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

Percentage Accurate: 73.8% → 85.2%

Time: 28.0s

Alternatives: 31

Speedup: 0.5×

• 58.7% 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: 73.8% accurate, 1.0× speedup

Math

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

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: 85.2% accurate, 0.2× speedup

Math

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

FPCore

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$1 + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(t$95$1 + N[(j * N[(a * c + N[(y * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(N[(t * b), $MachinePrecision] + N[(y * N[(N[(x * N[(z / i), $MachinePrecision]), $MachinePrecision] - 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 90.8%

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

      1. *-commutative 90.8%

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

      2. sub-neg 90.8%

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

      3. *-commutative 90.8%

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

      4. fma-define 90.8%

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

   3. Simplified 90.8%

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

   if +inf.0 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 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 30.3%

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

   4. Taylor expanded in i around -inf 42.0%

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

      1. mul-1-neg 42.0%

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

      2. *-commutative 42.0%

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

      3. distribute-rgt-neg-in 42.0%

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

   6. Simplified 51.3%

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

   7. Taylor expanded in y around inf 67.9%

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

      1. associate-/l* 67.9%

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

   9. Simplified 67.9%

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

4. Final simplification 87.0%

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

Alternative 2: 85.2% accurate, 0.2× speedup

Math

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

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* b (- (* t i) (* z c))) (* x (- (* t a) (* y z)))))
        (t_2 (- (* a c) (* y i))))
   (if (<= (+ t_1 (* j t_2)) INFINITY)
     (fma j t_2 t_1)
     (* i (+ (* t b) (* 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 = (b * ((t * i) - (z * c))) - (x * ((t * a) - (y * z)));
	double t_2 = (a * c) - (y * i);
	double tmp;
	if ((t_1 + (j * t_2)) <= ((double) INFINITY)) {
		tmp = fma(j, t_2, t_1);
	} else {
		tmp = i * ((t * b) + (y * ((x * (z / i)) - j)));
	}
	return tmp;
}

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$1 + N[(j * t$95$2), $MachinePrecision]), $MachinePrecision], Infinity], N[(j * t$95$2 + t$95$1), $MachinePrecision], N[(i * N[(N[(t * b), $MachinePrecision] + N[(y * N[(N[(x * N[(z / i), $MachinePrecision]), $MachinePrecision] - 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 90.8%

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

      1. +-commutative 90.8%

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

      2. fma-define 90.8%

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

      3. *-commutative 90.8%

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

      4. *-commutative 90.8%

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

   3. Simplified 90.8%

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

   if +inf.0 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 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 30.3%

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

   4. Taylor expanded in i around -inf 42.0%

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

      1. mul-1-neg 42.0%

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

      2. *-commutative 42.0%

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

      3. distribute-rgt-neg-in 42.0%

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

   6. Simplified 51.3%

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

   7. Taylor expanded in y around inf 67.9%

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

      1. associate-/l* 67.9%

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

   9. Simplified 67.9%

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

4. Final simplification 87.0%

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

Alternative 3: 85.2% accurate, 0.5× speedup

Math

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

FPCore

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

Python

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

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) - Float64(x * Float64(Float64(t * a) - Float64(y * z)))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(i * Float64(Float64(t * b) + Float64(y * Float64(Float64(x * Float64(z / i)) - j))));
	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))) - (x * ((t * a) - (y * z)))) + (j * ((a * c) - (y * i)));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = i * ((t * b) + (y * ((x * (z / i)) - j)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $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[(i * N[(N[(t * b), $MachinePrecision] + N[(y * N[(N[(x * N[(z / i), $MachinePrecision]), $MachinePrecision] - 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 90.8%

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

   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 30.3%

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

   4. Taylor expanded in i around -inf 42.0%

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

      1. mul-1-neg 42.0%

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

      2. *-commutative 42.0%

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

      3. distribute-rgt-neg-in 42.0%

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

   6. Simplified 51.3%

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

   7. Taylor expanded in y around inf 67.9%

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

      1. associate-/l* 67.9%

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

   9. Simplified 67.9%

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

4. Final simplification 87.0%

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

Alternative 4: 51.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_3 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -5.4 \cdot 10^{-23}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -5.7 \cdot 10^{-265}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-292}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-244}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-126}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-79}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+111}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i))))
        (t_2 (* z (- (* x y) (* b c))))
        (t_3 (* t (- (* b i) (* x a)))))
   (if (<= t -5.4e-23)
     t_3
     (if (<= t -5.7e-265)
       t_2
       (if (<= t 4.6e-292)
         t_1
         (if (<= t 5e-244)
           t_2
           (if (<= t 6.8e-126)
             (- (* a (* c j)) (* i (* y j)))
             (if (<= t 1.5e-79)
               (* b (- (* t i) (* z c)))
               (if (<= t 8.5e+111) t_1 t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = z * ((x * y) - (b * c));
	double t_3 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -5.4e-23) {
		tmp = t_3;
	} else if (t <= -5.7e-265) {
		tmp = t_2;
	} else if (t <= 4.6e-292) {
		tmp = t_1;
	} else if (t <= 5e-244) {
		tmp = t_2;
	} else if (t <= 6.8e-126) {
		tmp = (a * (c * j)) - (i * (y * j));
	} else if (t <= 1.5e-79) {
		tmp = b * ((t * i) - (z * c));
	} else if (t <= 8.5e+111) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = z * ((x * y) - (b * c))
    t_3 = t * ((b * i) - (x * a))
    if (t <= (-5.4d-23)) then
        tmp = t_3
    else if (t <= (-5.7d-265)) then
        tmp = t_2
    else if (t <= 4.6d-292) then
        tmp = t_1
    else if (t <= 5d-244) then
        tmp = t_2
    else if (t <= 6.8d-126) then
        tmp = (a * (c * j)) - (i * (y * j))
    else if (t <= 1.5d-79) then
        tmp = b * ((t * i) - (z * c))
    else if (t <= 8.5d+111) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = z * ((x * y) - (b * c));
	double t_3 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -5.4e-23) {
		tmp = t_3;
	} else if (t <= -5.7e-265) {
		tmp = t_2;
	} else if (t <= 4.6e-292) {
		tmp = t_1;
	} else if (t <= 5e-244) {
		tmp = t_2;
	} else if (t <= 6.8e-126) {
		tmp = (a * (c * j)) - (i * (y * j));
	} else if (t <= 1.5e-79) {
		tmp = b * ((t * i) - (z * c));
	} else if (t <= 8.5e+111) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = z * ((x * y) - (b * c))
	t_3 = t * ((b * i) - (x * a))
	tmp = 0
	if t <= -5.4e-23:
		tmp = t_3
	elif t <= -5.7e-265:
		tmp = t_2
	elif t <= 4.6e-292:
		tmp = t_1
	elif t <= 5e-244:
		tmp = t_2
	elif t <= 6.8e-126:
		tmp = (a * (c * j)) - (i * (y * j))
	elif t <= 1.5e-79:
		tmp = b * ((t * i) - (z * c))
	elif t <= 8.5e+111:
		tmp = t_1
	else:
		tmp = t_3
	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)))
	t_2 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	t_3 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	tmp = 0.0
	if (t <= -5.4e-23)
		tmp = t_3;
	elseif (t <= -5.7e-265)
		tmp = t_2;
	elseif (t <= 4.6e-292)
		tmp = t_1;
	elseif (t <= 5e-244)
		tmp = t_2;
	elseif (t <= 6.8e-126)
		tmp = Float64(Float64(a * Float64(c * j)) - Float64(i * Float64(y * j)));
	elseif (t <= 1.5e-79)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (t <= 8.5e+111)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = z * ((x * y) - (b * c));
	t_3 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -5.4e-23)
		tmp = t_3;
	elseif (t <= -5.7e-265)
		tmp = t_2;
	elseif (t <= 4.6e-292)
		tmp = t_1;
	elseif (t <= 5e-244)
		tmp = t_2;
	elseif (t <= 6.8e-126)
		tmp = (a * (c * j)) - (i * (y * j));
	elseif (t <= 1.5e-79)
		tmp = b * ((t * i) - (z * c));
	elseif (t <= 8.5e+111)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.4e-23], t$95$3, If[LessEqual[t, -5.7e-265], t$95$2, If[LessEqual[t, 4.6e-292], t$95$1, If[LessEqual[t, 5e-244], t$95$2, If[LessEqual[t, 6.8e-126], N[(N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.5e-79], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e+111], t$95$1, t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -5.3999999999999997e-23 or 8.49999999999999983e111 < t

   1. Initial program 69.7%

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

   3. Taylor expanded in t around inf 70.9%

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

      1. distribute-lft-out-- 70.9%

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

      2. *-commutative 70.9%

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

      3. *-commutative 70.9%

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

   5. Simplified 70.9%

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

   if -5.3999999999999997e-23 < t < -5.7e-265 or 4.5999999999999998e-292 < t < 4.99999999999999998e-244

   1. Initial program 76.0%

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

   3. Taylor expanded in z around inf 57.2%

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

      1. *-commutative 57.2%

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

   5. Simplified 57.2%

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

   if -5.7e-265 < t < 4.5999999999999998e-292 or 1.5e-79 < t < 8.49999999999999983e111

   1. Initial program 79.7%

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

   3. Taylor expanded in c around 0 75.6%

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

   4. Taylor expanded in j around inf 66.0%

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

      1. +-commutative 66.0%

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

      2. mul-1-neg 66.0%

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

      3. unsub-neg 66.0%

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

   6. Simplified 66.0%

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

   if 4.99999999999999998e-244 < t < 6.8e-126

   1. Initial program 91.7%

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

   3. Taylor expanded in c around 0 99.9%

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

   4. Taylor expanded in x around 0 78.7%

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

      1. +-commutative 78.7%

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

      2. neg-mul-1 78.7%

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

      3. unsub-neg 78.7%

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

      4. *-commutative 78.7%

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

      5. associate-*r* 70.8%

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

   6. Simplified 70.8%

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

   7. Taylor expanded in b around 0 65.9%

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

   if 6.8e-126 < t < 1.5e-79

   1. Initial program 85.5%

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

   3. Taylor expanded in b around inf 99.8%

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

      1. *-commutative 99.8%

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

      2. *-commutative 99.8%

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

   5. Simplified 99.8%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{-23}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -5.7 \cdot 10^{-265}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-292}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-244}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-126}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-79}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+111}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_3 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;b \leq -1.2 \cdot 10^{+87}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{-41}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{-152}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-229}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-136}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 1.26 \cdot 10^{+182}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i))))
        (t_2 (* b (- (* t i) (* z c))))
        (t_3 (* a (- (* c j) (* x t)))))
   (if (<= b -1.2e+87)
     t_2
     (if (<= b -2.3e-18)
       t_1
       (if (<= b -3.6e-41)
         (* t (- (* b i) (* x a)))
         (if (<= b -3.5e-152)
           t_1
           (if (<= b 9e-229)
             t_3
             (if (<= b 4.5e-136)
               (* y (- (* x z) (* i j)))
               (if (<= b 1.26e+182) t_3 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));
	double t_2 = b * ((t * i) - (z * c));
	double t_3 = a * ((c * j) - (x * t));
	double tmp;
	if (b <= -1.2e+87) {
		tmp = t_2;
	} else if (b <= -2.3e-18) {
		tmp = t_1;
	} else if (b <= -3.6e-41) {
		tmp = t * ((b * i) - (x * a));
	} else if (b <= -3.5e-152) {
		tmp = t_1;
	} else if (b <= 9e-229) {
		tmp = t_3;
	} else if (b <= 4.5e-136) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 1.26e+182) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = b * ((t * i) - (z * c))
    t_3 = a * ((c * j) - (x * t))
    if (b <= (-1.2d+87)) then
        tmp = t_2
    else if (b <= (-2.3d-18)) then
        tmp = t_1
    else if (b <= (-3.6d-41)) then
        tmp = t * ((b * i) - (x * a))
    else if (b <= (-3.5d-152)) then
        tmp = t_1
    else if (b <= 9d-229) then
        tmp = t_3
    else if (b <= 4.5d-136) then
        tmp = y * ((x * z) - (i * j))
    else if (b <= 1.26d+182) then
        tmp = t_3
    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));
	double t_2 = b * ((t * i) - (z * c));
	double t_3 = a * ((c * j) - (x * t));
	double tmp;
	if (b <= -1.2e+87) {
		tmp = t_2;
	} else if (b <= -2.3e-18) {
		tmp = t_1;
	} else if (b <= -3.6e-41) {
		tmp = t * ((b * i) - (x * a));
	} else if (b <= -3.5e-152) {
		tmp = t_1;
	} else if (b <= 9e-229) {
		tmp = t_3;
	} else if (b <= 4.5e-136) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 1.26e+182) {
		tmp = t_3;
	} 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))
	t_2 = b * ((t * i) - (z * c))
	t_3 = a * ((c * j) - (x * t))
	tmp = 0
	if b <= -1.2e+87:
		tmp = t_2
	elif b <= -2.3e-18:
		tmp = t_1
	elif b <= -3.6e-41:
		tmp = t * ((b * i) - (x * a))
	elif b <= -3.5e-152:
		tmp = t_1
	elif b <= 9e-229:
		tmp = t_3
	elif b <= 4.5e-136:
		tmp = y * ((x * z) - (i * j))
	elif b <= 1.26e+182:
		tmp = t_3
	else:
		tmp = t_2
	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)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_3 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (b <= -1.2e+87)
		tmp = t_2;
	elseif (b <= -2.3e-18)
		tmp = t_1;
	elseif (b <= -3.6e-41)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (b <= -3.5e-152)
		tmp = t_1;
	elseif (b <= 9e-229)
		tmp = t_3;
	elseif (b <= 4.5e-136)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (b <= 1.26e+182)
		tmp = t_3;
	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));
	t_2 = b * ((t * i) - (z * c));
	t_3 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (b <= -1.2e+87)
		tmp = t_2;
	elseif (b <= -2.3e-18)
		tmp = t_1;
	elseif (b <= -3.6e-41)
		tmp = t * ((b * i) - (x * a));
	elseif (b <= -3.5e-152)
		tmp = t_1;
	elseif (b <= 9e-229)
		tmp = t_3;
	elseif (b <= 4.5e-136)
		tmp = y * ((x * z) - (i * j));
	elseif (b <= 1.26e+182)
		tmp = t_3;
	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[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.2e+87], t$95$2, If[LessEqual[b, -2.3e-18], t$95$1, If[LessEqual[b, -3.6e-41], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.5e-152], t$95$1, If[LessEqual[b, 9e-229], t$95$3, If[LessEqual[b, 4.5e-136], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.26e+182], t$95$3, t$95$2]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.19999999999999991e87 or 1.2600000000000001e182 < b

   1. Initial program 69.5%

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

   3. Taylor expanded in b around inf 81.8%

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

      1. *-commutative 81.8%

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

      2. *-commutative 81.8%

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

   5. Simplified 81.8%

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

   if -1.19999999999999991e87 < b < -2.3000000000000001e-18 or -3.6e-41 < b < -3.5000000000000001e-152

   1. Initial program 85.2%

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

   3. Taylor expanded in c around 0 78.6%

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

   4. Taylor expanded in j around inf 56.0%

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

      1. +-commutative 56.0%

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

      2. mul-1-neg 56.0%

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

      3. unsub-neg 56.0%

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

   6. Simplified 56.0%

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

   if -2.3000000000000001e-18 < b < -3.6e-41

   1. Initial program 83.1%

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

   3. Taylor expanded in t around inf 83.1%

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

      1. distribute-lft-out-- 83.1%

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

      2. *-commutative 83.1%

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

      3. *-commutative 83.1%

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

   5. Simplified 83.1%

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

   if -3.5000000000000001e-152 < b < 9.0000000000000004e-229 or 4.49999999999999972e-136 < b < 1.2600000000000001e182

   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 inf 60.7%

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

      1. +-commutative 60.7%

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

      2. mul-1-neg 60.7%

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

      3. unsub-neg 60.7%

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

      4. *-commutative 60.7%

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

      5. *-commutative 60.7%

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

   5. Simplified 60.7%

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

   if 9.0000000000000004e-229 < b < 4.49999999999999972e-136

   1. Initial program 75.6%

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

   3. Taylor expanded in y around inf 70.7%

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

      1. +-commutative 70.7%

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

      2. mul-1-neg 70.7%

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

      3. unsub-neg 70.7%

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

      4. *-commutative 70.7%

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

   5. Simplified 70.7%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.2 \cdot 10^{+87}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-18}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{-41}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{-152}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-229}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-136}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 1.26 \cdot 10^{+182}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 49.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_3 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;b \leq -1.15 \cdot 10^{+87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{-28}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{-69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-156}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 1.26 \cdot 10^{-229}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{-136}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{+182}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c))))
        (t_2 (* j (- (* a c) (* y i))))
        (t_3 (* a (- (* c j) (* x t)))))
   (if (<= b -1.15e+87)
     t_1
     (if (<= b -2.7e-28)
       t_2
       (if (<= b -1.6e-69)
         t_1
         (if (<= b -1.7e-156)
           t_2
           (if (<= b 1.26e-229)
             t_3
             (if (<= b 3.6e-136)
               (* y (- (* x z) (* i j)))
               (if (<= b 1.45e+182) t_3 t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = j * ((a * c) - (y * i));
	double t_3 = a * ((c * j) - (x * t));
	double tmp;
	if (b <= -1.15e+87) {
		tmp = t_1;
	} else if (b <= -2.7e-28) {
		tmp = t_2;
	} else if (b <= -1.6e-69) {
		tmp = t_1;
	} else if (b <= -1.7e-156) {
		tmp = t_2;
	} else if (b <= 1.26e-229) {
		tmp = t_3;
	} else if (b <= 3.6e-136) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 1.45e+182) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = j * ((a * c) - (y * i))
    t_3 = a * ((c * j) - (x * t))
    if (b <= (-1.15d+87)) then
        tmp = t_1
    else if (b <= (-2.7d-28)) then
        tmp = t_2
    else if (b <= (-1.6d-69)) then
        tmp = t_1
    else if (b <= (-1.7d-156)) then
        tmp = t_2
    else if (b <= 1.26d-229) then
        tmp = t_3
    else if (b <= 3.6d-136) then
        tmp = y * ((x * z) - (i * j))
    else if (b <= 1.45d+182) then
        tmp = t_3
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = j * ((a * c) - (y * i));
	double t_3 = a * ((c * j) - (x * t));
	double tmp;
	if (b <= -1.15e+87) {
		tmp = t_1;
	} else if (b <= -2.7e-28) {
		tmp = t_2;
	} else if (b <= -1.6e-69) {
		tmp = t_1;
	} else if (b <= -1.7e-156) {
		tmp = t_2;
	} else if (b <= 1.26e-229) {
		tmp = t_3;
	} else if (b <= 3.6e-136) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 1.45e+182) {
		tmp = t_3;
	} 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))
	t_2 = j * ((a * c) - (y * i))
	t_3 = a * ((c * j) - (x * t))
	tmp = 0
	if b <= -1.15e+87:
		tmp = t_1
	elif b <= -2.7e-28:
		tmp = t_2
	elif b <= -1.6e-69:
		tmp = t_1
	elif b <= -1.7e-156:
		tmp = t_2
	elif b <= 1.26e-229:
		tmp = t_3
	elif b <= 3.6e-136:
		tmp = y * ((x * z) - (i * j))
	elif b <= 1.45e+182:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_3 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (b <= -1.15e+87)
		tmp = t_1;
	elseif (b <= -2.7e-28)
		tmp = t_2;
	elseif (b <= -1.6e-69)
		tmp = t_1;
	elseif (b <= -1.7e-156)
		tmp = t_2;
	elseif (b <= 1.26e-229)
		tmp = t_3;
	elseif (b <= 3.6e-136)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (b <= 1.45e+182)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = j * ((a * c) - (y * i));
	t_3 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (b <= -1.15e+87)
		tmp = t_1;
	elseif (b <= -2.7e-28)
		tmp = t_2;
	elseif (b <= -1.6e-69)
		tmp = t_1;
	elseif (b <= -1.7e-156)
		tmp = t_2;
	elseif (b <= 1.26e-229)
		tmp = t_3;
	elseif (b <= 3.6e-136)
		tmp = y * ((x * z) - (i * j));
	elseif (b <= 1.45e+182)
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.15e+87], t$95$1, If[LessEqual[b, -2.7e-28], t$95$2, If[LessEqual[b, -1.6e-69], t$95$1, If[LessEqual[b, -1.7e-156], t$95$2, If[LessEqual[b, 1.26e-229], t$95$3, If[LessEqual[b, 3.6e-136], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.45e+182], t$95$3, t$95$1]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.1500000000000001e87 or -2.6999999999999999e-28 < b < -1.59999999999999999e-69 or 1.4499999999999999e182 < b

   1. Initial program 71.3%

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

   3. Taylor expanded in b around inf 79.2%

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

      1. *-commutative 79.2%

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

      2. *-commutative 79.2%

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

   5. Simplified 79.2%

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

   if -1.1500000000000001e87 < b < -2.6999999999999999e-28 or -1.59999999999999999e-69 < b < -1.69999999999999995e-156

   1. Initial program 85.6%

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

   3. Taylor expanded in c around 0 76.0%

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

   4. Taylor expanded in j around inf 57.8%

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

      1. +-commutative 57.8%

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

      2. mul-1-neg 57.8%

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

      3. unsub-neg 57.8%

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

   6. Simplified 57.8%

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

   if -1.69999999999999995e-156 < b < 1.26000000000000008e-229 or 3.5999999999999998e-136 < b < 1.4499999999999999e182

   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 inf 60.7%

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

      1. +-commutative 60.7%

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

      2. mul-1-neg 60.7%

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

      3. unsub-neg 60.7%

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

      4. *-commutative 60.7%

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

      5. *-commutative 60.7%

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

   5. Simplified 60.7%

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

   if 1.26000000000000008e-229 < b < 3.5999999999999998e-136

   1. Initial program 75.6%

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

   3. Taylor expanded in y around inf 70.7%

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

      1. +-commutative 70.7%

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

      2. mul-1-neg 70.7%

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

      3. unsub-neg 70.7%

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

      4. *-commutative 70.7%

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

   5. Simplified 70.7%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{+87}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{-28}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{-69}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-156}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 1.26 \cdot 10^{-229}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{-136}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{+182}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 60.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := t\_1 + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;a \leq -8.5 \cdot 10^{+164}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-153}:\\ \;\;\;\;i \cdot \left(t \cdot b + y \cdot \left(x \cdot \frac{z}{i} - j\right)\right)\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{-81}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 520:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;a \leq 1.16 \cdot 10^{+108}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1 - x \cdot \left(t \cdot a - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i))))
        (t_2 (+ t_1 (* b (- (* t i) (* z c))))))
   (if (<= a -8.5e+164)
     (* a (- (* c j) (* x t)))
     (if (<= a -3.5e-153)
       (* i (+ (* t b) (* y (- (* x (/ z i)) j))))
       (if (<= a 8.8e-81)
         t_2
         (if (<= a 520.0)
           (- (* z (- (* x y) (* b c))) (* y (* i j)))
           (if (<= a 1.16e+108) t_2 (- t_1 (* x (- (* t a) (* y z)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = t_1 + (b * ((t * i) - (z * c)));
	double tmp;
	if (a <= -8.5e+164) {
		tmp = a * ((c * j) - (x * t));
	} else if (a <= -3.5e-153) {
		tmp = i * ((t * b) + (y * ((x * (z / i)) - j)));
	} else if (a <= 8.8e-81) {
		tmp = t_2;
	} else if (a <= 520.0) {
		tmp = (z * ((x * y) - (b * c))) - (y * (i * j));
	} else if (a <= 1.16e+108) {
		tmp = t_2;
	} else {
		tmp = t_1 - (x * ((t * a) - (y * z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = t_1 + (b * ((t * i) - (z * c)))
    if (a <= (-8.5d+164)) then
        tmp = a * ((c * j) - (x * t))
    else if (a <= (-3.5d-153)) then
        tmp = i * ((t * b) + (y * ((x * (z / i)) - j)))
    else if (a <= 8.8d-81) then
        tmp = t_2
    else if (a <= 520.0d0) then
        tmp = (z * ((x * y) - (b * c))) - (y * (i * j))
    else if (a <= 1.16d+108) then
        tmp = t_2
    else
        tmp = t_1 - (x * ((t * a) - (y * z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = t_1 + (b * ((t * i) - (z * c)));
	double tmp;
	if (a <= -8.5e+164) {
		tmp = a * ((c * j) - (x * t));
	} else if (a <= -3.5e-153) {
		tmp = i * ((t * b) + (y * ((x * (z / i)) - j)));
	} else if (a <= 8.8e-81) {
		tmp = t_2;
	} else if (a <= 520.0) {
		tmp = (z * ((x * y) - (b * c))) - (y * (i * j));
	} else if (a <= 1.16e+108) {
		tmp = t_2;
	} else {
		tmp = t_1 - (x * ((t * a) - (y * z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = t_1 + (b * ((t * i) - (z * c)))
	tmp = 0
	if a <= -8.5e+164:
		tmp = a * ((c * j) - (x * t))
	elif a <= -3.5e-153:
		tmp = i * ((t * b) + (y * ((x * (z / i)) - j)))
	elif a <= 8.8e-81:
		tmp = t_2
	elif a <= 520.0:
		tmp = (z * ((x * y) - (b * c))) - (y * (i * j))
	elif a <= 1.16e+108:
		tmp = t_2
	else:
		tmp = t_1 - (x * ((t * a) - (y * z)))
	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)))
	t_2 = Float64(t_1 + Float64(b * Float64(Float64(t * i) - Float64(z * c))))
	tmp = 0.0
	if (a <= -8.5e+164)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (a <= -3.5e-153)
		tmp = Float64(i * Float64(Float64(t * b) + Float64(y * Float64(Float64(x * Float64(z / i)) - j))));
	elseif (a <= 8.8e-81)
		tmp = t_2;
	elseif (a <= 520.0)
		tmp = Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) - Float64(y * Float64(i * j)));
	elseif (a <= 1.16e+108)
		tmp = t_2;
	else
		tmp = Float64(t_1 - Float64(x * Float64(Float64(t * a) - Float64(y * z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = t_1 + (b * ((t * i) - (z * c)));
	tmp = 0.0;
	if (a <= -8.5e+164)
		tmp = a * ((c * j) - (x * t));
	elseif (a <= -3.5e-153)
		tmp = i * ((t * b) + (y * ((x * (z / i)) - j)));
	elseif (a <= 8.8e-81)
		tmp = t_2;
	elseif (a <= 520.0)
		tmp = (z * ((x * y) - (b * c))) - (y * (i * j));
	elseif (a <= 1.16e+108)
		tmp = t_2;
	else
		tmp = t_1 - (x * ((t * a) - (y * z)));
	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]}, Block[{t$95$2 = N[(t$95$1 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.5e+164], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.5e-153], N[(i * N[(N[(t * b), $MachinePrecision] + N[(y * N[(N[(x * N[(z / i), $MachinePrecision]), $MachinePrecision] - j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.8e-81], t$95$2, If[LessEqual[a, 520.0], N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.16e+108], t$95$2, N[(t$95$1 - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -8.50000000000000027e164

   1. Initial program 77.3%

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

   3. Taylor expanded in a around inf 91.9%

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

      1. +-commutative 91.9%

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

      2. mul-1-neg 91.9%

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

      3. unsub-neg 91.9%

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

      4. *-commutative 91.9%

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

      5. *-commutative 91.9%

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

   5. Simplified 91.9%

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

   if -8.50000000000000027e164 < a < -3.49999999999999981e-153

   1. Initial program 63.6%

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

   3. Taylor expanded in a around 0 55.3%

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

   4. Taylor expanded in i around -inf 56.9%

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

      1. mul-1-neg 56.9%

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

      2. *-commutative 56.9%

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

      3. distribute-rgt-neg-in 56.9%

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

   6. Simplified 65.2%

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

   7. Taylor expanded in y around inf 64.1%

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

      1. associate-/l* 64.0%

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

   9. Simplified 64.0%

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

   if -3.49999999999999981e-153 < a < 8.7999999999999997e-81 or 520 < a < 1.15999999999999995e108

   1. Initial program 84.9%

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

   3. Taylor expanded in x around 0 80.0%

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

   if 8.7999999999999997e-81 < a < 520

   1. Initial program 72.3%

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

   3. Taylor expanded in a around 0 77.3%

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

   4. Taylor expanded in t around 0 72.9%

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

      1. sub-neg 72.9%

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

      2. associate-+r+ 72.9%

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

      3. sub-neg 72.9%

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

      4. associate-*r* 72.9%

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

      5. associate-*r* 72.9%

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

      6. distribute-rgt-out-- 72.9%

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

      7. +-commutative 72.9%

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

      8. neg-mul-1 72.9%

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

      9. unsub-neg 72.9%

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

      10. *-commutative 72.9%

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

      11. *-commutative 72.9%

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

      12. associate-*r* 73.1%

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

   6. Simplified 73.1%

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

   if 1.15999999999999995e108 < a

   1. Initial program 76.3%

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

   3. Taylor expanded in b around 0 78.6%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{+164}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-153}:\\ \;\;\;\;i \cdot \left(t \cdot b + y \cdot \left(x \cdot \frac{z}{i} - j\right)\right)\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{-81}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 520:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;a \leq 1.16 \cdot 10^{+108}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 50.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -9 \cdot 10^{+119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -460000:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -5.7 \cdot 10^{-139}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-60}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+81}:\\ \;\;\;\;i \cdot \left(y \cdot \left(z \cdot \left(\frac{x}{i} - \frac{j}{z}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -9e+119)
     t_1
     (if (<= a -460000.0)
       (* y (- (* x z) (* i j)))
       (if (<= a -3.8e-71)
         t_1
         (if (<= a -5.7e-139)
           (* i (- (* t b) (* y j)))
           (if (<= a 8e-60)
             (* b (- (* t i) (* z c)))
             (if (<= a 1.5e+81)
               (* i (* y (* z (- (/ x i) (/ j z)))))
               t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -9e+119) {
		tmp = t_1;
	} else if (a <= -460000.0) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= -3.8e-71) {
		tmp = t_1;
	} else if (a <= -5.7e-139) {
		tmp = i * ((t * b) - (y * j));
	} else if (a <= 8e-60) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 1.5e+81) {
		tmp = i * (y * (z * ((x / i) - (j / z))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (a <= (-9d+119)) then
        tmp = t_1
    else if (a <= (-460000.0d0)) then
        tmp = y * ((x * z) - (i * j))
    else if (a <= (-3.8d-71)) then
        tmp = t_1
    else if (a <= (-5.7d-139)) then
        tmp = i * ((t * b) - (y * j))
    else if (a <= 8d-60) then
        tmp = b * ((t * i) - (z * c))
    else if (a <= 1.5d+81) then
        tmp = i * (y * (z * ((x / i) - (j / z))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -9e+119) {
		tmp = t_1;
	} else if (a <= -460000.0) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= -3.8e-71) {
		tmp = t_1;
	} else if (a <= -5.7e-139) {
		tmp = i * ((t * b) - (y * j));
	} else if (a <= 8e-60) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 1.5e+81) {
		tmp = i * (y * (z * ((x / i) - (j / z))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -9e+119:
		tmp = t_1
	elif a <= -460000.0:
		tmp = y * ((x * z) - (i * j))
	elif a <= -3.8e-71:
		tmp = t_1
	elif a <= -5.7e-139:
		tmp = i * ((t * b) - (y * j))
	elif a <= 8e-60:
		tmp = b * ((t * i) - (z * c))
	elif a <= 1.5e+81:
		tmp = i * (y * (z * ((x / i) - (j / z))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -9e+119)
		tmp = t_1;
	elseif (a <= -460000.0)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (a <= -3.8e-71)
		tmp = t_1;
	elseif (a <= -5.7e-139)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (a <= 8e-60)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (a <= 1.5e+81)
		tmp = Float64(i * Float64(y * Float64(z * Float64(Float64(x / i) - Float64(j / z)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -9e+119)
		tmp = t_1;
	elseif (a <= -460000.0)
		tmp = y * ((x * z) - (i * j));
	elseif (a <= -3.8e-71)
		tmp = t_1;
	elseif (a <= -5.7e-139)
		tmp = i * ((t * b) - (y * j));
	elseif (a <= 8e-60)
		tmp = b * ((t * i) - (z * c));
	elseif (a <= 1.5e+81)
		tmp = i * (y * (z * ((x / i) - (j / z))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9e+119], t$95$1, If[LessEqual[a, -460000.0], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.8e-71], t$95$1, If[LessEqual[a, -5.7e-139], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8e-60], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.5e+81], N[(i * N[(y * N[(z * N[(N[(x / i), $MachinePrecision] - N[(j / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -9.00000000000000039e119 or -4.6e5 < a < -3.79999999999999992e-71 or 1.49999999999999999e81 < a

   1. Initial program 72.6%

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

   3. Taylor expanded in a around inf 72.9%

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

      1. +-commutative 72.9%

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

      2. mul-1-neg 72.9%

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

      3. unsub-neg 72.9%

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

      4. *-commutative 72.9%

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

      5. *-commutative 72.9%

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

   5. Simplified 72.9%

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

   if -9.00000000000000039e119 < a < -4.6e5

   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 y around inf 69.3%

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

      1. +-commutative 69.3%

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

      2. mul-1-neg 69.3%

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

      3. unsub-neg 69.3%

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

      4. *-commutative 69.3%

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

   5. Simplified 69.3%

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

   if -3.79999999999999992e-71 < a < -5.6999999999999997e-139

   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 i around inf 51.2%

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

      1. distribute-lft-out-- 51.2%

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

      2. *-commutative 51.2%

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

      3. *-commutative 51.2%

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

   5. Simplified 51.2%

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

   6. Taylor expanded in y around 0 44.8%

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

      1. +-commutative 44.8%

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

      2. neg-mul-1 44.8%

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

      3. unsub-neg 44.8%

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

      4. associate-*r* 44.8%

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

   8. Simplified 44.8%

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

   9. Taylor expanded in i around 0 51.2%

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

   if -5.6999999999999997e-139 < a < 7.9999999999999998e-60

   1. Initial program 82.7%

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

   3. Taylor expanded in b around inf 59.7%

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

      1. *-commutative 59.7%

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

      2. *-commutative 59.7%

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

   5. Simplified 59.7%

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

   if 7.9999999999999998e-60 < a < 1.49999999999999999e81

   1. Initial program 82.8%

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

   3. Taylor expanded in a around 0 75.9%

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

   4. Taylor expanded in i around -inf 79.3%

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

      1. mul-1-neg 79.3%

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

      2. *-commutative 79.3%

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

      3. distribute-rgt-neg-in 79.3%

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

   6. Simplified 75.9%

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

   7. Taylor expanded in y around inf 53.0%

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

      1. associate-*r* 53.0%

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

      2. neg-mul-1 53.0%

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

      3. associate-/l* 53.2%

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

   9. Simplified 53.2%

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

   10. Taylor expanded in z around inf 59.7%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{+119}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -460000:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-71}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -5.7 \cdot 10^{-139}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-60}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+81}:\\ \;\;\;\;i \cdot \left(y \cdot \left(z \cdot \left(\frac{x}{i} - \frac{j}{z}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b\right)\\ t_2 := a \cdot c - y \cdot i\\ t_3 := b \cdot \left(j \cdot \frac{t\_2}{b} + \left(t \cdot i - z \cdot c\right)\right)\\ \mathbf{if}\;b \leq -9.5:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{-82}:\\ \;\;\;\;i \cdot \left(t \cdot b - \left(y \cdot j + \frac{z \cdot \left(b \cdot c - x \cdot y\right)}{i}\right)\right)\\ \mathbf{elif}\;b \leq 7.4 \cdot 10^{-66}:\\ \;\;\;\;\left(t\_1 - a \cdot \left(x \cdot t\right)\right) + j \cdot t\_2\\ \mathbf{elif}\;b \leq 1.96 \cdot 10^{+136}:\\ \;\;\;\;\left(t\_1 - x \cdot \left(t \cdot a - y \cdot z\right)\right) + a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* t b)))
        (t_2 (- (* a c) (* y i)))
        (t_3 (* b (+ (* j (/ t_2 b)) (- (* t i) (* z c))))))
   (if (<= b -9.5)
     t_3
     (if (<= b -1.35e-82)
       (* i (- (* t b) (+ (* y j) (/ (* z (- (* b c) (* x y))) i))))
       (if (<= b 7.4e-66)
         (+ (- t_1 (* a (* x t))) (* j t_2))
         (if (<= b 1.96e+136)
           (+ (- t_1 (* x (- (* t a) (* y z)))) (* a (* c j)))
           t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (t * b);
	double t_2 = (a * c) - (y * i);
	double t_3 = b * ((j * (t_2 / b)) + ((t * i) - (z * c)));
	double tmp;
	if (b <= -9.5) {
		tmp = t_3;
	} else if (b <= -1.35e-82) {
		tmp = i * ((t * b) - ((y * j) + ((z * ((b * c) - (x * y))) / i)));
	} else if (b <= 7.4e-66) {
		tmp = (t_1 - (a * (x * t))) + (j * t_2);
	} else if (b <= 1.96e+136) {
		tmp = (t_1 - (x * ((t * a) - (y * z)))) + (a * (c * j));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = i * (t * b)
    t_2 = (a * c) - (y * i)
    t_3 = b * ((j * (t_2 / b)) + ((t * i) - (z * c)))
    if (b <= (-9.5d0)) then
        tmp = t_3
    else if (b <= (-1.35d-82)) then
        tmp = i * ((t * b) - ((y * j) + ((z * ((b * c) - (x * y))) / i)))
    else if (b <= 7.4d-66) then
        tmp = (t_1 - (a * (x * t))) + (j * t_2)
    else if (b <= 1.96d+136) then
        tmp = (t_1 - (x * ((t * a) - (y * z)))) + (a * (c * j))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (t * b);
	double t_2 = (a * c) - (y * i);
	double t_3 = b * ((j * (t_2 / b)) + ((t * i) - (z * c)));
	double tmp;
	if (b <= -9.5) {
		tmp = t_3;
	} else if (b <= -1.35e-82) {
		tmp = i * ((t * b) - ((y * j) + ((z * ((b * c) - (x * y))) / i)));
	} else if (b <= 7.4e-66) {
		tmp = (t_1 - (a * (x * t))) + (j * t_2);
	} else if (b <= 1.96e+136) {
		tmp = (t_1 - (x * ((t * a) - (y * z)))) + (a * (c * j));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (t * b)
	t_2 = (a * c) - (y * i)
	t_3 = b * ((j * (t_2 / b)) + ((t * i) - (z * c)))
	tmp = 0
	if b <= -9.5:
		tmp = t_3
	elif b <= -1.35e-82:
		tmp = i * ((t * b) - ((y * j) + ((z * ((b * c) - (x * y))) / i)))
	elif b <= 7.4e-66:
		tmp = (t_1 - (a * (x * t))) + (j * t_2)
	elif b <= 1.96e+136:
		tmp = (t_1 - (x * ((t * a) - (y * z)))) + (a * (c * j))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(t * b))
	t_2 = Float64(Float64(a * c) - Float64(y * i))
	t_3 = Float64(b * Float64(Float64(j * Float64(t_2 / b)) + Float64(Float64(t * i) - Float64(z * c))))
	tmp = 0.0
	if (b <= -9.5)
		tmp = t_3;
	elseif (b <= -1.35e-82)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(Float64(y * j) + Float64(Float64(z * Float64(Float64(b * c) - Float64(x * y))) / i))));
	elseif (b <= 7.4e-66)
		tmp = Float64(Float64(t_1 - Float64(a * Float64(x * t))) + Float64(j * t_2));
	elseif (b <= 1.96e+136)
		tmp = Float64(Float64(t_1 - Float64(x * Float64(Float64(t * a) - Float64(y * z)))) + Float64(a * Float64(c * j)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * (t * b);
	t_2 = (a * c) - (y * i);
	t_3 = b * ((j * (t_2 / b)) + ((t * i) - (z * c)));
	tmp = 0.0;
	if (b <= -9.5)
		tmp = t_3;
	elseif (b <= -1.35e-82)
		tmp = i * ((t * b) - ((y * j) + ((z * ((b * c) - (x * y))) / i)));
	elseif (b <= 7.4e-66)
		tmp = (t_1 - (a * (x * t))) + (j * t_2);
	elseif (b <= 1.96e+136)
		tmp = (t_1 - (x * ((t * a) - (y * z)))) + (a * (c * j));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(j * N[(t$95$2 / b), $MachinePrecision]), $MachinePrecision] + N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9.5], t$95$3, If[LessEqual[b, -1.35e-82], N[(i * N[(N[(t * b), $MachinePrecision] - N[(N[(y * j), $MachinePrecision] + N[(N[(z * N[(N[(b * c), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.4e-66], N[(N[(t$95$1 - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.96e+136], N[(N[(t$95$1 - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -9.5 or 1.96e136 < b

   1. Initial program 75.3%

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

   3. Taylor expanded in c around 0 68.6%

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

   4. Taylor expanded in x around 0 70.1%

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

      1. +-commutative 70.1%

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

      2. neg-mul-1 70.1%

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

      3. unsub-neg 70.1%

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

      4. *-commutative 70.1%

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

      5. associate-*r* 69.8%

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

   6. Simplified 69.8%

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

   7. Taylor expanded in b around -inf 72.1%

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

      1. associate-*r* 72.1%

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

      2. neg-mul-1 72.1%

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

      3. distribute-lft-out-- 72.1%

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

      4. associate-*r* 72.1%

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

      5. distribute-lft-neg-in 72.1%

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

      6. *-commutative 72.1%

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

      7. neg-mul-1 72.1%

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

      8. remove-double-neg 72.1%

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

   9. Simplified 79.8%

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

   if -9.5 < b < -1.3500000000000001e-82

   1. Initial program 82.9%

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

   3. Taylor expanded in a around 0 82.6%

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

   4. Taylor expanded in i around -inf 82.5%

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

      1. mul-1-neg 82.5%

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

      2. *-commutative 82.5%

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

      3. distribute-rgt-neg-in 82.5%

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

   6. Simplified 88.0%

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

   if -1.3500000000000001e-82 < b < 7.4000000000000004e-66

   1. Initial program 73.0%

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

   3. Taylor expanded in c around 0 76.0%

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

      1. mul-1-neg 76.0%

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

      2. *-commutative 76.0%

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

      3. associate-*r* 78.0%

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

      4. *-commutative 78.0%

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

      5. distribute-rgt-neg-out 78.0%

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

      6. *-commutative 78.0%

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

      7. distribute-rgt-neg-in 78.0%

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

   5. Simplified 78.0%

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

   6. Taylor expanded in y around 0 74.9%

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

      1. associate-*r* 74.9%

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

      2. neg-mul-1 74.9%

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

      3. *-commutative 74.9%

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

   8. Simplified 74.9%

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

   if 7.4000000000000004e-66 < b < 1.96e136

   1. Initial program 80.2%

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

   3. Taylor expanded in c around 0 72.0%

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

      1. mul-1-neg 72.0%

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

      2. *-commutative 72.0%

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

      3. associate-*r* 69.2%

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

      4. *-commutative 69.2%

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

      5. distribute-rgt-neg-out 69.2%

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

      6. *-commutative 69.2%

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

      7. distribute-rgt-neg-in 69.2%

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

   5. Simplified 69.2%

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

   6. Taylor expanded in c around inf 77.6%

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

      1. *-commutative 77.6%

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

   8. Simplified 77.6%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.5:\\ \;\;\;\;b \cdot \left(j \cdot \frac{a \cdot c - y \cdot i}{b} + \left(t \cdot i - z \cdot c\right)\right)\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{-82}:\\ \;\;\;\;i \cdot \left(t \cdot b - \left(y \cdot j + \frac{z \cdot \left(b \cdot c - x \cdot y\right)}{i}\right)\right)\\ \mathbf{elif}\;b \leq 7.4 \cdot 10^{-66}:\\ \;\;\;\;\left(i \cdot \left(t \cdot b\right) - a \cdot \left(x \cdot t\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 1.96 \cdot 10^{+136}:\\ \;\;\;\;\left(i \cdot \left(t \cdot b\right) - x \cdot \left(t \cdot a - y \cdot z\right)\right) + a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(j \cdot \frac{a \cdot c - y \cdot i}{b} + \left(t \cdot i - z \cdot c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 58.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;y \leq -1.02 \cdot 10^{+34}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-167}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-193}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-97}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b + y \cdot \left(x \cdot \frac{z}{i} - j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* a (* c j)) (* b (- (* t i) (* z c))))))
   (if (<= y -1.02e+34)
     (- (* z (- (* x y) (* b c))) (* y (* i j)))
     (if (<= y -1.9e-167)
       (* a (- (* c j) (* x t)))
       (if (<= y 1.55e-193)
         t_1
         (if (<= y 7e-97)
           (* t (- (* b i) (* x a)))
           (if (<= y 2.8e+17)
             t_1
             (* i (+ (* t b) (* 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 = (a * (c * j)) + (b * ((t * i) - (z * c)));
	double tmp;
	if (y <= -1.02e+34) {
		tmp = (z * ((x * y) - (b * c))) - (y * (i * j));
	} else if (y <= -1.9e-167) {
		tmp = a * ((c * j) - (x * t));
	} else if (y <= 1.55e-193) {
		tmp = t_1;
	} else if (y <= 7e-97) {
		tmp = t * ((b * i) - (x * a));
	} else if (y <= 2.8e+17) {
		tmp = t_1;
	} else {
		tmp = i * ((t * b) + (y * ((x * (z / i)) - j)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * (c * j)) + (b * ((t * i) - (z * c)))
    if (y <= (-1.02d+34)) then
        tmp = (z * ((x * y) - (b * c))) - (y * (i * j))
    else if (y <= (-1.9d-167)) then
        tmp = a * ((c * j) - (x * t))
    else if (y <= 1.55d-193) then
        tmp = t_1
    else if (y <= 7d-97) then
        tmp = t * ((b * i) - (x * a))
    else if (y <= 2.8d+17) then
        tmp = t_1
    else
        tmp = i * ((t * b) + (y * ((x * (z / i)) - j)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (a * (c * j)) + (b * ((t * i) - (z * c)));
	double tmp;
	if (y <= -1.02e+34) {
		tmp = (z * ((x * y) - (b * c))) - (y * (i * j));
	} else if (y <= -1.9e-167) {
		tmp = a * ((c * j) - (x * t));
	} else if (y <= 1.55e-193) {
		tmp = t_1;
	} else if (y <= 7e-97) {
		tmp = t * ((b * i) - (x * a));
	} else if (y <= 2.8e+17) {
		tmp = t_1;
	} else {
		tmp = i * ((t * b) + (y * ((x * (z / i)) - j)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (a * (c * j)) + (b * ((t * i) - (z * c)))
	tmp = 0
	if y <= -1.02e+34:
		tmp = (z * ((x * y) - (b * c))) - (y * (i * j))
	elif y <= -1.9e-167:
		tmp = a * ((c * j) - (x * t))
	elif y <= 1.55e-193:
		tmp = t_1
	elif y <= 7e-97:
		tmp = t * ((b * i) - (x * a))
	elif y <= 2.8e+17:
		tmp = t_1
	else:
		tmp = i * ((t * b) + (y * ((x * (z / i)) - j)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(a * Float64(c * j)) + Float64(b * Float64(Float64(t * i) - Float64(z * c))))
	tmp = 0.0
	if (y <= -1.02e+34)
		tmp = Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) - Float64(y * Float64(i * j)));
	elseif (y <= -1.9e-167)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (y <= 1.55e-193)
		tmp = t_1;
	elseif (y <= 7e-97)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (y <= 2.8e+17)
		tmp = t_1;
	else
		tmp = Float64(i * Float64(Float64(t * b) + Float64(y * Float64(Float64(x * Float64(z / i)) - j))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (a * (c * j)) + (b * ((t * i) - (z * c)));
	tmp = 0.0;
	if (y <= -1.02e+34)
		tmp = (z * ((x * y) - (b * c))) - (y * (i * j));
	elseif (y <= -1.9e-167)
		tmp = a * ((c * j) - (x * t));
	elseif (y <= 1.55e-193)
		tmp = t_1;
	elseif (y <= 7e-97)
		tmp = t * ((b * i) - (x * a));
	elseif (y <= 2.8e+17)
		tmp = t_1;
	else
		tmp = i * ((t * b) + (y * ((x * (z / i)) - j)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.02e+34], N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.9e-167], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.55e-193], t$95$1, If[LessEqual[y, 7e-97], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e+17], t$95$1, N[(i * N[(N[(t * b), $MachinePrecision] + N[(y * N[(N[(x * N[(z / i), $MachinePrecision]), $MachinePrecision] - j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.02e34

   1. Initial program 60.1%

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

   3. Taylor expanded in a around 0 49.4%

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

   4. Taylor expanded in t around 0 47.2%

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

      1. sub-neg 47.2%

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

      2. associate-+r+ 47.2%

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

      3. sub-neg 47.2%

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

      4. associate-*r* 53.5%

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

      5. associate-*r* 55.6%

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

      6. distribute-rgt-out-- 55.6%

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

      7. +-commutative 55.6%

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

      8. neg-mul-1 55.6%

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

      9. unsub-neg 55.6%

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

      10. *-commutative 55.6%

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

      11. *-commutative 55.6%

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

      12. associate-*r* 68.7%

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

   6. Simplified 68.7%

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

   if -1.02e34 < y < -1.89999999999999984e-167

   1. Initial program 79.9%

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

   3. Taylor expanded in a around inf 69.8%

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

      1. +-commutative 69.8%

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

      2. mul-1-neg 69.8%

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

      3. unsub-neg 69.8%

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

      4. *-commutative 69.8%

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

      5. *-commutative 69.8%

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

   5. Simplified 69.8%

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

   if -1.89999999999999984e-167 < y < 1.5500000000000001e-193 or 7.00000000000000038e-97 < y < 2.8e17

   1. Initial program 86.6%

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

   3. Taylor expanded in c around 0 86.4%

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

   4. Taylor expanded in x around 0 72.2%

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

      1. +-commutative 72.2%

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

      2. neg-mul-1 72.2%

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

      3. unsub-neg 72.2%

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

      4. *-commutative 72.2%

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

      5. associate-*r* 67.5%

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

   6. Simplified 67.5%

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

   7. Taylor expanded in y around 0 73.4%

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

      1. *-commutative 73.4%

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

   9. Simplified 73.4%

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

   if 1.5500000000000001e-193 < y < 7.00000000000000038e-97

   1. Initial program 90.1%

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

   3. Taylor expanded in t around inf 57.9%

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

      1. distribute-lft-out-- 57.9%

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

      2. *-commutative 57.9%

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

      3. *-commutative 57.9%

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

   5. Simplified 57.9%

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

   if 2.8e17 < y

   1. Initial program 66.6%

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

   3. Taylor expanded in a around 0 62.9%

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

   4. Taylor expanded in i around -inf 65.9%

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

      1. mul-1-neg 65.9%

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

      2. *-commutative 65.9%

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

      3. distribute-rgt-neg-in 65.9%

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

   6. Simplified 71.1%

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

   7. Taylor expanded in y around inf 75.1%

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

      1. associate-/l* 75.6%

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

   9. Simplified 75.6%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+34}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-167}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-193}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-97}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+17}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b + y \cdot \left(x \cdot \frac{z}{i} - j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 59.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right) - y \cdot \left(i \cdot j\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -8 \cdot 10^{+134}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{+38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-21}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 55000:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* z (- (* x y) (* b c))) (* y (* i j))))
        (t_2 (* x (- (* y z) (* t a)))))
   (if (<= x -8e+134)
     t_2
     (if (<= x -6.2e+38)
       t_1
       (if (<= x -5e-21)
         (* t (- (* b i) (* x a)))
         (if (<= x -1.25e-55)
           t_1
           (if (<= x 55000.0)
             (+ (* a (* c j)) (* b (- (* t i) (* z c))))
             t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (z * ((x * y) - (b * c))) - (y * (i * j));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -8e+134) {
		tmp = t_2;
	} else if (x <= -6.2e+38) {
		tmp = t_1;
	} else if (x <= -5e-21) {
		tmp = t * ((b * i) - (x * a));
	} else if (x <= -1.25e-55) {
		tmp = t_1;
	} else if (x <= 55000.0) {
		tmp = (a * (c * j)) + (b * ((t * i) - (z * c)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z * ((x * y) - (b * c))) - (y * (i * j))
    t_2 = x * ((y * z) - (t * a))
    if (x <= (-8d+134)) then
        tmp = t_2
    else if (x <= (-6.2d+38)) then
        tmp = t_1
    else if (x <= (-5d-21)) then
        tmp = t * ((b * i) - (x * a))
    else if (x <= (-1.25d-55)) then
        tmp = t_1
    else if (x <= 55000.0d0) then
        tmp = (a * (c * j)) + (b * ((t * i) - (z * c)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (z * ((x * y) - (b * c))) - (y * (i * j));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -8e+134) {
		tmp = t_2;
	} else if (x <= -6.2e+38) {
		tmp = t_1;
	} else if (x <= -5e-21) {
		tmp = t * ((b * i) - (x * a));
	} else if (x <= -1.25e-55) {
		tmp = t_1;
	} else if (x <= 55000.0) {
		tmp = (a * (c * j)) + (b * ((t * i) - (z * c)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (z * ((x * y) - (b * c))) - (y * (i * j))
	t_2 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -8e+134:
		tmp = t_2
	elif x <= -6.2e+38:
		tmp = t_1
	elif x <= -5e-21:
		tmp = t * ((b * i) - (x * a))
	elif x <= -1.25e-55:
		tmp = t_1
	elif x <= 55000.0:
		tmp = (a * (c * j)) + (b * ((t * i) - (z * c)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) - Float64(y * Float64(i * j)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -8e+134)
		tmp = t_2;
	elseif (x <= -6.2e+38)
		tmp = t_1;
	elseif (x <= -5e-21)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (x <= -1.25e-55)
		tmp = t_1;
	elseif (x <= 55000.0)
		tmp = Float64(Float64(a * Float64(c * j)) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (z * ((x * y) - (b * c))) - (y * (i * j));
	t_2 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -8e+134)
		tmp = t_2;
	elseif (x <= -6.2e+38)
		tmp = t_1;
	elseif (x <= -5e-21)
		tmp = t * ((b * i) - (x * a));
	elseif (x <= -1.25e-55)
		tmp = t_1;
	elseif (x <= 55000.0)
		tmp = (a * (c * j)) + (b * ((t * i) - (z * c)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8e+134], t$95$2, If[LessEqual[x, -6.2e+38], t$95$1, If[LessEqual[x, -5e-21], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.25e-55], t$95$1, If[LessEqual[x, 55000.0], N[(N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -7.99999999999999937e134 or 55000 < x

   1. Initial program 71.4%

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

   3. Taylor expanded in c around 0 69.0%

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

   4. Taylor expanded in x around inf 72.0%

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

   if -7.99999999999999937e134 < x < -6.20000000000000035e38 or -4.99999999999999973e-21 < x < -1.25e-55

   1. Initial program 85.4%

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

   3. Taylor expanded in a around 0 71.7%

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

   4. Taylor expanded in t around 0 68.3%

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

      1. sub-neg 68.3%

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

      2. associate-+r+ 68.3%

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

      3. sub-neg 68.3%

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

      4. associate-*r* 71.6%

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

      5. associate-*r* 71.6%

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

      6. distribute-rgt-out-- 71.6%

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

      7. +-commutative 71.6%

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

      8. neg-mul-1 71.6%

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

      9. unsub-neg 71.6%

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

      10. *-commutative 71.6%

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

      11. *-commutative 71.6%

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

      12. associate-*r* 75.5%

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

   6. Simplified 75.5%

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

   if -6.20000000000000035e38 < x < -4.99999999999999973e-21

   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 t around inf 75.5%

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

      1. distribute-lft-out-- 75.5%

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

      2. *-commutative 75.5%

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

      3. *-commutative 75.5%

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

   5. Simplified 75.5%

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

   if -1.25e-55 < x < 55000

   1. Initial program 76.3%

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

   3. Taylor expanded in c around 0 76.1%

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

   4. Taylor expanded in x around 0 74.0%

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

      1. +-commutative 74.0%

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

      2. neg-mul-1 74.0%

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

      3. unsub-neg 74.0%

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

      4. *-commutative 74.0%

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

      5. associate-*r* 74.4%

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

   6. Simplified 74.4%

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

   7. Taylor expanded in y around 0 66.1%

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

      1. *-commutative 66.1%

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

   9. Simplified 66.1%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+134}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{+38}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-21}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-55}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;x \leq 55000:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 58.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b + y \cdot \left(x \cdot \frac{z}{i} - j\right)\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.25 \cdot 10^{+165}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-152}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-58}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{+120}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+158}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+225}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (+ (* t b) (* y (- (* x (/ z i)) j)))))
        (t_2 (* a (- (* c j) (* x t)))))
   (if (<= a -1.25e+165)
     t_2
     (if (<= a -4.2e-152)
       t_1
       (if (<= a 1.45e-58)
         (- (* b (- (* t i) (* z c))) (* i (* y j)))
         (if (<= a 8.6e+120)
           t_1
           (if (<= a 1.25e+158)
             (* x (- (* y z) (* t a)))
             (if (<= a 1.15e+225) (* j (- (* a c) (* y i))) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) + (y * ((x * (z / i)) - j)));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.25e+165) {
		tmp = t_2;
	} else if (a <= -4.2e-152) {
		tmp = t_1;
	} else if (a <= 1.45e-58) {
		tmp = (b * ((t * i) - (z * c))) - (i * (y * j));
	} else if (a <= 8.6e+120) {
		tmp = t_1;
	} else if (a <= 1.25e+158) {
		tmp = x * ((y * z) - (t * a));
	} else if (a <= 1.15e+225) {
		tmp = j * ((a * c) - (y * i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i * ((t * b) + (y * ((x * (z / i)) - j)))
    t_2 = a * ((c * j) - (x * t))
    if (a <= (-1.25d+165)) then
        tmp = t_2
    else if (a <= (-4.2d-152)) then
        tmp = t_1
    else if (a <= 1.45d-58) then
        tmp = (b * ((t * i) - (z * c))) - (i * (y * j))
    else if (a <= 8.6d+120) then
        tmp = t_1
    else if (a <= 1.25d+158) then
        tmp = x * ((y * z) - (t * a))
    else if (a <= 1.15d+225) then
        tmp = j * ((a * c) - (y * i))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) + (y * ((x * (z / i)) - j)));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.25e+165) {
		tmp = t_2;
	} else if (a <= -4.2e-152) {
		tmp = t_1;
	} else if (a <= 1.45e-58) {
		tmp = (b * ((t * i) - (z * c))) - (i * (y * j));
	} else if (a <= 8.6e+120) {
		tmp = t_1;
	} else if (a <= 1.25e+158) {
		tmp = x * ((y * z) - (t * a));
	} else if (a <= 1.15e+225) {
		tmp = j * ((a * c) - (y * i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) + (y * ((x * (z / i)) - j)))
	t_2 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -1.25e+165:
		tmp = t_2
	elif a <= -4.2e-152:
		tmp = t_1
	elif a <= 1.45e-58:
		tmp = (b * ((t * i) - (z * c))) - (i * (y * j))
	elif a <= 8.6e+120:
		tmp = t_1
	elif a <= 1.25e+158:
		tmp = x * ((y * z) - (t * a))
	elif a <= 1.15e+225:
		tmp = j * ((a * c) - (y * i))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(t * b) + Float64(y * Float64(Float64(x * Float64(z / i)) - j))))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -1.25e+165)
		tmp = t_2;
	elseif (a <= -4.2e-152)
		tmp = t_1;
	elseif (a <= 1.45e-58)
		tmp = Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) - Float64(i * Float64(y * j)));
	elseif (a <= 8.6e+120)
		tmp = t_1;
	elseif (a <= 1.25e+158)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (a <= 1.15e+225)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((t * b) + (y * ((x * (z / i)) - j)));
	t_2 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -1.25e+165)
		tmp = t_2;
	elseif (a <= -4.2e-152)
		tmp = t_1;
	elseif (a <= 1.45e-58)
		tmp = (b * ((t * i) - (z * c))) - (i * (y * j));
	elseif (a <= 8.6e+120)
		tmp = t_1;
	elseif (a <= 1.25e+158)
		tmp = x * ((y * z) - (t * a));
	elseif (a <= 1.15e+225)
		tmp = j * ((a * c) - (y * i));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(t * b), $MachinePrecision] + N[(y * N[(N[(x * N[(z / i), $MachinePrecision]), $MachinePrecision] - j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.25e+165], t$95$2, If[LessEqual[a, -4.2e-152], t$95$1, If[LessEqual[a, 1.45e-58], N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.6e+120], t$95$1, If[LessEqual[a, 1.25e+158], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.15e+225], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.24999999999999993e165 or 1.15e225 < a

   1. Initial program 81.5%

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

   3. Taylor expanded in a around inf 93.5%

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

      1. +-commutative 93.5%

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

      2. mul-1-neg 93.5%

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

      3. unsub-neg 93.5%

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

      4. *-commutative 93.5%

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

      5. *-commutative 93.5%

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

   5. Simplified 93.5%

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

   if -1.24999999999999993e165 < a < -4.19999999999999998e-152 or 1.44999999999999995e-58 < a < 8.6000000000000003e120

   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 0 59.6%

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

   4. Taylor expanded in i around -inf 61.6%

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

      1. mul-1-neg 61.6%

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

      2. *-commutative 61.6%

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

      3. distribute-rgt-neg-in 61.6%

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

   6. Simplified 66.1%

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

   7. Taylor expanded in y around inf 65.4%

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

      1. associate-/l* 65.5%

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

   9. Simplified 65.5%

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

   if -4.19999999999999998e-152 < a < 1.44999999999999995e-58

   1. Initial program 83.9%

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

   3. Taylor expanded in a around 0 73.0%

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

   4. Taylor expanded in x around 0 73.6%

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

      1. neg-mul-1 73.6%

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

      2. distribute-rgt-neg-in 73.6%

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

      3. distribute-lft-neg-in 73.6%

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

   6. Simplified 73.6%

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

   if 8.6000000000000003e120 < a < 1.2499999999999999e158

   1. Initial program 70.6%

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

   3. Taylor expanded in c around 0 60.6%

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

   4. Taylor expanded in x around inf 80.9%

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

   if 1.2499999999999999e158 < a < 1.15e225

   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 c around 0 68.5%

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

   4. Taylor expanded in j around inf 68.6%

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

      1. +-commutative 68.6%

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

      2. mul-1-neg 68.6%

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

      3. unsub-neg 68.6%

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

   6. Simplified 68.6%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.25 \cdot 10^{+165}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-152}:\\ \;\;\;\;i \cdot \left(t \cdot b + y \cdot \left(x \cdot \frac{z}{i} - j\right)\right)\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-58}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{+120}:\\ \;\;\;\;i \cdot \left(t \cdot b + y \cdot \left(x \cdot \frac{z}{i} - j\right)\right)\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+158}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+225}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 48.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;j \leq -2.2 \cdot 10^{+193}:\\ \;\;\;\;i \cdot \frac{y \cdot \left(x \cdot z - i \cdot j\right)}{i}\\ \mathbf{elif}\;j \leq -2.2 \cdot 10^{-38}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq 3.5 \cdot 10^{-284}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 4.35 \cdot 10^{-234}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 7.2 \cdot 10^{-117}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 6.6 \cdot 10^{-45}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* b i) (* x a)))) (t_2 (* z (- (* x y) (* b c)))))
   (if (<= j -2.2e+193)
     (* i (/ (* y (- (* x z) (* i j))) i))
     (if (<= j -2.2e-38)
       (* c (- (* a j) (* z b)))
       (if (<= j 3.5e-284)
         t_1
         (if (<= j 4.35e-234)
           t_2
           (if (<= j 7.2e-117)
             t_1
             (if (<= j 6.6e-45) t_2 (* 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 t_1 = t * ((b * i) - (x * a));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (j <= -2.2e+193) {
		tmp = i * ((y * ((x * z) - (i * j))) / i);
	} else if (j <= -2.2e-38) {
		tmp = c * ((a * j) - (z * b));
	} else if (j <= 3.5e-284) {
		tmp = t_1;
	} else if (j <= 4.35e-234) {
		tmp = t_2;
	} else if (j <= 7.2e-117) {
		tmp = t_1;
	} else if (j <= 6.6e-45) {
		tmp = t_2;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((b * i) - (x * a))
    t_2 = z * ((x * y) - (b * c))
    if (j <= (-2.2d+193)) then
        tmp = i * ((y * ((x * z) - (i * j))) / i)
    else if (j <= (-2.2d-38)) then
        tmp = c * ((a * j) - (z * b))
    else if (j <= 3.5d-284) then
        tmp = t_1
    else if (j <= 4.35d-234) then
        tmp = t_2
    else if (j <= 7.2d-117) then
        tmp = t_1
    else if (j <= 6.6d-45) then
        tmp = t_2
    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 t_1 = t * ((b * i) - (x * a));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (j <= -2.2e+193) {
		tmp = i * ((y * ((x * z) - (i * j))) / i);
	} else if (j <= -2.2e-38) {
		tmp = c * ((a * j) - (z * b));
	} else if (j <= 3.5e-284) {
		tmp = t_1;
	} else if (j <= 4.35e-234) {
		tmp = t_2;
	} else if (j <= 7.2e-117) {
		tmp = t_1;
	} else if (j <= 6.6e-45) {
		tmp = t_2;
	} else {
		tmp = j * ((a * c) - (y * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((b * i) - (x * a))
	t_2 = z * ((x * y) - (b * c))
	tmp = 0
	if j <= -2.2e+193:
		tmp = i * ((y * ((x * z) - (i * j))) / i)
	elif j <= -2.2e-38:
		tmp = c * ((a * j) - (z * b))
	elif j <= 3.5e-284:
		tmp = t_1
	elif j <= 4.35e-234:
		tmp = t_2
	elif j <= 7.2e-117:
		tmp = t_1
	elif j <= 6.6e-45:
		tmp = t_2
	else:
		tmp = j * ((a * c) - (y * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	t_2 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (j <= -2.2e+193)
		tmp = Float64(i * Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) / i));
	elseif (j <= -2.2e-38)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (j <= 3.5e-284)
		tmp = t_1;
	elseif (j <= 4.35e-234)
		tmp = t_2;
	elseif (j <= 7.2e-117)
		tmp = t_1;
	elseif (j <= 6.6e-45)
		tmp = t_2;
	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)
	t_1 = t * ((b * i) - (x * a));
	t_2 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (j <= -2.2e+193)
		tmp = i * ((y * ((x * z) - (i * j))) / i);
	elseif (j <= -2.2e-38)
		tmp = c * ((a * j) - (z * b));
	elseif (j <= 3.5e-284)
		tmp = t_1;
	elseif (j <= 4.35e-234)
		tmp = t_2;
	elseif (j <= 7.2e-117)
		tmp = t_1;
	elseif (j <= 6.6e-45)
		tmp = t_2;
	else
		tmp = j * ((a * c) - (y * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.2e+193], N[(i * N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.2e-38], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.5e-284], t$95$1, If[LessEqual[j, 4.35e-234], t$95$2, If[LessEqual[j, 7.2e-117], t$95$1, If[LessEqual[j, 6.6e-45], t$95$2, N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -2.19999999999999986e193

   1. Initial program 62.4%

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

   3. Taylor expanded in a around 0 56.7%

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

   4. Taylor expanded in i around -inf 56.7%

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

      1. mul-1-neg 56.7%

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

      2. *-commutative 56.7%

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

      3. distribute-rgt-neg-in 56.7%

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

   6. Simplified 56.7%

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

   7. Taylor expanded in y around inf 76.4%

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

      1. associate-*r* 76.4%

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

      2. neg-mul-1 76.4%

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

      3. associate-/l* 76.4%

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

   9. Simplified 76.4%

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

   10. Taylor expanded in i around 0 69.9%

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

       1. mul-1-neg 69.9%

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

       2. *-commutative 69.9%

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

       3. associate-*r* 69.9%

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

       4. distribute-lft-neg-out 69.9%

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

       5. mul-1-neg 69.9%

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

       6. associate-*r* 75.8%

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

       7. distribute-rgt-in 82.1%

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

       8. +-commutative 82.1%

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

       9. mul-1-neg 82.1%

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

       10. sub-neg 82.1%

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

   12. Simplified 82.1%

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

   if -2.19999999999999986e193 < j < -2.20000000000000007e-38

   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 c around inf 63.4%

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

      1. *-commutative 63.4%

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

   5. Simplified 63.4%

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

   if -2.20000000000000007e-38 < j < 3.49999999999999975e-284 or 4.35e-234 < j < 7.2000000000000001e-117

   1. Initial program 76.7%

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

   3. Taylor expanded in t around inf 65.2%

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

      1. distribute-lft-out-- 65.2%

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

      2. *-commutative 65.2%

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

      3. *-commutative 65.2%

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

   5. Simplified 65.2%

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

   if 3.49999999999999975e-284 < j < 4.35e-234 or 7.2000000000000001e-117 < j < 6.6000000000000001e-45

   1. Initial program 72.5%

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

   3. Taylor expanded in z around inf 72.4%

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

      1. *-commutative 72.4%

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

   5. Simplified 72.4%

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

   if 6.6000000000000001e-45 < j

   1. Initial program 78.8%

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

   3. Taylor expanded in c around 0 72.1%

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

   4. Taylor expanded in j around inf 63.4%

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

      1. +-commutative 63.4%

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

      2. mul-1-neg 63.4%

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

      3. unsub-neg 63.4%

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

   6. Simplified 63.4%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.2 \cdot 10^{+193}:\\ \;\;\;\;i \cdot \frac{y \cdot \left(x \cdot z - i \cdot j\right)}{i}\\ \mathbf{elif}\;j \leq -2.2 \cdot 10^{-38}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq 3.5 \cdot 10^{-284}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 4.35 \cdot 10^{-234}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 7.2 \cdot 10^{-117}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 6.6 \cdot 10^{-45}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 68.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := x \cdot \left(t \cdot a - y \cdot z\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_4 := t\_3 - t\_2\\ \mathbf{if}\;j \leq -1.05 \cdot 10^{+52}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{-116}:\\ \;\;\;\;t\_1 - t\_2\\ \mathbf{elif}\;j \leq 1.75 \cdot 10^{-48}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;j \leq 0.00042:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;t\_3 + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c))))
        (t_2 (* x (- (* t a) (* y z))))
        (t_3 (* j (- (* a c) (* y i))))
        (t_4 (- t_3 t_2)))
   (if (<= j -1.05e+52)
     t_4
     (if (<= j 2.5e-116)
       (- t_1 t_2)
       (if (<= j 1.75e-48)
         (- (* z (- (* x y) (* b c))) (* y (* i j)))
         (if (<= j 0.00042) t_4 (+ t_3 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = x * ((t * a) - (y * z));
	double t_3 = j * ((a * c) - (y * i));
	double t_4 = t_3 - t_2;
	double tmp;
	if (j <= -1.05e+52) {
		tmp = t_4;
	} else if (j <= 2.5e-116) {
		tmp = t_1 - t_2;
	} else if (j <= 1.75e-48) {
		tmp = (z * ((x * y) - (b * c))) - (y * (i * j));
	} else if (j <= 0.00042) {
		tmp = t_4;
	} else {
		tmp = t_3 + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = x * ((t * a) - (y * z))
    t_3 = j * ((a * c) - (y * i))
    t_4 = t_3 - t_2
    if (j <= (-1.05d+52)) then
        tmp = t_4
    else if (j <= 2.5d-116) then
        tmp = t_1 - t_2
    else if (j <= 1.75d-48) then
        tmp = (z * ((x * y) - (b * c))) - (y * (i * j))
    else if (j <= 0.00042d0) then
        tmp = t_4
    else
        tmp = t_3 + 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 t_2 = x * ((t * a) - (y * z));
	double t_3 = j * ((a * c) - (y * i));
	double t_4 = t_3 - t_2;
	double tmp;
	if (j <= -1.05e+52) {
		tmp = t_4;
	} else if (j <= 2.5e-116) {
		tmp = t_1 - t_2;
	} else if (j <= 1.75e-48) {
		tmp = (z * ((x * y) - (b * c))) - (y * (i * j));
	} else if (j <= 0.00042) {
		tmp = t_4;
	} else {
		tmp = t_3 + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = x * ((t * a) - (y * z))
	t_3 = j * ((a * c) - (y * i))
	t_4 = t_3 - t_2
	tmp = 0
	if j <= -1.05e+52:
		tmp = t_4
	elif j <= 2.5e-116:
		tmp = t_1 - t_2
	elif j <= 1.75e-48:
		tmp = (z * ((x * y) - (b * c))) - (y * (i * j))
	elif j <= 0.00042:
		tmp = t_4
	else:
		tmp = t_3 + 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)))
	t_2 = Float64(x * Float64(Float64(t * a) - Float64(y * z)))
	t_3 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_4 = Float64(t_3 - t_2)
	tmp = 0.0
	if (j <= -1.05e+52)
		tmp = t_4;
	elseif (j <= 2.5e-116)
		tmp = Float64(t_1 - t_2);
	elseif (j <= 1.75e-48)
		tmp = Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) - Float64(y * Float64(i * j)));
	elseif (j <= 0.00042)
		tmp = t_4;
	else
		tmp = Float64(t_3 + 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));
	t_2 = x * ((t * a) - (y * z));
	t_3 = j * ((a * c) - (y * i));
	t_4 = t_3 - t_2;
	tmp = 0.0;
	if (j <= -1.05e+52)
		tmp = t_4;
	elseif (j <= 2.5e-116)
		tmp = t_1 - t_2;
	elseif (j <= 1.75e-48)
		tmp = (z * ((x * y) - (b * c))) - (y * (i * j));
	elseif (j <= 0.00042)
		tmp = t_4;
	else
		tmp = t_3 + 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]}, Block[{t$95$2 = N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 - t$95$2), $MachinePrecision]}, If[LessEqual[j, -1.05e+52], t$95$4, If[LessEqual[j, 2.5e-116], N[(t$95$1 - t$95$2), $MachinePrecision], If[LessEqual[j, 1.75e-48], N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 0.00042], t$95$4, N[(t$95$3 + t$95$1), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.05e52 or 1.74999999999999996e-48 < j < 4.2000000000000002e-4

   1. Initial program 73.1%

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

   3. Taylor expanded in b around 0 77.4%

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

   if -1.05e52 < j < 2.5000000000000001e-116

   1. Initial program 77.4%

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

   3. Taylor expanded in j around 0 75.1%

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

   if 2.5000000000000001e-116 < j < 1.74999999999999996e-48

   1. Initial program 58.6%

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

   3. Taylor expanded in a around 0 51.4%

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

   4. Taylor expanded in t around 0 51.4%

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

      1. sub-neg 51.4%

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

      2. associate-+r+ 51.4%

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

      3. sub-neg 51.4%

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

      4. associate-*r* 64.7%

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

      5. associate-*r* 64.7%

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

      6. distribute-rgt-out-- 79.0%

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

      7. +-commutative 79.0%

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

      8. neg-mul-1 79.0%

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

      9. unsub-neg 79.0%

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

      10. *-commutative 79.0%

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

      11. *-commutative 79.0%

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

      12. associate-*r* 75.9%

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

   6. Simplified 75.9%

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

   if 4.2000000000000002e-4 < j

   1. Initial program 78.5%

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

   3. Taylor expanded in x around 0 80.2%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.05 \cdot 10^{+52}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{-116}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;j \leq 1.75 \cdot 10^{-48}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;j \leq 0.00042:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 73.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot c - y \cdot i\\ \mathbf{if}\;b \leq -1.15 \cdot 10^{+35} \lor \neg \left(b \leq 3.4 \cdot 10^{+135}\right):\\ \;\;\;\;b \cdot \left(j \cdot \frac{t\_1}{b} + \left(t \cdot i - z \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot \left(t \cdot b\right) - x \cdot \left(t \cdot a - y \cdot z\right)\right) + j \cdot t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* a c) (* y i))))
   (if (or (<= b -1.15e+35) (not (<= b 3.4e+135)))
     (* b (+ (* j (/ t_1 b)) (- (* t i) (* z c))))
     (+ (- (* i (* t b)) (* x (- (* t a) (* y z)))) (* 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 = (a * c) - (y * i);
	double tmp;
	if ((b <= -1.15e+35) || !(b <= 3.4e+135)) {
		tmp = b * ((j * (t_1 / b)) + ((t * i) - (z * c)));
	} else {
		tmp = ((i * (t * b)) - (x * ((t * a) - (y * z)))) + (j * t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * c) - (y * i)
    if ((b <= (-1.15d+35)) .or. (.not. (b <= 3.4d+135))) then
        tmp = b * ((j * (t_1 / b)) + ((t * i) - (z * c)))
    else
        tmp = ((i * (t * b)) - (x * ((t * a) - (y * z)))) + (j * t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (a * c) - (y * i);
	double tmp;
	if ((b <= -1.15e+35) || !(b <= 3.4e+135)) {
		tmp = b * ((j * (t_1 / b)) + ((t * i) - (z * c)));
	} else {
		tmp = ((i * (t * b)) - (x * ((t * a) - (y * z)))) + (j * t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (a * c) - (y * i)
	tmp = 0
	if (b <= -1.15e+35) or not (b <= 3.4e+135):
		tmp = b * ((j * (t_1 / b)) + ((t * i) - (z * c)))
	else:
		tmp = ((i * (t * b)) - (x * ((t * a) - (y * z)))) + (j * t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(a * c) - Float64(y * i))
	tmp = 0.0
	if ((b <= -1.15e+35) || !(b <= 3.4e+135))
		tmp = Float64(b * Float64(Float64(j * Float64(t_1 / b)) + Float64(Float64(t * i) - Float64(z * c))));
	else
		tmp = Float64(Float64(Float64(i * Float64(t * b)) - Float64(x * Float64(Float64(t * a) - Float64(y * z)))) + Float64(j * t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (a * c) - (y * i);
	tmp = 0.0;
	if ((b <= -1.15e+35) || ~((b <= 3.4e+135)))
		tmp = b * ((j * (t_1 / b)) + ((t * i) - (z * c)));
	else
		tmp = ((i * (t * b)) - (x * ((t * a) - (y * z)))) + (j * t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[b, -1.15e+35], N[Not[LessEqual[b, 3.4e+135]], $MachinePrecision]], N[(b * N[(N[(j * N[(t$95$1 / b), $MachinePrecision]), $MachinePrecision] + N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.1499999999999999e35 or 3.4000000000000001e135 < b

   1. Initial program 72.4%

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

   3. Taylor expanded in c around 0 67.0%

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

   4. Taylor expanded in x around 0 71.4%

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

      1. +-commutative 71.4%

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

      2. neg-mul-1 71.4%

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

      3. unsub-neg 71.4%

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

      4. *-commutative 71.4%

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

      5. associate-*r* 72.0%

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

   6. Simplified 72.0%

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

   7. Taylor expanded in b around -inf 73.6%

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

      1. associate-*r* 73.6%

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

      2. neg-mul-1 73.6%

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

      3. distribute-lft-out-- 73.6%

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

      4. associate-*r* 73.6%

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

      5. distribute-lft-neg-in 73.6%

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

      6. *-commutative 73.6%

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

      7. neg-mul-1 73.6%

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

      8. remove-double-neg 73.6%

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

   9. Simplified 81.2%

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

   if -1.1499999999999999e35 < b < 3.4000000000000001e135

   1. Initial program 77.3%

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

   3. Taylor expanded in c around 0 75.2%

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

      1. mul-1-neg 75.2%

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

      2. *-commutative 75.2%

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

      3. associate-*r* 75.2%

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

      4. *-commutative 75.2%

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

      5. distribute-rgt-neg-out 75.2%

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

      6. *-commutative 75.2%

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

      7. distribute-rgt-neg-in 75.2%

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

   5. Simplified 75.2%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{+35} \lor \neg \left(b \leq 3.4 \cdot 10^{+135}\right):\\ \;\;\;\;b \cdot \left(j \cdot \frac{a \cdot c - y \cdot i}{b} + \left(t \cdot i - z \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot \left(t \cdot b\right) - x \cdot \left(t \cdot a - y \cdot z\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 50.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.45 \cdot 10^{+87}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.9 \cdot 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.55 \cdot 10^{-69}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{-153}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{+182}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))) (t_2 (* b (- (* t i) (* z c)))))
   (if (<= b -1.45e+87)
     t_2
     (if (<= b -1.9e-31)
       t_1
       (if (<= b -1.55e-69)
         t_2
         (if (<= b -3.6e-153)
           t_1
           (if (<= b 1.35e+182) (* a (- (* c j) (* x t))) 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));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -1.45e+87) {
		tmp = t_2;
	} else if (b <= -1.9e-31) {
		tmp = t_1;
	} else if (b <= -1.55e-69) {
		tmp = t_2;
	} else if (b <= -3.6e-153) {
		tmp = t_1;
	} else if (b <= 1.35e+182) {
		tmp = a * ((c * j) - (x * t));
	} 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))
    t_2 = b * ((t * i) - (z * c))
    if (b <= (-1.45d+87)) then
        tmp = t_2
    else if (b <= (-1.9d-31)) then
        tmp = t_1
    else if (b <= (-1.55d-69)) then
        tmp = t_2
    else if (b <= (-3.6d-153)) then
        tmp = t_1
    else if (b <= 1.35d+182) then
        tmp = a * ((c * j) - (x * t))
    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));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -1.45e+87) {
		tmp = t_2;
	} else if (b <= -1.9e-31) {
		tmp = t_1;
	} else if (b <= -1.55e-69) {
		tmp = t_2;
	} else if (b <= -3.6e-153) {
		tmp = t_1;
	} else if (b <= 1.35e+182) {
		tmp = a * ((c * j) - (x * t));
	} 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))
	t_2 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -1.45e+87:
		tmp = t_2
	elif b <= -1.9e-31:
		tmp = t_1
	elif b <= -1.55e-69:
		tmp = t_2
	elif b <= -3.6e-153:
		tmp = t_1
	elif b <= 1.35e+182:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = t_2
	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)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -1.45e+87)
		tmp = t_2;
	elseif (b <= -1.9e-31)
		tmp = t_1;
	elseif (b <= -1.55e-69)
		tmp = t_2;
	elseif (b <= -3.6e-153)
		tmp = t_1;
	elseif (b <= 1.35e+182)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	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));
	t_2 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -1.45e+87)
		tmp = t_2;
	elseif (b <= -1.9e-31)
		tmp = t_1;
	elseif (b <= -1.55e-69)
		tmp = t_2;
	elseif (b <= -3.6e-153)
		tmp = t_1;
	elseif (b <= 1.35e+182)
		tmp = a * ((c * j) - (x * t));
	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[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.45e+87], t$95$2, If[LessEqual[b, -1.9e-31], t$95$1, If[LessEqual[b, -1.55e-69], t$95$2, If[LessEqual[b, -3.6e-153], t$95$1, If[LessEqual[b, 1.35e+182], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.4499999999999999e87 or -1.9e-31 < b < -1.55e-69 or 1.3500000000000001e182 < b

   1. Initial program 71.3%

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

   3. Taylor expanded in b around inf 79.2%

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

      1. *-commutative 79.2%

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

      2. *-commutative 79.2%

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

   5. Simplified 79.2%

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

   if -1.4499999999999999e87 < b < -1.9e-31 or -1.55e-69 < b < -3.5999999999999998e-153

   1. Initial program 85.6%

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

   3. Taylor expanded in c around 0 76.0%

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

   4. Taylor expanded in j around inf 57.8%

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

      1. +-commutative 57.8%

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

      2. mul-1-neg 57.8%

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

      3. unsub-neg 57.8%

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

   6. Simplified 57.8%

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

   if -3.5999999999999998e-153 < b < 1.3500000000000001e182

   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 a around inf 56.4%

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

      1. +-commutative 56.4%

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

      2. mul-1-neg 56.4%

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

      3. unsub-neg 56.4%

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

      4. *-commutative 56.4%

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

      5. *-commutative 56.4%

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

   5. Simplified 56.4%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.45 \cdot 10^{+87}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.9 \cdot 10^{-31}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq -1.55 \cdot 10^{-69}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{-153}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{+182}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 60.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.6 \cdot 10^{+165}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-154}:\\ \;\;\;\;i \cdot \left(t \cdot b + y \cdot \left(x \cdot \frac{z}{i} - j\right)\right)\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-35}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -6.6e+165)
   (* a (- (* c j) (* x t)))
   (if (<= a -1.5e-154)
     (* i (+ (* t b) (* y (- (* x (/ z i)) j))))
     (if (<= a 3.3e-35)
       (- (* b (- (* t i) (* z c))) (* i (* y j)))
       (- (* j (- (* a c) (* y i))) (* x (- (* t a) (* y z))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -6.6e+165) {
		tmp = a * ((c * j) - (x * t));
	} else if (a <= -1.5e-154) {
		tmp = i * ((t * b) + (y * ((x * (z / i)) - j)));
	} else if (a <= 3.3e-35) {
		tmp = (b * ((t * i) - (z * c))) - (i * (y * j));
	} else {
		tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (a <= (-6.6d+165)) then
        tmp = a * ((c * j) - (x * t))
    else if (a <= (-1.5d-154)) then
        tmp = i * ((t * b) + (y * ((x * (z / i)) - j)))
    else if (a <= 3.3d-35) then
        tmp = (b * ((t * i) - (z * c))) - (i * (y * j))
    else
        tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -6.6e+165) {
		tmp = a * ((c * j) - (x * t));
	} else if (a <= -1.5e-154) {
		tmp = i * ((t * b) + (y * ((x * (z / i)) - j)));
	} else if (a <= 3.3e-35) {
		tmp = (b * ((t * i) - (z * c))) - (i * (y * j));
	} else {
		tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -6.6e+165:
		tmp = a * ((c * j) - (x * t))
	elif a <= -1.5e-154:
		tmp = i * ((t * b) + (y * ((x * (z / i)) - j)))
	elif a <= 3.3e-35:
		tmp = (b * ((t * i) - (z * c))) - (i * (y * j))
	else:
		tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -6.6e+165)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (a <= -1.5e-154)
		tmp = Float64(i * Float64(Float64(t * b) + Float64(y * Float64(Float64(x * Float64(z / i)) - j))));
	elseif (a <= 3.3e-35)
		tmp = Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) - Float64(i * Float64(y * j)));
	else
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) - Float64(x * Float64(Float64(t * a) - Float64(y * z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -6.6e+165)
		tmp = a * ((c * j) - (x * t));
	elseif (a <= -1.5e-154)
		tmp = i * ((t * b) + (y * ((x * (z / i)) - j)));
	elseif (a <= 3.3e-35)
		tmp = (b * ((t * i) - (z * c))) - (i * (y * j));
	else
		tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -6.6e+165], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.5e-154], N[(i * N[(N[(t * b), $MachinePrecision] + N[(y * N[(N[(x * N[(z / i), $MachinePrecision]), $MachinePrecision] - j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.3e-35], N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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]]]]

Derivation

1. Split input into 4 regimes

2. if a < -6.5999999999999997e165

   1. Initial program 77.3%

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

   3. Taylor expanded in a around inf 91.9%

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

      1. +-commutative 91.9%

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

      2. mul-1-neg 91.9%

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

      3. unsub-neg 91.9%

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

      4. *-commutative 91.9%

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

      5. *-commutative 91.9%

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

   5. Simplified 91.9%

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

   if -6.5999999999999997e165 < a < -1.5000000000000001e-154

   1. Initial program 63.6%

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

   3. Taylor expanded in a around 0 55.3%

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

   4. Taylor expanded in i around -inf 56.9%

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

      1. mul-1-neg 56.9%

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

      2. *-commutative 56.9%

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

      3. distribute-rgt-neg-in 56.9%

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

   6. Simplified 65.2%

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

   7. Taylor expanded in y around inf 64.1%

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

      1. associate-/l* 64.0%

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

   9. Simplified 64.0%

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

   if -1.5000000000000001e-154 < a < 3.3e-35

   1. Initial program 81.2%

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

   3. Taylor expanded in a around 0 71.2%

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

   4. Taylor expanded in x around 0 71.9%

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

      1. neg-mul-1 71.9%

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

      2. distribute-rgt-neg-in 71.9%

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

      3. distribute-lft-neg-in 71.9%

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

   6. Simplified 71.9%

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

   if 3.3e-35 < a

   1. Initial program 80.1%

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

   3. Taylor expanded in b around 0 74.2%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.6 \cdot 10^{+165}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-154}:\\ \;\;\;\;i \cdot \left(t \cdot b + y \cdot \left(x \cdot \frac{z}{i} - j\right)\right)\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-35}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 29.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;b \leq -1.7 \cdot 10^{+49}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;b \leq -0.0132:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-152}:\\ \;\;\;\;\left(-i\right) \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;b \leq -1.85 \cdot 10^{-159}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.22 \cdot 10^{+137}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))))
   (if (<= b -1.7e+49)
     (* z (* b (- c)))
     (if (<= b -0.0132)
       t_1
       (if (<= b -2.1e-152)
         (* (- i) (* y j))
         (if (<= b -1.85e-159)
           t_1
           (if (<= b 1.22e+137) (* a (* x (- t))) (* (* z b) (- c)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double tmp;
	if (b <= -1.7e+49) {
		tmp = z * (b * -c);
	} else if (b <= -0.0132) {
		tmp = t_1;
	} else if (b <= -2.1e-152) {
		tmp = -i * (y * j);
	} else if (b <= -1.85e-159) {
		tmp = t_1;
	} else if (b <= 1.22e+137) {
		tmp = a * (x * -t);
	} else {
		tmp = (z * b) * -c;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (c * j)
    if (b <= (-1.7d+49)) then
        tmp = z * (b * -c)
    else if (b <= (-0.0132d0)) then
        tmp = t_1
    else if (b <= (-2.1d-152)) then
        tmp = -i * (y * j)
    else if (b <= (-1.85d-159)) then
        tmp = t_1
    else if (b <= 1.22d+137) then
        tmp = a * (x * -t)
    else
        tmp = (z * b) * -c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double tmp;
	if (b <= -1.7e+49) {
		tmp = z * (b * -c);
	} else if (b <= -0.0132) {
		tmp = t_1;
	} else if (b <= -2.1e-152) {
		tmp = -i * (y * j);
	} else if (b <= -1.85e-159) {
		tmp = t_1;
	} else if (b <= 1.22e+137) {
		tmp = a * (x * -t);
	} else {
		tmp = (z * b) * -c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	tmp = 0
	if b <= -1.7e+49:
		tmp = z * (b * -c)
	elif b <= -0.0132:
		tmp = t_1
	elif b <= -2.1e-152:
		tmp = -i * (y * j)
	elif b <= -1.85e-159:
		tmp = t_1
	elif b <= 1.22e+137:
		tmp = a * (x * -t)
	else:
		tmp = (z * b) * -c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	tmp = 0.0
	if (b <= -1.7e+49)
		tmp = Float64(z * Float64(b * Float64(-c)));
	elseif (b <= -0.0132)
		tmp = t_1;
	elseif (b <= -2.1e-152)
		tmp = Float64(Float64(-i) * Float64(y * j));
	elseif (b <= -1.85e-159)
		tmp = t_1;
	elseif (b <= 1.22e+137)
		tmp = Float64(a * Float64(x * Float64(-t)));
	else
		tmp = Float64(Float64(z * b) * Float64(-c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (c * j);
	tmp = 0.0;
	if (b <= -1.7e+49)
		tmp = z * (b * -c);
	elseif (b <= -0.0132)
		tmp = t_1;
	elseif (b <= -2.1e-152)
		tmp = -i * (y * j);
	elseif (b <= -1.85e-159)
		tmp = t_1;
	elseif (b <= 1.22e+137)
		tmp = a * (x * -t);
	else
		tmp = (z * b) * -c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.7e+49], N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -0.0132], t$95$1, If[LessEqual[b, -2.1e-152], N[((-i) * N[(y * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.85e-159], t$95$1, If[LessEqual[b, 1.22e+137], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], N[(N[(z * b), $MachinePrecision] * (-c)), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.7e49

   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 c around 0 66.5%

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

   4. Taylor expanded in c around inf 54.7%

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

      1. *-commutative 54.7%

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

   6. Simplified 54.7%

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

   7. Taylor expanded in j around 0 43.7%

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

      1. mul-1-neg 43.7%

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

      2. associate-*r* 49.8%

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

      3. distribute-rgt-neg-in 49.8%

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

   9. Simplified 49.8%

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

   if -1.7e49 < b < -0.0132 or -2.09999999999999999e-152 < b < -1.8499999999999999e-159

   1. Initial program 94.2%

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

   3. Taylor expanded in a around inf 51.4%

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

      1. +-commutative 51.4%

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

      2. mul-1-neg 51.4%

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

      3. unsub-neg 51.4%

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

      4. *-commutative 51.4%

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

      5. *-commutative 51.4%

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

   5. Simplified 51.4%

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

   6. Taylor expanded in j around inf 45.8%

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

      1. *-commutative 45.8%

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

   8. Simplified 45.8%

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

   if -0.0132 < b < -2.09999999999999999e-152

   1. Initial program 77.8%

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

   3. Taylor expanded in i around inf 54.9%

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

      1. distribute-lft-out-- 54.9%

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

      2. *-commutative 54.9%

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

      3. *-commutative 54.9%

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

   5. Simplified 54.9%

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

   6. Taylor expanded in y around inf 39.9%

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

      1. neg-mul-1 39.9%

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

      2. distribute-rgt-neg-in 39.9%

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

      3. distribute-lft-neg-in 39.9%

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

   8. Simplified 39.9%

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

   if -1.8499999999999999e-159 < b < 1.2199999999999999e137

   1. Initial program 75.1%

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

   3. Taylor expanded in a around inf 56.5%

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

      1. +-commutative 56.5%

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

      2. mul-1-neg 56.5%

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

      3. unsub-neg 56.5%

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

      4. *-commutative 56.5%

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

      5. *-commutative 56.5%

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

   5. Simplified 56.5%

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

   6. Taylor expanded in j around 0 40.2%

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

      1. mul-1-neg 40.2%

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

      2. distribute-rgt-neg-in 40.2%

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

   8. Simplified 40.2%

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

   if 1.2199999999999999e137 < b

   1. Initial program 73.1%

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

   3. Taylor expanded in c around 0 67.8%

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

   4. Taylor expanded in c around inf 69.2%

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

      1. *-commutative 69.2%

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

   6. Simplified 69.2%

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

   7. Taylor expanded in j around 0 59.0%

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

      1. neg-mul-1 59.0%

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

      2. distribute-rgt-neg-in 59.0%

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

   9. Simplified 59.0%

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

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.7 \cdot 10^{+49}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;b \leq -0.0132:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-152}:\\ \;\;\;\;\left(-i\right) \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;b \leq -1.85 \cdot 10^{-159}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 1.22 \cdot 10^{+137}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 29.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ t_2 := \left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{if}\;b \leq -8.2 \cdot 10^{+51}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.45:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{-154}:\\ \;\;\;\;\left(-i\right) \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;b \leq -1.3 \cdot 10^{-159}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{+135}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))) (t_2 (* (* z b) (- c))))
   (if (<= b -8.2e+51)
     t_2
     (if (<= b -1.45)
       t_1
       (if (<= b -5.8e-154)
         (* (- i) (* y j))
         (if (<= b -1.3e-159)
           t_1
           (if (<= b 3.4e+135) (* a (* x (- t))) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double t_2 = (z * b) * -c;
	double tmp;
	if (b <= -8.2e+51) {
		tmp = t_2;
	} else if (b <= -1.45) {
		tmp = t_1;
	} else if (b <= -5.8e-154) {
		tmp = -i * (y * j);
	} else if (b <= -1.3e-159) {
		tmp = t_1;
	} else if (b <= 3.4e+135) {
		tmp = a * (x * -t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (c * j)
    t_2 = (z * b) * -c
    if (b <= (-8.2d+51)) then
        tmp = t_2
    else if (b <= (-1.45d0)) then
        tmp = t_1
    else if (b <= (-5.8d-154)) then
        tmp = -i * (y * j)
    else if (b <= (-1.3d-159)) then
        tmp = t_1
    else if (b <= 3.4d+135) then
        tmp = a * (x * -t)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double t_2 = (z * b) * -c;
	double tmp;
	if (b <= -8.2e+51) {
		tmp = t_2;
	} else if (b <= -1.45) {
		tmp = t_1;
	} else if (b <= -5.8e-154) {
		tmp = -i * (y * j);
	} else if (b <= -1.3e-159) {
		tmp = t_1;
	} else if (b <= 3.4e+135) {
		tmp = a * (x * -t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	t_2 = (z * b) * -c
	tmp = 0
	if b <= -8.2e+51:
		tmp = t_2
	elif b <= -1.45:
		tmp = t_1
	elif b <= -5.8e-154:
		tmp = -i * (y * j)
	elif b <= -1.3e-159:
		tmp = t_1
	elif b <= 3.4e+135:
		tmp = a * (x * -t)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	t_2 = Float64(Float64(z * b) * Float64(-c))
	tmp = 0.0
	if (b <= -8.2e+51)
		tmp = t_2;
	elseif (b <= -1.45)
		tmp = t_1;
	elseif (b <= -5.8e-154)
		tmp = Float64(Float64(-i) * Float64(y * j));
	elseif (b <= -1.3e-159)
		tmp = t_1;
	elseif (b <= 3.4e+135)
		tmp = Float64(a * Float64(x * Float64(-t)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (c * j);
	t_2 = (z * b) * -c;
	tmp = 0.0;
	if (b <= -8.2e+51)
		tmp = t_2;
	elseif (b <= -1.45)
		tmp = t_1;
	elseif (b <= -5.8e-154)
		tmp = -i * (y * j);
	elseif (b <= -1.3e-159)
		tmp = t_1;
	elseif (b <= 3.4e+135)
		tmp = a * (x * -t);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * b), $MachinePrecision] * (-c)), $MachinePrecision]}, If[LessEqual[b, -8.2e+51], t$95$2, If[LessEqual[b, -1.45], t$95$1, If[LessEqual[b, -5.8e-154], N[((-i) * N[(y * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.3e-159], t$95$1, If[LessEqual[b, 3.4e+135], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -8.20000000000000021e51 or 3.4000000000000001e135 < b

   1. Initial program 71.6%

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

   3. Taylor expanded in c around 0 67.1%

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

   4. Taylor expanded in c around inf 61.2%

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

      1. *-commutative 61.2%

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

   6. Simplified 61.2%

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

   7. Taylor expanded in j around 0 52.8%

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

      1. neg-mul-1 52.8%

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

      2. distribute-rgt-neg-in 52.8%

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

   9. Simplified 52.8%

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

   if -8.20000000000000021e51 < b < -1.44999999999999996 or -5.8e-154 < b < -1.2999999999999999e-159

   1. Initial program 94.2%

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

   3. Taylor expanded in a around inf 51.4%

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

      1. +-commutative 51.4%

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

      2. mul-1-neg 51.4%

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

      3. unsub-neg 51.4%

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

      4. *-commutative 51.4%

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

      5. *-commutative 51.4%

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

   5. Simplified 51.4%

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

   6. Taylor expanded in j around inf 45.8%

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

      1. *-commutative 45.8%

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

   8. Simplified 45.8%

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

   if -1.44999999999999996 < b < -5.8e-154

   1. Initial program 77.8%

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

   3. Taylor expanded in i around inf 54.9%

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

      1. distribute-lft-out-- 54.9%

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

      2. *-commutative 54.9%

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

      3. *-commutative 54.9%

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

   5. Simplified 54.9%

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

   6. Taylor expanded in y around inf 39.9%

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

      1. neg-mul-1 39.9%

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

      2. distribute-rgt-neg-in 39.9%

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

      3. distribute-lft-neg-in 39.9%

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

   8. Simplified 39.9%

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

   if -1.2999999999999999e-159 < b < 3.4000000000000001e135

   1. Initial program 75.1%

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

   3. Taylor expanded in a around inf 56.5%

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

      1. +-commutative 56.5%

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

      2. mul-1-neg 56.5%

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

      3. unsub-neg 56.5%

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

      4. *-commutative 56.5%

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

      5. *-commutative 56.5%

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

   5. Simplified 56.5%

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

   6. Taylor expanded in j around 0 40.2%

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

      1. mul-1-neg 40.2%

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

      2. distribute-rgt-neg-in 40.2%

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

   8. Simplified 40.2%

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

4. Final simplification 44.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{+51}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{elif}\;b \leq -1.45:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{-154}:\\ \;\;\;\;\left(-i\right) \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;b \leq -1.3 \cdot 10^{-159}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{+135}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 29.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(x \cdot \left(-t\right)\right)\\ t_2 := \left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{if}\;b \leq -7.6 \cdot 10^{+49}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-159}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{-230}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{-138}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 1.42 \cdot 10^{+137}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* x (- t)))) (t_2 (* (* z b) (- c))))
   (if (<= b -7.6e+49)
     t_2
     (if (<= b -2.6e-159)
       (* a (* c j))
       (if (<= b 1.3e-230)
         t_1
         (if (<= b 1.25e-138) (* x (* y z)) (if (<= b 1.42e+137) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (x * -t);
	double t_2 = (z * b) * -c;
	double tmp;
	if (b <= -7.6e+49) {
		tmp = t_2;
	} else if (b <= -2.6e-159) {
		tmp = a * (c * j);
	} else if (b <= 1.3e-230) {
		tmp = t_1;
	} else if (b <= 1.25e-138) {
		tmp = x * (y * z);
	} else if (b <= 1.42e+137) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (x * -t)
    t_2 = (z * b) * -c
    if (b <= (-7.6d+49)) then
        tmp = t_2
    else if (b <= (-2.6d-159)) then
        tmp = a * (c * j)
    else if (b <= 1.3d-230) then
        tmp = t_1
    else if (b <= 1.25d-138) then
        tmp = x * (y * z)
    else if (b <= 1.42d+137) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (x * -t);
	double t_2 = (z * b) * -c;
	double tmp;
	if (b <= -7.6e+49) {
		tmp = t_2;
	} else if (b <= -2.6e-159) {
		tmp = a * (c * j);
	} else if (b <= 1.3e-230) {
		tmp = t_1;
	} else if (b <= 1.25e-138) {
		tmp = x * (y * z);
	} else if (b <= 1.42e+137) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (x * -t)
	t_2 = (z * b) * -c
	tmp = 0
	if b <= -7.6e+49:
		tmp = t_2
	elif b <= -2.6e-159:
		tmp = a * (c * j)
	elif b <= 1.3e-230:
		tmp = t_1
	elif b <= 1.25e-138:
		tmp = x * (y * z)
	elif b <= 1.42e+137:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(x * Float64(-t)))
	t_2 = Float64(Float64(z * b) * Float64(-c))
	tmp = 0.0
	if (b <= -7.6e+49)
		tmp = t_2;
	elseif (b <= -2.6e-159)
		tmp = Float64(a * Float64(c * j));
	elseif (b <= 1.3e-230)
		tmp = t_1;
	elseif (b <= 1.25e-138)
		tmp = Float64(x * Float64(y * z));
	elseif (b <= 1.42e+137)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (x * -t);
	t_2 = (z * b) * -c;
	tmp = 0.0;
	if (b <= -7.6e+49)
		tmp = t_2;
	elseif (b <= -2.6e-159)
		tmp = a * (c * j);
	elseif (b <= 1.3e-230)
		tmp = t_1;
	elseif (b <= 1.25e-138)
		tmp = x * (y * z);
	elseif (b <= 1.42e+137)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * b), $MachinePrecision] * (-c)), $MachinePrecision]}, If[LessEqual[b, -7.6e+49], t$95$2, If[LessEqual[b, -2.6e-159], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.3e-230], t$95$1, If[LessEqual[b, 1.25e-138], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.42e+137], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -7.5999999999999997e49 or 1.42e137 < b

   1. Initial program 71.6%

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

   3. Taylor expanded in c around 0 67.1%

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

   4. Taylor expanded in c around inf 61.2%

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

      1. *-commutative 61.2%

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

   6. Simplified 61.2%

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

   7. Taylor expanded in j around 0 52.8%

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

      1. neg-mul-1 52.8%

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

      2. distribute-rgt-neg-in 52.8%

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

   9. Simplified 52.8%

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

   if -7.5999999999999997e49 < b < -2.5999999999999998e-159

   1. Initial program 84.5%

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

   3. Taylor expanded in a around inf 40.1%

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

      1. +-commutative 40.1%

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

      2. mul-1-neg 40.1%

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

      3. unsub-neg 40.1%

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

      4. *-commutative 40.1%

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

      5. *-commutative 40.1%

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

   5. Simplified 40.1%

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

   6. Taylor expanded in j around inf 31.2%

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

      1. *-commutative 31.2%

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

   8. Simplified 31.2%

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

   if -2.5999999999999998e-159 < b < 1.3000000000000001e-230 or 1.24999999999999997e-138 < b < 1.42e137

   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 a around inf 61.2%

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

      1. +-commutative 61.2%

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

      2. mul-1-neg 61.2%

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

      3. unsub-neg 61.2%

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

      4. *-commutative 61.2%

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

      5. *-commutative 61.2%

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

   5. Simplified 61.2%

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

   6. Taylor expanded in j around 0 43.6%

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

      1. mul-1-neg 43.6%

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

      2. distribute-rgt-neg-in 43.6%

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

   8. Simplified 43.6%

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

   if 1.3000000000000001e-230 < b < 1.24999999999999997e-138

   1. Initial program 75.6%

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

   3. Taylor expanded in a around 0 56.0%

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

   4. Taylor expanded in x around inf 41.8%

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

4. Final simplification 44.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.6 \cdot 10^{+49}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-159}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{-230}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{-138}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 1.42 \cdot 10^{+137}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 30.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b\right)\\ t_2 := a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{if}\;x \leq -3.2 \cdot 10^{-8}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-129}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{-189}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-252}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+33}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* t b))) (t_2 (* a (* x (- t)))))
   (if (<= x -3.2e-8)
     t_2
     (if (<= x -3e-129)
       t_1
       (if (<= x -3.6e-189)
         (* c (* a j))
         (if (<= x -3.5e-252) t_1 (if (<= x 1.5e+33) (* a (* c j)) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (t * b);
	double t_2 = a * (x * -t);
	double tmp;
	if (x <= -3.2e-8) {
		tmp = t_2;
	} else if (x <= -3e-129) {
		tmp = t_1;
	} else if (x <= -3.6e-189) {
		tmp = c * (a * j);
	} else if (x <= -3.5e-252) {
		tmp = t_1;
	} else if (x <= 1.5e+33) {
		tmp = a * (c * j);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i * (t * b)
    t_2 = a * (x * -t)
    if (x <= (-3.2d-8)) then
        tmp = t_2
    else if (x <= (-3d-129)) then
        tmp = t_1
    else if (x <= (-3.6d-189)) then
        tmp = c * (a * j)
    else if (x <= (-3.5d-252)) then
        tmp = t_1
    else if (x <= 1.5d+33) then
        tmp = a * (c * j)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (t * b);
	double t_2 = a * (x * -t);
	double tmp;
	if (x <= -3.2e-8) {
		tmp = t_2;
	} else if (x <= -3e-129) {
		tmp = t_1;
	} else if (x <= -3.6e-189) {
		tmp = c * (a * j);
	} else if (x <= -3.5e-252) {
		tmp = t_1;
	} else if (x <= 1.5e+33) {
		tmp = a * (c * j);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (t * b)
	t_2 = a * (x * -t)
	tmp = 0
	if x <= -3.2e-8:
		tmp = t_2
	elif x <= -3e-129:
		tmp = t_1
	elif x <= -3.6e-189:
		tmp = c * (a * j)
	elif x <= -3.5e-252:
		tmp = t_1
	elif x <= 1.5e+33:
		tmp = a * (c * j)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(t * b))
	t_2 = Float64(a * Float64(x * Float64(-t)))
	tmp = 0.0
	if (x <= -3.2e-8)
		tmp = t_2;
	elseif (x <= -3e-129)
		tmp = t_1;
	elseif (x <= -3.6e-189)
		tmp = Float64(c * Float64(a * j));
	elseif (x <= -3.5e-252)
		tmp = t_1;
	elseif (x <= 1.5e+33)
		tmp = Float64(a * Float64(c * j));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * (t * b);
	t_2 = a * (x * -t);
	tmp = 0.0;
	if (x <= -3.2e-8)
		tmp = t_2;
	elseif (x <= -3e-129)
		tmp = t_1;
	elseif (x <= -3.6e-189)
		tmp = c * (a * j);
	elseif (x <= -3.5e-252)
		tmp = t_1;
	elseif (x <= 1.5e+33)
		tmp = a * (c * j);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.2e-8], t$95$2, If[LessEqual[x, -3e-129], t$95$1, If[LessEqual[x, -3.6e-189], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.5e-252], t$95$1, If[LessEqual[x, 1.5e+33], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.2000000000000002e-8 or 1.49999999999999992e33 < x

   1. Initial program 72.6%

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

   3. Taylor expanded in a around inf 51.1%

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

      1. +-commutative 51.1%

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

      2. mul-1-neg 51.1%

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

      3. unsub-neg 51.1%

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

      4. *-commutative 51.1%

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

      5. *-commutative 51.1%

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

   5. Simplified 51.1%

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

   6. Taylor expanded in j around 0 45.8%

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

      1. mul-1-neg 45.8%

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

      2. distribute-rgt-neg-in 45.8%

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

   8. Simplified 45.8%

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

   if -3.2000000000000002e-8 < x < -2.9999999999999998e-129 or -3.60000000000000017e-189 < x < -3.49999999999999986e-252

   1. Initial program 73.6%

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

   3. Taylor expanded in c around 0 62.4%

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

      1. mul-1-neg 62.4%

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

      2. *-commutative 62.4%

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

      3. associate-*r* 62.3%

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

      4. *-commutative 62.3%

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

      5. distribute-rgt-neg-out 62.3%

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

      6. *-commutative 62.3%

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

      7. distribute-rgt-neg-in 62.3%

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

   5. Simplified 62.3%

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

   6. Taylor expanded in b around inf 42.0%

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

      1. *-commutative 42.0%

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

      2. associate-*r* 42.1%

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

      3. *-commutative 42.1%

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

   8. Simplified 42.1%

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

   if -2.9999999999999998e-129 < x < -3.60000000000000017e-189

   1. Initial program 78.2%

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

   3. Taylor expanded in c around 0 77.8%

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

   4. Taylor expanded in c around inf 55.6%

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

      1. *-commutative 55.6%

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

   6. Simplified 55.6%

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

   7. Taylor expanded in j around inf 40.9%

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

      1. *-commutative 40.9%

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

   9. Simplified 40.9%

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

   if -3.49999999999999986e-252 < x < 1.49999999999999992e33

   1. Initial program 79.5%

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

   3. Taylor expanded in a around inf 45.3%

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

      1. +-commutative 45.3%

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

      2. mul-1-neg 45.3%

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

      3. unsub-neg 45.3%

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

      4. *-commutative 45.3%

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

      5. *-commutative 45.3%

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

   5. Simplified 45.3%

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

   6. Taylor expanded in j around inf 40.5%

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

      1. *-commutative 40.5%

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

   8. Simplified 40.5%

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

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{-8}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-129}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{-189}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-252}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+33}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 29.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ t_2 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{+78}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{+38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -0.00192:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-188}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+103}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))) (t_2 (* x (* y z))))
   (if (<= z -1.9e+78)
     t_2
     (if (<= z -1.8e+38)
       t_1
       (if (<= z -0.00192)
         t_2
         (if (<= z -6.8e-188)
           (* i (* t b))
           (if (<= z 1.75e+103) t_1 (* z (* x y)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double t_2 = x * (y * z);
	double tmp;
	if (z <= -1.9e+78) {
		tmp = t_2;
	} else if (z <= -1.8e+38) {
		tmp = t_1;
	} else if (z <= -0.00192) {
		tmp = t_2;
	} else if (z <= -6.8e-188) {
		tmp = i * (t * b);
	} else if (z <= 1.75e+103) {
		tmp = t_1;
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (c * j)
    t_2 = x * (y * z)
    if (z <= (-1.9d+78)) then
        tmp = t_2
    else if (z <= (-1.8d+38)) then
        tmp = t_1
    else if (z <= (-0.00192d0)) then
        tmp = t_2
    else if (z <= (-6.8d-188)) then
        tmp = i * (t * b)
    else if (z <= 1.75d+103) then
        tmp = t_1
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double t_2 = x * (y * z);
	double tmp;
	if (z <= -1.9e+78) {
		tmp = t_2;
	} else if (z <= -1.8e+38) {
		tmp = t_1;
	} else if (z <= -0.00192) {
		tmp = t_2;
	} else if (z <= -6.8e-188) {
		tmp = i * (t * b);
	} else if (z <= 1.75e+103) {
		tmp = t_1;
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	t_2 = x * (y * z)
	tmp = 0
	if z <= -1.9e+78:
		tmp = t_2
	elif z <= -1.8e+38:
		tmp = t_1
	elif z <= -0.00192:
		tmp = t_2
	elif z <= -6.8e-188:
		tmp = i * (t * b)
	elif z <= 1.75e+103:
		tmp = t_1
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	t_2 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (z <= -1.9e+78)
		tmp = t_2;
	elseif (z <= -1.8e+38)
		tmp = t_1;
	elseif (z <= -0.00192)
		tmp = t_2;
	elseif (z <= -6.8e-188)
		tmp = Float64(i * Float64(t * b));
	elseif (z <= 1.75e+103)
		tmp = t_1;
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (c * j);
	t_2 = x * (y * z);
	tmp = 0.0;
	if (z <= -1.9e+78)
		tmp = t_2;
	elseif (z <= -1.8e+38)
		tmp = t_1;
	elseif (z <= -0.00192)
		tmp = t_2;
	elseif (z <= -6.8e-188)
		tmp = i * (t * b);
	elseif (z <= 1.75e+103)
		tmp = t_1;
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.9e+78], t$95$2, If[LessEqual[z, -1.8e+38], t$95$1, If[LessEqual[z, -0.00192], t$95$2, If[LessEqual[z, -6.8e-188], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.75e+103], t$95$1, N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.9e78 or -1.79999999999999985e38 < z < -0.00192000000000000005

   1. Initial program 66.7%

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

   3. Taylor expanded in a around 0 65.3%

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

   4. Taylor expanded in x around inf 44.4%

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

   if -1.9e78 < z < -1.79999999999999985e38 or -6.80000000000000055e-188 < z < 1.75e103

   1. Initial program 81.3%

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

   3. Taylor expanded in a around inf 61.2%

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

      1. +-commutative 61.2%

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

      2. mul-1-neg 61.2%

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

      3. unsub-neg 61.2%

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

      4. *-commutative 61.2%

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

      5. *-commutative 61.2%

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

   5. Simplified 61.2%

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

   6. Taylor expanded in j around inf 39.2%

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

      1. *-commutative 39.2%

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

   8. Simplified 39.2%

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

   if -0.00192000000000000005 < z < -6.80000000000000055e-188

   1. Initial program 86.3%

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

   3. Taylor expanded in c around 0 80.9%

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

      1. mul-1-neg 80.9%

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

      2. *-commutative 80.9%

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

      3. associate-*r* 81.1%

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

      4. *-commutative 81.1%

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

      5. distribute-rgt-neg-out 81.1%

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

      6. *-commutative 81.1%

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

      7. distribute-rgt-neg-in 81.1%

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

   5. Simplified 81.1%

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

   6. Taylor expanded in b around inf 31.7%

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

      1. *-commutative 31.7%

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

      2. associate-*r* 34.5%

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

      3. *-commutative 34.5%

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

   8. Simplified 34.5%

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

   if 1.75e103 < z

   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 a around 0 58.0%

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

   4. Taylor expanded in x around inf 46.6%

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

      1. associate-*r* 47.2%

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

      2. *-commutative 47.2%

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

   6. Simplified 47.2%

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

4. Final simplification 41.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+78}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{+38}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq -0.00192:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-188}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+103}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 29.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ t_2 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+77}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{+38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -0.0029:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-186}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+103}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))) (t_2 (* x (* y z))))
   (if (<= z -2.4e+77)
     t_2
     (if (<= z -3.1e+38)
       t_1
       (if (<= z -0.0029)
         t_2
         (if (<= z -1.15e-186) (* i (* t b)) (if (<= z 6.4e+103) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double t_2 = x * (y * z);
	double tmp;
	if (z <= -2.4e+77) {
		tmp = t_2;
	} else if (z <= -3.1e+38) {
		tmp = t_1;
	} else if (z <= -0.0029) {
		tmp = t_2;
	} else if (z <= -1.15e-186) {
		tmp = i * (t * b);
	} else if (z <= 6.4e+103) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (c * j)
    t_2 = x * (y * z)
    if (z <= (-2.4d+77)) then
        tmp = t_2
    else if (z <= (-3.1d+38)) then
        tmp = t_1
    else if (z <= (-0.0029d0)) then
        tmp = t_2
    else if (z <= (-1.15d-186)) then
        tmp = i * (t * b)
    else if (z <= 6.4d+103) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double t_2 = x * (y * z);
	double tmp;
	if (z <= -2.4e+77) {
		tmp = t_2;
	} else if (z <= -3.1e+38) {
		tmp = t_1;
	} else if (z <= -0.0029) {
		tmp = t_2;
	} else if (z <= -1.15e-186) {
		tmp = i * (t * b);
	} else if (z <= 6.4e+103) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	t_2 = x * (y * z)
	tmp = 0
	if z <= -2.4e+77:
		tmp = t_2
	elif z <= -3.1e+38:
		tmp = t_1
	elif z <= -0.0029:
		tmp = t_2
	elif z <= -1.15e-186:
		tmp = i * (t * b)
	elif z <= 6.4e+103:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	t_2 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (z <= -2.4e+77)
		tmp = t_2;
	elseif (z <= -3.1e+38)
		tmp = t_1;
	elseif (z <= -0.0029)
		tmp = t_2;
	elseif (z <= -1.15e-186)
		tmp = Float64(i * Float64(t * b));
	elseif (z <= 6.4e+103)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (c * j);
	t_2 = x * (y * z);
	tmp = 0.0;
	if (z <= -2.4e+77)
		tmp = t_2;
	elseif (z <= -3.1e+38)
		tmp = t_1;
	elseif (z <= -0.0029)
		tmp = t_2;
	elseif (z <= -1.15e-186)
		tmp = i * (t * b);
	elseif (z <= 6.4e+103)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.4e+77], t$95$2, If[LessEqual[z, -3.1e+38], t$95$1, If[LessEqual[z, -0.0029], t$95$2, If[LessEqual[z, -1.15e-186], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.4e+103], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.3999999999999999e77 or -3.10000000000000018e38 < z < -0.0029 or 6.39999999999999985e103 < z

   1. Initial program 65.9%

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

   3. Taylor expanded in a around 0 62.5%

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

   4. Taylor expanded in x around inf 45.3%

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

   if -2.3999999999999999e77 < z < -3.10000000000000018e38 or -1.15e-186 < z < 6.39999999999999985e103

   1. Initial program 81.3%

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

   3. Taylor expanded in a around inf 61.2%

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

      1. +-commutative 61.2%

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

      2. mul-1-neg 61.2%

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

      3. unsub-neg 61.2%

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

      4. *-commutative 61.2%

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

      5. *-commutative 61.2%

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

   5. Simplified 61.2%

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

   6. Taylor expanded in j around inf 39.2%

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

      1. *-commutative 39.2%

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

   8. Simplified 39.2%

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

   if -0.0029 < z < -1.15e-186

   1. Initial program 86.3%

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

   3. Taylor expanded in c around 0 80.9%

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

      1. mul-1-neg 80.9%

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

      2. *-commutative 80.9%

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

      3. associate-*r* 81.1%

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

      4. *-commutative 81.1%

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

      5. distribute-rgt-neg-out 81.1%

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

      6. *-commutative 81.1%

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

      7. distribute-rgt-neg-in 81.1%

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

   5. Simplified 81.1%

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

   6. Taylor expanded in b around inf 31.7%

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

      1. *-commutative 31.7%

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

      2. associate-*r* 34.5%

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

      3. *-commutative 34.5%

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

   8. Simplified 34.5%

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

4. Final simplification 41.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+77}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{+38}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq -0.0029:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-186}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+103}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 50.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.6 \cdot 10^{+42} \lor \neg \left(b \leq -1.05 \cdot 10^{-31}\right) \land \left(b \leq -9.5 \cdot 10^{-60} \lor \neg \left(b \leq 1.26 \cdot 10^{+182}\right)\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -5.6e+42)
         (and (not (<= b -1.05e-31))
              (or (<= b -9.5e-60) (not (<= b 1.26e+182)))))
   (* b (- (* t i) (* z c)))
   (* a (- (* c j) (* x t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -5.6e+42) || (!(b <= -1.05e-31) && ((b <= -9.5e-60) || !(b <= 1.26e+182)))) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-5.6d+42)) .or. (.not. (b <= (-1.05d-31))) .and. (b <= (-9.5d-60)) .or. (.not. (b <= 1.26d+182))) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = a * ((c * j) - (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -5.6e+42) || (!(b <= -1.05e-31) && ((b <= -9.5e-60) || !(b <= 1.26e+182)))) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -5.6e+42) or (not (b <= -1.05e-31) and ((b <= -9.5e-60) or not (b <= 1.26e+182))):
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = a * ((c * j) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -5.6e+42) || (!(b <= -1.05e-31) && ((b <= -9.5e-60) || !(b <= 1.26e+182))))
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -5.6e+42) || (~((b <= -1.05e-31)) && ((b <= -9.5e-60) || ~((b <= 1.26e+182)))))
		tmp = b * ((t * i) - (z * c));
	else
		tmp = a * ((c * j) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -5.6e+42], And[N[Not[LessEqual[b, -1.05e-31]], $MachinePrecision], Or[LessEqual[b, -9.5e-60], N[Not[LessEqual[b, 1.26e+182]], $MachinePrecision]]]], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.5999999999999999e42 or -1.04999999999999996e-31 < b < -9.49999999999999958e-60 or 1.2600000000000001e182 < b

   1. Initial program 73.4%

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

   3. Taylor expanded in b around inf 76.0%

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

      1. *-commutative 76.0%

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

      2. *-commutative 76.0%

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

   5. Simplified 76.0%

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

   if -5.5999999999999999e42 < b < -1.04999999999999996e-31 or -9.49999999999999958e-60 < b < 1.2600000000000001e182

   1. Initial program 76.7%

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

   3. Taylor expanded in a around inf 54.6%

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

      1. +-commutative 54.6%

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

      2. mul-1-neg 54.6%

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

      3. unsub-neg 54.6%

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

      4. *-commutative 54.6%

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

      5. *-commutative 54.6%

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

   5. Simplified 54.6%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.6 \cdot 10^{+42} \lor \neg \left(b \leq -1.05 \cdot 10^{-31}\right) \land \left(b \leq -9.5 \cdot 10^{-60} \lor \neg \left(b \leq 1.26 \cdot 10^{+182}\right)\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 50.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -2.85 \cdot 10^{+43}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -150:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{-152}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq 1.26 \cdot 10^{+182}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))) (t_2 (* b (- (* t i) (* z c)))))
   (if (<= b -2.85e+43)
     t_2
     (if (<= b -150.0)
       t_1
       (if (<= b -3.5e-152)
         (* i (- (* t b) (* y j)))
         (if (<= b 1.26e+182) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -2.85e+43) {
		tmp = t_2;
	} else if (b <= -150.0) {
		tmp = t_1;
	} else if (b <= -3.5e-152) {
		tmp = i * ((t * b) - (y * j));
	} else if (b <= 1.26e+182) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    t_2 = b * ((t * i) - (z * c))
    if (b <= (-2.85d+43)) then
        tmp = t_2
    else if (b <= (-150.0d0)) then
        tmp = t_1
    else if (b <= (-3.5d-152)) then
        tmp = i * ((t * b) - (y * j))
    else if (b <= 1.26d+182) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -2.85e+43) {
		tmp = t_2;
	} else if (b <= -150.0) {
		tmp = t_1;
	} else if (b <= -3.5e-152) {
		tmp = i * ((t * b) - (y * j));
	} else if (b <= 1.26e+182) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -2.85e+43:
		tmp = t_2
	elif b <= -150.0:
		tmp = t_1
	elif b <= -3.5e-152:
		tmp = i * ((t * b) - (y * j))
	elif b <= 1.26e+182:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -2.85e+43)
		tmp = t_2;
	elseif (b <= -150.0)
		tmp = t_1;
	elseif (b <= -3.5e-152)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (b <= 1.26e+182)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	t_2 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -2.85e+43)
		tmp = t_2;
	elseif (b <= -150.0)
		tmp = t_1;
	elseif (b <= -3.5e-152)
		tmp = i * ((t * b) - (y * j));
	elseif (b <= 1.26e+182)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.85e+43], t$95$2, If[LessEqual[b, -150.0], t$95$1, If[LessEqual[b, -3.5e-152], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.26e+182], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.8499999999999999e43 or 1.2600000000000001e182 < b

   1. Initial program 72.5%

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

   3. Taylor expanded in b around inf 76.8%

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

      1. *-commutative 76.8%

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

      2. *-commutative 76.8%

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

   5. Simplified 76.8%

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

   if -2.8499999999999999e43 < b < -150 or -3.5000000000000001e-152 < b < 1.2600000000000001e182

   1. Initial program 76.7%

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

   3. Taylor expanded in a around inf 56.3%

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

      1. +-commutative 56.3%

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

      2. mul-1-neg 56.3%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 56.3%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 56.3%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

      5. *-commutative 56.3%

         \[\leadsto a \cdot \left(j \cdot c - \color{blue}{x \cdot t}\right) \]

   5. Simplified 56.3%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - x \cdot t\right)} \]

   if -150 < b < -3.5000000000000001e-152

   1. Initial program 77.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 54.9%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 54.9%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

      2. *-commutative 54.9%

         \[\leadsto i \cdot \left(-1 \cdot \left(\color{blue}{y \cdot j} - b \cdot t\right)\right) \]

      3. *-commutative 54.9%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j - \color{blue}{t \cdot b}\right)\right) \]

   5. Simplified 54.9%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j - t \cdot b\right)\right)} \]

   6. Taylor expanded in y around 0 55.0%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + b \cdot \left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. +-commutative 55.0%

         \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right) + -1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]

      2. neg-mul-1 55.0%

         \[\leadsto b \cdot \left(i \cdot t\right) + \color{blue}{\left(-i \cdot \left(j \cdot y\right)\right)} \]

      3. unsub-neg 55.0%

         \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right) - i \cdot \left(j \cdot y\right)} \]

      4. associate-*r* 44.1%

         \[\leadsto b \cdot \left(i \cdot t\right) - \color{blue}{\left(i \cdot j\right) \cdot y} \]

   8. Simplified 44.1%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right) - \left(i \cdot j\right) \cdot y} \]

   9. Taylor expanded in i around 0 54.9%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot t - j \cdot y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.85 \cdot 10^{+43}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -150:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{-152}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq 1.26 \cdot 10^{+182}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 27.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -3.4 \cdot 10^{-109} \lor \neg \left(j \leq 3 \cdot 10^{-116} \lor \neg \left(j \leq 1.85 \cdot 10^{+43}\right) \land j \leq 4 \cdot 10^{+166}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -3.4e-109)
         (not (or (<= j 3e-116) (and (not (<= j 1.85e+43)) (<= j 4e+166)))))
   (* a (* c j))
   (* b (* 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 ((j <= -3.4e-109) || !((j <= 3e-116) || (!(j <= 1.85e+43) && (j <= 4e+166)))) {
		tmp = a * (c * j);
	} else {
		tmp = b * (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 ((j <= (-3.4d-109)) .or. (.not. (j <= 3d-116) .or. (.not. (j <= 1.85d+43)) .and. (j <= 4d+166))) then
        tmp = a * (c * j)
    else
        tmp = b * (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 ((j <= -3.4e-109) || !((j <= 3e-116) || (!(j <= 1.85e+43) && (j <= 4e+166)))) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -3.4e-109) or not ((j <= 3e-116) or (not (j <= 1.85e+43) and (j <= 4e+166))):
		tmp = a * (c * j)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -3.4e-109) || !((j <= 3e-116) || (!(j <= 1.85e+43) && (j <= 4e+166))))
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(b * 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 ((j <= -3.4e-109) || ~(((j <= 3e-116) || (~((j <= 1.85e+43)) && (j <= 4e+166)))))
		tmp = a * (c * j);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -3.4e-109], N[Not[Or[LessEqual[j, 3e-116], And[N[Not[LessEqual[j, 1.85e+43]], $MachinePrecision], LessEqual[j, 4e+166]]]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -3.40000000000000012e-109 or 3.00000000000000026e-116 < j < 1.85e43 or 3.99999999999999976e166 < j

   1. Initial program 75.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 55.4%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 55.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 55.4%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 55.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 55.4%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

      5. *-commutative 55.4%

         \[\leadsto a \cdot \left(j \cdot c - \color{blue}{x \cdot t}\right) \]

   5. Simplified 55.4%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - x \cdot t\right)} \]

   6. Taylor expanded in j around inf 39.1%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   7. Step-by-step derivation

      1. *-commutative 39.1%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   8. Simplified 39.1%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c\right)} \]

   if -3.40000000000000012e-109 < j < 3.00000000000000026e-116 or 1.85e43 < j < 3.99999999999999976e166

   1. Initial program 75.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 40.5%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 40.5%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

      2. *-commutative 40.5%

         \[\leadsto i \cdot \left(-1 \cdot \left(\color{blue}{y \cdot j} - b \cdot t\right)\right) \]

      3. *-commutative 40.5%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j - \color{blue}{t \cdot b}\right)\right) \]

   5. Simplified 40.5%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j - t \cdot b\right)\right)} \]

   6. Taylor expanded in y around 0 34.0%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 36.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.4 \cdot 10^{-109} \lor \neg \left(j \leq 3 \cdot 10^{-116} \lor \neg \left(j \leq 1.85 \cdot 10^{+43}\right) \land j \leq 4 \cdot 10^{+166}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 28.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;j \leq -1.45 \cdot 10^{+36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 3 \cdot 10^{-116}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;j \leq 2.4 \cdot 10^{+44}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;j \leq 4 \cdot 10^{+165}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))))
   (if (<= j -1.45e+36)
     t_1
     (if (<= j 3e-116)
       (* i (* t b))
       (if (<= j 2.4e+44)
         (* c (* a j))
         (if (<= j 4e+165) (* 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 = a * (c * j);
	double tmp;
	if (j <= -1.45e+36) {
		tmp = t_1;
	} else if (j <= 3e-116) {
		tmp = i * (t * b);
	} else if (j <= 2.4e+44) {
		tmp = c * (a * j);
	} else if (j <= 4e+165) {
		tmp = 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 = a * (c * j)
    if (j <= (-1.45d+36)) then
        tmp = t_1
    else if (j <= 3d-116) then
        tmp = i * (t * b)
    else if (j <= 2.4d+44) then
        tmp = c * (a * j)
    else if (j <= 4d+165) then
        tmp = 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 = a * (c * j);
	double tmp;
	if (j <= -1.45e+36) {
		tmp = t_1;
	} else if (j <= 3e-116) {
		tmp = i * (t * b);
	} else if (j <= 2.4e+44) {
		tmp = c * (a * j);
	} else if (j <= 4e+165) {
		tmp = b * (t * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	tmp = 0
	if j <= -1.45e+36:
		tmp = t_1
	elif j <= 3e-116:
		tmp = i * (t * b)
	elif j <= 2.4e+44:
		tmp = c * (a * j)
	elif j <= 4e+165:
		tmp = b * (t * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	tmp = 0.0
	if (j <= -1.45e+36)
		tmp = t_1;
	elseif (j <= 3e-116)
		tmp = Float64(i * Float64(t * b));
	elseif (j <= 2.4e+44)
		tmp = Float64(c * Float64(a * j));
	elseif (j <= 4e+165)
		tmp = 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 = a * (c * j);
	tmp = 0.0;
	if (j <= -1.45e+36)
		tmp = t_1;
	elseif (j <= 3e-116)
		tmp = i * (t * b);
	elseif (j <= 2.4e+44)
		tmp = c * (a * j);
	elseif (j <= 4e+165)
		tmp = 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[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.45e+36], t$95$1, If[LessEqual[j, 3e-116], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.4e+44], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4e+165], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.45e36 or 3.9999999999999996e165 < j

   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 a around inf 57.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 57.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 57.0%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 57.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 57.0%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

      5. *-commutative 57.0%

         \[\leadsto a \cdot \left(j \cdot c - \color{blue}{x \cdot t}\right) \]

   5. Simplified 57.0%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - x \cdot t\right)} \]

   6. Taylor expanded in j around inf 45.8%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   7. Step-by-step derivation

      1. *-commutative 45.8%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   8. Simplified 45.8%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c\right)} \]

   if -1.45e36 < j < 3.00000000000000026e-116

   1. Initial program 77.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0 64.5%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{-1 \cdot \left(b \cdot \left(i \cdot t\right)\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. mul-1-neg 64.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(-b \cdot \left(i \cdot t\right)\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 64.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\color{blue}{\left(i \cdot t\right) \cdot b}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. associate-*r* 64.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\color{blue}{i \cdot \left(t \cdot b\right)}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 64.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(-i \cdot \color{blue}{\left(b \cdot t\right)}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      5. distribute-rgt-neg-out 64.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{i \cdot \left(-b \cdot t\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      6. *-commutative 64.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(-\color{blue}{t \cdot b}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      7. distribute-rgt-neg-in 64.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \color{blue}{\left(t \cdot \left(-b\right)\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Simplified 64.7%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{i \cdot \left(t \cdot \left(-b\right)\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   6. Taylor expanded in b around inf 27.8%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 27.8%

         \[\leadsto \color{blue}{\left(i \cdot t\right) \cdot b} \]

      2. associate-*r* 28.7%

         \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]

      3. *-commutative 28.7%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t\right)} \]

   8. Simplified 28.7%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot t\right)} \]

   if 3.00000000000000026e-116 < j < 2.40000000000000013e44

   1. Initial program 70.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0 79.2%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + a \cdot \left(c \cdot j\right)\right)} \]

   4. Taylor expanded in c around inf 47.7%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]
   5. Step-by-step derivation

      1. *-commutative 47.7%

         \[\leadsto c \cdot \left(\color{blue}{j \cdot a} - b \cdot z\right) \]

   6. Simplified 47.7%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a - b \cdot z\right)} \]

   7. Taylor expanded in j around inf 36.3%

      \[\leadsto c \cdot \color{blue}{\left(a \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 36.3%

         \[\leadsto c \cdot \color{blue}{\left(j \cdot a\right)} \]

   9. Simplified 36.3%

      \[\leadsto c \cdot \color{blue}{\left(j \cdot a\right)} \]

   if 2.40000000000000013e44 < j < 3.9999999999999996e165

   1. Initial program 78.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 65.8%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 65.8%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

      2. *-commutative 65.8%

         \[\leadsto i \cdot \left(-1 \cdot \left(\color{blue}{y \cdot j} - b \cdot t\right)\right) \]

      3. *-commutative 65.8%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j - \color{blue}{t \cdot b}\right)\right) \]

   5. Simplified 65.8%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j - t \cdot b\right)\right)} \]

   6. Taylor expanded in y around 0 44.1%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 36.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.45 \cdot 10^{+36}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq 3 \cdot 10^{-116}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;j \leq 2.4 \cdot 10^{+44}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;j \leq 4 \cdot 10^{+165}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 27.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i\right)\\ t_2 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;j \leq -6 \cdot 10^{-110}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 2.8 \cdot 10^{-116}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 7.2 \cdot 10^{+44}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;j \leq 4.4 \cdot 10^{+165}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* t i))) (t_2 (* a (* c j))))
   (if (<= j -6e-110)
     t_2
     (if (<= j 2.8e-116)
       t_1
       (if (<= j 7.2e+44) (* c (* a j)) (if (<= j 4.4e+165) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (t * i);
	double t_2 = a * (c * j);
	double tmp;
	if (j <= -6e-110) {
		tmp = t_2;
	} else if (j <= 2.8e-116) {
		tmp = t_1;
	} else if (j <= 7.2e+44) {
		tmp = c * (a * j);
	} else if (j <= 4.4e+165) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (t * i)
    t_2 = a * (c * j)
    if (j <= (-6d-110)) then
        tmp = t_2
    else if (j <= 2.8d-116) then
        tmp = t_1
    else if (j <= 7.2d+44) then
        tmp = c * (a * j)
    else if (j <= 4.4d+165) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (t * i);
	double t_2 = a * (c * j);
	double tmp;
	if (j <= -6e-110) {
		tmp = t_2;
	} else if (j <= 2.8e-116) {
		tmp = t_1;
	} else if (j <= 7.2e+44) {
		tmp = c * (a * j);
	} else if (j <= 4.4e+165) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (t * i)
	t_2 = a * (c * j)
	tmp = 0
	if j <= -6e-110:
		tmp = t_2
	elif j <= 2.8e-116:
		tmp = t_1
	elif j <= 7.2e+44:
		tmp = c * (a * j)
	elif j <= 4.4e+165:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(t * i))
	t_2 = Float64(a * Float64(c * j))
	tmp = 0.0
	if (j <= -6e-110)
		tmp = t_2;
	elseif (j <= 2.8e-116)
		tmp = t_1;
	elseif (j <= 7.2e+44)
		tmp = Float64(c * Float64(a * j));
	elseif (j <= 4.4e+165)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (t * i);
	t_2 = a * (c * j);
	tmp = 0.0;
	if (j <= -6e-110)
		tmp = t_2;
	elseif (j <= 2.8e-116)
		tmp = t_1;
	elseif (j <= 7.2e+44)
		tmp = c * (a * j);
	elseif (j <= 4.4e+165)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -6e-110], t$95$2, If[LessEqual[j, 2.8e-116], t$95$1, If[LessEqual[j, 7.2e+44], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.4e+165], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -5.99999999999999972e-110 or 4.3999999999999998e165 < j

   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 a around inf 54.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 54.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 54.0%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 54.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 54.0%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

      5. *-commutative 54.0%

         \[\leadsto a \cdot \left(j \cdot c - \color{blue}{x \cdot t}\right) \]

   5. Simplified 54.0%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - x \cdot t\right)} \]

   6. Taylor expanded in j around inf 39.9%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   7. Step-by-step derivation

      1. *-commutative 39.9%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   8. Simplified 39.9%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c\right)} \]

   if -5.99999999999999972e-110 < j < 2.7999999999999999e-116 or 7.2e44 < j < 4.3999999999999998e165

   1. Initial program 75.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 40.5%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 40.5%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

      2. *-commutative 40.5%

         \[\leadsto i \cdot \left(-1 \cdot \left(\color{blue}{y \cdot j} - b \cdot t\right)\right) \]

      3. *-commutative 40.5%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j - \color{blue}{t \cdot b}\right)\right) \]

   5. Simplified 40.5%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j - t \cdot b\right)\right)} \]

   6. Taylor expanded in y around 0 34.0%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]

   if 2.7999999999999999e-116 < j < 7.2e44

   1. Initial program 70.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0 79.2%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + a \cdot \left(c \cdot j\right)\right)} \]

   4. Taylor expanded in c around inf 47.7%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]
   5. Step-by-step derivation

      1. *-commutative 47.7%

         \[\leadsto c \cdot \left(\color{blue}{j \cdot a} - b \cdot z\right) \]

   6. Simplified 47.7%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a - b \cdot z\right)} \]

   7. Taylor expanded in j around inf 36.3%

      \[\leadsto c \cdot \color{blue}{\left(a \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 36.3%

         \[\leadsto c \cdot \color{blue}{\left(j \cdot a\right)} \]

   9. Simplified 36.3%

      \[\leadsto c \cdot \color{blue}{\left(j \cdot a\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 36.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -6 \cdot 10^{-110}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq 2.8 \cdot 10^{-116}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;j \leq 7.2 \cdot 10^{+44}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;j \leq 4.4 \cdot 10^{+165}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 58.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.12 \cdot 10^{-42} \lor \neg \left(x \leq 250000\right):\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= x -1.12e-42) (not (<= x 250000.0)))
   (* x (- (* y z) (* t a)))
   (+ (* a (* c j)) (* b (- (* t i) (* z c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((x <= -1.12e-42) || !(x <= 250000.0)) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = (a * (c * j)) + (b * ((t * i) - (z * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((x <= (-1.12d-42)) .or. (.not. (x <= 250000.0d0))) then
        tmp = x * ((y * z) - (t * a))
    else
        tmp = (a * (c * j)) + (b * ((t * i) - (z * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((x <= -1.12e-42) || !(x <= 250000.0)) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = (a * (c * j)) + (b * ((t * i) - (z * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (x <= -1.12e-42) or not (x <= 250000.0):
		tmp = x * ((y * z) - (t * a))
	else:
		tmp = (a * (c * j)) + (b * ((t * i) - (z * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((x <= -1.12e-42) || !(x <= 250000.0))
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	else
		tmp = Float64(Float64(a * Float64(c * j)) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((x <= -1.12e-42) || ~((x <= 250000.0)))
		tmp = x * ((y * z) - (t * a));
	else
		tmp = (a * (c * j)) + (b * ((t * i) - (z * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[x, -1.12e-42], N[Not[LessEqual[x, 250000.0]], $MachinePrecision]], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.1199999999999999e-42 or 2.5e5 < x

   1. Initial program 74.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0 70.0%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + a \cdot \left(c \cdot j\right)\right)} \]

   4. Taylor expanded in x around inf 65.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]

   if -1.1199999999999999e-42 < x < 2.5e5

   1. Initial program 76.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0 76.7%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + a \cdot \left(c \cdot j\right)\right)} \]

   4. Taylor expanded in x around 0 73.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + a \cdot \left(c \cdot j\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   5. Step-by-step derivation

      1. +-commutative 73.8%

         \[\leadsto \color{blue}{\left(a \cdot \left(c \cdot j\right) + -1 \cdot \left(i \cdot \left(j \cdot y\right)\right)\right)} - b \cdot \left(c \cdot z - i \cdot t\right) \]

      2. neg-mul-1 73.8%

         \[\leadsto \left(a \cdot \left(c \cdot j\right) + \color{blue}{\left(-i \cdot \left(j \cdot y\right)\right)}\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      3. unsub-neg 73.8%

         \[\leadsto \color{blue}{\left(a \cdot \left(c \cdot j\right) - i \cdot \left(j \cdot y\right)\right)} - b \cdot \left(c \cdot z - i \cdot t\right) \]

      4. *-commutative 73.8%

         \[\leadsto \left(a \cdot \color{blue}{\left(j \cdot c\right)} - i \cdot \left(j \cdot y\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      5. associate-*r* 74.2%

         \[\leadsto \left(a \cdot \left(j \cdot c\right) - \color{blue}{\left(i \cdot j\right) \cdot y}\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

   6. Simplified 74.2%

      \[\leadsto \color{blue}{\left(a \cdot \left(j \cdot c\right) - \left(i \cdot j\right) \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   7. Taylor expanded in y around 0 65.4%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   8. Step-by-step derivation

      1. *-commutative 65.4%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} - b \cdot \left(c \cdot z - i \cdot t\right) \]

   9. Simplified 65.4%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.12 \cdot 10^{-42} \lor \neg \left(x \leq 250000\right):\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 42.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.65 \cdot 10^{+54}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;b \leq 1.68 \cdot 10^{+137}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -2.65e+54)
   (* z (* b (- c)))
   (if (<= b 1.68e+137) (* a (- (* c j) (* x t))) (* (* z b) (- c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -2.65e+54) {
		tmp = z * (b * -c);
	} else if (b <= 1.68e+137) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = (z * b) * -c;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-2.65d+54)) then
        tmp = z * (b * -c)
    else if (b <= 1.68d+137) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = (z * b) * -c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -2.65e+54) {
		tmp = z * (b * -c);
	} else if (b <= 1.68e+137) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = (z * b) * -c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -2.65e+54:
		tmp = z * (b * -c)
	elif b <= 1.68e+137:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = (z * b) * -c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -2.65e+54)
		tmp = Float64(z * Float64(b * Float64(-c)));
	elseif (b <= 1.68e+137)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = Float64(Float64(z * b) * Float64(-c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -2.65e+54)
		tmp = z * (b * -c);
	elseif (b <= 1.68e+137)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = (z * b) * -c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -2.65e+54], N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.68e+137], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * b), $MachinePrecision] * (-c)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.65000000000000009e54

   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 c around 0 66.5%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + a \cdot \left(c \cdot j\right)\right)} \]

   4. Taylor expanded in c around inf 54.7%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]
   5. Step-by-step derivation

      1. *-commutative 54.7%

         \[\leadsto c \cdot \left(\color{blue}{j \cdot a} - b \cdot z\right) \]

   6. Simplified 54.7%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a - b \cdot z\right)} \]

   7. Taylor expanded in j around 0 43.7%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 43.7%

         \[\leadsto \color{blue}{-b \cdot \left(c \cdot z\right)} \]

      2. associate-*r* 49.8%

         \[\leadsto -\color{blue}{\left(b \cdot c\right) \cdot z} \]

      3. distribute-rgt-neg-in 49.8%

         \[\leadsto \color{blue}{\left(b \cdot c\right) \cdot \left(-z\right)} \]

   9. Simplified 49.8%

      \[\leadsto \color{blue}{\left(b \cdot c\right) \cdot \left(-z\right)} \]

   if -2.65000000000000009e54 < b < 1.6799999999999999e137

   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 a around inf 52.3%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 52.3%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 52.3%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 52.3%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 52.3%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

      5. *-commutative 52.3%

         \[\leadsto a \cdot \left(j \cdot c - \color{blue}{x \cdot t}\right) \]

   5. Simplified 52.3%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - x \cdot t\right)} \]

   if 1.6799999999999999e137 < b

   1. Initial program 73.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0 67.8%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + a \cdot \left(c \cdot j\right)\right)} \]

   4. Taylor expanded in c around inf 69.2%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]
   5. Step-by-step derivation

      1. *-commutative 69.2%

         \[\leadsto c \cdot \left(\color{blue}{j \cdot a} - b \cdot z\right) \]

   6. Simplified 69.2%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a - b \cdot z\right)} \]

   7. Taylor expanded in j around 0 59.0%

      \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(b \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. neg-mul-1 59.0%

         \[\leadsto c \cdot \color{blue}{\left(-b \cdot z\right)} \]

      2. distribute-rgt-neg-in 59.0%

         \[\leadsto c \cdot \color{blue}{\left(b \cdot \left(-z\right)\right)} \]

   9. Simplified 59.0%

      \[\leadsto c \cdot \color{blue}{\left(b \cdot \left(-z\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.65 \cdot 10^{+54}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;b \leq 1.68 \cdot 10^{+137}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 31: 22.5% 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 75.6%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
2. Add Preprocessing

3. Taylor expanded in a around inf 45.0%

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
4. Step-by-step derivation

   1. +-commutative 45.0%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

   2. mul-1-neg 45.0%

      \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

   3. unsub-neg 45.0%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. *-commutative 45.0%

      \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. *-commutative 45.0%

      \[\leadsto a \cdot \left(j \cdot c - \color{blue}{x \cdot t}\right) \]

5. Simplified 45.0%

   \[\leadsto \color{blue}{a \cdot \left(j \cdot c - x \cdot t\right)} \]

6. Taylor expanded in j around inf 24.9%

   \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
7. Step-by-step derivation

   1. *-commutative 24.9%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

8. Simplified 24.9%

   \[\leadsto \color{blue}{a \cdot \left(j \cdot c\right)} \]

9. Final simplification 24.9%

   \[\leadsto a \cdot \left(c \cdot j\right) \]
10. Add Preprocessing

Developer target: 58.8% 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 2024084 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :alt
  (if (< x -1.469694296777705e-64) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 3.2113527362226803e-147) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i)))))