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

Percentage Accurate: 73.2% → 82.2%

Time: 19.3s

Alternatives: 21

Speedup: 0.5×

• 58.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 82.2% accurate, 0.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $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[(N[(a * c), $MachinePrecision] * N[(j - N[(b * N[(z / a), $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 91.6%

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

      1. +-commutative 91.6%

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

      2. fma-define 91.6%

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

      3. *-commutative 91.6%

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

      4. sub-neg 91.6%

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

      5. *-commutative 91.6%

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

      6. sub-neg 91.6%

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

      7. *-commutative 91.6%

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

      8. *-commutative 91.6%

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

   3. Simplified 91.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   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 -inf 22.9%

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

   5. Simplified 29.2%

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

   6. Taylor expanded in c around inf 52.6%

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

      1. associate-*r* 52.6%

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

      2. mul-1-neg 52.6%

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

      3. unsub-neg 52.6%

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

      4. associate-/l* 52.7%

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

   8. Simplified 52.7%

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

4. Final simplification 84.3%

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

Alternative 2: 82.2% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(a * c), $MachinePrecision] * N[(j - N[(b * N[(z / a), $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 91.6%

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

   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 -inf 22.9%

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

   5. Simplified 29.2%

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

   6. Taylor expanded in c around inf 52.6%

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

      1. associate-*r* 52.6%

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

      2. mul-1-neg 52.6%

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

      3. unsub-neg 52.6%

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

      4. associate-/l* 52.7%

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

   8. Simplified 52.7%

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

4. Final simplification 84.3%

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

Alternative 3: 58.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;t \leq -1.35 \cdot 10^{+53}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(b \cdot \frac{i}{a} - x\right)\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{-200}:\\ \;\;\;\;t\_1 - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{elif}\;t \leq 6.1 \cdot 10^{-96}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+142}:\\ \;\;\;\;a \cdot \left(c \cdot j + \left(\frac{t\_1}{a} - x \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))))
   (if (<= t -1.35e+53)
     (* (* t a) (- (* b (/ i a)) x))
     (if (<= t 5.3e-200)
       (- t_1 (* j (- (* y i) (* a c))))
       (if (<= t 6.1e-96)
         (* z (- (* x y) (* b c)))
         (if (<= t 1.6e+142)
           (* a (+ (* c j) (- (/ t_1 a) (* x t))))
           (* t (- (* b i) (* x a)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double tmp;
	if (t <= -1.35e+53) {
		tmp = (t * a) * ((b * (i / a)) - x);
	} else if (t <= 5.3e-200) {
		tmp = t_1 - (j * ((y * i) - (a * c)));
	} else if (t <= 6.1e-96) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 1.6e+142) {
		tmp = a * ((c * j) + ((t_1 / a) - (x * t)));
	} else {
		tmp = t * ((b * i) - (x * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y * z)
    if (t <= (-1.35d+53)) then
        tmp = (t * a) * ((b * (i / a)) - x)
    else if (t <= 5.3d-200) then
        tmp = t_1 - (j * ((y * i) - (a * c)))
    else if (t <= 6.1d-96) then
        tmp = z * ((x * y) - (b * c))
    else if (t <= 1.6d+142) then
        tmp = a * ((c * j) + ((t_1 / a) - (x * t)))
    else
        tmp = t * ((b * i) - (x * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double tmp;
	if (t <= -1.35e+53) {
		tmp = (t * a) * ((b * (i / a)) - x);
	} else if (t <= 5.3e-200) {
		tmp = t_1 - (j * ((y * i) - (a * c)));
	} else if (t <= 6.1e-96) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 1.6e+142) {
		tmp = a * ((c * j) + ((t_1 / a) - (x * t)));
	} else {
		tmp = t * ((b * i) - (x * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	tmp = 0
	if t <= -1.35e+53:
		tmp = (t * a) * ((b * (i / a)) - x)
	elif t <= 5.3e-200:
		tmp = t_1 - (j * ((y * i) - (a * c)))
	elif t <= 6.1e-96:
		tmp = z * ((x * y) - (b * c))
	elif t <= 1.6e+142:
		tmp = a * ((c * j) + ((t_1 / a) - (x * t)))
	else:
		tmp = t * ((b * i) - (x * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (t <= -1.35e+53)
		tmp = Float64(Float64(t * a) * Float64(Float64(b * Float64(i / a)) - x));
	elseif (t <= 5.3e-200)
		tmp = Float64(t_1 - Float64(j * Float64(Float64(y * i) - Float64(a * c))));
	elseif (t <= 6.1e-96)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (t <= 1.6e+142)
		tmp = Float64(a * Float64(Float64(c * j) + Float64(Float64(t_1 / a) - Float64(x * t))));
	else
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (y * z);
	tmp = 0.0;
	if (t <= -1.35e+53)
		tmp = (t * a) * ((b * (i / a)) - x);
	elseif (t <= 5.3e-200)
		tmp = t_1 - (j * ((y * i) - (a * c)));
	elseif (t <= 6.1e-96)
		tmp = z * ((x * y) - (b * c));
	elseif (t <= 1.6e+142)
		tmp = a * ((c * j) + ((t_1 / a) - (x * t)));
	else
		tmp = t * ((b * i) - (x * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.35e+53], N[(N[(t * a), $MachinePrecision] * N[(N[(b * N[(i / a), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.3e-200], N[(t$95$1 - N[(j * N[(N[(y * i), $MachinePrecision] - N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.1e-96], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.6e+142], N[(a * N[(N[(c * j), $MachinePrecision] + N[(N[(t$95$1 / a), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.3500000000000001e53

   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 a around -inf 59.9%

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

   5. Simplified 63.7%

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

   6. Taylor expanded in t around inf 60.1%

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

      1. associate-*r* 69.4%

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

      2. associate-/l* 71.3%

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

   8. Simplified 71.3%

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

   if -1.3500000000000001e53 < t < 5.29999999999999973e-200

   1. Initial program 81.7%

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

   3. Taylor expanded in b around 0 70.9%

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

   4. Taylor expanded in t around 0 63.3%

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

   if 5.29999999999999973e-200 < t < 6.1000000000000001e-96

   1. Initial program 76.9%

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

   3. Taylor expanded in z around inf 72.7%

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

      1. *-commutative 72.7%

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

   5. Simplified 72.7%

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

   if 6.1000000000000001e-96 < t < 1.60000000000000003e142

   1. Initial program 73.6%

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

   3. Taylor expanded in a around -inf 68.3%

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

   5. Simplified 72.1%

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

   6. Taylor expanded in x around inf 70.9%

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

   if 1.60000000000000003e142 < t

   1. Initial program 59.4%

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

   3. Taylor expanded in t around inf 83.0%

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

      1. distribute-lft-out-- 83.0%

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

   5. Simplified 83.0%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x - b \cdot i\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+53}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(b \cdot \frac{i}{a} - x\right)\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{-200}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{elif}\;t \leq 6.1 \cdot 10^{-96}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+142}:\\ \;\;\;\;a \cdot \left(c \cdot j + \left(\frac{x \cdot \left(y \cdot z\right)}{a} - x \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 29.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i\right)\\ t_2 := c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{if}\;b \leq -7.5 \cdot 10^{+95}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.1 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.22 \cdot 10^{-293}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{-117}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq 1.54 \cdot 10^{+97}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+204}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* t i))) (t_2 (* c (* z (- b)))))
   (if (<= b -7.5e+95)
     t_2
     (if (<= b -1.1e+19)
       t_1
       (if (<= b -2.22e-293)
         (* c (* a j))
         (if (<= b 9.2e-117)
           (* y (* x z))
           (if (<= b 1.54e+97)
             (* j (* a c))
             (if (<= b 1.15e+204) 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 = c * (z * -b);
	double tmp;
	if (b <= -7.5e+95) {
		tmp = t_2;
	} else if (b <= -1.1e+19) {
		tmp = t_1;
	} else if (b <= -2.22e-293) {
		tmp = c * (a * j);
	} else if (b <= 9.2e-117) {
		tmp = y * (x * z);
	} else if (b <= 1.54e+97) {
		tmp = j * (a * c);
	} else if (b <= 1.15e+204) {
		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 = c * (z * -b)
    if (b <= (-7.5d+95)) then
        tmp = t_2
    else if (b <= (-1.1d+19)) then
        tmp = t_1
    else if (b <= (-2.22d-293)) then
        tmp = c * (a * j)
    else if (b <= 9.2d-117) then
        tmp = y * (x * z)
    else if (b <= 1.54d+97) then
        tmp = j * (a * c)
    else if (b <= 1.15d+204) 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 = c * (z * -b);
	double tmp;
	if (b <= -7.5e+95) {
		tmp = t_2;
	} else if (b <= -1.1e+19) {
		tmp = t_1;
	} else if (b <= -2.22e-293) {
		tmp = c * (a * j);
	} else if (b <= 9.2e-117) {
		tmp = y * (x * z);
	} else if (b <= 1.54e+97) {
		tmp = j * (a * c);
	} else if (b <= 1.15e+204) {
		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 = c * (z * -b)
	tmp = 0
	if b <= -7.5e+95:
		tmp = t_2
	elif b <= -1.1e+19:
		tmp = t_1
	elif b <= -2.22e-293:
		tmp = c * (a * j)
	elif b <= 9.2e-117:
		tmp = y * (x * z)
	elif b <= 1.54e+97:
		tmp = j * (a * c)
	elif b <= 1.15e+204:
		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(c * Float64(z * Float64(-b)))
	tmp = 0.0
	if (b <= -7.5e+95)
		tmp = t_2;
	elseif (b <= -1.1e+19)
		tmp = t_1;
	elseif (b <= -2.22e-293)
		tmp = Float64(c * Float64(a * j));
	elseif (b <= 9.2e-117)
		tmp = Float64(y * Float64(x * z));
	elseif (b <= 1.54e+97)
		tmp = Float64(j * Float64(a * c));
	elseif (b <= 1.15e+204)
		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 = c * (z * -b);
	tmp = 0.0;
	if (b <= -7.5e+95)
		tmp = t_2;
	elseif (b <= -1.1e+19)
		tmp = t_1;
	elseif (b <= -2.22e-293)
		tmp = c * (a * j);
	elseif (b <= 9.2e-117)
		tmp = y * (x * z);
	elseif (b <= 1.54e+97)
		tmp = j * (a * c);
	elseif (b <= 1.15e+204)
		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[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.5e+95], t$95$2, If[LessEqual[b, -1.1e+19], t$95$1, If[LessEqual[b, -2.22e-293], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.2e-117], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.54e+97], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.15e+204], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -7.5000000000000001e95 or 1.14999999999999995e204 < b

   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 64.9%

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

   5. Simplified 67.6%

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

   6. Taylor expanded in z around inf 56.7%

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

      1. +-commutative 56.7%

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

      2. mul-1-neg 56.7%

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

      3. unsub-neg 56.7%

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

      4. *-commutative 56.7%

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

      5. *-commutative 56.7%

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

   8. Simplified 56.7%

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

   9. Taylor expanded in b around inf 51.1%

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

       1. mul-1-neg 51.1%

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

       2. *-commutative 51.1%

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

       3. associate-*r* 53.3%

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

       4. *-commutative 53.3%

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

       5. distribute-rgt-neg-out 53.3%

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

       6. distribute-rgt-neg-in 53.3%

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

   11. Simplified 53.3%

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

   if -7.5000000000000001e95 < b < -1.1e19 or 1.54000000000000002e97 < b < 1.14999999999999995e204

   1. Initial program 66.3%

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

   3. Taylor expanded in a around -inf 59.0%

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

   5. Simplified 61.7%

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

   6. Taylor expanded in b around -inf 65.0%

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

      1. *-commutative 65.0%

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

      2. *-commutative 65.0%

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

   8. Simplified 65.0%

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

   9. Taylor expanded in t around inf 48.5%

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

   if -1.1e19 < b < -2.2200000000000001e-293

   1. Initial program 68.1%

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

   3. Taylor expanded in a around -inf 64.5%

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

   5. Simplified 62.7%

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

   6. Taylor expanded in c around inf 41.9%

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

      1. associate-*r* 42.1%

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

      2. mul-1-neg 42.1%

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

      3. unsub-neg 42.1%

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

      4. associate-/l* 42.0%

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

   8. Simplified 42.0%

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

   9. Taylor expanded in a around inf 38.0%

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

       1. associate-*r* 34.5%

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

       2. *-commutative 34.5%

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

       3. associate-*l* 42.8%

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

   11. Simplified 42.8%

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

   if -2.2200000000000001e-293 < b < 9.19999999999999978e-117

   1. Initial program 79.3%

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

   3. Taylor expanded in y around inf 56.4%

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

      1. +-commutative 56.4%

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

      2. mul-1-neg 56.4%

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

      3. unsub-neg 56.4%

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

      4. *-commutative 56.4%

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

   5. Simplified 56.4%

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

   6. Taylor expanded in z around inf 44.7%

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

      1. *-commutative 44.7%

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

   8. Simplified 44.7%

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

   if 9.19999999999999978e-117 < b < 1.54000000000000002e97

   1. Initial program 80.6%

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

   3. Taylor expanded in a around inf 49.7%

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

      1. +-commutative 49.7%

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

      2. mul-1-neg 49.7%

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

      3. unsub-neg 49.7%

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

   5. Simplified 49.7%

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

   6. Taylor expanded in c around inf 29.4%

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

      1. associate-*r* 34.7%

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

   8. Simplified 34.7%

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

4. Final simplification 45.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+95}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;b \leq -1.1 \cdot 10^{+19}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq -2.22 \cdot 10^{-293}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{-117}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq 1.54 \cdot 10^{+97}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+204}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 65.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+54}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(b \cdot \frac{i}{a} - x\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+61}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z\right) - j \cdot \left(y \cdot i - a \cdot c\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+142}:\\ \;\;\;\;a \cdot \left(j \cdot \left(x \cdot \frac{y \cdot z}{a \cdot j} + \left(c - t \cdot \frac{x}{j}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -2.2e+54)
   (* (* t a) (- (* b (/ i a)) x))
   (if (<= t 4e+61)
     (- (- (* x (* y z)) (* j (- (* y i) (* a c)))) (* b (* z c)))
     (if (<= t 1.45e+142)
       (* a (* j (+ (* x (/ (* y z) (* a j))) (- c (* t (/ x j))))))
       (* t (- (* b i) (* x a)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -2.2e+54) {
		tmp = (t * a) * ((b * (i / a)) - x);
	} else if (t <= 4e+61) {
		tmp = ((x * (y * z)) - (j * ((y * i) - (a * c)))) - (b * (z * c));
	} else if (t <= 1.45e+142) {
		tmp = a * (j * ((x * ((y * z) / (a * j))) + (c - (t * (x / j)))));
	} else {
		tmp = t * ((b * i) - (x * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (t <= (-2.2d+54)) then
        tmp = (t * a) * ((b * (i / a)) - x)
    else if (t <= 4d+61) then
        tmp = ((x * (y * z)) - (j * ((y * i) - (a * c)))) - (b * (z * c))
    else if (t <= 1.45d+142) then
        tmp = a * (j * ((x * ((y * z) / (a * j))) + (c - (t * (x / j)))))
    else
        tmp = t * ((b * i) - (x * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -2.2e+54) {
		tmp = (t * a) * ((b * (i / a)) - x);
	} else if (t <= 4e+61) {
		tmp = ((x * (y * z)) - (j * ((y * i) - (a * c)))) - (b * (z * c));
	} else if (t <= 1.45e+142) {
		tmp = a * (j * ((x * ((y * z) / (a * j))) + (c - (t * (x / j)))));
	} else {
		tmp = t * ((b * i) - (x * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -2.2e+54:
		tmp = (t * a) * ((b * (i / a)) - x)
	elif t <= 4e+61:
		tmp = ((x * (y * z)) - (j * ((y * i) - (a * c)))) - (b * (z * c))
	elif t <= 1.45e+142:
		tmp = a * (j * ((x * ((y * z) / (a * j))) + (c - (t * (x / j)))))
	else:
		tmp = t * ((b * i) - (x * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -2.2e+54)
		tmp = Float64(Float64(t * a) * Float64(Float64(b * Float64(i / a)) - x));
	elseif (t <= 4e+61)
		tmp = Float64(Float64(Float64(x * Float64(y * z)) - Float64(j * Float64(Float64(y * i) - Float64(a * c)))) - Float64(b * Float64(z * c)));
	elseif (t <= 1.45e+142)
		tmp = Float64(a * Float64(j * Float64(Float64(x * Float64(Float64(y * z) / Float64(a * j))) + Float64(c - Float64(t * Float64(x / j))))));
	else
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -2.2e+54)
		tmp = (t * a) * ((b * (i / a)) - x);
	elseif (t <= 4e+61)
		tmp = ((x * (y * z)) - (j * ((y * i) - (a * c)))) - (b * (z * c));
	elseif (t <= 1.45e+142)
		tmp = a * (j * ((x * ((y * z) / (a * j))) + (c - (t * (x / j)))));
	else
		tmp = t * ((b * i) - (x * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -2.2e+54], N[(N[(t * a), $MachinePrecision] * N[(N[(b * N[(i / a), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e+61], N[(N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(y * i), $MachinePrecision] - N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.45e+142], N[(a * N[(j * N[(N[(x * N[(N[(y * z), $MachinePrecision] / N[(a * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c - N[(t * N[(x / j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.1999999999999999e54

   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 a around -inf 59.9%

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

   5. Simplified 63.7%

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

   6. Taylor expanded in t around inf 60.1%

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

      1. associate-*r* 69.4%

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

      2. associate-/l* 71.3%

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

   8. Simplified 71.3%

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

   if -2.1999999999999999e54 < t < 3.9999999999999998e61

   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 t around 0 72.9%

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

   if 3.9999999999999998e61 < t < 1.45000000000000007e142

   1. Initial program 50.0%

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

   3. Taylor expanded in a around -inf 49.9%

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

   5. Simplified 54.5%

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

   6. Taylor expanded in x around inf 82.0%

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

   7. Taylor expanded in j around inf 90.8%

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

      1. associate--r+ 90.8%

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

      2. associate-/l* 90.8%

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

      3. associate-/l* 95.4%

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

      4. *-commutative 95.4%

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

   9. Simplified 95.4%

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

   if 1.45000000000000007e142 < t

   1. Initial program 59.4%

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

   3. Taylor expanded in t around inf 83.0%

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

      1. distribute-lft-out-- 83.0%

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

   5. Simplified 83.0%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x - b \cdot i\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+54}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(b \cdot \frac{i}{a} - x\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+61}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z\right) - j \cdot \left(y \cdot i - a \cdot c\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+142}:\\ \;\;\;\;a \cdot \left(j \cdot \left(x \cdot \frac{y \cdot z}{a \cdot j} + \left(c - t \cdot \frac{x}{j}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 28.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j\right)\\ \mathbf{if}\;a \leq -6.3 \cdot 10^{+112}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -4.7 \cdot 10^{-163}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-223}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-122}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+203}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* a j))))
   (if (<= a -6.3e+112)
     t_1
     (if (<= a -4.7e-163)
       (* (* z c) (- b))
       (if (<= a 1.65e-223)
         (* z (* x y))
         (if (<= a 3.9e-122)
           (* c (* z (- b)))
           (if (<= a 2.7e+203) (* t (* x (- a))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (a * j);
	double tmp;
	if (a <= -6.3e+112) {
		tmp = t_1;
	} else if (a <= -4.7e-163) {
		tmp = (z * c) * -b;
	} else if (a <= 1.65e-223) {
		tmp = z * (x * y);
	} else if (a <= 3.9e-122) {
		tmp = c * (z * -b);
	} else if (a <= 2.7e+203) {
		tmp = t * (x * -a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (a * j)
    if (a <= (-6.3d+112)) then
        tmp = t_1
    else if (a <= (-4.7d-163)) then
        tmp = (z * c) * -b
    else if (a <= 1.65d-223) then
        tmp = z * (x * y)
    else if (a <= 3.9d-122) then
        tmp = c * (z * -b)
    else if (a <= 2.7d+203) then
        tmp = t * (x * -a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (a * j);
	double tmp;
	if (a <= -6.3e+112) {
		tmp = t_1;
	} else if (a <= -4.7e-163) {
		tmp = (z * c) * -b;
	} else if (a <= 1.65e-223) {
		tmp = z * (x * y);
	} else if (a <= 3.9e-122) {
		tmp = c * (z * -b);
	} else if (a <= 2.7e+203) {
		tmp = t * (x * -a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (a * j)
	tmp = 0
	if a <= -6.3e+112:
		tmp = t_1
	elif a <= -4.7e-163:
		tmp = (z * c) * -b
	elif a <= 1.65e-223:
		tmp = z * (x * y)
	elif a <= 3.9e-122:
		tmp = c * (z * -b)
	elif a <= 2.7e+203:
		tmp = t * (x * -a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(a * j))
	tmp = 0.0
	if (a <= -6.3e+112)
		tmp = t_1;
	elseif (a <= -4.7e-163)
		tmp = Float64(Float64(z * c) * Float64(-b));
	elseif (a <= 1.65e-223)
		tmp = Float64(z * Float64(x * y));
	elseif (a <= 3.9e-122)
		tmp = Float64(c * Float64(z * Float64(-b)));
	elseif (a <= 2.7e+203)
		tmp = Float64(t * Float64(x * Float64(-a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (a * j);
	tmp = 0.0;
	if (a <= -6.3e+112)
		tmp = t_1;
	elseif (a <= -4.7e-163)
		tmp = (z * c) * -b;
	elseif (a <= 1.65e-223)
		tmp = z * (x * y);
	elseif (a <= 3.9e-122)
		tmp = c * (z * -b);
	elseif (a <= 2.7e+203)
		tmp = t * (x * -a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.3e+112], t$95$1, If[LessEqual[a, -4.7e-163], N[(N[(z * c), $MachinePrecision] * (-b)), $MachinePrecision], If[LessEqual[a, 1.65e-223], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.9e-122], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.7e+203], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -6.2999999999999997e112 or 2.7e203 < a

   1. Initial program 57.5%

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

   3. Taylor expanded in a around -inf 68.3%

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

   5. Simplified 74.5%

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

   6. Taylor expanded in c around inf 61.6%

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

      1. associate-*r* 58.7%

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

      2. mul-1-neg 58.7%

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

      3. unsub-neg 58.7%

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

      4. associate-/l* 57.4%

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

   8. Simplified 57.4%

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

   9. Taylor expanded in a around inf 48.1%

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

       1. associate-*r* 48.2%

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

       2. *-commutative 48.2%

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

       3. associate-*l* 55.6%

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

   11. Simplified 55.6%

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

   if -6.2999999999999997e112 < a < -4.7e-163

   1. Initial program 77.0%

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

   3. Taylor expanded in a around -inf 65.6%

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

   5. Simplified 67.1%

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

   6. Taylor expanded in b around -inf 49.4%

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

      1. *-commutative 49.4%

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

      2. *-commutative 49.4%

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

   8. Simplified 49.4%

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

   9. Taylor expanded in t around 0 33.8%

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

       1. associate-*r* 33.8%

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

       2. neg-mul-1 33.8%

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

   11. Simplified 33.8%

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

   if -4.7e-163 < a < 1.64999999999999997e-223

   1. Initial program 89.6%

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

   3. Taylor expanded in a around -inf 52.6%

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

   5. Simplified 54.9%

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

   6. Taylor expanded in z around inf 43.6%

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

      1. +-commutative 43.6%

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

      2. mul-1-neg 43.6%

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

      3. unsub-neg 43.6%

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

      4. *-commutative 43.6%

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

      5. *-commutative 43.6%

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

   8. Simplified 43.6%

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

   9. Taylor expanded in y around inf 43.6%

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

       1. associate-*r* 43.6%

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

   11. Simplified 43.6%

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

   if 1.64999999999999997e-223 < a < 3.8999999999999999e-122

   1. Initial program 99.7%

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

   3. Taylor expanded in a around -inf 57.0%

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

   5. Simplified 52.1%

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

   6. Taylor expanded in z around inf 41.8%

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

      1. +-commutative 41.8%

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

      2. mul-1-neg 41.8%

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

      3. unsub-neg 41.8%

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

      4. *-commutative 41.8%

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

      5. *-commutative 41.8%

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

   8. Simplified 41.8%

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

   9. Taylor expanded in b around inf 46.6%

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

       1. mul-1-neg 46.6%

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

       2. *-commutative 46.6%

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

       3. associate-*r* 46.6%

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

       4. *-commutative 46.6%

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

       5. distribute-rgt-neg-out 46.6%

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

       6. distribute-rgt-neg-in 46.6%

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

   11. Simplified 46.6%

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

   if 3.8999999999999999e-122 < a < 2.7e203

   1. Initial program 69.9%

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

   3. Taylor expanded in a around -inf 72.6%

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

   5. Simplified 72.8%

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

   6. Taylor expanded in z around inf 72.6%

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

      1. +-commutative 72.6%

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

      2. mul-1-neg 72.6%

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

      3. unsub-neg 72.6%

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

      4. *-commutative 72.6%

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

      5. *-commutative 72.6%

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

   8. Simplified 72.6%

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

   9. Taylor expanded in t around inf 45.9%

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

       1. mul-1-neg 45.9%

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

       2. *-commutative 45.9%

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

       3. associate-*r* 44.5%

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

       4. *-commutative 44.5%

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

       5. distribute-rgt-neg-out 44.5%

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

       6. *-commutative 44.5%

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

       7. distribute-rgt-neg-in 44.5%

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

   11. Simplified 44.5%

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

4. Final simplification 44.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.3 \cdot 10^{+112}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;a \leq -4.7 \cdot 10^{-163}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-223}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-122}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+203}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.02 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+99}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z\right) - i \cdot \left(y \cdot j\right)\right) + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))))
   (if (<= b -1.02e+21)
     t_1
     (if (<= b 6.5e+99)
       (+ (* j (- (* a c) (* y i))) (* x (- (* y z) (* t a))))
       (+ (- (* x (* y z)) (* i (* y j))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -1.02e+21) {
		tmp = t_1;
	} else if (b <= 6.5e+99) {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else {
		tmp = ((x * (y * z)) - (i * (y * 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 = b * ((t * i) - (z * c))
    if (b <= (-1.02d+21)) then
        tmp = t_1
    else if (b <= 6.5d+99) then
        tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
    else
        tmp = ((x * (y * z)) - (i * (y * 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 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -1.02e+21) {
		tmp = t_1;
	} else if (b <= 6.5e+99) {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else {
		tmp = ((x * (y * z)) - (i * (y * j))) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -1.02e+21:
		tmp = t_1
	elif b <= 6.5e+99:
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
	else:
		tmp = ((x * (y * z)) - (i * (y * j))) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -1.02e+21)
		tmp = t_1;
	elseif (b <= 6.5e+99)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	else
		tmp = Float64(Float64(Float64(x * Float64(y * z)) - Float64(i * Float64(y * j))) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -1.02e+21)
		tmp = t_1;
	elseif (b <= 6.5e+99)
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	else
		tmp = ((x * (y * z)) - (i * (y * j))) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.02e+21], t$95$1, If[LessEqual[b, 6.5e+99], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.02e21

   1. Initial program 71.5%

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

   3. Taylor expanded in b around inf 65.5%

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

      1. *-commutative 65.5%

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

   5. Simplified 65.5%

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

   if -1.02e21 < b < 6.5000000000000004e99

   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 b around 0 79.0%

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

   if 6.5000000000000004e99 < b

   1. Initial program 74.1%

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

   3. Taylor expanded in a around 0 72.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.02 \cdot 10^{+21}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+99}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z\right) - i \cdot \left(y \cdot j\right)\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+53}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(b \cdot \frac{i}{a} - x\right)\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-170}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-21}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+142}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -5e+53)
   (* (* t a) (- (* b (/ i a)) x))
   (if (<= t 7.5e-170)
     (* c (- (* a j) (* z b)))
     (if (<= t 1.55e-21)
       (* z (- (* x y) (* b c)))
       (if (<= t 1.1e+142)
         (* a (- (* c j) (* x t)))
         (* t (- (* b i) (* x a))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -5e+53) {
		tmp = (t * a) * ((b * (i / a)) - x);
	} else if (t <= 7.5e-170) {
		tmp = c * ((a * j) - (z * b));
	} else if (t <= 1.55e-21) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 1.1e+142) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t * ((b * i) - (x * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (t <= (-5d+53)) then
        tmp = (t * a) * ((b * (i / a)) - x)
    else if (t <= 7.5d-170) then
        tmp = c * ((a * j) - (z * b))
    else if (t <= 1.55d-21) then
        tmp = z * ((x * y) - (b * c))
    else if (t <= 1.1d+142) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = t * ((b * i) - (x * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -5e+53) {
		tmp = (t * a) * ((b * (i / a)) - x);
	} else if (t <= 7.5e-170) {
		tmp = c * ((a * j) - (z * b));
	} else if (t <= 1.55e-21) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 1.1e+142) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t * ((b * i) - (x * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -5e+53:
		tmp = (t * a) * ((b * (i / a)) - x)
	elif t <= 7.5e-170:
		tmp = c * ((a * j) - (z * b))
	elif t <= 1.55e-21:
		tmp = z * ((x * y) - (b * c))
	elif t <= 1.1e+142:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = t * ((b * i) - (x * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -5e+53)
		tmp = Float64(Float64(t * a) * Float64(Float64(b * Float64(i / a)) - x));
	elseif (t <= 7.5e-170)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (t <= 1.55e-21)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (t <= 1.1e+142)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -5e+53)
		tmp = (t * a) * ((b * (i / a)) - x);
	elseif (t <= 7.5e-170)
		tmp = c * ((a * j) - (z * b));
	elseif (t <= 1.55e-21)
		tmp = z * ((x * y) - (b * c));
	elseif (t <= 1.1e+142)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = t * ((b * i) - (x * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -5e+53], N[(N[(t * a), $MachinePrecision] * N[(N[(b * N[(i / a), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.5e-170], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.55e-21], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.1e+142], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -5.0000000000000004e53

   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 a around -inf 59.9%

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

   5. Simplified 63.7%

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

   6. Taylor expanded in t around inf 60.1%

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

      1. associate-*r* 69.4%

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

      2. associate-/l* 71.3%

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

   8. Simplified 71.3%

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

   if -5.0000000000000004e53 < t < 7.4999999999999998e-170

   1. Initial program 82.5%

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

   3. Taylor expanded in c around inf 55.6%

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

   if 7.4999999999999998e-170 < t < 1.5499999999999999e-21

   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 z around inf 74.8%

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

      1. *-commutative 74.8%

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

   5. Simplified 74.8%

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

   if 1.5499999999999999e-21 < t < 1.09999999999999993e142

   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 a around inf 65.6%

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

      1. +-commutative 65.6%

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

      2. mul-1-neg 65.6%

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

      3. unsub-neg 65.6%

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

   5. Simplified 65.6%

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

   if 1.09999999999999993e142 < t

   1. Initial program 59.4%

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

   3. Taylor expanded in t around inf 83.0%

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

      1. distribute-lft-out-- 83.0%

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

   5. Simplified 83.0%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x - b \cdot i\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+53}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(b \cdot \frac{i}{a} - x\right)\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-170}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-21}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+142}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 51.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -8.5 \cdot 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-171}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{-22}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+142}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* b i) (* x a)))))
   (if (<= t -8.5e+59)
     t_1
     (if (<= t 5.2e-171)
       (* c (- (* a j) (* z b)))
       (if (<= t 1.22e-22)
         (* z (- (* x y) (* b c)))
         (if (<= t 1.7e+142) (* a (- (* c j) (* x t))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -8.5e+59) {
		tmp = t_1;
	} else if (t <= 5.2e-171) {
		tmp = c * ((a * j) - (z * b));
	} else if (t <= 1.22e-22) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 1.7e+142) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((b * i) - (x * a))
    if (t <= (-8.5d+59)) then
        tmp = t_1
    else if (t <= 5.2d-171) then
        tmp = c * ((a * j) - (z * b))
    else if (t <= 1.22d-22) then
        tmp = z * ((x * y) - (b * c))
    else if (t <= 1.7d+142) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -8.5e+59) {
		tmp = t_1;
	} else if (t <= 5.2e-171) {
		tmp = c * ((a * j) - (z * b));
	} else if (t <= 1.22e-22) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 1.7e+142) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((b * i) - (x * a))
	tmp = 0
	if t <= -8.5e+59:
		tmp = t_1
	elif t <= 5.2e-171:
		tmp = c * ((a * j) - (z * b))
	elif t <= 1.22e-22:
		tmp = z * ((x * y) - (b * c))
	elif t <= 1.7e+142:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	tmp = 0.0
	if (t <= -8.5e+59)
		tmp = t_1;
	elseif (t <= 5.2e-171)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (t <= 1.22e-22)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (t <= 1.7e+142)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -8.5e+59)
		tmp = t_1;
	elseif (t <= 5.2e-171)
		tmp = c * ((a * j) - (z * b));
	elseif (t <= 1.22e-22)
		tmp = z * ((x * y) - (b * c));
	elseif (t <= 1.7e+142)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.5e+59], t$95$1, If[LessEqual[t, 5.2e-171], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.22e-22], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.7e+142], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.4999999999999999e59 or 1.6999999999999999e142 < t

   1. Initial program 66.3%

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

   3. Taylor expanded in t around inf 71.9%

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

      1. distribute-lft-out-- 71.9%

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

   5. Simplified 71.9%

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

   if -8.4999999999999999e59 < t < 5.2000000000000001e-171

   1. Initial program 81.9%

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

   3. Taylor expanded in c around inf 55.5%

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

   if 5.2000000000000001e-171 < t < 1.2200000000000001e-22

   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 z around inf 74.8%

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

      1. *-commutative 74.8%

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

   5. Simplified 74.8%

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

   if 1.2200000000000001e-22 < t < 1.6999999999999999e142

   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 a around inf 65.6%

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

      1. +-commutative 65.6%

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

      2. mul-1-neg 65.6%

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

      3. unsub-neg 65.6%

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

   5. Simplified 65.6%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+59}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-171}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{-22}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+142}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.6 \cdot 10^{+21} \lor \neg \left(b \leq 1.62 \cdot 10^{+103}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -3.6e+21) (not (<= b 1.62e+103)))
   (* b (- (* t i) (* z c)))
   (+ (* j (- (* a c) (* y i))) (* x (- (* y z) (* t a))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -3.6e+21) || !(b <= 1.62e+103)) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-3.6d+21)) .or. (.not. (b <= 1.62d+103))) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -3.6e+21) || !(b <= 1.62e+103)) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -3.6e+21) or not (b <= 1.62e+103):
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -3.6e+21) || !(b <= 1.62e+103))
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -3.6e+21) || ~((b <= 1.62e+103)))
		tmp = b * ((t * i) - (z * c));
	else
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -3.6e+21], N[Not[LessEqual[b, 1.62e+103]], $MachinePrecision]], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.6e21 or 1.62000000000000007e103 < 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 66.6%

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

      1. *-commutative 66.6%

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

   5. Simplified 66.6%

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

   if -3.6e21 < b < 1.62000000000000007e103

   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 b around 0 79.0%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.6 \cdot 10^{+21} \lor \neg \left(b \leq 1.62 \cdot 10^{+103}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 66.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -3.2 \cdot 10^{+21}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 10^{+94}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_1 + t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (* b (- (* t i) (* z c)))))
   (if (<= b -3.2e+21)
     t_2
     (if (<= b 1e+94) (+ (* j (- (* a c) (* y i))) t_1) (+ t_1 t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -3.2e+21) {
		tmp = t_2;
	} else if (b <= 1e+94) {
		tmp = (j * ((a * c) - (y * i))) + t_1;
	} else {
		tmp = t_1 + t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = b * ((t * i) - (z * c))
    if (b <= (-3.2d+21)) then
        tmp = t_2
    else if (b <= 1d+94) then
        tmp = (j * ((a * c) - (y * i))) + t_1
    else
        tmp = t_1 + t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -3.2e+21) {
		tmp = t_2;
	} else if (b <= 1e+94) {
		tmp = (j * ((a * c) - (y * i))) + t_1;
	} else {
		tmp = t_1 + t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -3.2e+21:
		tmp = t_2
	elif b <= 1e+94:
		tmp = (j * ((a * c) - (y * i))) + t_1
	else:
		tmp = t_1 + t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -3.2e+21)
		tmp = t_2;
	elseif (b <= 1e+94)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + t_1);
	else
		tmp = Float64(t_1 + t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -3.2e+21)
		tmp = t_2;
	elseif (b <= 1e+94)
		tmp = (j * ((a * c) - (y * i))) + t_1;
	else
		tmp = t_1 + t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.2e+21], t$95$2, If[LessEqual[b, 1e+94], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(t$95$1 + t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.2e21

   1. Initial program 71.5%

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

   3. Taylor expanded in b around inf 65.5%

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

      1. *-commutative 65.5%

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

   5. Simplified 65.5%

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

   if -3.2e21 < b < 1e94

   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 b around 0 79.0%

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

   if 1e94 < b

   1. Initial program 74.1%

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

   3. Taylor expanded in j around 0 69.9%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.2 \cdot 10^{+21}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 10^{+94}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 28.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{+113}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-163}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-226}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-122}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -1.75e+113)
   (* c (* a j))
   (if (<= a -4.2e-163)
     (* (* z c) (- b))
     (if (<= a 4.8e-226)
       (* z (* x y))
       (if (<= a 3.9e-122) (* c (* z (- b))) (* a (* x (- t))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -1.75e+113) {
		tmp = c * (a * j);
	} else if (a <= -4.2e-163) {
		tmp = (z * c) * -b;
	} else if (a <= 4.8e-226) {
		tmp = z * (x * y);
	} else if (a <= 3.9e-122) {
		tmp = c * (z * -b);
	} else {
		tmp = a * (x * -t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (a <= (-1.75d+113)) then
        tmp = c * (a * j)
    else if (a <= (-4.2d-163)) then
        tmp = (z * c) * -b
    else if (a <= 4.8d-226) then
        tmp = z * (x * y)
    else if (a <= 3.9d-122) then
        tmp = c * (z * -b)
    else
        tmp = a * (x * -t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -1.75e+113) {
		tmp = c * (a * j);
	} else if (a <= -4.2e-163) {
		tmp = (z * c) * -b;
	} else if (a <= 4.8e-226) {
		tmp = z * (x * y);
	} else if (a <= 3.9e-122) {
		tmp = c * (z * -b);
	} else {
		tmp = a * (x * -t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -1.75e+113:
		tmp = c * (a * j)
	elif a <= -4.2e-163:
		tmp = (z * c) * -b
	elif a <= 4.8e-226:
		tmp = z * (x * y)
	elif a <= 3.9e-122:
		tmp = c * (z * -b)
	else:
		tmp = a * (x * -t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -1.75e+113)
		tmp = Float64(c * Float64(a * j));
	elseif (a <= -4.2e-163)
		tmp = Float64(Float64(z * c) * Float64(-b));
	elseif (a <= 4.8e-226)
		tmp = Float64(z * Float64(x * y));
	elseif (a <= 3.9e-122)
		tmp = Float64(c * Float64(z * Float64(-b)));
	else
		tmp = Float64(a * Float64(x * Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -1.75e+113)
		tmp = c * (a * j);
	elseif (a <= -4.2e-163)
		tmp = (z * c) * -b;
	elseif (a <= 4.8e-226)
		tmp = z * (x * y);
	elseif (a <= 3.9e-122)
		tmp = c * (z * -b);
	else
		tmp = a * (x * -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -1.75e+113], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.2e-163], N[(N[(z * c), $MachinePrecision] * (-b)), $MachinePrecision], If[LessEqual[a, 4.8e-226], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.9e-122], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.75e113

   1. Initial program 53.8%

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

   3. Taylor expanded in a around -inf 67.5%

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

   5. Simplified 71.9%

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

   6. Taylor expanded in c around inf 59.5%

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

      1. associate-*r* 57.4%

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

      2. mul-1-neg 57.4%

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

      3. unsub-neg 57.4%

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

      4. associate-/l* 55.2%

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

   8. Simplified 55.2%

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

   9. Taylor expanded in a around inf 44.2%

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

       1. associate-*r* 44.3%

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

       2. *-commutative 44.3%

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

       3. associate-*l* 50.7%

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

   11. Simplified 50.7%

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

   if -1.75e113 < a < -4.19999999999999996e-163

   1. Initial program 77.0%

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

   3. Taylor expanded in a around -inf 65.6%

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

   5. Simplified 67.1%

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

   6. Taylor expanded in b around -inf 49.4%

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

      1. *-commutative 49.4%

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

      2. *-commutative 49.4%

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

   8. Simplified 49.4%

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

   9. Taylor expanded in t around 0 33.8%

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

       1. associate-*r* 33.8%

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

       2. neg-mul-1 33.8%

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

   11. Simplified 33.8%

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

   if -4.19999999999999996e-163 < a < 4.7999999999999999e-226

   1. Initial program 89.6%

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

   3. Taylor expanded in a around -inf 52.6%

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

   5. Simplified 54.9%

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

   6. Taylor expanded in z around inf 43.6%

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

      1. +-commutative 43.6%

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

      2. mul-1-neg 43.6%

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

      3. unsub-neg 43.6%

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

      4. *-commutative 43.6%

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

      5. *-commutative 43.6%

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

   8. Simplified 43.6%

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

   9. Taylor expanded in y around inf 43.6%

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

       1. associate-*r* 43.6%

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

   11. Simplified 43.6%

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

   if 4.7999999999999999e-226 < a < 3.8999999999999999e-122

   1. Initial program 99.7%

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

   3. Taylor expanded in a around -inf 57.0%

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

   5. Simplified 52.1%

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

   6. Taylor expanded in z around inf 41.8%

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

      1. +-commutative 41.8%

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

      2. mul-1-neg 41.8%

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

      3. unsub-neg 41.8%

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

      4. *-commutative 41.8%

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

      5. *-commutative 41.8%

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

   8. Simplified 41.8%

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

   9. Taylor expanded in b around inf 46.6%

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

       1. mul-1-neg 46.6%

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

       2. *-commutative 46.6%

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

       3. associate-*r* 46.6%

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

       4. *-commutative 46.6%

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

       5. distribute-rgt-neg-out 46.6%

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

       6. distribute-rgt-neg-in 46.6%

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

   11. Simplified 46.6%

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

   if 3.8999999999999999e-122 < a

   1. Initial program 68.9%

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

   3. Taylor expanded in a around inf 65.6%

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

      1. +-commutative 65.6%

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

      2. mul-1-neg 65.6%

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

      3. unsub-neg 65.6%

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

   5. Simplified 65.6%

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

   6. Taylor expanded in c around 0 46.9%

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

      1. mul-1-neg 46.9%

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

      2. *-commutative 46.9%

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

      3. distribute-rgt-neg-in 46.9%

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

   8. Simplified 46.9%

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

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{+113}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-163}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-226}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-122}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 59.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+54}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(b \cdot \frac{i}{a} - x\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+87}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -2.3e+54)
   (* (* t a) (- (* b (/ i a)) x))
   (if (<= t 2e+87)
     (- (* x (* y z)) (* j (- (* y i) (* a c))))
     (* t (- (* b i) (* x a))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -2.3e+54) {
		tmp = (t * a) * ((b * (i / a)) - x);
	} else if (t <= 2e+87) {
		tmp = (x * (y * z)) - (j * ((y * i) - (a * c)));
	} else {
		tmp = t * ((b * i) - (x * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (t <= (-2.3d+54)) then
        tmp = (t * a) * ((b * (i / a)) - x)
    else if (t <= 2d+87) then
        tmp = (x * (y * z)) - (j * ((y * i) - (a * c)))
    else
        tmp = t * ((b * i) - (x * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -2.3e+54) {
		tmp = (t * a) * ((b * (i / a)) - x);
	} else if (t <= 2e+87) {
		tmp = (x * (y * z)) - (j * ((y * i) - (a * c)));
	} else {
		tmp = t * ((b * i) - (x * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -2.3e+54:
		tmp = (t * a) * ((b * (i / a)) - x)
	elif t <= 2e+87:
		tmp = (x * (y * z)) - (j * ((y * i) - (a * c)))
	else:
		tmp = t * ((b * i) - (x * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -2.3e+54)
		tmp = Float64(Float64(t * a) * Float64(Float64(b * Float64(i / a)) - x));
	elseif (t <= 2e+87)
		tmp = Float64(Float64(x * Float64(y * z)) - Float64(j * Float64(Float64(y * i) - Float64(a * c))));
	else
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -2.3e+54)
		tmp = (t * a) * ((b * (i / a)) - x);
	elseif (t <= 2e+87)
		tmp = (x * (y * z)) - (j * ((y * i) - (a * c)));
	else
		tmp = t * ((b * i) - (x * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -2.3e+54], N[(N[(t * a), $MachinePrecision] * N[(N[(b * N[(i / a), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2e+87], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(y * i), $MachinePrecision] - N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.29999999999999994e54

   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 a around -inf 59.9%

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

   5. Simplified 63.7%

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

   6. Taylor expanded in t around inf 60.1%

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

      1. associate-*r* 69.4%

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

      2. associate-/l* 71.3%

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

   8. Simplified 71.3%

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

   if -2.29999999999999994e54 < t < 1.9999999999999999e87

   1. Initial program 80.7%

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

   3. Taylor expanded in b around 0 67.4%

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

   4. Taylor expanded in t around 0 61.3%

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

   if 1.9999999999999999e87 < t

   1. Initial program 57.0%

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

   3. Taylor expanded in t around inf 76.8%

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

      1. distribute-lft-out-- 76.8%

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

   5. Simplified 76.8%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x - b \cdot i\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+54}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(b \cdot \frac{i}{a} - x\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+87}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.9 \cdot 10^{-5} \lor \neg \left(c \leq 5.1 \cdot 10^{-55}\right):\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -1.9e-5) (not (<= c 5.1e-55)))
   (* c (- (* a j) (* z b)))
   (* x (- (* y z) (* t a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -1.9e-5) || !(c <= 5.1e-55)) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = x * ((y * z) - (t * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((c <= (-1.9d-5)) .or. (.not. (c <= 5.1d-55))) then
        tmp = c * ((a * j) - (z * b))
    else
        tmp = x * ((y * z) - (t * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -1.9e-5) || !(c <= 5.1e-55)) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = x * ((y * z) - (t * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -1.9e-5) or not (c <= 5.1e-55):
		tmp = c * ((a * j) - (z * b))
	else:
		tmp = x * ((y * z) - (t * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -1.9e-5) || !(c <= 5.1e-55))
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	else
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -1.9e-5) || ~((c <= 5.1e-55)))
		tmp = c * ((a * j) - (z * b));
	else
		tmp = x * ((y * z) - (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -1.9e-5], N[Not[LessEqual[c, 5.1e-55]], $MachinePrecision]], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.9000000000000001e-5 or 5.09999999999999995e-55 < c

   1. Initial program 67.3%

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

   3. Taylor expanded in c around inf 63.4%

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

   if -1.9000000000000001e-5 < c < 5.09999999999999995e-55

   1. Initial program 83.8%

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

   3. Taylor expanded in b around 0 72.8%

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

   4. Taylor expanded in j around 0 56.9%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.9 \cdot 10^{-5} \lor \neg \left(c \leq 5.1 \cdot 10^{-55}\right):\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 51.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{+20} \lor \neg \left(b \leq 1.65 \cdot 10^{+94}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -5.5e+20) (not (<= b 1.65e+94)))
   (* 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 <= -5.5e+20) || !(b <= 1.65e+94)) {
		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 <= (-5.5d+20)) .or. (.not. (b <= 1.65d+94))) 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 <= -5.5e+20) || !(b <= 1.65e+94)) {
		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 <= -5.5e+20) or not (b <= 1.65e+94):
		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 <= -5.5e+20) || !(b <= 1.65e+94))
		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 <= -5.5e+20) || ~((b <= 1.65e+94)))
		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, -5.5e+20], N[Not[LessEqual[b, 1.65e+94]], $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 < -5.5e20 or 1.65e94 < 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 66.6%

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

      1. *-commutative 66.6%

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

   5. Simplified 66.6%

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

   if -5.5e20 < b < 1.65e94

   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 52.7%

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

      1. +-commutative 52.7%

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

      2. mul-1-neg 52.7%

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

      3. unsub-neg 52.7%

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

   5. Simplified 52.7%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{+20} \lor \neg \left(b \leq 1.65 \cdot 10^{+94}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 41.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.12 \cdot 10^{+198}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+208}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -1.12e+198)
   (* (* z c) (- b))
   (if (<= b 1.05e+208) (* a (- (* c j) (* x t))) (* c (* z (- b))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -1.12e+198) {
		tmp = (z * c) * -b;
	} else if (b <= 1.05e+208) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = c * (z * -b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-1.12d+198)) then
        tmp = (z * c) * -b
    else if (b <= 1.05d+208) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = c * (z * -b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -1.12e+198) {
		tmp = (z * c) * -b;
	} else if (b <= 1.05e+208) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = c * (z * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -1.12e+198:
		tmp = (z * c) * -b
	elif b <= 1.05e+208:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = c * (z * -b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -1.12e+198)
		tmp = Float64(Float64(z * c) * Float64(-b));
	elseif (b <= 1.05e+208)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = Float64(c * Float64(z * Float64(-b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -1.12e+198)
		tmp = (z * c) * -b;
	elseif (b <= 1.05e+208)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = c * (z * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -1.12e+198], N[(N[(z * c), $MachinePrecision] * (-b)), $MachinePrecision], If[LessEqual[b, 1.05e+208], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.1199999999999999e198

   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 a around -inf 66.2%

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

   5. Simplified 63.0%

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

   6. Taylor expanded in b around -inf 82.4%

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

      1. *-commutative 82.4%

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

      2. *-commutative 82.4%

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

   8. Simplified 82.4%

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

   9. Taylor expanded in t around 0 63.8%

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

       1. associate-*r* 63.8%

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

       2. neg-mul-1 63.8%

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

   11. Simplified 63.8%

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

   if -1.1199999999999999e198 < b < 1.0499999999999999e208

   1. Initial program 74.0%

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

   3. Taylor expanded in a around inf 48.6%

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

      1. +-commutative 48.6%

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

      2. mul-1-neg 48.6%

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

      3. unsub-neg 48.6%

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

   5. Simplified 48.6%

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

   if 1.0499999999999999e208 < b

   1. Initial program 80.8%

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

   3. Taylor expanded in a around -inf 72.7%

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

   5. Simplified 72.7%

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

   6. Taylor expanded in z around inf 72.9%

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

      1. +-commutative 72.9%

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

      2. mul-1-neg 72.9%

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

      3. unsub-neg 72.9%

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

      4. *-commutative 72.9%

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

      5. *-commutative 72.9%

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

   8. Simplified 72.9%

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

   9. Taylor expanded in b around inf 63.3%

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

       1. mul-1-neg 63.3%

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

       2. *-commutative 63.3%

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

       3. associate-*r* 72.0%

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

       4. *-commutative 72.0%

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

       5. distribute-rgt-neg-out 72.0%

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

       6. distribute-rgt-neg-in 72.0%

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

   11. Simplified 72.0%

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

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.12 \cdot 10^{+198}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+208}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 29.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -9.8:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;c \leq 5.1 \cdot 10^{-54}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -9.8)
   (* j (* a c))
   (if (<= c 5.1e-54) (* t (* x (- a))) (* a (* c j)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -9.8) {
		tmp = j * (a * c);
	} else if (c <= 5.1e-54) {
		tmp = t * (x * -a);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (c <= (-9.8d0)) then
        tmp = j * (a * c)
    else if (c <= 5.1d-54) then
        tmp = t * (x * -a)
    else
        tmp = a * (c * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -9.8) {
		tmp = j * (a * c);
	} else if (c <= 5.1e-54) {
		tmp = t * (x * -a);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -9.8:
		tmp = j * (a * c)
	elif c <= 5.1e-54:
		tmp = t * (x * -a)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -9.8)
		tmp = Float64(j * Float64(a * c));
	elseif (c <= 5.1e-54)
		tmp = Float64(t * Float64(x * Float64(-a)));
	else
		tmp = Float64(a * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -9.8)
		tmp = j * (a * c);
	elseif (c <= 5.1e-54)
		tmp = t * (x * -a);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -9.8], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.1e-54], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -9.8000000000000007

   1. Initial program 70.3%

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

   3. Taylor expanded in a around inf 46.2%

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

      1. +-commutative 46.2%

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

      2. mul-1-neg 46.2%

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

      3. unsub-neg 46.2%

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

   5. Simplified 46.2%

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

   6. Taylor expanded in c around inf 39.3%

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

      1. associate-*r* 42.4%

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

   8. Simplified 42.4%

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

   if -9.8000000000000007 < c < 5.1000000000000001e-54

   1. Initial program 83.4%

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

   3. Taylor expanded in a around -inf 68.6%

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

   5. Simplified 68.6%

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

   6. Taylor expanded in z around inf 53.5%

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

      1. +-commutative 53.5%

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

      2. mul-1-neg 53.5%

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

      3. unsub-neg 53.5%

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

      4. *-commutative 53.5%

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

      5. *-commutative 53.5%

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

   8. Simplified 53.5%

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

   9. Taylor expanded in t around inf 38.9%

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

       1. mul-1-neg 38.9%

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

       2. *-commutative 38.9%

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

       3. associate-*r* 37.2%

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

       4. *-commutative 37.2%

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

       5. distribute-rgt-neg-out 37.2%

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

       6. *-commutative 37.2%

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

       7. distribute-rgt-neg-in 37.2%

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

   11. Simplified 37.2%

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

   if 5.1000000000000001e-54 < c

   1. Initial program 65.0%

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

   3. Taylor expanded in a around inf 48.0%

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

      1. +-commutative 48.0%

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

      2. mul-1-neg 48.0%

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

      3. unsub-neg 48.0%

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

   5. Simplified 48.0%

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

   6. Taylor expanded in c around inf 41.9%

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

4. Final simplification 39.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -9.8:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;c \leq 5.1 \cdot 10^{-54}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 29.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -2.15 \cdot 10^{-52} \lor \neg \left(j \leq 1.3 \cdot 10^{-24}\right):\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -2.15e-52) (not (<= j 1.3e-24))) (* c (* a j)) (* y (* x z))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -2.15e-52) || !(j <= 1.3e-24)) {
		tmp = c * (a * j);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((j <= (-2.15d-52)) .or. (.not. (j <= 1.3d-24))) then
        tmp = c * (a * j)
    else
        tmp = y * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -2.15e-52) || !(j <= 1.3e-24)) {
		tmp = c * (a * j);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -2.15e-52) or not (j <= 1.3e-24):
		tmp = c * (a * j)
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -2.15e-52) || !(j <= 1.3e-24))
		tmp = Float64(c * Float64(a * j));
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -2.15e-52) || ~((j <= 1.3e-24)))
		tmp = c * (a * j);
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -2.15e-52], N[Not[LessEqual[j, 1.3e-24]], $MachinePrecision]], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -2.1500000000000002e-52 or 1.3e-24 < 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 61.5%

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

   5. Simplified 64.3%

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

   6. Taylor expanded in c around inf 47.9%

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

      1. associate-*r* 49.5%

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

      2. mul-1-neg 49.5%

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

      3. unsub-neg 49.5%

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

      4. associate-/l* 48.9%

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

   8. Simplified 48.9%

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

   9. Taylor expanded in a around inf 37.9%

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

       1. associate-*r* 36.4%

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

       2. *-commutative 36.4%

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

       3. associate-*l* 41.0%

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

   11. Simplified 41.0%

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

   if -2.1500000000000002e-52 < j < 1.3e-24

   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 y around inf 36.6%

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

      1. +-commutative 36.6%

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

      2. mul-1-neg 36.6%

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

      3. unsub-neg 36.6%

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

      4. *-commutative 36.6%

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

   5. Simplified 36.6%

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

   6. Taylor expanded in z around inf 33.2%

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

      1. *-commutative 33.2%

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

   8. Simplified 33.2%

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

4. Final simplification 37.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.15 \cdot 10^{-52} \lor \neg \left(j \leq 1.3 \cdot 10^{-24}\right):\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 30.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.3 \cdot 10^{+51} \lor \neg \left(j \leq 1.8 \cdot 10^{-58}\right):\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -1.3e+51) (not (<= j 1.8e-58))) (* c (* a 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 <= -1.3e+51) || !(j <= 1.8e-58)) {
		tmp = c * (a * 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 <= (-1.3d+51)) .or. (.not. (j <= 1.8d-58))) then
        tmp = c * (a * 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 <= -1.3e+51) || !(j <= 1.8e-58)) {
		tmp = c * (a * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -1.3e+51) or not (j <= 1.8e-58):
		tmp = c * (a * 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 <= -1.3e+51) || !(j <= 1.8e-58))
		tmp = Float64(c * Float64(a * 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 <= -1.3e+51) || ~((j <= 1.8e-58)))
		tmp = c * (a * 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, -1.3e+51], N[Not[LessEqual[j, 1.8e-58]], $MachinePrecision]], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -1.3000000000000001e51 or 1.80000000000000005e-58 < j

   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 60.8%

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

   5. Simplified 64.0%

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

   6. Taylor expanded in c around inf 48.3%

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

      1. associate-*r* 50.2%

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

      2. mul-1-neg 50.2%

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

      3. unsub-neg 50.2%

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

      4. associate-/l* 48.8%

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

   8. Simplified 48.8%

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

   9. Taylor expanded in a around inf 39.3%

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

       1. associate-*r* 37.6%

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

       2. *-commutative 37.6%

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

       3. associate-*l* 42.5%

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

   11. Simplified 42.5%

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

   if -1.3000000000000001e51 < j < 1.80000000000000005e-58

   1. Initial program 73.3%

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

   3. Taylor expanded in a around -inf 69.2%

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

   5. Simplified 69.9%

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

   6. Taylor expanded in b around -inf 45.0%

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

      1. *-commutative 45.0%

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

      2. *-commutative 45.0%

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

   8. Simplified 45.0%

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

   9. Taylor expanded in t around inf 25.9%

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

4. Final simplification 34.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.3 \cdot 10^{+51} \lor \neg \left(j \leq 1.8 \cdot 10^{-58}\right):\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 29.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -6.3 \cdot 10^{-55} \lor \neg \left(c \leq 3.1 \cdot 10^{-89}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -6.3e-55) (not (<= c 3.1e-89))) (* 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 ((c <= -6.3e-55) || !(c <= 3.1e-89)) {
		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 ((c <= (-6.3d-55)) .or. (.not. (c <= 3.1d-89))) 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 ((c <= -6.3e-55) || !(c <= 3.1e-89)) {
		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 (c <= -6.3e-55) or not (c <= 3.1e-89):
		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 ((c <= -6.3e-55) || !(c <= 3.1e-89))
		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 ((c <= -6.3e-55) || ~((c <= 3.1e-89)))
		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[c, -6.3e-55], N[Not[LessEqual[c, 3.1e-89]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -6.2999999999999997e-55 or 3.09999999999999996e-89 < c

   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 a around inf 47.7%

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

      1. +-commutative 47.7%

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

      2. mul-1-neg 47.7%

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

      3. unsub-neg 47.7%

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

   5. Simplified 47.7%

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

   6. Taylor expanded in c around inf 38.1%

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

   if -6.2999999999999997e-55 < c < 3.09999999999999996e-89

   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 -inf 66.7%

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

   5. Simplified 67.8%

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

   6. Taylor expanded in b around -inf 33.1%

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

      1. *-commutative 33.1%

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

      2. *-commutative 33.1%

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

   8. Simplified 33.1%

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

   9. Taylor expanded in t around inf 25.6%

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

4. Final simplification 33.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.3 \cdot 10^{-55} \lor \neg \left(c \leq 3.1 \cdot 10^{-89}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 22.2% 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 74.4%

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

3. Taylor expanded in a around inf 44.7%

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

   1. +-commutative 44.7%

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

   2. mul-1-neg 44.7%

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

   3. unsub-neg 44.7%

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

5. Simplified 44.7%

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

6. Taylor expanded in c around inf 25.5%

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

Developer Target 1: 59.5% 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 2024152 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

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

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