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

Percentage Accurate: 73.6% → 82.0%

Time: 18.7s

Alternatives: 19

Speedup: 0.5×

• 58.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 82.0% accurate, 0.2× speedup

Math

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

FPCore

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

C

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 90.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in y around inf 16.1%

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

      1. *-commutative 16.1%

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

      2. associate-*l* 26.8%

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

   5. Simplified 26.8%

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

   6. Taylor expanded in c around 0 32.4%

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

   8. Simplified 53.9%

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

4. Final simplification 82.1%

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

Alternative 2: 82.0% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((z * c) - (t * i)))) + (j * ((a * c) - (y * i)))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = (y * ((x * z) - (i * j))) + (i * (b * (t - (c * (z / i)))))
	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(z * c) - Float64(t * i)))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(i * Float64(b * Float64(t - Float64(c * Float64(z / i))))));
	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 * ((z * c) - (t * i)))) + (j * ((a * c) - (y * i)));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = (y * ((x * z) - (i * j))) + (i * (b * (t - (c * (z / i)))));
	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[(z * c), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(b * N[(t - N[(c * N[(z / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 90.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in a around 0 27.1%

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

   5. Simplified 46.7%

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

   6. Taylor expanded in i around inf 48.5%

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

      1. +-commutative 48.5%

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

      2. mul-1-neg 48.5%

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

      3. unsub-neg 48.5%

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

      4. *-commutative 48.5%

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

      5. associate-/l* 48.5%

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

      6. associate-/l* 51.9%

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

   8. Simplified 51.9%

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

   9. Taylor expanded in i around inf 48.5%

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

       1. *-commutative 48.5%

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

       2. +-commutative 48.5%

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

       3. mul-1-neg 48.5%

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

       4. associate-*r* 52.0%

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

       5. associate-*r/ 50.1%

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

       6. sub-neg 50.1%

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

       7. associate-*l* 51.9%

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

       8. distribute-lft-out-- 53.7%

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

       9. associate-*r/ 50.3%

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

       10. associate-*r* 46.8%

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

       11. *-commutative 46.8%

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

       12. *-commutative 46.8%

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

       13. associate-*l* 50.3%

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

       14. associate-*r/ 53.7%

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

   11. Simplified 53.7%

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

4. Final simplification 82.1%

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

Alternative 3: 63.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ t_2 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -3.3 \cdot 10^{+91}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -1.4 \cdot 10^{-154}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{-279}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;c \leq 7.5 \cdot 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* j (- (* a c) (* y i))) (* x (- (* t a) (* y z)))))
        (t_2 (* c (- (* a j) (* z b)))))
   (if (<= c -3.3e+91)
     t_2
     (if (<= c -1.4e-154)
       t_1
       (if (<= c 3.2e-279)
         (+ (* y (- (* x z) (* i j))) (* b (* t i)))
         (if (<= c 7.5e+59) 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 * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)));
	double t_2 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -3.3e+91) {
		tmp = t_2;
	} else if (c <= -1.4e-154) {
		tmp = t_1;
	} else if (c <= 3.2e-279) {
		tmp = (y * ((x * z) - (i * j))) + (b * (t * i));
	} else if (c <= 7.5e+59) {
		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 * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)))
    t_2 = c * ((a * j) - (z * b))
    if (c <= (-3.3d+91)) then
        tmp = t_2
    else if (c <= (-1.4d-154)) then
        tmp = t_1
    else if (c <= 3.2d-279) then
        tmp = (y * ((x * z) - (i * j))) + (b * (t * i))
    else if (c <= 7.5d+59) 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 * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)));
	double t_2 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -3.3e+91) {
		tmp = t_2;
	} else if (c <= -1.4e-154) {
		tmp = t_1;
	} else if (c <= 3.2e-279) {
		tmp = (y * ((x * z) - (i * j))) + (b * (t * i));
	} else if (c <= 7.5e+59) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)))
	t_2 = c * ((a * j) - (z * b))
	tmp = 0
	if c <= -3.3e+91:
		tmp = t_2
	elif c <= -1.4e-154:
		tmp = t_1
	elif c <= 3.2e-279:
		tmp = (y * ((x * z) - (i * j))) + (b * (t * i))
	elif c <= 7.5e+59:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) - Float64(x * Float64(Float64(t * a) - Float64(y * z))))
	t_2 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -3.3e+91)
		tmp = t_2;
	elseif (c <= -1.4e-154)
		tmp = t_1;
	elseif (c <= 3.2e-279)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(b * Float64(t * i)));
	elseif (c <= 7.5e+59)
		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 * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)));
	t_2 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -3.3e+91)
		tmp = t_2;
	elseif (c <= -1.4e-154)
		tmp = t_1;
	elseif (c <= 3.2e-279)
		tmp = (y * ((x * z) - (i * j))) + (b * (t * i));
	elseif (c <= 7.5e+59)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.3e+91], t$95$2, If[LessEqual[c, -1.4e-154], t$95$1, If[LessEqual[c, 3.2e-279], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 7.5e+59], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -3.30000000000000017e91 or 7.4999999999999996e59 < c

   1. Initial program 64.6%

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

   3. Taylor expanded in c around inf 75.1%

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

   if -3.30000000000000017e91 < c < -1.40000000000000006e-154 or 3.1999999999999999e-279 < c < 7.4999999999999996e59

   1. Initial program 77.5%

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

   3. Taylor expanded in b around 0 72.3%

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

   if -1.40000000000000006e-154 < c < 3.1999999999999999e-279

   1. Initial program 61.3%

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

   3. Taylor expanded in a around 0 63.5%

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

   5. Simplified 80.1%

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

   6. Taylor expanded in t around inf 77.6%

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

      1. *-commutative 77.6%

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

   8. Simplified 77.6%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.3 \cdot 10^{+91}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -1.4 \cdot 10^{-154}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{-279}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;c \leq 7.5 \cdot 10^{+59}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 64.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -8 \cdot 10^{+90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -2.5 \cdot 10^{-154}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;c \leq 3.5 \cdot 10^{+73}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* a j) (* z b)))))
   (if (<= c -8e+90)
     t_1
     (if (<= c -2.5e-154)
       (- (* j (- (* a c) (* y i))) (* x (- (* t a) (* y z))))
       (if (<= c 3.5e+73)
         (+ (* y (- (* x z) (* i j))) (* b (- (* t i) (* z c))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -8e+90) {
		tmp = t_1;
	} else if (c <= -2.5e-154) {
		tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)));
	} else if (c <= 3.5e+73) {
		tmp = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((a * j) - (z * b))
    if (c <= (-8d+90)) then
        tmp = t_1
    else if (c <= (-2.5d-154)) then
        tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)))
    else if (c <= 3.5d+73) then
        tmp = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -8e+90) {
		tmp = t_1;
	} else if (c <= -2.5e-154) {
		tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)));
	} else if (c <= 3.5e+73) {
		tmp = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((a * j) - (z * b))
	tmp = 0
	if c <= -8e+90:
		tmp = t_1
	elif c <= -2.5e-154:
		tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)))
	elif c <= 3.5e+73:
		tmp = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -8e+90)
		tmp = t_1;
	elseif (c <= -2.5e-154)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) - Float64(x * Float64(Float64(t * a) - Float64(y * z))));
	elseif (c <= 3.5e+73)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -8e+90)
		tmp = t_1;
	elseif (c <= -2.5e-154)
		tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)));
	elseif (c <= 3.5e+73)
		tmp = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -8e+90], t$95$1, If[LessEqual[c, -2.5e-154], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.5e+73], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -7.99999999999999973e90 or 3.50000000000000002e73 < c

   1. Initial program 64.8%

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

   3. Taylor expanded in c around inf 76.6%

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

   if -7.99999999999999973e90 < c < -2.5000000000000001e-154

   1. Initial program 68.9%

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

   3. Taylor expanded in b around 0 67.1%

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

   if -2.5000000000000001e-154 < c < 3.50000000000000002e73

   1. Initial program 74.9%

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

   3. Taylor expanded in a around 0 61.4%

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

   5. Simplified 74.1%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -8 \cdot 10^{+90}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -2.5 \cdot 10^{-154}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;c \leq 3.5 \cdot 10^{+73}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 30.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j\right)\\ \mathbf{if}\;c \leq -3.5 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -3.2 \cdot 10^{+29}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;c \leq -3.2 \cdot 10^{-219}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 5.6 \cdot 10^{-267}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq 4.5 \cdot 10^{+43}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* a j))))
   (if (<= c -3.5e+96)
     t_1
     (if (<= c -3.2e+29)
       (* b (* t i))
       (if (<= c -3.2e-219)
         (* y (* i (- j)))
         (if (<= c 5.6e-267)
           (* t (* b i))
           (if (<= c 4.5e+43) (* z (* x y)) 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 = c * (a * j);
	double tmp;
	if (c <= -3.5e+96) {
		tmp = t_1;
	} else if (c <= -3.2e+29) {
		tmp = b * (t * i);
	} else if (c <= -3.2e-219) {
		tmp = y * (i * -j);
	} else if (c <= 5.6e-267) {
		tmp = t * (b * i);
	} else if (c <= 4.5e+43) {
		tmp = z * (x * y);
	} 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 = c * (a * j)
    if (c <= (-3.5d+96)) then
        tmp = t_1
    else if (c <= (-3.2d+29)) then
        tmp = b * (t * i)
    else if (c <= (-3.2d-219)) then
        tmp = y * (i * -j)
    else if (c <= 5.6d-267) then
        tmp = t * (b * i)
    else if (c <= 4.5d+43) then
        tmp = z * (x * y)
    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 = c * (a * j);
	double tmp;
	if (c <= -3.5e+96) {
		tmp = t_1;
	} else if (c <= -3.2e+29) {
		tmp = b * (t * i);
	} else if (c <= -3.2e-219) {
		tmp = y * (i * -j);
	} else if (c <= 5.6e-267) {
		tmp = t * (b * i);
	} else if (c <= 4.5e+43) {
		tmp = z * (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (a * j)
	tmp = 0
	if c <= -3.5e+96:
		tmp = t_1
	elif c <= -3.2e+29:
		tmp = b * (t * i)
	elif c <= -3.2e-219:
		tmp = y * (i * -j)
	elif c <= 5.6e-267:
		tmp = t * (b * i)
	elif c <= 4.5e+43:
		tmp = z * (x * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(a * j))
	tmp = 0.0
	if (c <= -3.5e+96)
		tmp = t_1;
	elseif (c <= -3.2e+29)
		tmp = Float64(b * Float64(t * i));
	elseif (c <= -3.2e-219)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (c <= 5.6e-267)
		tmp = Float64(t * Float64(b * i));
	elseif (c <= 4.5e+43)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (a * j);
	tmp = 0.0;
	if (c <= -3.5e+96)
		tmp = t_1;
	elseif (c <= -3.2e+29)
		tmp = b * (t * i);
	elseif (c <= -3.2e-219)
		tmp = y * (i * -j);
	elseif (c <= 5.6e-267)
		tmp = t * (b * i);
	elseif (c <= 4.5e+43)
		tmp = z * (x * y);
	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[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.5e+96], t$95$1, If[LessEqual[c, -3.2e+29], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -3.2e-219], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.6e-267], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.5e+43], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -3.4999999999999999e96 or 4.5e43 < c

   1. Initial program 66.4%

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

   3. Taylor expanded in y around inf 65.5%

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

      1. *-commutative 65.5%

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

      2. associate-*l* 66.5%

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

   5. Simplified 66.5%

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

   6. Taylor expanded in c around inf 63.3%

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

      1. *-commutative 63.3%

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

      2. *-commutative 63.3%

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

      3. associate-*l* 69.0%

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

      4. *-commutative 69.0%

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

   8. Simplified 69.0%

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

   9. Taylor expanded in a around inf 42.1%

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

       1. *-commutative 42.1%

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

       2. associate-*l* 46.0%

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

       3. *-commutative 46.0%

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

   11. Simplified 46.0%

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

   if -3.4999999999999999e96 < c < -3.19999999999999987e29

   1. Initial program 68.5%

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

   3. Taylor expanded in y around inf 58.6%

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

      1. *-commutative 58.6%

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

      2. associate-*l* 64.0%

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

   5. Simplified 64.0%

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

   6. Taylor expanded in t around inf 37.8%

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

      1. *-commutative 37.8%

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

   8. Simplified 37.8%

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

   if -3.19999999999999987e29 < c < -3.19999999999999998e-219

   1. Initial program 67.3%

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

   3. Taylor expanded in y around inf 51.1%

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

      1. +-commutative 51.1%

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

      2. mul-1-neg 51.1%

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

      3. unsub-neg 51.1%

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

      4. *-commutative 51.1%

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

   5. Simplified 51.1%

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

   6. Taylor expanded in z around 0 38.9%

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

      1. mul-1-neg 38.9%

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

      2. *-commutative 38.9%

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

      3. distribute-lft-neg-in 38.9%

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

   8. Simplified 38.9%

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

   if -3.19999999999999998e-219 < c < 5.60000000000000009e-267

   1. Initial program 64.3%

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

   3. Taylor expanded in z around inf 58.4%

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

      1. +-commutative 58.4%

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

      2. mul-1-neg 58.4%

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

      3. unsub-neg 58.4%

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

      4. associate-/l* 55.1%

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

      5. associate-/l* 58.1%

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

   5. Simplified 58.1%

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

   6. Taylor expanded in t around inf 71.2%

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

      1. distribute-lft-out-- 71.2%

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

      2. *-commutative 71.2%

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

   8. Simplified 71.2%

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

   9. Taylor expanded in x around 0 48.6%

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

   if 5.60000000000000009e-267 < c < 4.5e43

   1. Initial program 81.0%

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

   3. Taylor expanded in z around inf 40.1%

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

      1. *-commutative 40.1%

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

   5. Simplified 40.1%

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

   6. Taylor expanded in y around inf 34.1%

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

4. Final simplification 41.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.5 \cdot 10^{+96}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;c \leq -3.2 \cdot 10^{+29}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;c \leq -3.2 \cdot 10^{-219}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 5.6 \cdot 10^{-267}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq 4.5 \cdot 10^{+43}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 59.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -3.9 \cdot 10^{+89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -2.75 \cdot 10^{-154}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{+61}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* a j) (* z b)))))
   (if (<= c -3.9e+89)
     t_1
     (if (<= c -2.75e-154)
       (+ (* x (* y z)) (* j (- (* a c) (* y i))))
       (if (<= c 1.15e+61) (+ (* y (- (* x z) (* i j))) (* b (* t i))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -3.9e+89) {
		tmp = t_1;
	} else if (c <= -2.75e-154) {
		tmp = (x * (y * z)) + (j * ((a * c) - (y * i)));
	} else if (c <= 1.15e+61) {
		tmp = (y * ((x * z) - (i * j))) + (b * (t * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((a * j) - (z * b))
    if (c <= (-3.9d+89)) then
        tmp = t_1
    else if (c <= (-2.75d-154)) then
        tmp = (x * (y * z)) + (j * ((a * c) - (y * i)))
    else if (c <= 1.15d+61) then
        tmp = (y * ((x * z) - (i * j))) + (b * (t * i))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -3.9e+89) {
		tmp = t_1;
	} else if (c <= -2.75e-154) {
		tmp = (x * (y * z)) + (j * ((a * c) - (y * i)));
	} else if (c <= 1.15e+61) {
		tmp = (y * ((x * z) - (i * j))) + (b * (t * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((a * j) - (z * b))
	tmp = 0
	if c <= -3.9e+89:
		tmp = t_1
	elif c <= -2.75e-154:
		tmp = (x * (y * z)) + (j * ((a * c) - (y * i)))
	elif c <= 1.15e+61:
		tmp = (y * ((x * z) - (i * j))) + (b * (t * i))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -3.9e+89)
		tmp = t_1;
	elseif (c <= -2.75e-154)
		tmp = Float64(Float64(x * Float64(y * z)) + Float64(j * Float64(Float64(a * c) - Float64(y * i))));
	elseif (c <= 1.15e+61)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(b * Float64(t * i)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -3.9e+89)
		tmp = t_1;
	elseif (c <= -2.75e-154)
		tmp = (x * (y * z)) + (j * ((a * c) - (y * i)));
	elseif (c <= 1.15e+61)
		tmp = (y * ((x * z) - (i * j))) + (b * (t * i));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.9e+89], t$95$1, If[LessEqual[c, -2.75e-154], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.15e+61], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -3.90000000000000011e89 or 1.15e61 < c

   1. Initial program 64.6%

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

   3. Taylor expanded in c around inf 75.1%

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

   if -3.90000000000000011e89 < c < -2.75000000000000001e-154

   1. Initial program 68.9%

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

   3. Taylor expanded in y around inf 61.2%

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

      1. *-commutative 61.2%

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

      2. associate-*l* 61.4%

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

   5. Simplified 61.4%

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

   6. Taylor expanded in b around 0 55.4%

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

   if -2.75000000000000001e-154 < c < 1.15e61

   1. Initial program 75.5%

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

   3. Taylor expanded in a around 0 62.3%

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

   5. Simplified 73.8%

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

   6. Taylor expanded in t around inf 70.3%

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

      1. *-commutative 70.3%

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

   8. Simplified 70.3%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.9 \cdot 10^{+89}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -2.75 \cdot 10^{-154}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{+61}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 52.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -2.05 \cdot 10^{+38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 5 \cdot 10^{-168}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 230:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 4.8 \cdot 10^{+76}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (<= j -2.05e+38)
     t_1
     (if (<= j 5e-168)
       (* z (- (* x y) (* b c)))
       (if (<= j 230.0)
         (* b (- (* t i) (* z c)))
         (if (<= j 4.8e+76) (* y (- (* x z) (* i j))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -2.05e+38) {
		tmp = t_1;
	} else if (j <= 5e-168) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 230.0) {
		tmp = b * ((t * i) - (z * c));
	} else if (j <= 4.8e+76) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    if (j <= (-2.05d+38)) then
        tmp = t_1
    else if (j <= 5d-168) then
        tmp = z * ((x * y) - (b * c))
    else if (j <= 230.0d0) then
        tmp = b * ((t * i) - (z * c))
    else if (j <= 4.8d+76) then
        tmp = y * ((x * z) - (i * j))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -2.05e+38) {
		tmp = t_1;
	} else if (j <= 5e-168) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 230.0) {
		tmp = b * ((t * i) - (z * c));
	} else if (j <= 4.8e+76) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -2.05e+38:
		tmp = t_1
	elif j <= 5e-168:
		tmp = z * ((x * y) - (b * c))
	elif j <= 230.0:
		tmp = b * ((t * i) - (z * c))
	elif j <= 4.8e+76:
		tmp = y * ((x * z) - (i * j))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -2.05e+38)
		tmp = t_1;
	elseif (j <= 5e-168)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (j <= 230.0)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (j <= 4.8e+76)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -2.05e+38)
		tmp = t_1;
	elseif (j <= 5e-168)
		tmp = z * ((x * y) - (b * c));
	elseif (j <= 230.0)
		tmp = b * ((t * i) - (z * c));
	elseif (j <= 4.8e+76)
		tmp = y * ((x * z) - (i * j));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.05e+38], t$95$1, If[LessEqual[j, 5e-168], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 230.0], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.8e+76], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -2.0500000000000002e38 or 4.8e76 < j

   1. Initial program 69.6%

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

   3. Taylor expanded in y around inf 72.5%

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

      1. *-commutative 72.5%

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

      2. associate-*l* 75.5%

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

   5. Simplified 75.5%

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

   6. Taylor expanded in j around inf 75.7%

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

      1. *-commutative 75.7%

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

      2. *-commutative 75.7%

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

      3. *-commutative 75.7%

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

   8. Simplified 75.7%

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

   if -2.0500000000000002e38 < j < 5.00000000000000001e-168

   1. Initial program 68.5%

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

   3. Taylor expanded in z around inf 57.4%

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

      1. *-commutative 57.4%

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

   5. Simplified 57.4%

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

   if 5.00000000000000001e-168 < j < 230

   1. Initial program 74.8%

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

   3. Taylor expanded in b around inf 49.1%

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

      1. *-commutative 49.1%

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

   5. Simplified 49.1%

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

   if 230 < j < 4.8e76

   1. Initial program 74.1%

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

   3. Taylor expanded in y around inf 74.3%

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

      1. +-commutative 74.3%

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

      2. mul-1-neg 74.3%

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

      3. unsub-neg 74.3%

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

      4. *-commutative 74.3%

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

   5. Simplified 74.3%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.05 \cdot 10^{+38}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 5 \cdot 10^{-168}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 230:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 4.8 \cdot 10^{+76}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+205} \lor \neg \left(t \leq 7 \cdot 10^{+160}\right):\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -3.4e+205) (not (<= t 7e+160)))
   (* t (- (* b i) (* x a)))
   (+ (* z (- (* x y) (* b c))) (* j (- (* a c) (* y i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -3.4e+205) || !(t <= 7e+160)) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = (z * ((x * y) - (b * c))) + (j * ((a * c) - (y * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((t <= (-3.4d+205)) .or. (.not. (t <= 7d+160))) then
        tmp = t * ((b * i) - (x * a))
    else
        tmp = (z * ((x * y) - (b * c))) + (j * ((a * c) - (y * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -3.4e+205) || !(t <= 7e+160)) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = (z * ((x * y) - (b * c))) + (j * ((a * c) - (y * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -3.4e+205) or not (t <= 7e+160):
		tmp = t * ((b * i) - (x * a))
	else:
		tmp = (z * ((x * y) - (b * c))) + (j * ((a * c) - (y * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -3.4e+205) || !(t <= 7e+160))
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	else
		tmp = Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -3.4e+205) || ~((t <= 7e+160)))
		tmp = t * ((b * i) - (x * a));
	else
		tmp = (z * ((x * y) - (b * c))) + (j * ((a * c) - (y * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -3.4e+205], N[Not[LessEqual[t, 7e+160]], $MachinePrecision]], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.4e205 or 7.00000000000000051e160 < t

   1. Initial program 62.0%

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

   3. Taylor expanded in z around inf 57.7%

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

      1. +-commutative 57.7%

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

      2. mul-1-neg 57.7%

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

      3. unsub-neg 57.7%

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

      4. associate-/l* 51.4%

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

      5. associate-/l* 49.5%

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

   5. Simplified 49.5%

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

   6. Taylor expanded in t around inf 83.8%

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

      1. distribute-lft-out-- 83.8%

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

      2. *-commutative 83.8%

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

   8. Simplified 83.8%

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

   9. Taylor expanded in t around 0 83.8%

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

       1. mul-1-neg 83.8%

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

       2. *-commutative 83.8%

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

       3. fmm-undef 83.8%

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

       4. distribute-rgt-neg-out 83.8%

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

       5. neg-sub0 83.8%

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

       6. fmm-undef 83.8%

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

       7. associate--r- 83.8%

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

       8. neg-sub0 83.8%

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

       9. *-commutative 83.8%

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

       10. mul-1-neg 83.8%

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

       11. +-commutative 83.8%

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

       12. mul-1-neg 83.8%

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

       13. *-commutative 83.8%

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

       14. unsub-neg 83.8%

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

   11. Simplified 83.8%

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

   if -3.4e205 < t < 7.00000000000000051e160

   1. Initial program 72.2%

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

   3. Taylor expanded in y around inf 69.2%

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

      1. *-commutative 69.2%

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

      2. associate-*l* 71.0%

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

   5. Simplified 71.0%

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

   6. Taylor expanded in c around inf 66.7%

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

      1. *-commutative 66.7%

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

      2. *-commutative 66.7%

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

      3. associate-*l* 69.5%

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

      4. *-commutative 69.5%

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

   8. Simplified 69.5%

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

   9. Taylor expanded in y around 0 64.9%

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

       1. associate-*r* 68.2%

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

       2. associate-*r* 70.9%

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

       3. distribute-rgt-out-- 72.3%

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

   11. Simplified 72.3%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+205} \lor \neg \left(t \leq 7 \cdot 10^{+160}\right):\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 67.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.4 \cdot 10^{+67}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+24}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -5.4e+67)
   (+ (* y (- (* x z) (* i j))) (* b (- (* t i) (* z c))))
   (if (<= b 4e+24)
     (+ (* z (- (* x y) (* b c))) (* j (- (* a c) (* y i))))
     (- (* x (- (* y z) (* t a))) (* b (- (* z c) (* t i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -5.4e+67) {
		tmp = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)));
	} else if (b <= 4e+24) {
		tmp = (z * ((x * y) - (b * c))) + (j * ((a * c) - (y * i)));
	} else {
		tmp = (x * ((y * z) - (t * a))) - (b * ((z * c) - (t * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-5.4d+67)) then
        tmp = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)))
    else if (b <= 4d+24) then
        tmp = (z * ((x * y) - (b * c))) + (j * ((a * c) - (y * i)))
    else
        tmp = (x * ((y * z) - (t * a))) - (b * ((z * c) - (t * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -5.4e+67) {
		tmp = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)));
	} else if (b <= 4e+24) {
		tmp = (z * ((x * y) - (b * c))) + (j * ((a * c) - (y * i)));
	} else {
		tmp = (x * ((y * z) - (t * a))) - (b * ((z * c) - (t * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -5.4e+67:
		tmp = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)))
	elif b <= 4e+24:
		tmp = (z * ((x * y) - (b * c))) + (j * ((a * c) - (y * i)))
	else:
		tmp = (x * ((y * z) - (t * a))) - (b * ((z * c) - (t * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -5.4e+67)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	elseif (b <= 4e+24)
		tmp = Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))));
	else
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(z * c) - Float64(t * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -5.4e+67)
		tmp = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)));
	elseif (b <= 4e+24)
		tmp = (z * ((x * y) - (b * c))) + (j * ((a * c) - (y * i)));
	else
		tmp = (x * ((y * z) - (t * a))) - (b * ((z * c) - (t * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -5.4e+67], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4e+24], N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(z * c), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.3999999999999998e67

   1. Initial program 66.5%

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

   3. Taylor expanded in a around 0 66.9%

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

   5. Simplified 76.2%

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

   if -5.3999999999999998e67 < b < 3.9999999999999999e24

   1. Initial program 70.1%

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

   3. Taylor expanded in y around inf 64.9%

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

      1. *-commutative 64.9%

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

      2. associate-*l* 66.2%

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

   5. Simplified 66.2%

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

   6. Taylor expanded in c around inf 66.2%

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

      1. *-commutative 66.2%

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

      2. *-commutative 66.2%

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

      3. associate-*l* 70.7%

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

      4. *-commutative 70.7%

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

   8. Simplified 70.7%

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

   9. Taylor expanded in y around 0 65.0%

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

       1. associate-*r* 68.7%

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

       2. associate-*r* 73.2%

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

       3. distribute-rgt-out-- 73.8%

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

   11. Simplified 73.8%

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

   if 3.9999999999999999e24 < b

   1. Initial program 73.9%

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

   3. Taylor expanded in j around 0 82.7%

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

      1. *-commutative 82.7%

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

      2. *-commutative 82.7%

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

   5. Simplified 82.7%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.4 \cdot 10^{+67}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+24}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 30.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.35 \cdot 10^{+15}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq -1.5 \cdot 10^{-216}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 6.5 \cdot 10^{-267}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq 9 \cdot 10^{+44}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -1.35e+15)
   (* z (* b (- c)))
   (if (<= c -1.5e-216)
     (* y (* i (- j)))
     (if (<= c 6.5e-267)
       (* t (* b i))
       (if (<= c 9e+44) (* z (* x y)) (* c (* a 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 (c <= -1.35e+15) {
		tmp = z * (b * -c);
	} else if (c <= -1.5e-216) {
		tmp = y * (i * -j);
	} else if (c <= 6.5e-267) {
		tmp = t * (b * i);
	} else if (c <= 9e+44) {
		tmp = z * (x * y);
	} else {
		tmp = c * (a * 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 (c <= (-1.35d+15)) then
        tmp = z * (b * -c)
    else if (c <= (-1.5d-216)) then
        tmp = y * (i * -j)
    else if (c <= 6.5d-267) then
        tmp = t * (b * i)
    else if (c <= 9d+44) then
        tmp = z * (x * y)
    else
        tmp = c * (a * 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 (c <= -1.35e+15) {
		tmp = z * (b * -c);
	} else if (c <= -1.5e-216) {
		tmp = y * (i * -j);
	} else if (c <= 6.5e-267) {
		tmp = t * (b * i);
	} else if (c <= 9e+44) {
		tmp = z * (x * y);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -1.35e+15:
		tmp = z * (b * -c)
	elif c <= -1.5e-216:
		tmp = y * (i * -j)
	elif c <= 6.5e-267:
		tmp = t * (b * i)
	elif c <= 9e+44:
		tmp = z * (x * y)
	else:
		tmp = c * (a * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -1.35e+15)
		tmp = Float64(z * Float64(b * Float64(-c)));
	elseif (c <= -1.5e-216)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (c <= 6.5e-267)
		tmp = Float64(t * Float64(b * i));
	elseif (c <= 9e+44)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = Float64(c * Float64(a * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -1.35e+15)
		tmp = z * (b * -c);
	elseif (c <= -1.5e-216)
		tmp = y * (i * -j);
	elseif (c <= 6.5e-267)
		tmp = t * (b * i);
	elseif (c <= 9e+44)
		tmp = z * (x * y);
	else
		tmp = c * (a * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -1.35e+15], N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.5e-216], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.5e-267], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 9e+44], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -1.35e15

   1. Initial program 61.7%

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

   3. Taylor expanded in z around inf 57.0%

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

      1. *-commutative 57.0%

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

   5. Simplified 57.0%

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

   6. Taylor expanded in y around 0 42.8%

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

      1. *-commutative 42.8%

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

      2. neg-mul-1 42.8%

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

      3. distribute-lft-neg-in 42.8%

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

   8. Simplified 42.8%

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

   if -1.35e15 < c < -1.50000000000000006e-216

   1. Initial program 70.5%

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

   3. Taylor expanded in y around inf 52.3%

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

      1. +-commutative 52.3%

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

      2. mul-1-neg 52.3%

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

      3. unsub-neg 52.3%

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

      4. *-commutative 52.3%

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

   5. Simplified 52.3%

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

   6. Taylor expanded in z around 0 40.9%

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

      1. mul-1-neg 40.9%

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

      2. *-commutative 40.9%

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

      3. distribute-lft-neg-in 40.9%

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

   8. Simplified 40.9%

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

   if -1.50000000000000006e-216 < c < 6.4999999999999999e-267

   1. Initial program 64.3%

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

   3. Taylor expanded in z around inf 58.4%

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

      1. +-commutative 58.4%

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

      2. mul-1-neg 58.4%

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

      3. unsub-neg 58.4%

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

      4. associate-/l* 55.1%

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

      5. associate-/l* 58.1%

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

   5. Simplified 58.1%

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

   6. Taylor expanded in t around inf 71.2%

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

      1. distribute-lft-out-- 71.2%

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

      2. *-commutative 71.2%

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

   8. Simplified 71.2%

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

   9. Taylor expanded in x around 0 48.6%

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

   if 6.4999999999999999e-267 < c < 9e44

   1. Initial program 81.0%

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

   3. Taylor expanded in z around inf 40.1%

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

      1. *-commutative 40.1%

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

   5. Simplified 40.1%

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

   6. Taylor expanded in y around inf 34.1%

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

   if 9e44 < c

   1. Initial program 69.4%

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

   3. Taylor expanded in y around inf 66.2%

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

      1. *-commutative 66.2%

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

      2. associate-*l* 69.6%

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

   5. Simplified 69.6%

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

   6. Taylor expanded in c around inf 66.1%

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

      1. *-commutative 66.1%

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

      2. *-commutative 66.1%

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

      3. associate-*l* 71.1%

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

      4. *-commutative 71.1%

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

   8. Simplified 71.1%

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

   9. Taylor expanded in a around inf 47.9%

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

       1. *-commutative 47.9%

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

       2. associate-*l* 50.8%

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

       3. *-commutative 50.8%

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

   11. Simplified 50.8%

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

4. Final simplification 42.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.35 \cdot 10^{+15}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq -1.5 \cdot 10^{-216}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 6.5 \cdot 10^{-267}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq 9 \cdot 10^{+44}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 59.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.75 \cdot 10^{+59} \lor \neg \left(b \leq 4.3 \cdot 10^{-29}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -1.75e+59) (not (<= b 4.3e-29)))
   (* b (- (* t i) (* z c)))
   (+ (* z (* x y)) (* j (- (* a c) (* y i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -1.75e+59) || !(b <= 4.3e-29)) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = (z * (x * y)) + (j * ((a * c) - (y * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-1.75d+59)) .or. (.not. (b <= 4.3d-29))) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = (z * (x * y)) + (j * ((a * c) - (y * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -1.75e+59) || !(b <= 4.3e-29)) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = (z * (x * y)) + (j * ((a * c) - (y * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -1.75e+59) or not (b <= 4.3e-29):
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = (z * (x * y)) + (j * ((a * c) - (y * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -1.75e+59) || !(b <= 4.3e-29))
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = Float64(Float64(z * Float64(x * y)) + Float64(j * Float64(Float64(a * c) - Float64(y * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -1.75e+59) || ~((b <= 4.3e-29)))
		tmp = b * ((t * i) - (z * c));
	else
		tmp = (z * (x * y)) + (j * ((a * c) - (y * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -1.75e+59], N[Not[LessEqual[b, 4.3e-29]], $MachinePrecision]], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.75e59 or 4.2999999999999998e-29 < b

   1. Initial program 71.0%

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

   3. Taylor expanded in b around inf 67.8%

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

      1. *-commutative 67.8%

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

   5. Simplified 67.8%

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

   if -1.75e59 < b < 4.2999999999999998e-29

   1. Initial program 69.9%

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

   3. Taylor expanded in y around inf 64.9%

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

      1. *-commutative 64.9%

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

      2. associate-*l* 66.9%

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

   5. Simplified 66.9%

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

   6. Taylor expanded in c around inf 67.1%

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

      1. *-commutative 67.1%

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

      2. *-commutative 67.1%

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

      3. associate-*l* 71.9%

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

      4. *-commutative 71.9%

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

   8. Simplified 71.9%

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

   9. Taylor expanded in y around inf 65.5%

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

       1. *-commutative 65.5%

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

       2. *-commutative 65.5%

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

       3. associate-*l* 69.2%

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

       4. *-commutative 69.2%

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

   11. Simplified 69.2%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.75 \cdot 10^{+59} \lor \neg \left(b \leq 4.3 \cdot 10^{-29}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 59.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.7 \cdot 10^{+57} \lor \neg \left(b \leq 3.5 \cdot 10^{-26}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -1.7e+57) (not (<= b 3.5e-26)))
   (* b (- (* t i) (* z c)))
   (+ (* x (* y z)) (* j (- (* a c) (* y i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -1.7e+57) || !(b <= 3.5e-26)) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = (x * (y * z)) + (j * ((a * c) - (y * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-1.7d+57)) .or. (.not. (b <= 3.5d-26))) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = (x * (y * z)) + (j * ((a * c) - (y * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -1.7e+57) || !(b <= 3.5e-26)) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = (x * (y * z)) + (j * ((a * c) - (y * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -1.7e+57) or not (b <= 3.5e-26):
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = (x * (y * z)) + (j * ((a * c) - (y * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -1.7e+57) || !(b <= 3.5e-26))
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = Float64(Float64(x * Float64(y * z)) + Float64(j * Float64(Float64(a * c) - Float64(y * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -1.7e+57) || ~((b <= 3.5e-26)))
		tmp = b * ((t * i) - (z * c));
	else
		tmp = (x * (y * z)) + (j * ((a * c) - (y * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -1.7e+57], N[Not[LessEqual[b, 3.5e-26]], $MachinePrecision]], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.69999999999999996e57 or 3.49999999999999985e-26 < b

   1. Initial program 71.0%

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

   3. Taylor expanded in b around inf 67.8%

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

      1. *-commutative 67.8%

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

   5. Simplified 67.8%

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

   if -1.69999999999999996e57 < b < 3.49999999999999985e-26

   1. Initial program 69.9%

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

   3. Taylor expanded in y around inf 64.9%

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

      1. *-commutative 64.9%

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

      2. associate-*l* 66.9%

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

   5. Simplified 66.9%

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

   6. Taylor expanded in b around 0 65.5%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.7 \cdot 10^{+57} \lor \neg \left(b \leq 3.5 \cdot 10^{-26}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 50.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.2 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{-102}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-54}:\\ \;\;\;\;\left(-i\right) \cdot \left(y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))))
   (if (<= b -1.2e+34)
     t_1
     (if (<= b 7.5e-102)
       (* a (- (* c j) (* x t)))
       (if (<= b 1.05e-54) (* (- i) (* y j)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -1.2e+34) {
		tmp = t_1;
	} else if (b <= 7.5e-102) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= 1.05e-54) {
		tmp = -i * (y * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    if (b <= (-1.2d+34)) then
        tmp = t_1
    else if (b <= 7.5d-102) then
        tmp = a * ((c * j) - (x * t))
    else if (b <= 1.05d-54) then
        tmp = -i * (y * j)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -1.2e+34) {
		tmp = t_1;
	} else if (b <= 7.5e-102) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= 1.05e-54) {
		tmp = -i * (y * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -1.2e+34:
		tmp = t_1
	elif b <= 7.5e-102:
		tmp = a * ((c * j) - (x * t))
	elif b <= 1.05e-54:
		tmp = -i * (y * j)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -1.2e+34)
		tmp = t_1;
	elseif (b <= 7.5e-102)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (b <= 1.05e-54)
		tmp = Float64(Float64(-i) * Float64(y * j));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -1.2e+34)
		tmp = t_1;
	elseif (b <= 7.5e-102)
		tmp = a * ((c * j) - (x * t));
	elseif (b <= 1.05e-54)
		tmp = -i * (y * j);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.2e+34], t$95$1, If[LessEqual[b, 7.5e-102], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.05e-54], N[((-i) * N[(y * j), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.19999999999999993e34 or 1.05e-54 < b

   1. Initial program 71.2%

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

   3. Taylor expanded in b around inf 66.7%

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

      1. *-commutative 66.7%

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

   5. Simplified 66.7%

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

   if -1.19999999999999993e34 < b < 7.5000000000000008e-102

   1. Initial program 68.8%

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

   3. Taylor expanded in a around inf 44.4%

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

      1. +-commutative 44.4%

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

      2. mul-1-neg 44.4%

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

      3. unsub-neg 44.4%

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

   5. Simplified 44.4%

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

   if 7.5000000000000008e-102 < b < 1.05e-54

   1. Initial program 74.5%

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

   3. Taylor expanded in y around inf 79.7%

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

      1. *-commutative 79.7%

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

      2. associate-*l* 85.5%

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

   5. Simplified 85.5%

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

   6. Taylor expanded in c around inf 85.5%

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

      1. *-commutative 85.5%

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

      2. *-commutative 85.5%

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

      3. associate-*l* 85.5%

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

      4. *-commutative 85.5%

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

   8. Simplified 85.5%

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

   9. Taylor expanded in i around inf 49.3%

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

       1. associate-*r* 49.3%

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

       2. neg-mul-1 49.3%

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

       3. *-commutative 49.3%

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

   11. Simplified 49.3%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.2 \cdot 10^{+34}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{-102}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-54}:\\ \;\;\;\;\left(-i\right) \cdot \left(y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 42.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-i\right) \cdot \left(y \cdot j\right)\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{+66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+60}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+145}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (- i) (* y j))))
   (if (<= y -1.2e+66)
     t_1
     (if (<= y 2.6e+60)
       (* a (- (* c j) (* x t)))
       (if (<= y 1.7e+145) (* z (* x y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = -i * (y * j);
	double tmp;
	if (y <= -1.2e+66) {
		tmp = t_1;
	} else if (y <= 2.6e+60) {
		tmp = a * ((c * j) - (x * t));
	} else if (y <= 1.7e+145) {
		tmp = z * (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -i * (y * j)
    if (y <= (-1.2d+66)) then
        tmp = t_1
    else if (y <= 2.6d+60) then
        tmp = a * ((c * j) - (x * t))
    else if (y <= 1.7d+145) then
        tmp = z * (x * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = -i * (y * j);
	double tmp;
	if (y <= -1.2e+66) {
		tmp = t_1;
	} else if (y <= 2.6e+60) {
		tmp = a * ((c * j) - (x * t));
	} else if (y <= 1.7e+145) {
		tmp = z * (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = -i * (y * j)
	tmp = 0
	if y <= -1.2e+66:
		tmp = t_1
	elif y <= 2.6e+60:
		tmp = a * ((c * j) - (x * t))
	elif y <= 1.7e+145:
		tmp = z * (x * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(-i) * Float64(y * j))
	tmp = 0.0
	if (y <= -1.2e+66)
		tmp = t_1;
	elseif (y <= 2.6e+60)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (y <= 1.7e+145)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = -i * (y * j);
	tmp = 0.0;
	if (y <= -1.2e+66)
		tmp = t_1;
	elseif (y <= 2.6e+60)
		tmp = a * ((c * j) - (x * t));
	elseif (y <= 1.7e+145)
		tmp = z * (x * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[((-i) * N[(y * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.2e+66], t$95$1, If[LessEqual[y, 2.6e+60], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e+145], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.2000000000000001e66 or 1.7e145 < y

   1. Initial program 46.2%

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

   3. Taylor expanded in y around inf 51.9%

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

      1. *-commutative 51.9%

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

      2. associate-*l* 62.8%

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

   5. Simplified 62.8%

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

   6. Taylor expanded in c around inf 63.0%

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

      1. *-commutative 63.0%

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

      2. *-commutative 63.0%

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

      3. associate-*l* 65.3%

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

      4. *-commutative 65.3%

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

   8. Simplified 65.3%

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

   9. Taylor expanded in i around inf 46.6%

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

       1. associate-*r* 46.6%

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

       2. neg-mul-1 46.6%

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

       3. *-commutative 46.6%

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

   11. Simplified 46.6%

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

   if -1.2000000000000001e66 < y < 2.60000000000000008e60

   1. Initial program 84.0%

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

   3. Taylor expanded in a around inf 46.5%

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

      1. +-commutative 46.5%

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

      2. mul-1-neg 46.5%

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

      3. unsub-neg 46.5%

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

   5. Simplified 46.5%

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

   if 2.60000000000000008e60 < y < 1.7e145

   1. Initial program 75.0%

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

   3. Taylor expanded in z around inf 65.6%

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

      1. *-commutative 65.6%

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

   5. Simplified 65.6%

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

   6. Taylor expanded in y around inf 50.9%

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

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+66}:\\ \;\;\;\;\left(-i\right) \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+60}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+145}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-i\right) \cdot \left(y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 52.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.1 \cdot 10^{+34} \lor \neg \left(b \leq 1.2 \cdot 10^{-26}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -2.1e+34) (not (<= b 1.2e-26)))
   (* b (- (* t i) (* z c)))
   (* j (- (* a c) (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -2.1e+34) || !(b <= 1.2e-26)) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = j * ((a * c) - (y * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-2.1d+34)) .or. (.not. (b <= 1.2d-26))) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = j * ((a * c) - (y * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -2.1e+34) || !(b <= 1.2e-26)) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = j * ((a * c) - (y * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -2.1e+34) or not (b <= 1.2e-26):
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = j * ((a * c) - (y * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -2.1e+34) || !(b <= 1.2e-26))
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -2.1e+34) || ~((b <= 1.2e-26)))
		tmp = b * ((t * i) - (z * c));
	else
		tmp = j * ((a * c) - (y * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -2.1e+34], N[Not[LessEqual[b, 1.2e-26]], $MachinePrecision]], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.10000000000000017e34 or 1.2e-26 < b

   1. Initial program 70.7%

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

   3. Taylor expanded in b around inf 66.9%

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

      1. *-commutative 66.9%

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

   5. Simplified 66.9%

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

   if -2.10000000000000017e34 < b < 1.2e-26

   1. Initial program 70.0%

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

   3. Taylor expanded in y around inf 64.1%

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

      1. *-commutative 64.1%

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

      2. associate-*l* 67.6%

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

   5. Simplified 67.6%

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

   6. Taylor expanded in j around inf 56.7%

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

      1. *-commutative 56.7%

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

      2. *-commutative 56.7%

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

      3. *-commutative 56.7%

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

   8. Simplified 56.7%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.1 \cdot 10^{+34} \lor \neg \left(b \leq 1.2 \cdot 10^{-26}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 30.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.35 \cdot 10^{+73} \lor \neg \left(b \leq 6.4 \cdot 10^{-27}\right):\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -1.35e+73) (not (<= b 6.4e-27))) (* t (* b i)) (* c (* a 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 ((b <= -1.35e+73) || !(b <= 6.4e-27)) {
		tmp = t * (b * i);
	} else {
		tmp = c * (a * 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 ((b <= (-1.35d+73)) .or. (.not. (b <= 6.4d-27))) then
        tmp = t * (b * i)
    else
        tmp = c * (a * 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 ((b <= -1.35e+73) || !(b <= 6.4e-27)) {
		tmp = t * (b * i);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -1.35e+73) or not (b <= 6.4e-27):
		tmp = t * (b * i)
	else:
		tmp = c * (a * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -1.35e+73) || !(b <= 6.4e-27))
		tmp = Float64(t * Float64(b * i));
	else
		tmp = Float64(c * Float64(a * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -1.35e+73) || ~((b <= 6.4e-27)))
		tmp = t * (b * i);
	else
		tmp = c * (a * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -1.35e+73], N[Not[LessEqual[b, 6.4e-27]], $MachinePrecision]], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.35e73 or 6.39999999999999982e-27 < b

   1. Initial program 70.7%

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

   3. Taylor expanded in z around inf 58.1%

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

      1. +-commutative 58.1%

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

      2. mul-1-neg 58.1%

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

      3. unsub-neg 58.1%

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

      4. associate-/l* 59.9%

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

      5. associate-/l* 59.0%

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

   5. Simplified 59.0%

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

   6. Taylor expanded in t around inf 48.9%

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

      1. distribute-lft-out-- 48.9%

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

      2. *-commutative 48.9%

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

   8. Simplified 48.9%

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

   9. Taylor expanded in x around 0 39.8%

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

   if -1.35e73 < b < 6.39999999999999982e-27

   1. Initial program 70.1%

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

   3. Taylor expanded in y around inf 64.5%

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

      1. *-commutative 64.5%

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

      2. associate-*l* 66.5%

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

   5. Simplified 66.5%

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

   6. Taylor expanded in c around inf 66.6%

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

      1. *-commutative 66.6%

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

      2. *-commutative 66.6%

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

      3. associate-*l* 71.4%

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

      4. *-commutative 71.4%

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

   8. Simplified 71.4%

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

   9. Taylor expanded in a around inf 30.7%

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

       1. *-commutative 30.7%

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

       2. associate-*l* 32.4%

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

       3. *-commutative 32.4%

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

   11. Simplified 32.4%

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

4. Final simplification 35.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.35 \cdot 10^{+73} \lor \neg \left(b \leq 6.4 \cdot 10^{-27}\right):\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 29.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{+75} \lor \neg \left(b \leq 3.55 \cdot 10^{-28}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -1.3e+75) (not (<= b 3.55e-28))) (* b (* t i)) (* c (* a 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 ((b <= -1.3e+75) || !(b <= 3.55e-28)) {
		tmp = b * (t * i);
	} else {
		tmp = c * (a * 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 ((b <= (-1.3d+75)) .or. (.not. (b <= 3.55d-28))) then
        tmp = b * (t * i)
    else
        tmp = c * (a * 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 ((b <= -1.3e+75) || !(b <= 3.55e-28)) {
		tmp = b * (t * i);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -1.3e+75) or not (b <= 3.55e-28):
		tmp = b * (t * i)
	else:
		tmp = c * (a * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -1.3e+75) || !(b <= 3.55e-28))
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(c * Float64(a * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -1.3e+75) || ~((b <= 3.55e-28)))
		tmp = b * (t * i);
	else
		tmp = c * (a * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -1.3e+75], N[Not[LessEqual[b, 3.55e-28]], $MachinePrecision]], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.29999999999999992e75 or 3.5499999999999999e-28 < b

   1. Initial program 70.7%

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

   3. Taylor expanded in y around inf 67.1%

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

      1. *-commutative 67.1%

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

      2. associate-*l* 71.5%

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

   5. Simplified 71.5%

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

   6. Taylor expanded in t around inf 38.1%

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

      1. *-commutative 38.1%

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

   8. Simplified 38.1%

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

   if -1.29999999999999992e75 < b < 3.5499999999999999e-28

   1. Initial program 70.1%

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

   3. Taylor expanded in y around inf 64.5%

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

      1. *-commutative 64.5%

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

      2. associate-*l* 66.5%

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

   5. Simplified 66.5%

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

   6. Taylor expanded in c around inf 66.6%

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

      1. *-commutative 66.6%

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

      2. *-commutative 66.6%

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

      3. associate-*l* 71.4%

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

      4. *-commutative 71.4%

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

   8. Simplified 71.4%

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

   9. Taylor expanded in a around inf 30.7%

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

       1. *-commutative 30.7%

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

       2. associate-*l* 32.4%

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

       3. *-commutative 32.4%

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

   11. Simplified 32.4%

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

4. Final simplification 34.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{+75} \lor \neg \left(b \leq 3.55 \cdot 10^{-28}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 29.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -132000000 \lor \neg \left(t \leq 8.8 \cdot 10^{+175}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -132000000.0) (not (<= t 8.8e+175)))
   (* b (* t i))
   (* a (* c j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -132000000.0) || !(t <= 8.8e+175)) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((t <= (-132000000.0d0)) .or. (.not. (t <= 8.8d+175))) then
        tmp = b * (t * i)
    else
        tmp = a * (c * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -132000000.0) || !(t <= 8.8e+175)) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -132000000.0) or not (t <= 8.8e+175):
		tmp = b * (t * i)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -132000000.0) || !(t <= 8.8e+175))
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(a * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -132000000.0) || ~((t <= 8.8e+175)))
		tmp = b * (t * i);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -132000000.0], N[Not[LessEqual[t, 8.8e+175]], $MachinePrecision]], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.32e8 or 8.7999999999999997e175 < t

   1. Initial program 64.4%

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

   3. Taylor expanded in y around inf 56.8%

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

      1. *-commutative 56.8%

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

      2. associate-*l* 63.2%

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

   5. Simplified 63.2%

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

   6. Taylor expanded in t around inf 47.8%

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

      1. *-commutative 47.8%

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

   8. Simplified 47.8%

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

   if -1.32e8 < t < 8.7999999999999997e175

   1. Initial program 72.8%

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

   3. Taylor expanded in a around inf 34.0%

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

      1. +-commutative 34.0%

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

      2. mul-1-neg 34.0%

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

      3. unsub-neg 34.0%

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

   5. Simplified 34.0%

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

   6. Taylor expanded in c around inf 28.3%

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

4. Final simplification 34.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -132000000 \lor \neg \left(t \leq 8.8 \cdot 10^{+175}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 22.7% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(c \cdot j\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 70.3%

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

3. Taylor expanded in a around inf 35.3%

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

   1. +-commutative 35.3%

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

   2. mul-1-neg 35.3%

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

   3. unsub-neg 35.3%

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

5. Simplified 35.3%

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

6. Taylor expanded in c around inf 22.9%

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

Developer Target 1: 60.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right)\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + t\_1\\ \mathbf{if}\;x < -1.469694296777705 \cdot 10^{-64}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x < 3.2113527362226803 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* c a) (* y i))))
        (t_2
         (+
          (-
           (* x (- (* y z) (* t a)))
           (/
            (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0)))
            (+ (* c z) (* t i))))
          t_1)))
   (if (< x -1.469694296777705e-64)
     t_2
     (if (< x 3.2113527362226803e-147)
       (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) t_1))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (pow((c * z), 2.0) - pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((c * a) - (y * i))
    t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ** 2.0d0) - ((t * i) ** 2.0d0))) / ((c * z) + (t * i)))) + t_1
    if (x < (-1.469694296777705d-64)) then
        tmp = t_2
    else if (x < 3.2113527362226803d-147) then
        tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (Math.pow((c * z), 2.0) - Math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((c * a) - (y * i))
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (math.pow((c * z), 2.0) - math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1
	tmp = 0
	if x < -1.469694296777705e-64:
		tmp = t_2
	elif x < 3.2113527362226803e-147:
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(c * a) - Float64(y * i)))
	t_2 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(Float64(b * Float64((Float64(c * z) ^ 2.0) - (Float64(t * i) ^ 2.0))) / Float64(Float64(c * z) + Float64(t * i)))) + t_1)
	tmp = 0.0
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = Float64(Float64(Float64(Float64(b * i) - Float64(x * a)) * t) - Float64(Float64(z * Float64(c * b)) - t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((c * a) - (y * i));
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ^ 2.0) - ((t * i) ^ 2.0))) / ((c * z) + (t * i)))) + t_1;
	tmp = 0.0;
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[Power[N[(c * z), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(t * i), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * z), $MachinePrecision] + N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[Less[x, -1.469694296777705e-64], t$95$2, If[Less[x, 3.2113527362226803e-147], N[(N[(N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] - N[(N[(z * N[(c * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024170 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< x -293938859355541/2000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2) (pow (* t i) 2))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 32113527362226803/10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2) (pow (* t i) 2))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))))))

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