -9.5000000000000001e151 < b < -3.8999999999999999e27

   1. Initial program 66.7%

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

   3. Taylor expanded in z around inf 75.5%

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

      1. *-commutative 75.5%

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

      2. *-commutative 75.5%

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

   5. Simplified 75.5%

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

   if -2.4999999999999998e-94 < b < -3.80000000000000021e-171

   1. Initial program 75.2%

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

   3. Taylor expanded in y around inf 53.3%

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

      1. +-commutative 53.3%

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

      2. mul-1-neg 53.3%

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

      3. unsub-neg 53.3%

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

   5. Simplified 53.3%

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

   if -3.80000000000000021e-171 < b < 2.05e-45

   1. Initial program 71.6%

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

   3. Taylor expanded in z around inf 70.7%

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

   4. Taylor expanded in t around inf 57.8%

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

      1. +-commutative 57.8%

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

      2. mul-1-neg 57.8%

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

      3. unsub-neg 57.8%

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

      4. *-commutative 57.8%

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

   6. Simplified 57.8%

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

   if 2.05e-45 < b < 9.5000000000000004e44

   1. Initial program 73.5%

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

   3. Taylor expanded in t around -inf 66.4%

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

   5. Simplified 66.5%

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

   6. Taylor expanded in x around inf 51.6%

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

      1. associate-*r* 51.6%

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

      2. neg-mul-1 51.6%

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

      3. associate-/l* 51.6%

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

   8. Simplified 51.6%

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

   if 9.5000000000000004e44 < b

   1. Initial program 71.7%

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

   3. Taylor expanded in b around inf 76.8%

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

      1. *-commutative 76.8%

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

   5. Simplified 76.8%

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

   6. Taylor expanded in c around inf 78.8%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.2 \cdot 10^{+227}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -9.5 \cdot 10^{+151}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq -3.9 \cdot 10^{+27}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-94}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq -3.8 \cdot 10^{-171}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{-45}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+44}:\\ \;\;\;\;t \cdot \left(x \cdot \left(y \cdot \frac{z}{t} - a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(c \cdot \left(\frac{a \cdot i}{c} - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 49.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;b \leq -6.4 \cdot 10^{+227}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -9.2 \cdot 10^{+151}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -4.8 \cdot 10^{+27}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq -2.15 \cdot 10^{-94}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.26 \cdot 10^{-170}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{-27}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+45}:\\ \;\;\;\;a \cdot \left(x \cdot \left(\frac{y \cdot z}{a} - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(c \cdot \left(\frac{a \cdot i}{c} - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* a b) (* y j)))))
   (if (<= b -6.4e+227)
     (* b (- (* a i) (* z c)))
     (if (<= b -9.2e+151)
       t_1
       (if (<= b -4.8e+27)
         (* z (- (* x y) (* b c)))
         (if (<= b -2.15e-94)
           t_1
           (if (<= b -1.26e-170)
             (* y (- (* x z) (* i j)))
             (if (<= b 1.3e-27)
               (* t (- (* c j) (* x a)))
               (if (<= b 1.05e+45)
                 (* a (* x (- (/ (* y z) a) t)))
                 (* b (* c (- (/ (* a i) c) 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 = i * ((a * b) - (y * j));
	double tmp;
	if (b <= -6.4e+227) {
		tmp = b * ((a * i) - (z * c));
	} else if (b <= -9.2e+151) {
		tmp = t_1;
	} else if (b <= -4.8e+27) {
		tmp = z * ((x * y) - (b * c));
	} else if (b <= -2.15e-94) {
		tmp = t_1;
	} else if (b <= -1.26e-170) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 1.3e-27) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= 1.05e+45) {
		tmp = a * (x * (((y * z) / a) - t));
	} else {
		tmp = b * (c * (((a * i) / c) - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * ((a * b) - (y * j))
    if (b <= (-6.4d+227)) then
        tmp = b * ((a * i) - (z * c))
    else if (b <= (-9.2d+151)) then
        tmp = t_1
    else if (b <= (-4.8d+27)) then
        tmp = z * ((x * y) - (b * c))
    else if (b <= (-2.15d-94)) then
        tmp = t_1
    else if (b <= (-1.26d-170)) then
        tmp = y * ((x * z) - (i * j))
    else if (b <= 1.3d-27) then
        tmp = t * ((c * j) - (x * a))
    else if (b <= 1.05d+45) then
        tmp = a * (x * (((y * z) / a) - t))
    else
        tmp = b * (c * (((a * i) / c) - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double tmp;
	if (b <= -6.4e+227) {
		tmp = b * ((a * i) - (z * c));
	} else if (b <= -9.2e+151) {
		tmp = t_1;
	} else if (b <= -4.8e+27) {
		tmp = z * ((x * y) - (b * c));
	} else if (b <= -2.15e-94) {
		tmp = t_1;
	} else if (b <= -1.26e-170) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 1.3e-27) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= 1.05e+45) {
		tmp = a * (x * (((y * z) / a) - t));
	} else {
		tmp = b * (c * (((a * i) / c) - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((a * b) - (y * j))
	tmp = 0
	if b <= -6.4e+227:
		tmp = b * ((a * i) - (z * c))
	elif b <= -9.2e+151:
		tmp = t_1
	elif b <= -4.8e+27:
		tmp = z * ((x * y) - (b * c))
	elif b <= -2.15e-94:
		tmp = t_1
	elif b <= -1.26e-170:
		tmp = y * ((x * z) - (i * j))
	elif b <= 1.3e-27:
		tmp = t * ((c * j) - (x * a))
	elif b <= 1.05e+45:
		tmp = a * (x * (((y * z) / a) - t))
	else:
		tmp = b * (c * (((a * i) / c) - z))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	tmp = 0.0
	if (b <= -6.4e+227)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (b <= -9.2e+151)
		tmp = t_1;
	elseif (b <= -4.8e+27)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (b <= -2.15e-94)
		tmp = t_1;
	elseif (b <= -1.26e-170)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (b <= 1.3e-27)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (b <= 1.05e+45)
		tmp = Float64(a * Float64(x * Float64(Float64(Float64(y * z) / a) - t)));
	else
		tmp = Float64(b * Float64(c * Float64(Float64(Float64(a * i) / c) - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((a * b) - (y * j));
	tmp = 0.0;
	if (b <= -6.4e+227)
		tmp = b * ((a * i) - (z * c));
	elseif (b <= -9.2e+151)
		tmp = t_1;
	elseif (b <= -4.8e+27)
		tmp = z * ((x * y) - (b * c));
	elseif (b <= -2.15e-94)
		tmp = t_1;
	elseif (b <= -1.26e-170)
		tmp = y * ((x * z) - (i * j));
	elseif (b <= 1.3e-27)
		tmp = t * ((c * j) - (x * a));
	elseif (b <= 1.05e+45)
		tmp = a * (x * (((y * z) / a) - t));
	else
		tmp = b * (c * (((a * i) / c) - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.4e+227], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -9.2e+151], t$95$1, If[LessEqual[b, -4.8e+27], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.15e-94], t$95$1, If[LessEqual[b, -1.26e-170], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.3e-27], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.05e+45], N[(a * N[(x * N[(N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(c * N[(N[(N[(a * i), $MachinePrecision] / c), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -6.39999999999999975e227

   1. Initial program 61.7%

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

   3. Taylor expanded in b around inf 84.0%

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

      1. *-commutative 84.0%

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

   5. Simplified 84.0%

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

   if -6.39999999999999975e227 < b < -9.2000000000000003e151 or -4.79999999999999995e27 < b < -2.1499999999999999e-94

   1. Initial program 61.8%

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

   3. Taylor expanded in i around inf 60.6%

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

      1. distribute-lft-out-- 60.6%

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

   5. Simplified 60.6%

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

   if -9.2000000000000003e151 < b < -4.79999999999999995e27

   1. Initial program 66.7%

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

   3. Taylor expanded in z around inf 75.5%

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

      1. *-commutative 75.5%

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

      2. *-commutative 75.5%

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

   5. Simplified 75.5%

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

   if -2.1499999999999999e-94 < b < -1.26e-170

   1. Initial program 75.2%

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

   3. Taylor expanded in y around inf 53.3%

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

      1. +-commutative 53.3%

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

      2. mul-1-neg 53.3%

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

      3. unsub-neg 53.3%

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

   5. Simplified 53.3%

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

   if -1.26e-170 < b < 1.30000000000000009e-27

   1. Initial program 73.1%

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

   3. Taylor expanded in z around inf 71.3%

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

   4. Taylor expanded in t around inf 56.9%

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

      1. +-commutative 56.9%

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

      2. mul-1-neg 56.9%

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

      3. unsub-neg 56.9%

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

      4. *-commutative 56.9%

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

   6. Simplified 56.9%

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

   if 1.30000000000000009e-27 < b < 1.04999999999999997e45

   1. Initial program 67.3%

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

   3. Taylor expanded in j around 0 58.5%

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

   4. Taylor expanded in a around -inf 63.4%

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

      1. mul-1-neg 63.4%

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

      2. *-commutative 63.4%

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

      3. distribute-rgt-neg-in 63.4%

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

   6. Simplified 63.4%

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

   7. Taylor expanded in x around inf 54.2%

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

   if 1.04999999999999997e45 < b

   1. Initial program 71.7%

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

   3. Taylor expanded in b around inf 76.8%

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

      1. *-commutative 76.8%

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

   5. Simplified 76.8%

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

   6. Taylor expanded in c around inf 78.8%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.4 \cdot 10^{+227}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -9.2 \cdot 10^{+151}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq -4.8 \cdot 10^{+27}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq -2.15 \cdot 10^{-94}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq -1.26 \cdot 10^{-170}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{-27}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+45}:\\ \;\;\;\;a \cdot \left(x \cdot \left(\frac{y \cdot z}{a} - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(c \cdot \left(\frac{a \cdot i}{c} - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 30.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ t_2 := c \cdot \left(t \cdot j\right)\\ t_3 := \left(z \cdot c\right) \cdot \left(-b\right)\\ t_4 := b \cdot \left(a \cdot i\right)\\ \mathbf{if}\;i \leq -4500000000:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;i \leq -4.3 \cdot 10^{-125}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq -1.25 \cdot 10^{-227}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;i \leq -1.4 \cdot 10^{-259}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 1.4 \cdot 10^{-229}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq 2.7 \cdot 10^{-125}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 1.65 \cdot 10^{-63}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;i \leq 4.2 \cdot 10^{+85}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* x y)))
        (t_2 (* c (* t j)))
        (t_3 (* (* z c) (- b)))
        (t_4 (* b (* a i))))
   (if (<= i -4500000000.0)
     t_4
     (if (<= i -4.3e-125)
       (* x (* y z))
       (if (<= i -1.25e-227)
         t_3
         (if (<= i -1.4e-259)
           t_1
           (if (<= i 1.4e-229)
             t_2
             (if (<= i 2.7e-125)
               t_1
               (if (<= i 1.65e-63) t_3 (if (<= i 4.2e+85) t_2 t_4))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (x * y);
	double t_2 = c * (t * j);
	double t_3 = (z * c) * -b;
	double t_4 = b * (a * i);
	double tmp;
	if (i <= -4500000000.0) {
		tmp = t_4;
	} else if (i <= -4.3e-125) {
		tmp = x * (y * z);
	} else if (i <= -1.25e-227) {
		tmp = t_3;
	} else if (i <= -1.4e-259) {
		tmp = t_1;
	} else if (i <= 1.4e-229) {
		tmp = t_2;
	} else if (i <= 2.7e-125) {
		tmp = t_1;
	} else if (i <= 1.65e-63) {
		tmp = t_3;
	} else if (i <= 4.2e+85) {
		tmp = t_2;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = z * (x * y)
    t_2 = c * (t * j)
    t_3 = (z * c) * -b
    t_4 = b * (a * i)
    if (i <= (-4500000000.0d0)) then
        tmp = t_4
    else if (i <= (-4.3d-125)) then
        tmp = x * (y * z)
    else if (i <= (-1.25d-227)) then
        tmp = t_3
    else if (i <= (-1.4d-259)) then
        tmp = t_1
    else if (i <= 1.4d-229) then
        tmp = t_2
    else if (i <= 2.7d-125) then
        tmp = t_1
    else if (i <= 1.65d-63) then
        tmp = t_3
    else if (i <= 4.2d+85) then
        tmp = t_2
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (x * y);
	double t_2 = c * (t * j);
	double t_3 = (z * c) * -b;
	double t_4 = b * (a * i);
	double tmp;
	if (i <= -4500000000.0) {
		tmp = t_4;
	} else if (i <= -4.3e-125) {
		tmp = x * (y * z);
	} else if (i <= -1.25e-227) {
		tmp = t_3;
	} else if (i <= -1.4e-259) {
		tmp = t_1;
	} else if (i <= 1.4e-229) {
		tmp = t_2;
	} else if (i <= 2.7e-125) {
		tmp = t_1;
	} else if (i <= 1.65e-63) {
		tmp = t_3;
	} else if (i <= 4.2e+85) {
		tmp = t_2;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (x * y)
	t_2 = c * (t * j)
	t_3 = (z * c) * -b
	t_4 = b * (a * i)
	tmp = 0
	if i <= -4500000000.0:
		tmp = t_4
	elif i <= -4.3e-125:
		tmp = x * (y * z)
	elif i <= -1.25e-227:
		tmp = t_3
	elif i <= -1.4e-259:
		tmp = t_1
	elif i <= 1.4e-229:
		tmp = t_2
	elif i <= 2.7e-125:
		tmp = t_1
	elif i <= 1.65e-63:
		tmp = t_3
	elif i <= 4.2e+85:
		tmp = t_2
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(x * y))
	t_2 = Float64(c * Float64(t * j))
	t_3 = Float64(Float64(z * c) * Float64(-b))
	t_4 = Float64(b * Float64(a * i))
	tmp = 0.0
	if (i <= -4500000000.0)
		tmp = t_4;
	elseif (i <= -4.3e-125)
		tmp = Float64(x * Float64(y * z));
	elseif (i <= -1.25e-227)
		tmp = t_3;
	elseif (i <= -1.4e-259)
		tmp = t_1;
	elseif (i <= 1.4e-229)
		tmp = t_2;
	elseif (i <= 2.7e-125)
		tmp = t_1;
	elseif (i <= 1.65e-63)
		tmp = t_3;
	elseif (i <= 4.2e+85)
		tmp = t_2;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * (x * y);
	t_2 = c * (t * j);
	t_3 = (z * c) * -b;
	t_4 = b * (a * i);
	tmp = 0.0;
	if (i <= -4500000000.0)
		tmp = t_4;
	elseif (i <= -4.3e-125)
		tmp = x * (y * z);
	elseif (i <= -1.25e-227)
		tmp = t_3;
	elseif (i <= -1.4e-259)
		tmp = t_1;
	elseif (i <= 1.4e-229)
		tmp = t_2;
	elseif (i <= 2.7e-125)
		tmp = t_1;
	elseif (i <= 1.65e-63)
		tmp = t_3;
	elseif (i <= 4.2e+85)
		tmp = t_2;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z * c), $MachinePrecision] * (-b)), $MachinePrecision]}, Block[{t$95$4 = N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -4500000000.0], t$95$4, If[LessEqual[i, -4.3e-125], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.25e-227], t$95$3, If[LessEqual[i, -1.4e-259], t$95$1, If[LessEqual[i, 1.4e-229], t$95$2, If[LessEqual[i, 2.7e-125], t$95$1, If[LessEqual[i, 1.65e-63], t$95$3, If[LessEqual[i, 4.2e+85], t$95$2, t$95$4]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -4.5e9 or 4.2000000000000002e85 < i

   1. Initial program 58.9%

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

   3. Taylor expanded in b around inf 50.8%

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

      1. *-commutative 50.8%

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

   5. Simplified 50.8%

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

   6. Taylor expanded in i around inf 43.7%

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

   if -4.5e9 < i < -4.3000000000000002e-125

   1. Initial program 92.0%

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

   3. Taylor expanded in j around 0 80.6%

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

   4. Taylor expanded in a around -inf 73.2%

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

      1. mul-1-neg 73.2%

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

      2. *-commutative 73.2%

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

      3. distribute-rgt-neg-in 73.2%

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

   6. Simplified 73.1%

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

   7. Taylor expanded in y around inf 42.1%

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

      1. *-commutative 42.1%

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

   9. Simplified 42.1%

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

   if -4.3000000000000002e-125 < i < -1.2499999999999999e-227 or 2.6999999999999998e-125 < i < 1.64999999999999997e-63

   1. Initial program 72.5%

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

   3. Taylor expanded in b around inf 47.6%

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

      1. *-commutative 47.6%

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

   5. Simplified 47.6%

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

   6. Taylor expanded in i around 0 47.5%

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

      1. associate-*r* 47.5%

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

      2. neg-mul-1 47.5%

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

      3. *-commutative 47.5%

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

   8. Simplified 47.5%

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

   if -1.2499999999999999e-227 < i < -1.4e-259 or 1.39999999999999995e-229 < i < 2.6999999999999998e-125

   1. Initial program 77.3%

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

   3. Taylor expanded in z around inf 53.5%

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

      1. *-commutative 53.5%

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

      2. *-commutative 53.5%

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

   5. Simplified 53.5%

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

   6. Taylor expanded in y around inf 48.0%

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

   if -1.4e-259 < i < 1.39999999999999995e-229 or 1.64999999999999997e-63 < i < 4.2000000000000002e85

   1. Initial program 73.9%

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

   3. Taylor expanded in t around -inf 72.3%

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

   5. Simplified 81.1%

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

   6. Taylor expanded in c around inf 69.3%

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

      1. associate-*r/ 69.3%

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

      2. associate-*r* 69.3%

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

      3. neg-mul-1 69.3%

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

   8. Simplified 69.3%

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

   9. Taylor expanded in j around inf 38.2%

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

       1. *-commutative 38.2%

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

   11. Simplified 38.2%

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

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4500000000:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;i \leq -4.3 \cdot 10^{-125}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq -1.25 \cdot 10^{-227}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;i \leq -1.4 \cdot 10^{-259}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 1.4 \cdot 10^{-229}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;i \leq 2.7 \cdot 10^{-125}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 1.65 \cdot 10^{-63}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;i \leq 4.2 \cdot 10^{+85}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 50.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -5.5 \cdot 10^{+220}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.56 \cdot 10^{+209}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -8 \cdot 10^{+151}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{+27}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq -4.8 \cdot 10^{-97}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-169}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a)))) (t_2 (* b (- (* a i) (* z c)))))
   (if (<= b -5.5e+220)
     t_2
     (if (<= b -1.56e+209)
       t_1
       (if (<= b -8e+151)
         t_2
         (if (<= b -4.5e+27)
           (* z (- (* x y) (* b c)))
           (if (<= b -4.8e-97)
             (* a (- (* b i) (* x t)))
             (if (<= b -2e-169)
               (* y (- (* x z) (* i j)))
               (if (<= b 1.7e-15) 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 = t * ((c * j) - (x * a));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -5.5e+220) {
		tmp = t_2;
	} else if (b <= -1.56e+209) {
		tmp = t_1;
	} else if (b <= -8e+151) {
		tmp = t_2;
	} else if (b <= -4.5e+27) {
		tmp = z * ((x * y) - (b * c));
	} else if (b <= -4.8e-97) {
		tmp = a * ((b * i) - (x * t));
	} else if (b <= -2e-169) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 1.7e-15) {
		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 = t * ((c * j) - (x * a))
    t_2 = b * ((a * i) - (z * c))
    if (b <= (-5.5d+220)) then
        tmp = t_2
    else if (b <= (-1.56d+209)) then
        tmp = t_1
    else if (b <= (-8d+151)) then
        tmp = t_2
    else if (b <= (-4.5d+27)) then
        tmp = z * ((x * y) - (b * c))
    else if (b <= (-4.8d-97)) then
        tmp = a * ((b * i) - (x * t))
    else if (b <= (-2d-169)) then
        tmp = y * ((x * z) - (i * j))
    else if (b <= 1.7d-15) 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 = t * ((c * j) - (x * a));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -5.5e+220) {
		tmp = t_2;
	} else if (b <= -1.56e+209) {
		tmp = t_1;
	} else if (b <= -8e+151) {
		tmp = t_2;
	} else if (b <= -4.5e+27) {
		tmp = z * ((x * y) - (b * c));
	} else if (b <= -4.8e-97) {
		tmp = a * ((b * i) - (x * t));
	} else if (b <= -2e-169) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 1.7e-15) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -5.5e+220:
		tmp = t_2
	elif b <= -1.56e+209:
		tmp = t_1
	elif b <= -8e+151:
		tmp = t_2
	elif b <= -4.5e+27:
		tmp = z * ((x * y) - (b * c))
	elif b <= -4.8e-97:
		tmp = a * ((b * i) - (x * t))
	elif b <= -2e-169:
		tmp = y * ((x * z) - (i * j))
	elif b <= 1.7e-15:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -5.5e+220)
		tmp = t_2;
	elseif (b <= -1.56e+209)
		tmp = t_1;
	elseif (b <= -8e+151)
		tmp = t_2;
	elseif (b <= -4.5e+27)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (b <= -4.8e-97)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (b <= -2e-169)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (b <= 1.7e-15)
		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 = t * ((c * j) - (x * a));
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -5.5e+220)
		tmp = t_2;
	elseif (b <= -1.56e+209)
		tmp = t_1;
	elseif (b <= -8e+151)
		tmp = t_2;
	elseif (b <= -4.5e+27)
		tmp = z * ((x * y) - (b * c));
	elseif (b <= -4.8e-97)
		tmp = a * ((b * i) - (x * t));
	elseif (b <= -2e-169)
		tmp = y * ((x * z) - (i * j));
	elseif (b <= 1.7e-15)
		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[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.5e+220], t$95$2, If[LessEqual[b, -1.56e+209], t$95$1, If[LessEqual[b, -8e+151], t$95$2, If[LessEqual[b, -4.5e+27], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.8e-97], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2e-169], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.7e-15], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -5.4999999999999999e220 or -1.56e209 < b < -8.00000000000000014e151 or 1.7e-15 < b

   1. Initial program 69.4%

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

   3. Taylor expanded in b around inf 68.4%

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

      1. *-commutative 68.4%

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

   5. Simplified 68.4%

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

   if -5.4999999999999999e220 < b < -1.56e209 or -2.00000000000000004e-169 < b < 1.7e-15

   1. Initial program 69.3%

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

   3. Taylor expanded in z around inf 68.5%

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

   4. Taylor expanded in t around inf 57.7%

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

      1. +-commutative 57.7%

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

      2. mul-1-neg 57.7%

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

      3. unsub-neg 57.7%

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

      4. *-commutative 57.7%

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

   6. Simplified 57.7%

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

   if -8.00000000000000014e151 < b < -4.4999999999999999e27

   1. Initial program 66.7%

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

   3. Taylor expanded in z around inf 75.5%

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

      1. *-commutative 75.5%

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

      2. *-commutative 75.5%

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

   5. Simplified 75.5%

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

   if -4.4999999999999999e27 < b < -4.8e-97

   1. Initial program 70.0%

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

   3. Taylor expanded in a around inf 50.1%

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

      1. distribute-lft-out-- 50.1%

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

      2. *-commutative 50.1%

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

   5. Simplified 50.1%

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

   if -4.8e-97 < b < -2.00000000000000004e-169

   1. Initial program 73.7%

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

   3. Taylor expanded in y around inf 56.5%

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

      1. +-commutative 56.5%

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

      2. mul-1-neg 56.5%

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

      3. unsub-neg 56.5%

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

   5. Simplified 56.5%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{+220}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.56 \cdot 10^{+209}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq -8 \cdot 10^{+151}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{+27}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq -4.8 \cdot 10^{-97}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-169}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-15}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 53.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.55 \cdot 10^{+110}:\\ \;\;\;\;a \cdot \left(\frac{x \cdot \left(y \cdot z\right)}{a} - x \cdot t\right)\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{+27}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(b \cdot \frac{i}{t} - x\right)\\ \mathbf{elif}\;x \leq -2800000000000:\\ \;\;\;\;t \cdot \left(x \cdot \left(y \cdot \frac{z}{t} - a\right)\right)\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-251}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-7}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+28}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+80}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x -2.55e+110)
   (* a (- (/ (* x (* y z)) a) (* x t)))
   (if (<= x -9.2e+27)
     (* (* t a) (- (* b (/ i t)) x))
     (if (<= x -2800000000000.0)
       (* t (* x (- (* y (/ z t)) a)))
       (if (<= x 1.45e-251)
         (+ (* c (* t j)) (* b (- (* a i) (* z c))))
         (if (<= x 5e-7)
           (- (* j (- (* t c) (* y i))) (* b (* z c)))
           (if (<= x 1.6e+28)
             (* t (- (* c j) (* x a)))
             (if (<= x 7.2e+80)
               (* i (- (* a b) (* y j)))
               (* z (- (* x y) (* b 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 (x <= -2.55e+110) {
		tmp = a * (((x * (y * z)) / a) - (x * t));
	} else if (x <= -9.2e+27) {
		tmp = (t * a) * ((b * (i / t)) - x);
	} else if (x <= -2800000000000.0) {
		tmp = t * (x * ((y * (z / t)) - a));
	} else if (x <= 1.45e-251) {
		tmp = (c * (t * j)) + (b * ((a * i) - (z * c)));
	} else if (x <= 5e-7) {
		tmp = (j * ((t * c) - (y * i))) - (b * (z * c));
	} else if (x <= 1.6e+28) {
		tmp = t * ((c * j) - (x * a));
	} else if (x <= 7.2e+80) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = z * ((x * y) - (b * 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 (x <= (-2.55d+110)) then
        tmp = a * (((x * (y * z)) / a) - (x * t))
    else if (x <= (-9.2d+27)) then
        tmp = (t * a) * ((b * (i / t)) - x)
    else if (x <= (-2800000000000.0d0)) then
        tmp = t * (x * ((y * (z / t)) - a))
    else if (x <= 1.45d-251) then
        tmp = (c * (t * j)) + (b * ((a * i) - (z * c)))
    else if (x <= 5d-7) then
        tmp = (j * ((t * c) - (y * i))) - (b * (z * c))
    else if (x <= 1.6d+28) then
        tmp = t * ((c * j) - (x * a))
    else if (x <= 7.2d+80) then
        tmp = i * ((a * b) - (y * j))
    else
        tmp = z * ((x * y) - (b * 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 (x <= -2.55e+110) {
		tmp = a * (((x * (y * z)) / a) - (x * t));
	} else if (x <= -9.2e+27) {
		tmp = (t * a) * ((b * (i / t)) - x);
	} else if (x <= -2800000000000.0) {
		tmp = t * (x * ((y * (z / t)) - a));
	} else if (x <= 1.45e-251) {
		tmp = (c * (t * j)) + (b * ((a * i) - (z * c)));
	} else if (x <= 5e-7) {
		tmp = (j * ((t * c) - (y * i))) - (b * (z * c));
	} else if (x <= 1.6e+28) {
		tmp = t * ((c * j) - (x * a));
	} else if (x <= 7.2e+80) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if x <= -2.55e+110:
		tmp = a * (((x * (y * z)) / a) - (x * t))
	elif x <= -9.2e+27:
		tmp = (t * a) * ((b * (i / t)) - x)
	elif x <= -2800000000000.0:
		tmp = t * (x * ((y * (z / t)) - a))
	elif x <= 1.45e-251:
		tmp = (c * (t * j)) + (b * ((a * i) - (z * c)))
	elif x <= 5e-7:
		tmp = (j * ((t * c) - (y * i))) - (b * (z * c))
	elif x <= 1.6e+28:
		tmp = t * ((c * j) - (x * a))
	elif x <= 7.2e+80:
		tmp = i * ((a * b) - (y * j))
	else:
		tmp = z * ((x * y) - (b * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= -2.55e+110)
		tmp = Float64(a * Float64(Float64(Float64(x * Float64(y * z)) / a) - Float64(x * t)));
	elseif (x <= -9.2e+27)
		tmp = Float64(Float64(t * a) * Float64(Float64(b * Float64(i / t)) - x));
	elseif (x <= -2800000000000.0)
		tmp = Float64(t * Float64(x * Float64(Float64(y * Float64(z / t)) - a)));
	elseif (x <= 1.45e-251)
		tmp = Float64(Float64(c * Float64(t * j)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (x <= 5e-7)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) - Float64(b * Float64(z * c)));
	elseif (x <= 1.6e+28)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (x <= 7.2e+80)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	else
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (x <= -2.55e+110)
		tmp = a * (((x * (y * z)) / a) - (x * t));
	elseif (x <= -9.2e+27)
		tmp = (t * a) * ((b * (i / t)) - x);
	elseif (x <= -2800000000000.0)
		tmp = t * (x * ((y * (z / t)) - a));
	elseif (x <= 1.45e-251)
		tmp = (c * (t * j)) + (b * ((a * i) - (z * c)));
	elseif (x <= 5e-7)
		tmp = (j * ((t * c) - (y * i))) - (b * (z * c));
	elseif (x <= 1.6e+28)
		tmp = t * ((c * j) - (x * a));
	elseif (x <= 7.2e+80)
		tmp = i * ((a * b) - (y * j));
	else
		tmp = z * ((x * y) - (b * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, -2.55e+110], N[(a * N[(N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -9.2e+27], N[(N[(t * a), $MachinePrecision] * N[(N[(b * N[(i / t), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2800000000000.0], N[(t * N[(x * N[(N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.45e-251], N[(N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5e-7], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.6e+28], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.2e+80], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if x < -2.5500000000000001e110

   1. Initial program 72.4%

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

   3. Taylor expanded in j around 0 66.6%

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

   4. Taylor expanded in a around -inf 71.8%

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

      1. mul-1-neg 71.8%

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

      2. *-commutative 71.8%

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

      3. distribute-rgt-neg-in 71.8%

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

   6. Simplified 72.0%

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

   7. Taylor expanded in b around 0 74.5%

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

   if -2.5500000000000001e110 < x < -9.2000000000000002e27

   1. Initial program 86.8%

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

   3. Taylor expanded in t around -inf 78.7%

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

   5. Simplified 70.0%

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

   6. Taylor expanded in a around -inf 56.6%

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

      1. associate-*r* 60.7%

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

      2. *-commutative 60.7%

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

      3. +-commutative 60.7%

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

      4. mul-1-neg 60.7%

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

      5. unsub-neg 60.7%

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

      6. associate-/l* 64.8%

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

   8. Simplified 64.8%

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

   if -9.2000000000000002e27 < x < -2.8e12

   1. Initial program 74.6%

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

   3. Taylor expanded in t around -inf 74.4%

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

   5. Simplified 75.0%

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

   6. Taylor expanded in x around inf 79.8%

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

      1. associate-*r* 79.8%

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

      2. neg-mul-1 79.8%

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

      3. associate-/l* 80.4%

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

   8. Simplified 80.4%

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

   if -2.8e12 < x < 1.45e-251

   1. Initial program 67.1%

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

   3. Taylor expanded in z around inf 77.1%

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

   4. Taylor expanded in x around 0 66.8%

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

      1. *-commutative 66.8%

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

      2. *-commutative 66.8%

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

      3. *-commutative 66.8%

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

   6. Simplified 66.8%

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

   7. Taylor expanded in t around inf 65.7%

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

      1. *-commutative 65.7%

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

   9. Simplified 65.7%

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

   if 1.45e-251 < x < 4.99999999999999977e-7

   1. Initial program 69.5%

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

   3. Taylor expanded in z around inf 80.4%

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

   4. Taylor expanded in x around 0 81.2%

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

      1. *-commutative 81.2%

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

      2. *-commutative 81.2%

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

      3. *-commutative 81.2%

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

   6. Simplified 81.2%

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

   7. Taylor expanded in z around inf 71.9%

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

   if 4.99999999999999977e-7 < x < 1.6e28

   1. Initial program 84.3%

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

   3. Taylor expanded in z around inf 70.4%

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

   4. Taylor expanded in t around inf 77.2%

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

      1. +-commutative 77.2%

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

      2. mul-1-neg 77.2%

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

      3. unsub-neg 77.2%

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

      4. *-commutative 77.2%

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

   6. Simplified 77.2%

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

   if 1.6e28 < x < 7.1999999999999999e80

   1. Initial program 59.1%

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

   3. Taylor expanded in i around inf 68.2%

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

      1. distribute-lft-out-- 68.2%

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

   5. Simplified 68.2%

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

   if 7.1999999999999999e80 < x

   1. Initial program 58.6%

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

   3. Taylor expanded in z around inf 63.4%

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

      1. *-commutative 63.4%

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

      2. *-commutative 63.4%

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

   5. Simplified 63.4%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.55 \cdot 10^{+110}:\\ \;\;\;\;a \cdot \left(\frac{x \cdot \left(y \cdot z\right)}{a} - x \cdot t\right)\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{+27}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(b \cdot \frac{i}{t} - x\right)\\ \mathbf{elif}\;x \leq -2800000000000:\\ \;\;\;\;t \cdot \left(x \cdot \left(y \cdot \frac{z}{t} - a\right)\right)\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-251}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-7}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+28}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+80}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 53.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;x \leq -2.4 \cdot 10^{+110}:\\ \;\;\;\;a \cdot \left(\frac{t\_1}{a} - x \cdot t\right)\\ \mathbf{elif}\;x \leq -4.7 \cdot 10^{+26}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(b \cdot \frac{i}{t} - x\right)\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-23}:\\ \;\;\;\;t\_1 + t\_2\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-257}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) + t\_2\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-6}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+28}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+82}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))) (t_2 (* b (- (* a i) (* z c)))))
   (if (<= x -2.4e+110)
     (* a (- (/ t_1 a) (* x t)))
     (if (<= x -4.7e+26)
       (* (* t a) (- (* b (/ i t)) x))
       (if (<= x -2e-23)
         (+ t_1 t_2)
         (if (<= x 3e-257)
           (+ (* c (* t j)) t_2)
           (if (<= x 1.65e-6)
             (- (* j (- (* t c) (* y i))) (* b (* z c)))
             (if (<= x 3.5e+28)
               (* t (- (* c j) (* x a)))
               (if (<= x 4.6e+82)
                 (* i (- (* a b) (* y j)))
                 (* z (- (* x y) (* b 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);
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (x <= -2.4e+110) {
		tmp = a * ((t_1 / a) - (x * t));
	} else if (x <= -4.7e+26) {
		tmp = (t * a) * ((b * (i / t)) - x);
	} else if (x <= -2e-23) {
		tmp = t_1 + t_2;
	} else if (x <= 3e-257) {
		tmp = (c * (t * j)) + t_2;
	} else if (x <= 1.65e-6) {
		tmp = (j * ((t * c) - (y * i))) - (b * (z * c));
	} else if (x <= 3.5e+28) {
		tmp = t * ((c * j) - (x * a));
	} else if (x <= 4.6e+82) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (y * z)
    t_2 = b * ((a * i) - (z * c))
    if (x <= (-2.4d+110)) then
        tmp = a * ((t_1 / a) - (x * t))
    else if (x <= (-4.7d+26)) then
        tmp = (t * a) * ((b * (i / t)) - x)
    else if (x <= (-2d-23)) then
        tmp = t_1 + t_2
    else if (x <= 3d-257) then
        tmp = (c * (t * j)) + t_2
    else if (x <= 1.65d-6) then
        tmp = (j * ((t * c) - (y * i))) - (b * (z * c))
    else if (x <= 3.5d+28) then
        tmp = t * ((c * j) - (x * a))
    else if (x <= 4.6d+82) then
        tmp = i * ((a * b) - (y * j))
    else
        tmp = z * ((x * y) - (b * 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);
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (x <= -2.4e+110) {
		tmp = a * ((t_1 / a) - (x * t));
	} else if (x <= -4.7e+26) {
		tmp = (t * a) * ((b * (i / t)) - x);
	} else if (x <= -2e-23) {
		tmp = t_1 + t_2;
	} else if (x <= 3e-257) {
		tmp = (c * (t * j)) + t_2;
	} else if (x <= 1.65e-6) {
		tmp = (j * ((t * c) - (y * i))) - (b * (z * c));
	} else if (x <= 3.5e+28) {
		tmp = t * ((c * j) - (x * a));
	} else if (x <= 4.6e+82) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if x <= -2.4e+110:
		tmp = a * ((t_1 / a) - (x * t))
	elif x <= -4.7e+26:
		tmp = (t * a) * ((b * (i / t)) - x)
	elif x <= -2e-23:
		tmp = t_1 + t_2
	elif x <= 3e-257:
		tmp = (c * (t * j)) + t_2
	elif x <= 1.65e-6:
		tmp = (j * ((t * c) - (y * i))) - (b * (z * c))
	elif x <= 3.5e+28:
		tmp = t * ((c * j) - (x * a))
	elif x <= 4.6e+82:
		tmp = i * ((a * b) - (y * j))
	else:
		tmp = z * ((x * y) - (b * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(y * z))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (x <= -2.4e+110)
		tmp = Float64(a * Float64(Float64(t_1 / a) - Float64(x * t)));
	elseif (x <= -4.7e+26)
		tmp = Float64(Float64(t * a) * Float64(Float64(b * Float64(i / t)) - x));
	elseif (x <= -2e-23)
		tmp = Float64(t_1 + t_2);
	elseif (x <= 3e-257)
		tmp = Float64(Float64(c * Float64(t * j)) + t_2);
	elseif (x <= 1.65e-6)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) - Float64(b * Float64(z * c)));
	elseif (x <= 3.5e+28)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (x <= 4.6e+82)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	else
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * 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_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (x <= -2.4e+110)
		tmp = a * ((t_1 / a) - (x * t));
	elseif (x <= -4.7e+26)
		tmp = (t * a) * ((b * (i / t)) - x);
	elseif (x <= -2e-23)
		tmp = t_1 + t_2;
	elseif (x <= 3e-257)
		tmp = (c * (t * j)) + t_2;
	elseif (x <= 1.65e-6)
		tmp = (j * ((t * c) - (y * i))) - (b * (z * c));
	elseif (x <= 3.5e+28)
		tmp = t * ((c * j) - (x * a));
	elseif (x <= 4.6e+82)
		tmp = i * ((a * b) - (y * j));
	else
		tmp = z * ((x * y) - (b * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.4e+110], N[(a * N[(N[(t$95$1 / a), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.7e+26], N[(N[(t * a), $MachinePrecision] * N[(N[(b * N[(i / t), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2e-23], N[(t$95$1 + t$95$2), $MachinePrecision], If[LessEqual[x, 3e-257], N[(N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[x, 1.65e-6], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.5e+28], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.6e+82], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if x < -2.40000000000000012e110

   1. Initial program 72.4%

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

   3. Taylor expanded in j around 0 66.6%

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

   4. Taylor expanded in a around -inf 71.8%

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

      1. mul-1-neg 71.8%

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

      2. *-commutative 71.8%

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

      3. distribute-rgt-neg-in 71.8%

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

   6. Simplified 72.0%

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

   7. Taylor expanded in b around 0 74.5%

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

   if -2.40000000000000012e110 < x < -4.6999999999999998e26

   1. Initial program 87.4%

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

   3. Taylor expanded in t around -inf 79.6%

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

   5. Simplified 71.3%

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

   6. Taylor expanded in a around -inf 58.4%

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

      1. associate-*r* 62.3%

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

      2. *-commutative 62.3%

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

      3. +-commutative 62.3%

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

      4. mul-1-neg 62.3%

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

      5. unsub-neg 62.3%

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

      6. associate-/l* 66.3%

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

   8. Simplified 66.3%

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

   if -4.6999999999999998e26 < x < -1.99999999999999992e-23

   1. Initial program 70.7%

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

   3. Taylor expanded in j around 0 61.0%

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

   4. Taylor expanded in t around 0 60.8%

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

      1. *-commutative 60.8%

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

   6. Simplified 60.8%

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

   if -1.99999999999999992e-23 < x < 2.9999999999999999e-257

   1. Initial program 66.5%

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

   3. Taylor expanded in z around inf 76.3%

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

   4. Taylor expanded in x around 0 69.1%

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

      1. *-commutative 69.1%

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

      2. *-commutative 69.1%

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

      3. *-commutative 69.1%

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

   6. Simplified 69.1%

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

   7. Taylor expanded in t around inf 67.9%

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

      1. *-commutative 67.9%

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

   9. Simplified 67.9%

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

   if 2.9999999999999999e-257 < x < 1.65000000000000008e-6

   1. Initial program 69.5%

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

   3. Taylor expanded in z around inf 80.4%

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

   4. Taylor expanded in x around 0 81.2%

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

      1. *-commutative 81.2%

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

      2. *-commutative 81.2%

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

      3. *-commutative 81.2%

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

   6. Simplified 81.2%

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

   7. Taylor expanded in z around inf 71.9%

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

   if 1.65000000000000008e-6 < x < 3.5e28

   1. Initial program 84.3%

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

   3. Taylor expanded in z around inf 70.4%

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

   4. Taylor expanded in t around inf 77.2%

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

      1. +-commutative 77.2%

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

      2. mul-1-neg 77.2%

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

      3. unsub-neg 77.2%

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

      4. *-commutative 77.2%

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

   6. Simplified 77.2%

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

   if 3.5e28 < x < 4.59999999999999976e82

   1. Initial program 59.1%

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

   3. Taylor expanded in i around inf 68.2%

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

      1. distribute-lft-out-- 68.2%

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

   5. Simplified 68.2%

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

   if 4.59999999999999976e82 < x

   1. Initial program 58.6%

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

   3. Taylor expanded in z around inf 63.4%

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

      1. *-commutative 63.4%

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

      2. *-commutative 63.4%

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

   5. Simplified 63.4%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+110}:\\ \;\;\;\;a \cdot \left(\frac{x \cdot \left(y \cdot z\right)}{a} - x \cdot t\right)\\ \mathbf{elif}\;x \leq -4.7 \cdot 10^{+26}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(b \cdot \frac{i}{t} - x\right)\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-23}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-257}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-6}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+28}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+82}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 57.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;b \leq -1.7 \cdot 10^{+109}:\\ \;\;\;\;t\_1 + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{-95}:\\ \;\;\;\;a \cdot \left(b \cdot i - \frac{z \cdot \left(b \cdot c - x \cdot y\right)}{a}\right)\\ \mathbf{elif}\;b \leq -5.9 \cdot 10^{-117}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-27}:\\ \;\;\;\;t \cdot \left(c \cdot j + \left(\frac{t\_1}{t} - x \cdot a\right)\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+44}:\\ \;\;\;\;a \cdot \left(\frac{t\_1}{a} - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(c \cdot \left(\frac{a \cdot i}{c} - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))))
   (if (<= b -1.7e+109)
     (+ t_1 (* b (- (* a i) (* z c))))
     (if (<= b -1.6e-95)
       (* a (- (* b i) (/ (* z (- (* b c) (* x y))) a)))
       (if (<= b -5.9e-117)
         (- (* x (- (* y z) (* t a))) (* b (* z c)))
         (if (<= b 1.9e-27)
           (* t (+ (* c j) (- (/ t_1 t) (* x a))))
           (if (<= b 7.5e+44)
             (* a (- (/ t_1 a) (* x t)))
             (* b (* c (- (/ (* a i) c) 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 = x * (y * z);
	double tmp;
	if (b <= -1.7e+109) {
		tmp = t_1 + (b * ((a * i) - (z * c)));
	} else if (b <= -1.6e-95) {
		tmp = a * ((b * i) - ((z * ((b * c) - (x * y))) / a));
	} else if (b <= -5.9e-117) {
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c));
	} else if (b <= 1.9e-27) {
		tmp = t * ((c * j) + ((t_1 / t) - (x * a)));
	} else if (b <= 7.5e+44) {
		tmp = a * ((t_1 / a) - (x * t));
	} else {
		tmp = b * (c * (((a * i) / c) - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y * z)
    if (b <= (-1.7d+109)) then
        tmp = t_1 + (b * ((a * i) - (z * c)))
    else if (b <= (-1.6d-95)) then
        tmp = a * ((b * i) - ((z * ((b * c) - (x * y))) / a))
    else if (b <= (-5.9d-117)) then
        tmp = (x * ((y * z) - (t * a))) - (b * (z * c))
    else if (b <= 1.9d-27) then
        tmp = t * ((c * j) + ((t_1 / t) - (x * a)))
    else if (b <= 7.5d+44) then
        tmp = a * ((t_1 / a) - (x * t))
    else
        tmp = b * (c * (((a * i) / c) - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double tmp;
	if (b <= -1.7e+109) {
		tmp = t_1 + (b * ((a * i) - (z * c)));
	} else if (b <= -1.6e-95) {
		tmp = a * ((b * i) - ((z * ((b * c) - (x * y))) / a));
	} else if (b <= -5.9e-117) {
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c));
	} else if (b <= 1.9e-27) {
		tmp = t * ((c * j) + ((t_1 / t) - (x * a)));
	} else if (b <= 7.5e+44) {
		tmp = a * ((t_1 / a) - (x * t));
	} else {
		tmp = b * (c * (((a * i) / c) - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	tmp = 0
	if b <= -1.7e+109:
		tmp = t_1 + (b * ((a * i) - (z * c)))
	elif b <= -1.6e-95:
		tmp = a * ((b * i) - ((z * ((b * c) - (x * y))) / a))
	elif b <= -5.9e-117:
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c))
	elif b <= 1.9e-27:
		tmp = t * ((c * j) + ((t_1 / t) - (x * a)))
	elif b <= 7.5e+44:
		tmp = a * ((t_1 / a) - (x * t))
	else:
		tmp = b * (c * (((a * i) / c) - z))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (b <= -1.7e+109)
		tmp = Float64(t_1 + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (b <= -1.6e-95)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(Float64(z * Float64(Float64(b * c) - Float64(x * y))) / a)));
	elseif (b <= -5.9e-117)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(z * c)));
	elseif (b <= 1.9e-27)
		tmp = Float64(t * Float64(Float64(c * j) + Float64(Float64(t_1 / t) - Float64(x * a))));
	elseif (b <= 7.5e+44)
		tmp = Float64(a * Float64(Float64(t_1 / a) - Float64(x * t)));
	else
		tmp = Float64(b * Float64(c * Float64(Float64(Float64(a * i) / c) - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (y * z);
	tmp = 0.0;
	if (b <= -1.7e+109)
		tmp = t_1 + (b * ((a * i) - (z * c)));
	elseif (b <= -1.6e-95)
		tmp = a * ((b * i) - ((z * ((b * c) - (x * y))) / a));
	elseif (b <= -5.9e-117)
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c));
	elseif (b <= 1.9e-27)
		tmp = t * ((c * j) + ((t_1 / t) - (x * a)));
	elseif (b <= 7.5e+44)
		tmp = a * ((t_1 / a) - (x * t));
	else
		tmp = b * (c * (((a * i) / c) - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.7e+109], N[(t$95$1 + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.6e-95], N[(a * N[(N[(b * i), $MachinePrecision] - N[(N[(z * N[(N[(b * c), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -5.9e-117], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.9e-27], N[(t * N[(N[(c * j), $MachinePrecision] + N[(N[(t$95$1 / t), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.5e+44], N[(a * N[(N[(t$95$1 / a), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(c * N[(N[(N[(a * i), $MachinePrecision] / c), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -1.70000000000000003e109

   1. Initial program 59.2%

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

   3. Taylor expanded in j around 0 59.3%

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

   4. Taylor expanded in t around 0 72.1%

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

      1. *-commutative 72.1%

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

   6. Simplified 72.1%

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

   if -1.70000000000000003e109 < b < -1.5999999999999999e-95

   1. Initial program 66.9%

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

   3. Taylor expanded in j around 0 59.4%

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

   4. Taylor expanded in a around -inf 59.3%

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

      1. mul-1-neg 59.3%

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

      2. *-commutative 59.3%

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

      3. distribute-rgt-neg-in 59.3%

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

   6. Simplified 73.5%

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

   7. Taylor expanded in t around 0 68.9%

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

   if -1.5999999999999999e-95 < b < -5.9000000000000003e-117

   1. Initial program 79.4%

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

   3. Taylor expanded in j around 0 99.4%

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

   4. Taylor expanded in c around inf 99.4%

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

      1. *-commutative 99.4%

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

   6. Simplified 99.4%

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

   if -5.9000000000000003e-117 < b < 1.9e-27

   1. Initial program 73.1%

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

   3. Taylor expanded in t around -inf 71.0%

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

   5. Simplified 77.2%

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

   6. Taylor expanded in x around inf 68.4%

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

   if 1.9e-27 < b < 7.50000000000000027e44

   1. Initial program 67.3%

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

   3. Taylor expanded in j around 0 58.5%

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

   4. Taylor expanded in a around -inf 63.4%

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

      1. mul-1-neg 63.4%

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

      2. *-commutative 63.4%

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

      3. distribute-rgt-neg-in 63.4%

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

   6. Simplified 63.4%

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

   7. Taylor expanded in b around 0 59.0%

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

   if 7.50000000000000027e44 < b

   1. Initial program 71.7%

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

   3. Taylor expanded in b around inf 76.8%

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

      1. *-commutative 76.8%

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

   5. Simplified 76.8%

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

   6. Taylor expanded in c around inf 78.8%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.7 \cdot 10^{+109}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{-95}:\\ \;\;\;\;a \cdot \left(b \cdot i - \frac{z \cdot \left(b \cdot c - x \cdot y\right)}{a}\right)\\ \mathbf{elif}\;b \leq -5.9 \cdot 10^{-117}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-27}:\\ \;\;\;\;t \cdot \left(c \cdot j + \left(\frac{x \cdot \left(y \cdot z\right)}{t} - x \cdot a\right)\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+44}:\\ \;\;\;\;a \cdot \left(\frac{x \cdot \left(y \cdot z\right)}{a} - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(c \cdot \left(\frac{a \cdot i}{c} - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 29.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+39}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-85}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-150}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-294}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-201}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+79}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -7.2e+39)
   (* c (* t j))
   (if (<= t -1e-85)
     (* x (* y z))
     (if (<= t -4.2e-150)
       (* i (* j (- y)))
       (if (<= t -7.5e-294)
         (* y (* x z))
         (if (<= t 3.1e-201)
           (* a (* b i))
           (if (<= t 1.45e+79) (* z (* x y)) (* t (* x (- a))))))))))

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 <= -7.2e+39) {
		tmp = c * (t * j);
	} else if (t <= -1e-85) {
		tmp = x * (y * z);
	} else if (t <= -4.2e-150) {
		tmp = i * (j * -y);
	} else if (t <= -7.5e-294) {
		tmp = y * (x * z);
	} else if (t <= 3.1e-201) {
		tmp = a * (b * i);
	} else if (t <= 1.45e+79) {
		tmp = z * (x * y);
	} else {
		tmp = t * (x * -a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (t <= (-7.2d+39)) then
        tmp = c * (t * j)
    else if (t <= (-1d-85)) then
        tmp = x * (y * z)
    else if (t <= (-4.2d-150)) then
        tmp = i * (j * -y)
    else if (t <= (-7.5d-294)) then
        tmp = y * (x * z)
    else if (t <= 3.1d-201) then
        tmp = a * (b * i)
    else if (t <= 1.45d+79) then
        tmp = z * (x * y)
    else
        tmp = t * (x * -a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -7.2e+39) {
		tmp = c * (t * j);
	} else if (t <= -1e-85) {
		tmp = x * (y * z);
	} else if (t <= -4.2e-150) {
		tmp = i * (j * -y);
	} else if (t <= -7.5e-294) {
		tmp = y * (x * z);
	} else if (t <= 3.1e-201) {
		tmp = a * (b * i);
	} else if (t <= 1.45e+79) {
		tmp = z * (x * y);
	} else {
		tmp = t * (x * -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -7.2e+39:
		tmp = c * (t * j)
	elif t <= -1e-85:
		tmp = x * (y * z)
	elif t <= -4.2e-150:
		tmp = i * (j * -y)
	elif t <= -7.5e-294:
		tmp = y * (x * z)
	elif t <= 3.1e-201:
		tmp = a * (b * i)
	elif t <= 1.45e+79:
		tmp = z * (x * y)
	else:
		tmp = t * (x * -a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -7.2e+39)
		tmp = Float64(c * Float64(t * j));
	elseif (t <= -1e-85)
		tmp = Float64(x * Float64(y * z));
	elseif (t <= -4.2e-150)
		tmp = Float64(i * Float64(j * Float64(-y)));
	elseif (t <= -7.5e-294)
		tmp = Float64(y * Float64(x * z));
	elseif (t <= 3.1e-201)
		tmp = Float64(a * Float64(b * i));
	elseif (t <= 1.45e+79)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = Float64(t * Float64(x * Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -7.2e+39)
		tmp = c * (t * j);
	elseif (t <= -1e-85)
		tmp = x * (y * z);
	elseif (t <= -4.2e-150)
		tmp = i * (j * -y);
	elseif (t <= -7.5e-294)
		tmp = y * (x * z);
	elseif (t <= 3.1e-201)
		tmp = a * (b * i);
	elseif (t <= 1.45e+79)
		tmp = z * (x * y);
	else
		tmp = t * (x * -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -7.2e+39], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1e-85], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.2e-150], N[(i * N[(j * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -7.5e-294], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.1e-201], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.45e+79], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -7.19999999999999969e39

   1. Initial program 56.2%

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

   3. Taylor expanded in t around -inf 64.1%

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

   5. Simplified 68.1%

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

   6. Taylor expanded in c around inf 70.9%

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

      1. associate-*r/ 70.9%

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

      2. associate-*r* 70.9%

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

      3. neg-mul-1 70.9%

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

   8. Simplified 70.9%

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

   9. Taylor expanded in j around inf 44.5%

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

       1. *-commutative 44.5%

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

   11. Simplified 44.5%

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

   if -7.19999999999999969e39 < t < -9.9999999999999998e-86

   1. Initial program 71.8%

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

   3. Taylor expanded in j around 0 68.4%

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

   4. Taylor expanded in a around -inf 72.3%

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

      1. mul-1-neg 72.3%

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

      2. *-commutative 72.3%

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

      3. distribute-rgt-neg-in 72.3%

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

   6. Simplified 72.3%

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

   7. Taylor expanded in y around inf 46.3%

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

      1. *-commutative 46.3%

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

   9. Simplified 46.3%

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

   if -9.9999999999999998e-86 < t < -4.2000000000000002e-150

   1. Initial program 82.3%

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

   3. Taylor expanded in i around inf 60.0%

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

      1. distribute-lft-out-- 60.0%

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

   5. Simplified 60.0%

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

   6. Taylor expanded in j around inf 43.1%

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

      1. associate-*r* 43.1%

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

      2. neg-mul-1 43.1%

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

      3. *-commutative 43.1%

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

   8. Simplified 43.1%

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

   if -4.2000000000000002e-150 < t < -7.5000000000000004e-294

   1. Initial program 77.9%

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

   3. Taylor expanded in t around -inf 57.0%

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

   5. Simplified 60.6%

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

   6. Taylor expanded in y around -inf 48.9%

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

      1. *-commutative 48.9%

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

   8. Simplified 48.9%

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

   9. Taylor expanded in z around inf 34.6%

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

       1. *-commutative 34.6%

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

   11. Simplified 34.6%

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

   if -7.5000000000000004e-294 < t < 3.0999999999999999e-201

   1. Initial program 83.9%

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

   3. Taylor expanded in b around inf 55.2%

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

      1. *-commutative 55.2%

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

   5. Simplified 55.2%

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

   6. Taylor expanded in i around inf 50.2%

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

      1. *-commutative 50.2%

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

   8. Simplified 50.2%

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

   if 3.0999999999999999e-201 < t < 1.44999999999999996e79

   1. Initial program 78.9%

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

   3. Taylor expanded in z around inf 49.3%

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

      1. *-commutative 49.3%

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

      2. *-commutative 49.3%

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

   5. Simplified 49.3%

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

   6. Taylor expanded in y around inf 31.8%

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

   if 1.44999999999999996e79 < t

   1. Initial program 50.6%

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

   3. Taylor expanded in t around -inf 71.7%

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

   5. Simplified 70.0%

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

   6. Taylor expanded in c around inf 68.2%

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

      1. associate-*r/ 68.2%

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

      2. associate-*r* 68.2%

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

      3. neg-mul-1 68.2%

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

   8. Simplified 68.2%

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

   9. Taylor expanded in x around inf 47.8%

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

4. Final simplification 41.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+39}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-85}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-150}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-294}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-201}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+79}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 29.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+39}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-84}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-151}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;t \leq -6.3 \cdot 10^{-291}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 1.36 \cdot 10^{-201}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+68}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -5.2e+39)
   (* c (* t j))
   (if (<= t -3.5e-84)
     (* x (* y z))
     (if (<= t -9e-151)
       (* i (* j (- y)))
       (if (<= t -6.3e-291)
         (* y (* x z))
         (if (<= t 1.36e-201)
           (* a (* b i))
           (if (<= t 2.7e+68) (* z (* x y)) (* x (* t (- a))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -5.2e+39) {
		tmp = c * (t * j);
	} else if (t <= -3.5e-84) {
		tmp = x * (y * z);
	} else if (t <= -9e-151) {
		tmp = i * (j * -y);
	} else if (t <= -6.3e-291) {
		tmp = y * (x * z);
	} else if (t <= 1.36e-201) {
		tmp = a * (b * i);
	} else if (t <= 2.7e+68) {
		tmp = z * (x * y);
	} else {
		tmp = x * (t * -a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (t <= (-5.2d+39)) then
        tmp = c * (t * j)
    else if (t <= (-3.5d-84)) then
        tmp = x * (y * z)
    else if (t <= (-9d-151)) then
        tmp = i * (j * -y)
    else if (t <= (-6.3d-291)) then
        tmp = y * (x * z)
    else if (t <= 1.36d-201) then
        tmp = a * (b * i)
    else if (t <= 2.7d+68) then
        tmp = z * (x * y)
    else
        tmp = x * (t * -a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -5.2e+39) {
		tmp = c * (t * j);
	} else if (t <= -3.5e-84) {
		tmp = x * (y * z);
	} else if (t <= -9e-151) {
		tmp = i * (j * -y);
	} else if (t <= -6.3e-291) {
		tmp = y * (x * z);
	} else if (t <= 1.36e-201) {
		tmp = a * (b * i);
	} else if (t <= 2.7e+68) {
		tmp = z * (x * y);
	} else {
		tmp = x * (t * -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -5.2e+39:
		tmp = c * (t * j)
	elif t <= -3.5e-84:
		tmp = x * (y * z)
	elif t <= -9e-151:
		tmp = i * (j * -y)
	elif t <= -6.3e-291:
		tmp = y * (x * z)
	elif t <= 1.36e-201:
		tmp = a * (b * i)
	elif t <= 2.7e+68:
		tmp = z * (x * y)
	else:
		tmp = x * (t * -a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -5.2e+39)
		tmp = Float64(c * Float64(t * j));
	elseif (t <= -3.5e-84)
		tmp = Float64(x * Float64(y * z));
	elseif (t <= -9e-151)
		tmp = Float64(i * Float64(j * Float64(-y)));
	elseif (t <= -6.3e-291)
		tmp = Float64(y * Float64(x * z));
	elseif (t <= 1.36e-201)
		tmp = Float64(a * Float64(b * i));
	elseif (t <= 2.7e+68)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = Float64(x * Float64(t * Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -5.2e+39)
		tmp = c * (t * j);
	elseif (t <= -3.5e-84)
		tmp = x * (y * z);
	elseif (t <= -9e-151)
		tmp = i * (j * -y);
	elseif (t <= -6.3e-291)
		tmp = y * (x * z);
	elseif (t <= 1.36e-201)
		tmp = a * (b * i);
	elseif (t <= 2.7e+68)
		tmp = z * (x * y);
	else
		tmp = x * (t * -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -5.2e+39], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.5e-84], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -9e-151], N[(i * N[(j * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6.3e-291], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.36e-201], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.7e+68], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -5.2e39

   1. Initial program 56.2%

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

   3. Taylor expanded in t around -inf 64.1%

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

   5. Simplified 68.1%

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

   6. Taylor expanded in c around inf 70.9%

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

      1. associate-*r/ 70.9%

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

      2. associate-*r* 70.9%

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

      3. neg-mul-1 70.9%

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

   8. Simplified 70.9%

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

   9. Taylor expanded in j around inf 44.5%

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

       1. *-commutative 44.5%

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

   11. Simplified 44.5%

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

   if -5.2e39 < t < -3.5000000000000001e-84

   1. Initial program 71.8%

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

   3. Taylor expanded in j around 0 68.4%

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

   4. Taylor expanded in a around -inf 72.3%

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

      1. mul-1-neg 72.3%

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

      2. *-commutative 72.3%

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

      3. distribute-rgt-neg-in 72.3%

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

   6. Simplified 72.3%

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

   7. Taylor expanded in y around inf 46.3%

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

      1. *-commutative 46.3%

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

   9. Simplified 46.3%

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

   if -3.5000000000000001e-84 < t < -9.0000000000000005e-151

   1. Initial program 82.3%

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

   3. Taylor expanded in i around inf 60.0%

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

      1. distribute-lft-out-- 60.0%

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

   5. Simplified 60.0%

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

   6. Taylor expanded in j around inf 43.1%

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

      1. associate-*r* 43.1%

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

      2. neg-mul-1 43.1%

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

      3. *-commutative 43.1%

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

   8. Simplified 43.1%

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

   if -9.0000000000000005e-151 < t < -6.29999999999999992e-291

   1. Initial program 77.9%

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

   3. Taylor expanded in t around -inf 57.0%

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

   5. Simplified 60.6%

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

   6. Taylor expanded in y around -inf 48.9%

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

      1. *-commutative 48.9%

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

   8. Simplified 48.9%

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

   9. Taylor expanded in z around inf 34.6%

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

       1. *-commutative 34.6%

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

   11. Simplified 34.6%

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

   if -6.29999999999999992e-291 < t < 1.36000000000000005e-201

   1. Initial program 83.9%

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

   3. Taylor expanded in b around inf 55.2%

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

      1. *-commutative 55.2%

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

   5. Simplified 55.2%

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

   6. Taylor expanded in i around inf 50.2%

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

      1. *-commutative 50.2%

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

   8. Simplified 50.2%

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

   if 1.36000000000000005e-201 < t < 2.69999999999999991e68

   1. Initial program 78.9%

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

   3. Taylor expanded in z around inf 49.3%

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

      1. *-commutative 49.3%

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

      2. *-commutative 49.3%

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

   5. Simplified 49.3%

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

   6. Taylor expanded in y around inf 31.8%

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

   if 2.69999999999999991e68 < t

   1. Initial program 50.6%

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

   3. Taylor expanded in j around 0 46.7%

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

   4. Taylor expanded in a around -inf 52.0%

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

      1. mul-1-neg 52.0%

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

      2. *-commutative 52.0%

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

      3. distribute-rgt-neg-in 52.0%

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

   6. Simplified 54.1%

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

   7. Taylor expanded in t around inf 47.7%

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

      1. mul-1-neg 47.7%

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

      2. associate-*r* 51.0%

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

      3. distribute-lft-neg-in 51.0%

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

      4. distribute-rgt-neg-in 51.0%

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

   9. Simplified 51.0%

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

4. Final simplification 42.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+39}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-84}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-151}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;t \leq -6.3 \cdot 10^{-291}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 1.36 \cdot 10^{-201}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+68}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 50.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t \cdot a\right) \cdot \left(b \cdot \frac{i}{t} - x\right)\\ \mathbf{if}\;a \leq -2.1 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -5.6 \cdot 10^{-27}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-121}:\\ \;\;\;\;t \cdot \left(c \cdot j - b \cdot \left(z \cdot \frac{c}{t}\right)\right)\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-285}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-59}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* t a) (- (* b (/ i t)) x))))
   (if (<= a -2.1e+58)
     t_1
     (if (<= a -5.6e-27)
       (* y (- (* x z) (* i j)))
       (if (<= a -1.3e-121)
         (* t (- (* c j) (* b (* z (/ c t)))))
         (if (<= a -9.5e-285)
           (* j (- (* t c) (* y i)))
           (if (<= a 9.2e-59) (* z (- (* x y) (* b c))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (t * a) * ((b * (i / t)) - x);
	double tmp;
	if (a <= -2.1e+58) {
		tmp = t_1;
	} else if (a <= -5.6e-27) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= -1.3e-121) {
		tmp = t * ((c * j) - (b * (z * (c / t))));
	} else if (a <= -9.5e-285) {
		tmp = j * ((t * c) - (y * i));
	} else if (a <= 9.2e-59) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t * a) * ((b * (i / t)) - x)
    if (a <= (-2.1d+58)) then
        tmp = t_1
    else if (a <= (-5.6d-27)) then
        tmp = y * ((x * z) - (i * j))
    else if (a <= (-1.3d-121)) then
        tmp = t * ((c * j) - (b * (z * (c / t))))
    else if (a <= (-9.5d-285)) then
        tmp = j * ((t * c) - (y * i))
    else if (a <= 9.2d-59) then
        tmp = z * ((x * y) - (b * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (t * a) * ((b * (i / t)) - x);
	double tmp;
	if (a <= -2.1e+58) {
		tmp = t_1;
	} else if (a <= -5.6e-27) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= -1.3e-121) {
		tmp = t * ((c * j) - (b * (z * (c / t))));
	} else if (a <= -9.5e-285) {
		tmp = j * ((t * c) - (y * i));
	} else if (a <= 9.2e-59) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (t * a) * ((b * (i / t)) - x)
	tmp = 0
	if a <= -2.1e+58:
		tmp = t_1
	elif a <= -5.6e-27:
		tmp = y * ((x * z) - (i * j))
	elif a <= -1.3e-121:
		tmp = t * ((c * j) - (b * (z * (c / t))))
	elif a <= -9.5e-285:
		tmp = j * ((t * c) - (y * i))
	elif a <= 9.2e-59:
		tmp = z * ((x * y) - (b * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(t * a) * Float64(Float64(b * Float64(i / t)) - x))
	tmp = 0.0
	if (a <= -2.1e+58)
		tmp = t_1;
	elseif (a <= -5.6e-27)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (a <= -1.3e-121)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(b * Float64(z * Float64(c / t)))));
	elseif (a <= -9.5e-285)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (a <= 9.2e-59)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (t * a) * ((b * (i / t)) - x);
	tmp = 0.0;
	if (a <= -2.1e+58)
		tmp = t_1;
	elseif (a <= -5.6e-27)
		tmp = y * ((x * z) - (i * j));
	elseif (a <= -1.3e-121)
		tmp = t * ((c * j) - (b * (z * (c / t))));
	elseif (a <= -9.5e-285)
		tmp = j * ((t * c) - (y * i));
	elseif (a <= 9.2e-59)
		tmp = z * ((x * y) - (b * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(t * a), $MachinePrecision] * N[(N[(b * N[(i / t), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.1e+58], t$95$1, If[LessEqual[a, -5.6e-27], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.3e-121], N[(t * N[(N[(c * j), $MachinePrecision] - N[(b * N[(z * N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -9.5e-285], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.2e-59], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.10000000000000012e58 or 9.19999999999999918e-59 < a

   1. Initial program 62.2%

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

   3. Taylor expanded in t around -inf 61.1%

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

   5. Simplified 61.1%

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

   6. Taylor expanded in a around -inf 65.0%

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

      1. associate-*r* 64.7%

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

      2. *-commutative 64.7%

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

      3. +-commutative 64.7%

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

      4. mul-1-neg 64.7%

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

      5. unsub-neg 64.7%

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

      6. associate-/l* 65.5%

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

   8. Simplified 65.5%

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

   if -2.10000000000000012e58 < a < -5.5999999999999999e-27

   1. Initial program 74.1%

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

   3. Taylor expanded in y around inf 50.2%

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

      1. +-commutative 50.2%

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

      2. mul-1-neg 50.2%

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

      3. unsub-neg 50.2%

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

   5. Simplified 50.2%

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

   if -5.5999999999999999e-27 < a < -1.29999999999999993e-121

   1. Initial program 78.9%

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

   3. Taylor expanded in t around -inf 64.7%

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

   5. Simplified 79.0%

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

   6. Taylor expanded in c around inf 65.8%

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

      1. associate-*r/ 65.8%

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

      2. associate-*r* 65.8%

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

      3. neg-mul-1 65.8%

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

   8. Simplified 65.8%

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

   9. Taylor expanded in x around 0 65.8%

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

       1. distribute-rgt-in 65.8%

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

       2. *-commutative 65.8%

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

       3. neg-mul-1 65.8%

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

       4. unsub-neg 65.8%

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

       5. mul-1-neg 65.8%

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

       6. distribute-lft-neg-in 65.8%

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

       7. *-commutative 65.8%

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

       8. mul-1-neg 65.8%

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

       9. remove-double-neg 65.8%

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

       10. associate-/l* 79.7%

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

       11. *-commutative 79.7%

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

       12. associate-/l* 79.7%

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

   11. Simplified 79.7%

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

   if -1.29999999999999993e-121 < a < -9.4999999999999997e-285

   1. Initial program 89.6%

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

   3. Taylor expanded in z around inf 73.2%

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

   4. Taylor expanded in j around inf 49.4%

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

      1. *-commutative 49.4%

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

      2. *-commutative 49.4%

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

   6. Simplified 49.4%

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

   if -9.4999999999999997e-285 < a < 9.19999999999999918e-59

   1. Initial program 71.2%

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

   3. Taylor expanded in z around inf 60.2%

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

      1. *-commutative 60.2%

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

      2. *-commutative 60.2%

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

   5. Simplified 60.2%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{+58}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(b \cdot \frac{i}{t} - x\right)\\ \mathbf{elif}\;a \leq -5.6 \cdot 10^{-27}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-121}:\\ \;\;\;\;t \cdot \left(c \cdot j - b \cdot \left(z \cdot \frac{c}{t}\right)\right)\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-285}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-59}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(b \cdot \frac{i}{t} - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 67.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;x \leq -1.62 \cdot 10^{+137}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + t\_2\\ \mathbf{elif}\;x \leq -5.3 \cdot 10^{-58}:\\ \;\;\;\;t\_1 - x \cdot \left(z \cdot \left(a \cdot \frac{t}{z} - y\right)\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-7}:\\ \;\;\;\;t\_2 + t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - \left(x \cdot t + \frac{z \cdot \left(b \cdot c - x \cdot y\right)}{a}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))) (t_2 (* j (- (* t c) (* y i)))))
   (if (<= x -1.62e+137)
     (+ (* x (- (* y z) (* t a))) t_2)
     (if (<= x -5.3e-58)
       (- t_1 (* x (* z (- (* a (/ t z)) y))))
       (if (<= x 4.5e-7)
         (+ t_2 t_1)
         (* a (- (* b i) (+ (* x t) (/ (* z (- (* b c) (* x y))) a)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (x <= -1.62e+137) {
		tmp = (x * ((y * z) - (t * a))) + t_2;
	} else if (x <= -5.3e-58) {
		tmp = t_1 - (x * (z * ((a * (t / z)) - y)));
	} else if (x <= 4.5e-7) {
		tmp = t_2 + t_1;
	} else {
		tmp = a * ((b * i) - ((x * t) + ((z * ((b * c) - (x * y))) / a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = j * ((t * c) - (y * i))
    if (x <= (-1.62d+137)) then
        tmp = (x * ((y * z) - (t * a))) + t_2
    else if (x <= (-5.3d-58)) then
        tmp = t_1 - (x * (z * ((a * (t / z)) - y)))
    else if (x <= 4.5d-7) then
        tmp = t_2 + t_1
    else
        tmp = a * ((b * i) - ((x * t) + ((z * ((b * c) - (x * y))) / a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (x <= -1.62e+137) {
		tmp = (x * ((y * z) - (t * a))) + t_2;
	} else if (x <= -5.3e-58) {
		tmp = t_1 - (x * (z * ((a * (t / z)) - y)));
	} else if (x <= 4.5e-7) {
		tmp = t_2 + t_1;
	} else {
		tmp = a * ((b * i) - ((x * t) + ((z * ((b * c) - (x * y))) / a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = j * ((t * c) - (y * i))
	tmp = 0
	if x <= -1.62e+137:
		tmp = (x * ((y * z) - (t * a))) + t_2
	elif x <= -5.3e-58:
		tmp = t_1 - (x * (z * ((a * (t / z)) - y)))
	elif x <= 4.5e-7:
		tmp = t_2 + t_1
	else:
		tmp = a * ((b * i) - ((x * t) + ((z * ((b * c) - (x * y))) / a)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (x <= -1.62e+137)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_2);
	elseif (x <= -5.3e-58)
		tmp = Float64(t_1 - Float64(x * Float64(z * Float64(Float64(a * Float64(t / z)) - y))));
	elseif (x <= 4.5e-7)
		tmp = Float64(t_2 + t_1);
	else
		tmp = Float64(a * Float64(Float64(b * i) - Float64(Float64(x * t) + Float64(Float64(z * Float64(Float64(b * c) - Float64(x * y))) / a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (x <= -1.62e+137)
		tmp = (x * ((y * z) - (t * a))) + t_2;
	elseif (x <= -5.3e-58)
		tmp = t_1 - (x * (z * ((a * (t / z)) - y)));
	elseif (x <= 4.5e-7)
		tmp = t_2 + t_1;
	else
		tmp = a * ((b * i) - ((x * t) + ((z * ((b * c) - (x * y))) / a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.62e+137], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[x, -5.3e-58], N[(t$95$1 - N[(x * N[(z * N[(N[(a * N[(t / z), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.5e-7], N[(t$95$2 + t$95$1), $MachinePrecision], N[(a * N[(N[(b * i), $MachinePrecision] - N[(N[(x * t), $MachinePrecision] + N[(N[(z * N[(N[(b * c), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.6200000000000001e137

   1. Initial program 71.0%

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

   3. Taylor expanded in b around 0 79.2%

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

   if -1.6200000000000001e137 < x < -5.3000000000000003e-58

   1. Initial program 84.7%

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

   3. Taylor expanded in j around 0 76.9%

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

   4. Taylor expanded in z around inf 79.0%

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

      1. mul-1-neg 79.0%

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

      2. unsub-neg 79.0%

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

      3. associate-/l* 79.0%

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

   6. Simplified 79.0%

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

   if -5.3000000000000003e-58 < x < 4.4999999999999998e-7

   1. Initial program 65.9%

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

   3. Taylor expanded in x around 0 74.5%

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

      1. *-commutative 74.5%

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

   5. Simplified 74.5%

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

   if 4.4999999999999998e-7 < x

   1. Initial program 63.7%

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

   3. Taylor expanded in j around 0 62.5%

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

   4. Taylor expanded in a around -inf 62.7%

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

      1. mul-1-neg 62.7%

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

      2. *-commutative 62.7%

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

      3. distribute-rgt-neg-in 62.7%

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

   6. Simplified 67.3%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.62 \cdot 10^{+137}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq -5.3 \cdot 10^{-58}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - x \cdot \left(z \cdot \left(a \cdot \frac{t}{z} - y\right)\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-7}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - \left(x \cdot t + \frac{z \cdot \left(b \cdot c - x \cdot y\right)}{a}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 43.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -3.5 \cdot 10^{+145}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -2.6 \cdot 10^{-169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -7.8 \cdot 10^{-215}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq -3.7 \cdot 10^{-304}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 7.2 \cdot 10^{-59}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))) (t_2 (* c (- (* t j) (* z b)))))
   (if (<= c -3.5e+145)
     t_2
     (if (<= c -2.6e-169)
       t_1
       (if (<= c -7.8e-215)
         (* y (* x z))
         (if (<= c -3.7e-304)
           t_1
           (if (<= c 7.2e-59) (* x (* t (- a))) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -3.5e+145) {
		tmp = t_2;
	} else if (c <= -2.6e-169) {
		tmp = t_1;
	} else if (c <= -7.8e-215) {
		tmp = y * (x * z);
	} else if (c <= -3.7e-304) {
		tmp = t_1;
	} else if (c <= 7.2e-59) {
		tmp = x * (t * -a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = c * ((t * j) - (z * b))
    if (c <= (-3.5d+145)) then
        tmp = t_2
    else if (c <= (-2.6d-169)) then
        tmp = t_1
    else if (c <= (-7.8d-215)) then
        tmp = y * (x * z)
    else if (c <= (-3.7d-304)) then
        tmp = t_1
    else if (c <= 7.2d-59) then
        tmp = x * (t * -a)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -3.5e+145) {
		tmp = t_2;
	} else if (c <= -2.6e-169) {
		tmp = t_1;
	} else if (c <= -7.8e-215) {
		tmp = y * (x * z);
	} else if (c <= -3.7e-304) {
		tmp = t_1;
	} else if (c <= 7.2e-59) {
		tmp = x * (t * -a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -3.5e+145:
		tmp = t_2
	elif c <= -2.6e-169:
		tmp = t_1
	elif c <= -7.8e-215:
		tmp = y * (x * z)
	elif c <= -3.7e-304:
		tmp = t_1
	elif c <= 7.2e-59:
		tmp = x * (t * -a)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -3.5e+145)
		tmp = t_2;
	elseif (c <= -2.6e-169)
		tmp = t_1;
	elseif (c <= -7.8e-215)
		tmp = Float64(y * Float64(x * z));
	elseif (c <= -3.7e-304)
		tmp = t_1;
	elseif (c <= 7.2e-59)
		tmp = Float64(x * Float64(t * Float64(-a)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -3.5e+145)
		tmp = t_2;
	elseif (c <= -2.6e-169)
		tmp = t_1;
	elseif (c <= -7.8e-215)
		tmp = y * (x * z);
	elseif (c <= -3.7e-304)
		tmp = t_1;
	elseif (c <= 7.2e-59)
		tmp = x * (t * -a);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.5e+145], t$95$2, If[LessEqual[c, -2.6e-169], t$95$1, If[LessEqual[c, -7.8e-215], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -3.7e-304], t$95$1, If[LessEqual[c, 7.2e-59], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -3.5000000000000001e145 or 7.20000000000000001e-59 < c

   1. Initial program 51.3%

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

   3. Taylor expanded in c around inf 61.9%

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

      1. *-commutative 61.9%

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

   5. Simplified 61.9%

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

   if -3.5000000000000001e145 < c < -2.60000000000000014e-169 or -7.7999999999999999e-215 < c < -3.7000000000000003e-304

   1. Initial program 82.6%

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

   3. Taylor expanded in b around inf 50.2%

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

      1. *-commutative 50.2%

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

   5. Simplified 50.2%

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

   if -2.60000000000000014e-169 < c < -7.7999999999999999e-215

   1. Initial program 68.2%

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

   3. Taylor expanded in t around -inf 68.0%

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

   5. Simplified 91.5%

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

   6. Taylor expanded in y around -inf 67.7%

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

      1. *-commutative 67.7%

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

   8. Simplified 67.7%

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

   9. Taylor expanded in z around inf 67.6%

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

       1. *-commutative 67.6%

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

   11. Simplified 67.6%

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

   if -3.7000000000000003e-304 < c < 7.20000000000000001e-59

   1. Initial program 79.1%

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

   3. Taylor expanded in j around 0 63.2%

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

   4. Taylor expanded in a around -inf 69.8%

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

      1. mul-1-neg 69.8%

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

      2. *-commutative 69.8%

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

      3. distribute-rgt-neg-in 69.8%

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

   6. Simplified 69.9%

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

   7. Taylor expanded in t around inf 37.1%

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

      1. mul-1-neg 37.1%

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

      2. associate-*r* 39.7%

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

      3. distribute-lft-neg-in 39.7%

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

      4. distribute-rgt-neg-in 39.7%

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

   9. Simplified 39.7%

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

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.5 \cdot 10^{+145}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -2.6 \cdot 10^{-169}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq -7.8 \cdot 10^{-215}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq -3.7 \cdot 10^{-304}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq 7.2 \cdot 10^{-59}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 50.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -5.5 \cdot 10^{+220}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.56 \cdot 10^{+209}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -9.2 \cdot 10^{+151}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{+14}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a)))) (t_2 (* b (- (* a i) (* z c)))))
   (if (<= b -5.5e+220)
     t_2
     (if (<= b -1.56e+209)
       t_1
       (if (<= b -9.2e+151)
         t_2
         (if (<= b -3.6e+14)
           (* z (- (* x y) (* b c)))
           (if (<= b 1.9e-15) 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 = t * ((c * j) - (x * a));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -5.5e+220) {
		tmp = t_2;
	} else if (b <= -1.56e+209) {
		tmp = t_1;
	} else if (b <= -9.2e+151) {
		tmp = t_2;
	} else if (b <= -3.6e+14) {
		tmp = z * ((x * y) - (b * c));
	} else if (b <= 1.9e-15) {
		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 = t * ((c * j) - (x * a))
    t_2 = b * ((a * i) - (z * c))
    if (b <= (-5.5d+220)) then
        tmp = t_2
    else if (b <= (-1.56d+209)) then
        tmp = t_1
    else if (b <= (-9.2d+151)) then
        tmp = t_2
    else if (b <= (-3.6d+14)) then
        tmp = z * ((x * y) - (b * c))
    else if (b <= 1.9d-15) 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 = t * ((c * j) - (x * a));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -5.5e+220) {
		tmp = t_2;
	} else if (b <= -1.56e+209) {
		tmp = t_1;
	} else if (b <= -9.2e+151) {
		tmp = t_2;
	} else if (b <= -3.6e+14) {
		tmp = z * ((x * y) - (b * c));
	} else if (b <= 1.9e-15) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -5.5e+220:
		tmp = t_2
	elif b <= -1.56e+209:
		tmp = t_1
	elif b <= -9.2e+151:
		tmp = t_2
	elif b <= -3.6e+14:
		tmp = z * ((x * y) - (b * c))
	elif b <= 1.9e-15:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -5.5e+220)
		tmp = t_2;
	elseif (b <= -1.56e+209)
		tmp = t_1;
	elseif (b <= -9.2e+151)
		tmp = t_2;
	elseif (b <= -3.6e+14)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (b <= 1.9e-15)
		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 = t * ((c * j) - (x * a));
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -5.5e+220)
		tmp = t_2;
	elseif (b <= -1.56e+209)
		tmp = t_1;
	elseif (b <= -9.2e+151)
		tmp = t_2;
	elseif (b <= -3.6e+14)
		tmp = z * ((x * y) - (b * c));
	elseif (b <= 1.9e-15)
		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[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.5e+220], t$95$2, If[LessEqual[b, -1.56e+209], t$95$1, If[LessEqual[b, -9.2e+151], t$95$2, If[LessEqual[b, -3.6e+14], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.9e-15], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.4999999999999999e220 or -1.56e209 < b < -9.2000000000000003e151 or 1.9000000000000001e-15 < b

   1. Initial program 69.4%

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

   3. Taylor expanded in b around inf 68.4%

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

      1. *-commutative 68.4%

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

   5. Simplified 68.4%

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

   if -5.4999999999999999e220 < b < -1.56e209 or -3.6e14 < b < 1.9000000000000001e-15

   1. Initial program 70.0%

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

   3. Taylor expanded in z around inf 68.1%

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

   4. Taylor expanded in t around inf 53.3%

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

      1. +-commutative 53.3%

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

      2. mul-1-neg 53.3%

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

      3. unsub-neg 53.3%

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

      4. *-commutative 53.3%

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

   6. Simplified 53.3%

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

   if -9.2000000000000003e151 < b < -3.6e14

   1. Initial program 66.7%

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

   3. Taylor expanded in z around inf 70.5%

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

      1. *-commutative 70.5%

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

      2. *-commutative 70.5%

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

   5. Simplified 70.5%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{+220}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.56 \cdot 10^{+209}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq -9.2 \cdot 10^{+151}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{+14}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-15}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 56.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(z \cdot c\right)\\ \mathbf{if}\;x \leq -4.5 \cdot 10^{-29}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - t\_1\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-252}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-7}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - t\_1\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+27}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+91}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* z c))))
   (if (<= x -4.5e-29)
     (- (* x (- (* y z) (* t a))) t_1)
     (if (<= x 1.85e-252)
       (+ (* c (* t j)) (* b (- (* a i) (* z c))))
       (if (<= x 2.4e-7)
         (- (* j (- (* t c) (* y i))) t_1)
         (if (<= x 6.5e+27)
           (* t (- (* c j) (* x a)))
           (if (<= x 7.5e+91)
             (* i (- (* a b) (* y j)))
             (* z (- (* x y) (* b 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 = b * (z * c);
	double tmp;
	if (x <= -4.5e-29) {
		tmp = (x * ((y * z) - (t * a))) - t_1;
	} else if (x <= 1.85e-252) {
		tmp = (c * (t * j)) + (b * ((a * i) - (z * c)));
	} else if (x <= 2.4e-7) {
		tmp = (j * ((t * c) - (y * i))) - t_1;
	} else if (x <= 6.5e+27) {
		tmp = t * ((c * j) - (x * a));
	} else if (x <= 7.5e+91) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = z * ((x * y) - (b * 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 = b * (z * c)
    if (x <= (-4.5d-29)) then
        tmp = (x * ((y * z) - (t * a))) - t_1
    else if (x <= 1.85d-252) then
        tmp = (c * (t * j)) + (b * ((a * i) - (z * c)))
    else if (x <= 2.4d-7) then
        tmp = (j * ((t * c) - (y * i))) - t_1
    else if (x <= 6.5d+27) then
        tmp = t * ((c * j) - (x * a))
    else if (x <= 7.5d+91) then
        tmp = i * ((a * b) - (y * j))
    else
        tmp = z * ((x * y) - (b * 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 = b * (z * c);
	double tmp;
	if (x <= -4.5e-29) {
		tmp = (x * ((y * z) - (t * a))) - t_1;
	} else if (x <= 1.85e-252) {
		tmp = (c * (t * j)) + (b * ((a * i) - (z * c)));
	} else if (x <= 2.4e-7) {
		tmp = (j * ((t * c) - (y * i))) - t_1;
	} else if (x <= 6.5e+27) {
		tmp = t * ((c * j) - (x * a));
	} else if (x <= 7.5e+91) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (z * c)
	tmp = 0
	if x <= -4.5e-29:
		tmp = (x * ((y * z) - (t * a))) - t_1
	elif x <= 1.85e-252:
		tmp = (c * (t * j)) + (b * ((a * i) - (z * c)))
	elif x <= 2.4e-7:
		tmp = (j * ((t * c) - (y * i))) - t_1
	elif x <= 6.5e+27:
		tmp = t * ((c * j) - (x * a))
	elif x <= 7.5e+91:
		tmp = i * ((a * b) - (y * j))
	else:
		tmp = z * ((x * y) - (b * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(z * c))
	tmp = 0.0
	if (x <= -4.5e-29)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - t_1);
	elseif (x <= 1.85e-252)
		tmp = Float64(Float64(c * Float64(t * j)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (x <= 2.4e-7)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) - t_1);
	elseif (x <= 6.5e+27)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (x <= 7.5e+91)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	else
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (z * c);
	tmp = 0.0;
	if (x <= -4.5e-29)
		tmp = (x * ((y * z) - (t * a))) - t_1;
	elseif (x <= 1.85e-252)
		tmp = (c * (t * j)) + (b * ((a * i) - (z * c)));
	elseif (x <= 2.4e-7)
		tmp = (j * ((t * c) - (y * i))) - t_1;
	elseif (x <= 6.5e+27)
		tmp = t * ((c * j) - (x * a));
	elseif (x <= 7.5e+91)
		tmp = i * ((a * b) - (y * j));
	else
		tmp = z * ((x * y) - (b * c));
	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]}, If[LessEqual[x, -4.5e-29], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[x, 1.85e-252], N[(N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.4e-7], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[x, 6.5e+27], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.5e+91], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -4.4999999999999998e-29

   1. Initial program 77.3%

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

   3. Taylor expanded in j around 0 72.0%

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

   4. Taylor expanded in c around inf 66.2%

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

      1. *-commutative 66.2%

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

   6. Simplified 66.2%

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

   if -4.4999999999999998e-29 < x < 1.8500000000000001e-252

   1. Initial program 66.0%

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

   3. Taylor expanded in z around inf 75.9%

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

   4. Taylor expanded in x around 0 68.7%

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

      1. *-commutative 68.7%

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

      2. *-commutative 68.7%

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

      3. *-commutative 68.7%

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

   6. Simplified 68.7%

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

   7. Taylor expanded in t around inf 67.4%

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

      1. *-commutative 67.4%

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

   9. Simplified 67.4%

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

   if 1.8500000000000001e-252 < x < 2.39999999999999979e-7

   1. Initial program 69.5%

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

   3. Taylor expanded in z around inf 80.4%

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

   4. Taylor expanded in x around 0 81.2%

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

      1. *-commutative 81.2%

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

      2. *-commutative 81.2%

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

      3. *-commutative 81.2%

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

   6. Simplified 81.2%

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

   7. Taylor expanded in z around inf 71.9%

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

   if 2.39999999999999979e-7 < x < 6.5000000000000005e27

   1. Initial program 84.3%

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

   3. Taylor expanded in z around inf 70.4%

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

   4. Taylor expanded in t around inf 77.2%

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

      1. +-commutative 77.2%

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

      2. mul-1-neg 77.2%

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

      3. unsub-neg 77.2%

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

      4. *-commutative 77.2%

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

   6. Simplified 77.2%

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

   if 6.5000000000000005e27 < x < 7.50000000000000033e91

   1. Initial program 59.1%

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

   3. Taylor expanded in i around inf 68.2%

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

      1. distribute-lft-out-- 68.2%

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

   5. Simplified 68.2%

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

   if 7.50000000000000033e91 < x

   1. Initial program 58.6%

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

   3. Taylor expanded in z around inf 63.4%

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

      1. *-commutative 63.4%

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

      2. *-commutative 63.4%

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

   5. Simplified 63.4%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-29}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-252}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-7}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+27}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+91}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 64.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.9 \cdot 10^{+112}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-94}:\\ \;\;\;\;a \cdot \left(b \cdot i - \frac{z \cdot \left(b \cdot c - x \cdot y\right)}{a}\right)\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{+44}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(c \cdot \left(\frac{a \cdot i}{c} - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -2.9e+112)
   (+ (* x (* y z)) (* b (- (* a i) (* z c))))
   (if (<= b -2.5e-94)
     (* a (- (* b i) (/ (* z (- (* b c) (* x y))) a)))
     (if (<= b 6.4e+44)
       (+ (* x (- (* y z) (* t a))) (* j (- (* t c) (* y i))))
       (* b (* c (- (/ (* a i) c) 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 (b <= -2.9e+112) {
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)));
	} else if (b <= -2.5e-94) {
		tmp = a * ((b * i) - ((z * ((b * c) - (x * y))) / a));
	} else if (b <= 6.4e+44) {
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	} else {
		tmp = b * (c * (((a * i) / c) - 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 (b <= (-2.9d+112)) then
        tmp = (x * (y * z)) + (b * ((a * i) - (z * c)))
    else if (b <= (-2.5d-94)) then
        tmp = a * ((b * i) - ((z * ((b * c) - (x * y))) / a))
    else if (b <= 6.4d+44) then
        tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)))
    else
        tmp = b * (c * (((a * i) / c) - 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 (b <= -2.9e+112) {
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)));
	} else if (b <= -2.5e-94) {
		tmp = a * ((b * i) - ((z * ((b * c) - (x * y))) / a));
	} else if (b <= 6.4e+44) {
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	} else {
		tmp = b * (c * (((a * i) / c) - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -2.9e+112:
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)))
	elif b <= -2.5e-94:
		tmp = a * ((b * i) - ((z * ((b * c) - (x * y))) / a))
	elif b <= 6.4e+44:
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)))
	else:
		tmp = b * (c * (((a * i) / c) - z))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -2.9e+112)
		tmp = Float64(Float64(x * Float64(y * z)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (b <= -2.5e-94)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(Float64(z * Float64(Float64(b * c) - Float64(x * y))) / a)));
	elseif (b <= 6.4e+44)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))));
	else
		tmp = Float64(b * Float64(c * Float64(Float64(Float64(a * i) / c) - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -2.9e+112)
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)));
	elseif (b <= -2.5e-94)
		tmp = a * ((b * i) - ((z * ((b * c) - (x * y))) / a));
	elseif (b <= 6.4e+44)
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	else
		tmp = b * (c * (((a * i) / c) - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -2.9e+112], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.5e-94], N[(a * N[(N[(b * i), $MachinePrecision] - N[(N[(z * N[(N[(b * c), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.4e+44], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(c * N[(N[(N[(a * i), $MachinePrecision] / c), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.9000000000000002e112

   1. Initial program 59.2%

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

   3. Taylor expanded in j around 0 59.3%

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

   4. Taylor expanded in t around 0 72.1%

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

      1. *-commutative 72.1%

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

   6. Simplified 72.1%

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

   if -2.9000000000000002e112 < b < -2.4999999999999998e-94

   1. Initial program 66.9%

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

   3. Taylor expanded in j around 0 59.4%

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

   4. Taylor expanded in a around -inf 59.3%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \frac{x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)}{a} + t \cdot x\right) - b \cdot i\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 59.3%

         \[\leadsto \color{blue}{-a \cdot \left(\left(-1 \cdot \frac{x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)}{a} + t \cdot x\right) - b \cdot i\right)} \]

      2. *-commutative 59.3%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \frac{x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)}{a} + t \cdot x\right) - b \cdot i\right) \cdot a} \]

      3. distribute-rgt-neg-in 59.3%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \frac{x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)}{a} + t \cdot x\right) - b \cdot i\right) \cdot \left(-a\right)} \]

   6. Simplified 73.5%

      \[\leadsto \color{blue}{\left(\left(t \cdot x - \frac{z \cdot \left(x \cdot y - c \cdot b\right)}{a}\right) - i \cdot b\right) \cdot \left(-a\right)} \]

   7. Taylor expanded in t around 0 68.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i + \frac{z \cdot \left(x \cdot y - b \cdot c\right)}{a}\right)} \]

   if -2.4999999999999998e-94 < b < 6.40000000000000009e44

   1. Initial program 72.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 71.5%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   if 6.40000000000000009e44 < b

   1. Initial program 71.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 76.8%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 76.8%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

   5. Simplified 76.8%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

   6. Taylor expanded in c around inf 78.8%

      \[\leadsto b \cdot \color{blue}{\left(c \cdot \left(\frac{a \cdot i}{c} - z\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.9 \cdot 10^{+112}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-94}:\\ \;\;\;\;a \cdot \left(b \cdot i - \frac{z \cdot \left(b \cdot c - x \cdot y\right)}{a}\right)\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{+44}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(c \cdot \left(\frac{a \cdot i}{c} - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 30.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := c \cdot \left(t \cdot j\right)\\ t_3 := b \cdot \left(a \cdot i\right)\\ \mathbf{if}\;i \leq -3800000000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;i \leq -1.4 \cdot 10^{-260}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 5.8 \cdot 10^{-230}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq 6 \cdot 10^{-112}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 1.45 \cdot 10^{+85}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))) (t_2 (* c (* t j))) (t_3 (* b (* a i))))
   (if (<= i -3800000000.0)
     t_3
     (if (<= i -1.4e-260)
       t_1
       (if (<= i 5.8e-230)
         t_2
         (if (<= i 6e-112) t_1 (if (<= i 1.45e+85) t_2 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double t_2 = c * (t * j);
	double t_3 = b * (a * i);
	double tmp;
	if (i <= -3800000000.0) {
		tmp = t_3;
	} else if (i <= -1.4e-260) {
		tmp = t_1;
	} else if (i <= 5.8e-230) {
		tmp = t_2;
	} else if (i <= 6e-112) {
		tmp = t_1;
	} else if (i <= 1.45e+85) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * (y * z)
    t_2 = c * (t * j)
    t_3 = b * (a * i)
    if (i <= (-3800000000.0d0)) then
        tmp = t_3
    else if (i <= (-1.4d-260)) then
        tmp = t_1
    else if (i <= 5.8d-230) then
        tmp = t_2
    else if (i <= 6d-112) then
        tmp = t_1
    else if (i <= 1.45d+85) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double t_2 = c * (t * j);
	double t_3 = b * (a * i);
	double tmp;
	if (i <= -3800000000.0) {
		tmp = t_3;
	} else if (i <= -1.4e-260) {
		tmp = t_1;
	} else if (i <= 5.8e-230) {
		tmp = t_2;
	} else if (i <= 6e-112) {
		tmp = t_1;
	} else if (i <= 1.45e+85) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	t_2 = c * (t * j)
	t_3 = b * (a * i)
	tmp = 0
	if i <= -3800000000.0:
		tmp = t_3
	elif i <= -1.4e-260:
		tmp = t_1
	elif i <= 5.8e-230:
		tmp = t_2
	elif i <= 6e-112:
		tmp = t_1
	elif i <= 1.45e+85:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(y * z))
	t_2 = Float64(c * Float64(t * j))
	t_3 = Float64(b * Float64(a * i))
	tmp = 0.0
	if (i <= -3800000000.0)
		tmp = t_3;
	elseif (i <= -1.4e-260)
		tmp = t_1;
	elseif (i <= 5.8e-230)
		tmp = t_2;
	elseif (i <= 6e-112)
		tmp = t_1;
	elseif (i <= 1.45e+85)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (y * z);
	t_2 = c * (t * j);
	t_3 = b * (a * i);
	tmp = 0.0;
	if (i <= -3800000000.0)
		tmp = t_3;
	elseif (i <= -1.4e-260)
		tmp = t_1;
	elseif (i <= 5.8e-230)
		tmp = t_2;
	elseif (i <= 6e-112)
		tmp = t_1;
	elseif (i <= 1.45e+85)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -3800000000.0], t$95$3, If[LessEqual[i, -1.4e-260], t$95$1, If[LessEqual[i, 5.8e-230], t$95$2, If[LessEqual[i, 6e-112], t$95$1, If[LessEqual[i, 1.45e+85], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -3.8e9 or 1.44999999999999999e85 < i

   1. Initial program 58.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 50.8%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 50.8%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

   5. Simplified 50.8%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

   6. Taylor expanded in i around inf 43.7%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]

   if -3.8e9 < i < -1.3999999999999999e-260 or 5.80000000000000011e-230 < i < 6.0000000000000002e-112

   1. Initial program 81.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around 0 66.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]

   4. Taylor expanded in a around -inf 59.4%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \frac{x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)}{a} + t \cdot x\right) - b \cdot i\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 59.4%

         \[\leadsto \color{blue}{-a \cdot \left(\left(-1 \cdot \frac{x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)}{a} + t \cdot x\right) - b \cdot i\right)} \]

      2. *-commutative 59.4%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \frac{x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)}{a} + t \cdot x\right) - b \cdot i\right) \cdot a} \]

      3. distribute-rgt-neg-in 59.4%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \frac{x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)}{a} + t \cdot x\right) - b \cdot i\right) \cdot \left(-a\right)} \]

   6. Simplified 67.1%

      \[\leadsto \color{blue}{\left(\left(t \cdot x - \frac{z \cdot \left(x \cdot y - c \cdot b\right)}{a}\right) - i \cdot b\right) \cdot \left(-a\right)} \]

   7. Taylor expanded in y around inf 31.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   8. Step-by-step derivation

      1. *-commutative 31.8%

         \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

   9. Simplified 31.8%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y\right)} \]

   if -1.3999999999999999e-260 < i < 5.80000000000000011e-230 or 6.0000000000000002e-112 < i < 1.44999999999999999e85

   1. Initial program 72.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around -inf 72.5%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-1 \cdot \left(c \cdot j\right) + \left(-1 \cdot \frac{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)}{t} + a \cdot x\right)\right)\right)} \]

   5. Simplified 79.5%

      \[\leadsto \color{blue}{\left(\left(x \cdot a - \frac{y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)}{t}\right) - j \cdot c\right) \cdot \left(-t\right)} \]

   6. Taylor expanded in c around inf 71.3%

      \[\leadsto \left(\left(x \cdot a - \color{blue}{-1 \cdot \frac{b \cdot \left(c \cdot z\right)}{t}}\right) - j \cdot c\right) \cdot \left(-t\right) \]
   7. Step-by-step derivation

      1. associate-*r/ 71.3%

         \[\leadsto \left(\left(x \cdot a - \color{blue}{\frac{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)}{t}}\right) - j \cdot c\right) \cdot \left(-t\right) \]

      2. associate-*r* 71.3%

         \[\leadsto \left(\left(x \cdot a - \frac{\color{blue}{\left(-1 \cdot b\right) \cdot \left(c \cdot z\right)}}{t}\right) - j \cdot c\right) \cdot \left(-t\right) \]

      3. neg-mul-1 71.3%

         \[\leadsto \left(\left(x \cdot a - \frac{\color{blue}{\left(-b\right)} \cdot \left(c \cdot z\right)}{t}\right) - j \cdot c\right) \cdot \left(-t\right) \]

   8. Simplified 71.3%

      \[\leadsto \left(\left(x \cdot a - \color{blue}{\frac{\left(-b\right) \cdot \left(c \cdot z\right)}{t}}\right) - j \cdot c\right) \cdot \left(-t\right) \]

   9. Taylor expanded in j around inf 36.7%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   10. Step-by-step derivation

       1. *-commutative 36.7%

          \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

   11. Simplified 36.7%

       \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 38.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3800000000:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;i \leq -1.4 \cdot 10^{-260}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 5.8 \cdot 10^{-230}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;i \leq 6 \cdot 10^{-112}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 1.45 \cdot 10^{+85}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 30.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ t_2 := c \cdot \left(t \cdot j\right)\\ t_3 := b \cdot \left(a \cdot i\right)\\ \mathbf{if}\;i \leq -450000000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;i \leq -3 \cdot 10^{-260}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 5.2 \cdot 10^{-230}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq 2.6 \cdot 10^{-111}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 6.3 \cdot 10^{+84}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* x z))) (t_2 (* c (* t j))) (t_3 (* b (* a i))))
   (if (<= i -450000000.0)
     t_3
     (if (<= i -3e-260)
       t_1
       (if (<= i 5.2e-230)
         t_2
         (if (<= i 2.6e-111) t_1 (if (<= i 6.3e+84) t_2 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (x * z);
	double t_2 = c * (t * j);
	double t_3 = b * (a * i);
	double tmp;
	if (i <= -450000000.0) {
		tmp = t_3;
	} else if (i <= -3e-260) {
		tmp = t_1;
	} else if (i <= 5.2e-230) {
		tmp = t_2;
	} else if (i <= 2.6e-111) {
		tmp = t_1;
	} else if (i <= 6.3e+84) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y * (x * z)
    t_2 = c * (t * j)
    t_3 = b * (a * i)
    if (i <= (-450000000.0d0)) then
        tmp = t_3
    else if (i <= (-3d-260)) then
        tmp = t_1
    else if (i <= 5.2d-230) then
        tmp = t_2
    else if (i <= 2.6d-111) then
        tmp = t_1
    else if (i <= 6.3d+84) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (x * z);
	double t_2 = c * (t * j);
	double t_3 = b * (a * i);
	double tmp;
	if (i <= -450000000.0) {
		tmp = t_3;
	} else if (i <= -3e-260) {
		tmp = t_1;
	} else if (i <= 5.2e-230) {
		tmp = t_2;
	} else if (i <= 2.6e-111) {
		tmp = t_1;
	} else if (i <= 6.3e+84) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (x * z)
	t_2 = c * (t * j)
	t_3 = b * (a * i)
	tmp = 0
	if i <= -450000000.0:
		tmp = t_3
	elif i <= -3e-260:
		tmp = t_1
	elif i <= 5.2e-230:
		tmp = t_2
	elif i <= 2.6e-111:
		tmp = t_1
	elif i <= 6.3e+84:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(x * z))
	t_2 = Float64(c * Float64(t * j))
	t_3 = Float64(b * Float64(a * i))
	tmp = 0.0
	if (i <= -450000000.0)
		tmp = t_3;
	elseif (i <= -3e-260)
		tmp = t_1;
	elseif (i <= 5.2e-230)
		tmp = t_2;
	elseif (i <= 2.6e-111)
		tmp = t_1;
	elseif (i <= 6.3e+84)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * (x * z);
	t_2 = c * (t * j);
	t_3 = b * (a * i);
	tmp = 0.0;
	if (i <= -450000000.0)
		tmp = t_3;
	elseif (i <= -3e-260)
		tmp = t_1;
	elseif (i <= 5.2e-230)
		tmp = t_2;
	elseif (i <= 2.6e-111)
		tmp = t_1;
	elseif (i <= 6.3e+84)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -450000000.0], t$95$3, If[LessEqual[i, -3e-260], t$95$1, If[LessEqual[i, 5.2e-230], t$95$2, If[LessEqual[i, 2.6e-111], t$95$1, If[LessEqual[i, 6.3e+84], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -4.5e8 or 6.30000000000000013e84 < i

   1. Initial program 58.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 50.8%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 50.8%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

   5. Simplified 50.8%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

   6. Taylor expanded in i around inf 43.7%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]

   if -4.5e8 < i < -3.0000000000000001e-260 or 5.2000000000000003e-230 < i < 2.59999999999999982e-111

   1. Initial program 81.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around -inf 74.1%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-1 \cdot \left(c \cdot j\right) + \left(-1 \cdot \frac{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)}{t} + a \cdot x\right)\right)\right)} \]

   5. Simplified 79.3%

      \[\leadsto \color{blue}{\left(\left(x \cdot a - \frac{y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)}{t}\right) - j \cdot c\right) \cdot \left(-t\right)} \]

   6. Taylor expanded in y around -inf 42.6%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z - i \cdot j\right)} \]
   7. Step-by-step derivation

      1. *-commutative 42.6%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   8. Simplified 42.6%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   9. Taylor expanded in z around inf 35.1%

      \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} \]
   10. Step-by-step derivation

       1. *-commutative 35.1%

          \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} \]

   11. Simplified 35.1%

       \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} \]

   if -3.0000000000000001e-260 < i < 5.2000000000000003e-230 or 2.59999999999999982e-111 < i < 6.30000000000000013e84

   1. Initial program 72.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around -inf 72.5%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-1 \cdot \left(c \cdot j\right) + \left(-1 \cdot \frac{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)}{t} + a \cdot x\right)\right)\right)} \]

   5. Simplified 79.5%

      \[\leadsto \color{blue}{\left(\left(x \cdot a - \frac{y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)}{t}\right) - j \cdot c\right) \cdot \left(-t\right)} \]

   6. Taylor expanded in c around inf 71.3%

      \[\leadsto \left(\left(x \cdot a - \color{blue}{-1 \cdot \frac{b \cdot \left(c \cdot z\right)}{t}}\right) - j \cdot c\right) \cdot \left(-t\right) \]
   7. Step-by-step derivation

      1. associate-*r/ 71.3%

         \[\leadsto \left(\left(x \cdot a - \color{blue}{\frac{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)}{t}}\right) - j \cdot c\right) \cdot \left(-t\right) \]

      2. associate-*r* 71.3%

         \[\leadsto \left(\left(x \cdot a - \frac{\color{blue}{\left(-1 \cdot b\right) \cdot \left(c \cdot z\right)}}{t}\right) - j \cdot c\right) \cdot \left(-t\right) \]

      3. neg-mul-1 71.3%

         \[\leadsto \left(\left(x \cdot a - \frac{\color{blue}{\left(-b\right)} \cdot \left(c \cdot z\right)}{t}\right) - j \cdot c\right) \cdot \left(-t\right) \]

   8. Simplified 71.3%

      \[\leadsto \left(\left(x \cdot a - \color{blue}{\frac{\left(-b\right) \cdot \left(c \cdot z\right)}{t}}\right) - j \cdot c\right) \cdot \left(-t\right) \]

   9. Taylor expanded in j around inf 36.7%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   10. Step-by-step derivation

       1. *-commutative 36.7%

          \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

   11. Simplified 36.7%

       \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 39.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -450000000:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;i \leq -3 \cdot 10^{-260}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 5.2 \cdot 10^{-230}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;i \leq 2.6 \cdot 10^{-111}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 6.3 \cdot 10^{+84}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 30.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ t_2 := b \cdot \left(a \cdot i\right)\\ \mathbf{if}\;i \leq -4100000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -1.15 \cdot 10^{-260}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 6.8 \cdot 10^{-229}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 6.8 \cdot 10^{-111}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 3.7 \cdot 10^{+85}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j))) (t_2 (* b (* a i))))
   (if (<= i -4100000000.0)
     t_2
     (if (<= i -1.15e-260)
       (* y (* x z))
       (if (<= i 6.8e-229)
         t_1
         (if (<= i 6.8e-111) (* z (* x y)) (if (<= i 3.7e+85) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double t_2 = b * (a * i);
	double tmp;
	if (i <= -4100000000.0) {
		tmp = t_2;
	} else if (i <= -1.15e-260) {
		tmp = y * (x * z);
	} else if (i <= 6.8e-229) {
		tmp = t_1;
	} else if (i <= 6.8e-111) {
		tmp = z * (x * y);
	} else if (i <= 3.7e+85) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * (t * j)
    t_2 = b * (a * i)
    if (i <= (-4100000000.0d0)) then
        tmp = t_2
    else if (i <= (-1.15d-260)) then
        tmp = y * (x * z)
    else if (i <= 6.8d-229) then
        tmp = t_1
    else if (i <= 6.8d-111) then
        tmp = z * (x * y)
    else if (i <= 3.7d+85) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double t_2 = b * (a * i);
	double tmp;
	if (i <= -4100000000.0) {
		tmp = t_2;
	} else if (i <= -1.15e-260) {
		tmp = y * (x * z);
	} else if (i <= 6.8e-229) {
		tmp = t_1;
	} else if (i <= 6.8e-111) {
		tmp = z * (x * y);
	} else if (i <= 3.7e+85) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (t * j)
	t_2 = b * (a * i)
	tmp = 0
	if i <= -4100000000.0:
		tmp = t_2
	elif i <= -1.15e-260:
		tmp = y * (x * z)
	elif i <= 6.8e-229:
		tmp = t_1
	elif i <= 6.8e-111:
		tmp = z * (x * y)
	elif i <= 3.7e+85:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(t * j))
	t_2 = Float64(b * Float64(a * i))
	tmp = 0.0
	if (i <= -4100000000.0)
		tmp = t_2;
	elseif (i <= -1.15e-260)
		tmp = Float64(y * Float64(x * z));
	elseif (i <= 6.8e-229)
		tmp = t_1;
	elseif (i <= 6.8e-111)
		tmp = Float64(z * Float64(x * y));
	elseif (i <= 3.7e+85)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (t * j);
	t_2 = b * (a * i);
	tmp = 0.0;
	if (i <= -4100000000.0)
		tmp = t_2;
	elseif (i <= -1.15e-260)
		tmp = y * (x * z);
	elseif (i <= 6.8e-229)
		tmp = t_1;
	elseif (i <= 6.8e-111)
		tmp = z * (x * y);
	elseif (i <= 3.7e+85)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -4100000000.0], t$95$2, If[LessEqual[i, -1.15e-260], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 6.8e-229], t$95$1, If[LessEqual[i, 6.8e-111], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.7e+85], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -4.1e9 or 3.7000000000000002e85 < i

   1. Initial program 58.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 50.8%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 50.8%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

   5. Simplified 50.8%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

   6. Taylor expanded in i around inf 43.7%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]

   if -4.1e9 < i < -1.15e-260

   1. Initial program 87.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around -inf 79.6%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-1 \cdot \left(c \cdot j\right) + \left(-1 \cdot \frac{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)}{t} + a \cdot x\right)\right)\right)} \]

   5. Simplified 83.4%

      \[\leadsto \color{blue}{\left(\left(x \cdot a - \frac{y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)}{t}\right) - j \cdot c\right) \cdot \left(-t\right)} \]

   6. Taylor expanded in y around -inf 39.8%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z - i \cdot j\right)} \]
   7. Step-by-step derivation

      1. *-commutative 39.8%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   8. Simplified 39.8%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   9. Taylor expanded in z around inf 36.2%

      \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} \]
   10. Step-by-step derivation

       1. *-commutative 36.2%

          \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} \]

   11. Simplified 36.2%

       \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} \]

   if -1.15e-260 < i < 6.7999999999999998e-229 or 6.79999999999999993e-111 < i < 3.7000000000000002e85

   1. Initial program 72.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around -inf 72.5%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-1 \cdot \left(c \cdot j\right) + \left(-1 \cdot \frac{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)}{t} + a \cdot x\right)\right)\right)} \]

   5. Simplified 79.5%

      \[\leadsto \color{blue}{\left(\left(x \cdot a - \frac{y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)}{t}\right) - j \cdot c\right) \cdot \left(-t\right)} \]

   6. Taylor expanded in c around inf 71.3%

      \[\leadsto \left(\left(x \cdot a - \color{blue}{-1 \cdot \frac{b \cdot \left(c \cdot z\right)}{t}}\right) - j \cdot c\right) \cdot \left(-t\right) \]
   7. Step-by-step derivation

      1. associate-*r/ 71.3%

         \[\leadsto \left(\left(x \cdot a - \color{blue}{\frac{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)}{t}}\right) - j \cdot c\right) \cdot \left(-t\right) \]

      2. associate-*r* 71.3%

         \[\leadsto \left(\left(x \cdot a - \frac{\color{blue}{\left(-1 \cdot b\right) \cdot \left(c \cdot z\right)}}{t}\right) - j \cdot c\right) \cdot \left(-t\right) \]

      3. neg-mul-1 71.3%

         \[\leadsto \left(\left(x \cdot a - \frac{\color{blue}{\left(-b\right)} \cdot \left(c \cdot z\right)}{t}\right) - j \cdot c\right) \cdot \left(-t\right) \]

   8. Simplified 71.3%

      \[\leadsto \left(\left(x \cdot a - \color{blue}{\frac{\left(-b\right) \cdot \left(c \cdot z\right)}{t}}\right) - j \cdot c\right) \cdot \left(-t\right) \]

   9. Taylor expanded in j around inf 36.7%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   10. Step-by-step derivation

       1. *-commutative 36.7%

          \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

   11. Simplified 36.7%

       \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if 6.7999999999999998e-229 < i < 6.79999999999999993e-111

   1. Initial program 70.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 44.8%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 44.8%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

      2. *-commutative 44.8%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) \]

   5. Simplified 44.8%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   6. Taylor expanded in y around inf 34.2%

      \[\leadsto z \cdot \color{blue}{\left(x \cdot y\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 39.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4100000000:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;i \leq -1.15 \cdot 10^{-260}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 6.8 \cdot 10^{-229}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;i \leq 6.8 \cdot 10^{-111}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 3.7 \cdot 10^{+85}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 51.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{+220} \lor \neg \left(b \leq -1.56 \cdot 10^{+209}\right) \land \left(b \leq -23000000000 \lor \neg \left(b \leq 5.6 \cdot 10^{-16}\right)\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -5.5e+220)
         (and (not (<= b -1.56e+209))
              (or (<= b -23000000000.0) (not (<= b 5.6e-16)))))
   (* b (- (* a i) (* z c)))
   (* t (- (* c j) (* x a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -5.5e+220) || (!(b <= -1.56e+209) && ((b <= -23000000000.0) || !(b <= 5.6e-16)))) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = t * ((c * j) - (x * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-5.5d+220)) .or. (.not. (b <= (-1.56d+209))) .and. (b <= (-23000000000.0d0)) .or. (.not. (b <= 5.6d-16))) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = t * ((c * j) - (x * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -5.5e+220) || (!(b <= -1.56e+209) && ((b <= -23000000000.0) || !(b <= 5.6e-16)))) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = t * ((c * j) - (x * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -5.5e+220) or (not (b <= -1.56e+209) and ((b <= -23000000000.0) or not (b <= 5.6e-16))):
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = t * ((c * j) - (x * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -5.5e+220) || (!(b <= -1.56e+209) && ((b <= -23000000000.0) || !(b <= 5.6e-16))))
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -5.5e+220) || (~((b <= -1.56e+209)) && ((b <= -23000000000.0) || ~((b <= 5.6e-16)))))
		tmp = b * ((a * i) - (z * c));
	else
		tmp = t * ((c * j) - (x * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -5.5e+220], And[N[Not[LessEqual[b, -1.56e+209]], $MachinePrecision], Or[LessEqual[b, -23000000000.0], N[Not[LessEqual[b, 5.6e-16]], $MachinePrecision]]]], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.4999999999999999e220 or -1.56e209 < b < -2.3e10 or 5.6000000000000003e-16 < b

   1. Initial program 68.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 64.4%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 64.4%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

   5. Simplified 64.4%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

   if -5.4999999999999999e220 < b < -1.56e209 or -2.3e10 < b < 5.6000000000000003e-16

   1. Initial program 70.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 68.6%

      \[\leadsto \left(\color{blue}{z \cdot \left(-1 \cdot \frac{a \cdot \left(t \cdot x\right)}{z} + x \cdot y\right)} - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in t around inf 53.6%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 53.6%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 53.6%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 53.6%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

      4. *-commutative 53.6%

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) \]

   6. Simplified 53.6%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - a \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{+220} \lor \neg \left(b \leq -1.56 \cdot 10^{+209}\right) \land \left(b \leq -23000000000 \lor \neg \left(b \leq 5.6 \cdot 10^{-16}\right)\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 48.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -3.8 \cdot 10^{-109}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 3.25 \cdot 10^{-279}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-174}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))) (t_2 (* b (- (* a i) (* z c)))))
   (if (<= b -3.8e-109)
     t_2
     (if (<= b 3.25e-279)
       t_1
       (if (<= b 1.15e-174) (* x (* t (- a))) (if (<= b 1.45e-15) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -3.8e-109) {
		tmp = t_2;
	} else if (b <= 3.25e-279) {
		tmp = t_1;
	} else if (b <= 1.15e-174) {
		tmp = x * (t * -a);
	} else if (b <= 1.45e-15) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = b * ((a * i) - (z * c))
    if (b <= (-3.8d-109)) then
        tmp = t_2
    else if (b <= 3.25d-279) then
        tmp = t_1
    else if (b <= 1.15d-174) then
        tmp = x * (t * -a)
    else if (b <= 1.45d-15) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -3.8e-109) {
		tmp = t_2;
	} else if (b <= 3.25e-279) {
		tmp = t_1;
	} else if (b <= 1.15e-174) {
		tmp = x * (t * -a);
	} else if (b <= 1.45e-15) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -3.8e-109:
		tmp = t_2
	elif b <= 3.25e-279:
		tmp = t_1
	elif b <= 1.15e-174:
		tmp = x * (t * -a)
	elif b <= 1.45e-15:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -3.8e-109)
		tmp = t_2;
	elseif (b <= 3.25e-279)
		tmp = t_1;
	elseif (b <= 1.15e-174)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (b <= 1.45e-15)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -3.8e-109)
		tmp = t_2;
	elseif (b <= 3.25e-279)
		tmp = t_1;
	elseif (b <= 1.15e-174)
		tmp = x * (t * -a);
	elseif (b <= 1.45e-15)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.8e-109], t$95$2, If[LessEqual[b, 3.25e-279], t$95$1, If[LessEqual[b, 1.15e-174], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.45e-15], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.80000000000000002e-109 or 1.45000000000000009e-15 < b

   1. Initial program 67.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 58.3%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 58.3%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

   5. Simplified 58.3%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

   if -3.80000000000000002e-109 < b < 3.2499999999999998e-279 or 1.1499999999999999e-174 < b < 1.45000000000000009e-15

   1. Initial program 71.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 72.6%

      \[\leadsto \left(\color{blue}{z \cdot \left(-1 \cdot \frac{a \cdot \left(t \cdot x\right)}{z} + x \cdot y\right)} - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   4. Taylor expanded in j around inf 46.5%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]
   5. Step-by-step derivation

      1. *-commutative 46.5%

         \[\leadsto j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      2. *-commutative 46.5%

         \[\leadsto j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   6. Simplified 46.5%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot c - y \cdot i\right)} \]

   if 3.2499999999999998e-279 < b < 1.1499999999999999e-174

   1. Initial program 73.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around 0 49.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]

   4. Taylor expanded in a around -inf 57.8%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \frac{x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)}{a} + t \cdot x\right) - b \cdot i\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 57.8%

         \[\leadsto \color{blue}{-a \cdot \left(\left(-1 \cdot \frac{x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)}{a} + t \cdot x\right) - b \cdot i\right)} \]

      2. *-commutative 57.8%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \frac{x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)}{a} + t \cdot x\right) - b \cdot i\right) \cdot a} \]

      3. distribute-rgt-neg-in 57.8%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \frac{x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)}{a} + t \cdot x\right) - b \cdot i\right) \cdot \left(-a\right)} \]

   6. Simplified 62.2%

      \[\leadsto \color{blue}{\left(\left(t \cdot x - \frac{z \cdot \left(x \cdot y - c \cdot b\right)}{a}\right) - i \cdot b\right) \cdot \left(-a\right)} \]

   7. Taylor expanded in t around inf 50.7%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 50.7%

         \[\leadsto \color{blue}{-a \cdot \left(t \cdot x\right)} \]

      2. associate-*r* 50.8%

         \[\leadsto -\color{blue}{\left(a \cdot t\right) \cdot x} \]

      3. distribute-lft-neg-in 50.8%

         \[\leadsto \color{blue}{\left(-a \cdot t\right) \cdot x} \]

      4. distribute-rgt-neg-in 50.8%

         \[\leadsto \color{blue}{\left(a \cdot \left(-t\right)\right)} \cdot x \]

   9. Simplified 50.8%

      \[\leadsto \color{blue}{\left(a \cdot \left(-t\right)\right) \cdot x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{-109}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 3.25 \cdot 10^{-279}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-174}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-15}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 40.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{-286} \lor \neg \left(b \leq 4.25 \cdot 10^{-16}\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -7.5e-286) (not (<= b 4.25e-16)))
   (* b (- (* a i) (* z c)))
   (* x (* t (- a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -7.5e-286) || !(b <= 4.25e-16)) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = x * (t * -a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-7.5d-286)) .or. (.not. (b <= 4.25d-16))) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = x * (t * -a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -7.5e-286) || !(b <= 4.25e-16)) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = x * (t * -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -7.5e-286) or not (b <= 4.25e-16):
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = x * (t * -a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -7.5e-286) || !(b <= 4.25e-16))
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = Float64(x * Float64(t * Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -7.5e-286) || ~((b <= 4.25e-16)))
		tmp = b * ((a * i) - (z * c));
	else
		tmp = x * (t * -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -7.5e-286], N[Not[LessEqual[b, 4.25e-16]], $MachinePrecision]], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -7.50000000000000009e-286 or 4.25e-16 < b

   1. Initial program 67.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 52.6%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 52.6%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

   5. Simplified 52.6%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

   if -7.50000000000000009e-286 < b < 4.25e-16

   1. Initial program 73.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around 0 48.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]

   4. Taylor expanded in a around -inf 51.3%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(\left(-1 \cdot \frac{x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)}{a} + t \cdot x\right) - b \cdot i\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 51.3%

         \[\leadsto \color{blue}{-a \cdot \left(\left(-1 \cdot \frac{x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)}{a} + t \cdot x\right) - b \cdot i\right)} \]

      2. *-commutative 51.3%

         \[\leadsto -\color{blue}{\left(\left(-1 \cdot \frac{x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)}{a} + t \cdot x\right) - b \cdot i\right) \cdot a} \]

      3. distribute-rgt-neg-in 51.3%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot \frac{x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)}{a} + t \cdot x\right) - b \cdot i\right) \cdot \left(-a\right)} \]

   6. Simplified 55.5%

      \[\leadsto \color{blue}{\left(\left(t \cdot x - \frac{z \cdot \left(x \cdot y - c \cdot b\right)}{a}\right) - i \cdot b\right) \cdot \left(-a\right)} \]

   7. Taylor expanded in t around inf 34.0%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 34.0%

         \[\leadsto \color{blue}{-a \cdot \left(t \cdot x\right)} \]

      2. associate-*r* 36.1%

         \[\leadsto -\color{blue}{\left(a \cdot t\right) \cdot x} \]

      3. distribute-lft-neg-in 36.1%

         \[\leadsto \color{blue}{\left(-a \cdot t\right) \cdot x} \]

      4. distribute-rgt-neg-in 36.1%

         \[\leadsto \color{blue}{\left(a \cdot \left(-t\right)\right)} \cdot x \]

   9. Simplified 36.1%

      \[\leadsto \color{blue}{\left(a \cdot \left(-t\right)\right) \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{-286} \lor \neg \left(b \leq 4.25 \cdot 10^{-16}\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 29.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -8 \cdot 10^{-101} \lor \neg \left(i \leq 9.6 \cdot 10^{+84}\right):\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -8e-101) (not (<= i 9.6e+84))) (* b (* a i)) (* c (* t j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -8e-101) || !(i <= 9.6e+84)) {
		tmp = b * (a * i);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((i <= (-8d-101)) .or. (.not. (i <= 9.6d+84))) then
        tmp = b * (a * i)
    else
        tmp = c * (t * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -8e-101) || !(i <= 9.6e+84)) {
		tmp = b * (a * i);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (i <= -8e-101) or not (i <= 9.6e+84):
		tmp = b * (a * i)
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((i <= -8e-101) || !(i <= 9.6e+84))
		tmp = Float64(b * Float64(a * i));
	else
		tmp = Float64(c * Float64(t * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((i <= -8e-101) || ~((i <= 9.6e+84)))
		tmp = b * (a * i);
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[i, -8e-101], N[Not[LessEqual[i, 9.6e+84]], $MachinePrecision]], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -8.00000000000000041e-101 or 9.5999999999999999e84 < i

   1. Initial program 64.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 50.7%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 50.7%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

   5. Simplified 50.7%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

   6. Taylor expanded in i around inf 40.9%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]

   if -8.00000000000000041e-101 < i < 9.5999999999999999e84

   1. Initial program 74.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around -inf 72.5%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-1 \cdot \left(c \cdot j\right) + \left(-1 \cdot \frac{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)}{t} + a \cdot x\right)\right)\right)} \]

   5. Simplified 80.1%

      \[\leadsto \color{blue}{\left(\left(x \cdot a - \frac{y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(c \cdot z - i \cdot a\right)}{t}\right) - j \cdot c\right) \cdot \left(-t\right)} \]

   6. Taylor expanded in c around inf 64.4%

      \[\leadsto \left(\left(x \cdot a - \color{blue}{-1 \cdot \frac{b \cdot \left(c \cdot z\right)}{t}}\right) - j \cdot c\right) \cdot \left(-t\right) \]
   7. Step-by-step derivation

      1. associate-*r/ 64.4%

         \[\leadsto \left(\left(x \cdot a - \color{blue}{\frac{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)}{t}}\right) - j \cdot c\right) \cdot \left(-t\right) \]

      2. associate-*r* 64.4%

         \[\leadsto \left(\left(x \cdot a - \frac{\color{blue}{\left(-1 \cdot b\right) \cdot \left(c \cdot z\right)}}{t}\right) - j \cdot c\right) \cdot \left(-t\right) \]

      3. neg-mul-1 64.4%

         \[\leadsto \left(\left(x \cdot a - \frac{\color{blue}{\left(-b\right)} \cdot \left(c \cdot z\right)}{t}\right) - j \cdot c\right) \cdot \left(-t\right) \]

   8. Simplified 64.4%

      \[\leadsto \left(\left(x \cdot a - \color{blue}{\frac{\left(-b\right) \cdot \left(c \cdot z\right)}{t}}\right) - j \cdot c\right) \cdot \left(-t\right) \]

   9. Taylor expanded in j around inf 26.1%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   10. Step-by-step derivation

       1. *-commutative 26.1%

          \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

   11. Simplified 26.1%

       \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 33.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -8 \cdot 10^{-101} \lor \neg \left(i \leq 9.6 \cdot 10^{+84}\right):\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 22.2% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(b \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* b i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (b * i);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = a * (b * i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (b * i);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (b * i)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(b * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (b * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 69.4%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
2. Add Preprocessing

3. Taylor expanded in b around inf 41.2%

   \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
4. Step-by-step derivation

   1. *-commutative 41.2%

      \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

5. Simplified 41.2%

   \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

6. Taylor expanded in i around inf 22.6%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
7. Step-by-step derivation

   1. *-commutative 22.6%

      \[\leadsto a \cdot \color{blue}{\left(i \cdot b\right)} \]

8. Simplified 22.6%

   \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]

9. Final simplification 22.6%

   \[\leadsto a \cdot \left(b \cdot i\right) \]
10. Add Preprocessing

Alternative 29: 22.4% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ b \cdot \left(a \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* b (* a i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return b * (a * i);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = b * (a * i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return b * (a * i);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return b * (a * i)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(b * Float64(a * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = b * (a * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 69.4%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
2. Add Preprocessing

3. Taylor expanded in b around inf 41.2%

   \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
4. Step-by-step derivation

   1. *-commutative 41.2%

      \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

5. Simplified 41.2%

   \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

6. Taylor expanded in i around inf 23.4%

   \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]

7. Final simplification 23.4%

   \[\leadsto b \cdot \left(a \cdot i\right) \]
8. Add Preprocessing

Developer target: 68.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ t_2 := x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{if}\;t < -8.120978919195912 \cdot 10^{-33}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < -4.712553818218485 \cdot 10^{-169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t < -7.633533346031584 \cdot 10^{-308}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 1.0535888557455487 \cdot 10^{-139}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
          (/
           (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0)))
           (+ (* c t) (* i y)))))
        (t_2
         (-
          (* x (- (* z y) (* a t)))
          (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))
   (if (< t -8.120978919195912e-33)
     t_2
     (if (< t -4.712553818218485e-169)
       t_1
       (if (< t -7.633533346031584e-308)
         t_2
         (if (< t 1.0535888557455487e-139) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (pow((c * t), 2.0) - pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ** 2.0d0) - ((i * y) ** 2.0d0))) / ((c * t) + (i * y)))
    t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
    if (t < (-8.120978919195912d-33)) then
        tmp = t_2
    else if (t < (-4.712553818218485d-169)) then
        tmp = t_1
    else if (t < (-7.633533346031584d-308)) then
        tmp = t_2
    else if (t < 1.0535888557455487d-139) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (Math.pow((c * t), 2.0) - Math.pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (math.pow((c * t), 2.0) - math.pow((i * y), 2.0))) / ((c * t) + (i * y)))
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
	tmp = 0
	if t < -8.120978919195912e-33:
		tmp = t_2
	elif t < -4.712553818218485e-169:
		tmp = t_1
	elif t < -7.633533346031584e-308:
		tmp = t_2
	elif t < 1.0535888557455487e-139:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(Float64(j * Float64((Float64(c * t) ^ 2.0) - (Float64(i * y) ^ 2.0))) / Float64(Float64(c * t) + Float64(i * y))))
	t_2 = Float64(Float64(x * Float64(Float64(z * y) - Float64(a * t))) - Float64(Float64(b * Float64(Float64(z * c) - Float64(a * i))) - Float64(Float64(Float64(c * t) - Float64(y * i)) * j)))
	tmp = 0.0
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ^ 2.0) - ((i * y) ^ 2.0))) / ((c * t) + (i * y)));
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	tmp = 0.0;
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[Power[N[(c * t), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(i * y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * t), $MachinePrecision] + N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(c * t), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -8.120978919195912e-33], t$95$2, If[Less[t, -4.712553818218485e-169], t$95$1, If[Less[t, -7.633533346031584e-308], t$95$2, If[Less[t, 1.0535888557455487e-139], t$95$1, t$95$2]]]]]]

Reproduce

herbie shell --seed 2024082 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :alt
  (if (< t -8.120978919195912e-33) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -4.712553818218485e-169) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (if (< t -7.633533346031584e-308) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 1.0535888557455487e-139) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))