Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.5% → 79.7%

Time: 35.3s

Alternatives: 24

Speedup: 0.5×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 79.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = t_1 + (b * ((a * i) - (z * c)));
	double tmp;
	if ((t_2 + (j * ((t * c) - (y * i)))) <= ((double) INFINITY)) {
		tmp = t_2 + ((j * (t * c)) - (j * (y * i)));
	} else {
		tmp = t_1;
	}
	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));
	double t_2 = t_1 + (b * ((a * i) - (z * c)));
	double tmp;
	if ((t_2 + (j * ((t * c) - (y * i)))) <= Double.POSITIVE_INFINITY) {
		tmp = t_2 + ((j * (t * c)) - (j * (y * i)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = t_1 + (b * ((a * i) - (z * c)))
	tmp = 0
	if (t_2 + (j * ((t * c) - (y * i)))) <= math.inf:
		tmp = t_2 + ((j * (t * c)) - (j * (y * i)))
	else:
		tmp = t_1
	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(t_1 + Float64(b * Float64(Float64(a * i) - Float64(z * c))))
	tmp = 0.0
	if (Float64(t_2 + Float64(j * Float64(Float64(t * c) - Float64(y * i)))) <= Inf)
		tmp = Float64(t_2 + Float64(Float64(j * Float64(t * c)) - Float64(j * Float64(y * i))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 91.1%

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

      1. *-commutative 91.1%

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

      2. *-commutative 91.1%

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

      3. sub-neg 91.1%

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

      4. distribute-rgt-in 91.1%

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

      5. distribute-rgt-neg-in 91.1%

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

   4. Applied egg-rr 91.1%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x around inf 48.0%

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

      1. *-commutative 48.0%

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

   5. Simplified 48.0%

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

4. Final simplification 81.9%

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

Alternative 2: 81.0% accurate, 0.5× speedup

Math

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

FPCore

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

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = (t_1 + (b * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)))
	tmp = 0
	if t_2 <= math.inf:
		tmp = t_2
	else:
		tmp = t_1
	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(Float64(t_1 + Float64(b * Float64(Float64(a * i) - Float64(z * c)))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))))
	tmp = 0.0
	if (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = t_1;
	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 = (t_1 + (b * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)));
	tmp = 0.0;
	if (t_2 <= Inf)
		tmp = t_2;
	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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t$95$1 + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, Infinity], t$95$2, t$95$1]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 91.1%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x around inf 48.0%

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

      1. *-commutative 48.0%

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

   5. Simplified 48.0%

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

4. Final simplification 81.9%

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

Alternative 3: 56.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := c \cdot \left(t \cdot j\right) + t\_1\\ t_3 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -1 \cdot 10^{+108}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-52}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-95}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-14}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) + t\_1\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+66}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+80}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+149}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c))))
        (t_2 (+ (* c (* t j)) t_1))
        (t_3 (* t (- (* c j) (* x a)))))
   (if (<= t -1e+108)
     t_3
     (if (<= t -1.65e-52)
       (* x (- (* y z) (* t a)))
       (if (<= t -6.5e-95)
         t_2
         (if (<= t 1.35e-14)
           (+ (* y (* x z)) t_1)
           (if (<= t 8e+66)
             t_3
             (if (<= t 5.8e+80)
               t_2
               (if (<= t 2.2e+149) (* i (- (* a b) (* y j))) t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = (c * (t * j)) + t_1;
	double t_3 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -1e+108) {
		tmp = t_3;
	} else if (t <= -1.65e-52) {
		tmp = x * ((y * z) - (t * a));
	} else if (t <= -6.5e-95) {
		tmp = t_2;
	} else if (t <= 1.35e-14) {
		tmp = (y * (x * z)) + t_1;
	} else if (t <= 8e+66) {
		tmp = t_3;
	} else if (t <= 5.8e+80) {
		tmp = t_2;
	} else if (t <= 2.2e+149) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = (c * (t * j)) + t_1
    t_3 = t * ((c * j) - (x * a))
    if (t <= (-1d+108)) then
        tmp = t_3
    else if (t <= (-1.65d-52)) then
        tmp = x * ((y * z) - (t * a))
    else if (t <= (-6.5d-95)) then
        tmp = t_2
    else if (t <= 1.35d-14) then
        tmp = (y * (x * z)) + t_1
    else if (t <= 8d+66) then
        tmp = t_3
    else if (t <= 5.8d+80) then
        tmp = t_2
    else if (t <= 2.2d+149) then
        tmp = i * ((a * b) - (y * j))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = (c * (t * j)) + t_1;
	double t_3 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -1e+108) {
		tmp = t_3;
	} else if (t <= -1.65e-52) {
		tmp = x * ((y * z) - (t * a));
	} else if (t <= -6.5e-95) {
		tmp = t_2;
	} else if (t <= 1.35e-14) {
		tmp = (y * (x * z)) + t_1;
	} else if (t <= 8e+66) {
		tmp = t_3;
	} else if (t <= 5.8e+80) {
		tmp = t_2;
	} else if (t <= 2.2e+149) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = (c * (t * j)) + t_1
	t_3 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -1e+108:
		tmp = t_3
	elif t <= -1.65e-52:
		tmp = x * ((y * z) - (t * a))
	elif t <= -6.5e-95:
		tmp = t_2
	elif t <= 1.35e-14:
		tmp = (y * (x * z)) + t_1
	elif t <= 8e+66:
		tmp = t_3
	elif t <= 5.8e+80:
		tmp = t_2
	elif t <= 2.2e+149:
		tmp = i * ((a * b) - (y * j))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(Float64(c * Float64(t * j)) + t_1)
	t_3 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -1e+108)
		tmp = t_3;
	elseif (t <= -1.65e-52)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (t <= -6.5e-95)
		tmp = t_2;
	elseif (t <= 1.35e-14)
		tmp = Float64(Float64(y * Float64(x * z)) + t_1);
	elseif (t <= 8e+66)
		tmp = t_3;
	elseif (t <= 5.8e+80)
		tmp = t_2;
	elseif (t <= 2.2e+149)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = (c * (t * j)) + t_1;
	t_3 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -1e+108)
		tmp = t_3;
	elseif (t <= -1.65e-52)
		tmp = x * ((y * z) - (t * a));
	elseif (t <= -6.5e-95)
		tmp = t_2;
	elseif (t <= 1.35e-14)
		tmp = (y * (x * z)) + t_1;
	elseif (t <= 8e+66)
		tmp = t_3;
	elseif (t <= 5.8e+80)
		tmp = t_2;
	elseif (t <= 2.2e+149)
		tmp = i * ((a * b) - (y * j));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1e+108], t$95$3, If[LessEqual[t, -1.65e-52], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6.5e-95], t$95$2, If[LessEqual[t, 1.35e-14], N[(N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t, 8e+66], t$95$3, If[LessEqual[t, 5.8e+80], t$95$2, If[LessEqual[t, 2.2e+149], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1e108 or 1.3499999999999999e-14 < t < 7.99999999999999956e66 or 2.2e149 < t

   1. Initial program 65.0%

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

   3. Taylor expanded in t around inf 67.0%

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

   if -1e108 < t < -1.64999999999999998e-52

   1. Initial program 61.0%

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

   3. Taylor expanded in x around inf 58.0%

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

      1. *-commutative 58.0%

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

   5. Simplified 58.0%

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

   if -1.64999999999999998e-52 < t < -6.49999999999999985e-95 or 7.99999999999999956e66 < t < 5.79999999999999971e80

   1. Initial program 85.6%

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

   3. Taylor expanded in x around 0 78.6%

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

      1. *-commutative 78.6%

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

   5. Simplified 78.6%

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

   6. Taylor expanded in y around 0 85.7%

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

      1. *-commutative 85.7%

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

      2. *-commutative 85.7%

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

      3. *-commutative 85.7%

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

      4. *-commutative 85.7%

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

      5. sub-neg 85.7%

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

      6. +-commutative 85.7%

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

      7. +-commutative 85.7%

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

      8. sub-neg 85.7%

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

      9. *-commutative 85.7%

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

   8. Simplified 85.7%

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

   if -6.49999999999999985e-95 < t < 1.3499999999999999e-14

   1. Initial program 79.8%

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

   3. Taylor expanded in j around 0 72.4%

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

      1. *-commutative 72.4%

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

      2. *-commutative 72.4%

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

   5. Simplified 72.4%

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

   6. Taylor expanded in y around inf 70.6%

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

      1. *-commutative 32.6%

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

      2. associate-*l* 36.1%

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

   8. Simplified 71.4%

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

   if 5.79999999999999971e80 < t < 2.2e149

   1. Initial program 60.3%

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

   3. Taylor expanded in i around inf 60.6%

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

      1. distribute-lft-out-- 60.6%

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

      2. *-commutative 60.6%

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

   5. Simplified 60.6%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+108}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-52}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-95}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-14}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+66}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+80}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+149}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.22 \cdot 10^{+55}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -5 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{-240}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{-200}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{-36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.55 \cdot 10^{+140} \lor \neg \left(b \leq 7.2 \cdot 10^{+174}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (* b (- (* a i) (* z c)))))
   (if (<= b -1.22e+55)
     t_2
     (if (<= b -5e+27)
       t_1
       (if (<= b 2.15e-240)
         (* y (- (* x z) (* i j)))
         (if (<= b 3.6e-200)
           (* c (- (* t j) (* z b)))
           (if (<= b 7.8e-36)
             t_1
             (if (or (<= b 3.55e+140) (not (<= b 7.2e+174)))
               t_2
               (* j (- (* t c) (* y i)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.22e+55) {
		tmp = t_2;
	} else if (b <= -5e+27) {
		tmp = t_1;
	} else if (b <= 2.15e-240) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 3.6e-200) {
		tmp = c * ((t * j) - (z * b));
	} else if (b <= 7.8e-36) {
		tmp = t_1;
	} else if ((b <= 3.55e+140) || !(b <= 7.2e+174)) {
		tmp = t_2;
	} else {
		tmp = j * ((t * c) - (y * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = b * ((a * i) - (z * c))
    if (b <= (-1.22d+55)) then
        tmp = t_2
    else if (b <= (-5d+27)) then
        tmp = t_1
    else if (b <= 2.15d-240) then
        tmp = y * ((x * z) - (i * j))
    else if (b <= 3.6d-200) then
        tmp = c * ((t * j) - (z * b))
    else if (b <= 7.8d-36) then
        tmp = t_1
    else if ((b <= 3.55d+140) .or. (.not. (b <= 7.2d+174))) then
        tmp = t_2
    else
        tmp = j * ((t * c) - (y * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.22e+55) {
		tmp = t_2;
	} else if (b <= -5e+27) {
		tmp = t_1;
	} else if (b <= 2.15e-240) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 3.6e-200) {
		tmp = c * ((t * j) - (z * b));
	} else if (b <= 7.8e-36) {
		tmp = t_1;
	} else if ((b <= 3.55e+140) || !(b <= 7.2e+174)) {
		tmp = t_2;
	} else {
		tmp = j * ((t * c) - (y * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -1.22e+55:
		tmp = t_2
	elif b <= -5e+27:
		tmp = t_1
	elif b <= 2.15e-240:
		tmp = y * ((x * z) - (i * j))
	elif b <= 3.6e-200:
		tmp = c * ((t * j) - (z * b))
	elif b <= 7.8e-36:
		tmp = t_1
	elif (b <= 3.55e+140) or not (b <= 7.2e+174):
		tmp = t_2
	else:
		tmp = j * ((t * c) - (y * i))
	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(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -1.22e+55)
		tmp = t_2;
	elseif (b <= -5e+27)
		tmp = t_1;
	elseif (b <= 2.15e-240)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (b <= 3.6e-200)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (b <= 7.8e-36)
		tmp = t_1;
	elseif ((b <= 3.55e+140) || !(b <= 7.2e+174))
		tmp = t_2;
	else
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -1.22e+55)
		tmp = t_2;
	elseif (b <= -5e+27)
		tmp = t_1;
	elseif (b <= 2.15e-240)
		tmp = y * ((x * z) - (i * j));
	elseif (b <= 3.6e-200)
		tmp = c * ((t * j) - (z * b));
	elseif (b <= 7.8e-36)
		tmp = t_1;
	elseif ((b <= 3.55e+140) || ~((b <= 7.2e+174)))
		tmp = t_2;
	else
		tmp = j * ((t * c) - (y * i));
	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[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.22e+55], t$95$2, If[LessEqual[b, -5e+27], t$95$1, If[LessEqual[b, 2.15e-240], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.6e-200], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.8e-36], t$95$1, If[Or[LessEqual[b, 3.55e+140], N[Not[LessEqual[b, 7.2e+174]], $MachinePrecision]], t$95$2, N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.22e55 or 7.8000000000000001e-36 < b < 3.55000000000000014e140 or 7.2000000000000003e174 < b

   1. Initial program 76.0%

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

   3. Taylor expanded in b around inf 65.6%

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

      1. *-commutative 65.6%

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

   5. Simplified 65.6%

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

   if -1.22e55 < b < -4.99999999999999979e27 or 3.6000000000000002e-200 < b < 7.8000000000000001e-36

   1. Initial program 75.5%

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

   3. Taylor expanded in x around inf 56.5%

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

      1. *-commutative 56.5%

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

   5. Simplified 56.5%

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

   if -4.99999999999999979e27 < b < 2.15000000000000007e-240

   1. Initial program 68.9%

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

      1. *-commutative 68.9%

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

      2. *-commutative 68.9%

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

      3. sub-neg 68.9%

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

      4. distribute-rgt-in 68.9%

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

      5. distribute-rgt-neg-in 68.9%

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

   4. Applied egg-rr 68.9%

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

   5. Taylor expanded in y around inf 61.2%

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

      1. mul-1-neg 61.2%

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

      2. distribute-lft-neg-out 61.2%

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

      3. +-commutative 61.2%

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

      4. distribute-lft-neg-out 61.2%

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

      5. unsub-neg 61.2%

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

      6. *-commutative 61.2%

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

   7. Simplified 61.2%

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

   if 2.15000000000000007e-240 < b < 3.6000000000000002e-200

   1. Initial program 72.2%

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

   3. Taylor expanded in c around inf 85.9%

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

   if 3.55000000000000014e140 < b < 7.2000000000000003e174

   1. Initial program 33.8%

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

   3. Taylor expanded in j around inf 59.2%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.22 \cdot 10^{+55}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -5 \cdot 10^{+27}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{-240}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{-200}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{-36}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 3.55 \cdot 10^{+140} \lor \neg \left(b \leq 7.2 \cdot 10^{+174}\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 57.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{+121}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -7.4 \cdot 10^{+33}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-264}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-264}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+72}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* c (* t j)) (* b (- (* a i) (* z c)))))
        (t_2 (* y (- (* x z) (* i j)))))
   (if (<= y -6.5e+121)
     t_2
     (if (<= y -7.4e+33)
       (* a (- (* b i) (* x t)))
       (if (<= y -7e-264)
         t_1
         (if (<= y 3.8e-264)
           (* t (- (* c j) (* x a)))
           (if (<= y 1.1e+38)
             t_1
             (if (<= y 3.3e+68)
               (* x (- (* y z) (* t a)))
               (if (<= y 1.25e+72) (* a (* b i)) t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (c * (t * j)) + (b * ((a * i) - (z * c)));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -6.5e+121) {
		tmp = t_2;
	} else if (y <= -7.4e+33) {
		tmp = a * ((b * i) - (x * t));
	} else if (y <= -7e-264) {
		tmp = t_1;
	} else if (y <= 3.8e-264) {
		tmp = t * ((c * j) - (x * a));
	} else if (y <= 1.1e+38) {
		tmp = t_1;
	} else if (y <= 3.3e+68) {
		tmp = x * ((y * z) - (t * a));
	} else if (y <= 1.25e+72) {
		tmp = a * (b * i);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (c * (t * j)) + (b * ((a * i) - (z * c)))
    t_2 = y * ((x * z) - (i * j))
    if (y <= (-6.5d+121)) then
        tmp = t_2
    else if (y <= (-7.4d+33)) then
        tmp = a * ((b * i) - (x * t))
    else if (y <= (-7d-264)) then
        tmp = t_1
    else if (y <= 3.8d-264) then
        tmp = t * ((c * j) - (x * a))
    else if (y <= 1.1d+38) then
        tmp = t_1
    else if (y <= 3.3d+68) then
        tmp = x * ((y * z) - (t * a))
    else if (y <= 1.25d+72) then
        tmp = a * (b * i)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (c * (t * j)) + (b * ((a * i) - (z * c)));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -6.5e+121) {
		tmp = t_2;
	} else if (y <= -7.4e+33) {
		tmp = a * ((b * i) - (x * t));
	} else if (y <= -7e-264) {
		tmp = t_1;
	} else if (y <= 3.8e-264) {
		tmp = t * ((c * j) - (x * a));
	} else if (y <= 1.1e+38) {
		tmp = t_1;
	} else if (y <= 3.3e+68) {
		tmp = x * ((y * z) - (t * a));
	} else if (y <= 1.25e+72) {
		tmp = a * (b * i);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (c * (t * j)) + (b * ((a * i) - (z * c)))
	t_2 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -6.5e+121:
		tmp = t_2
	elif y <= -7.4e+33:
		tmp = a * ((b * i) - (x * t))
	elif y <= -7e-264:
		tmp = t_1
	elif y <= 3.8e-264:
		tmp = t * ((c * j) - (x * a))
	elif y <= 1.1e+38:
		tmp = t_1
	elif y <= 3.3e+68:
		tmp = x * ((y * z) - (t * a))
	elif y <= 1.25e+72:
		tmp = a * (b * i)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(c * Float64(t * j)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -6.5e+121)
		tmp = t_2;
	elseif (y <= -7.4e+33)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (y <= -7e-264)
		tmp = t_1;
	elseif (y <= 3.8e-264)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (y <= 1.1e+38)
		tmp = t_1;
	elseif (y <= 3.3e+68)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (y <= 1.25e+72)
		tmp = Float64(a * Float64(b * i));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (c * (t * j)) + (b * ((a * i) - (z * c)));
	t_2 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -6.5e+121)
		tmp = t_2;
	elseif (y <= -7.4e+33)
		tmp = a * ((b * i) - (x * t));
	elseif (y <= -7e-264)
		tmp = t_1;
	elseif (y <= 3.8e-264)
		tmp = t * ((c * j) - (x * a));
	elseif (y <= 1.1e+38)
		tmp = t_1;
	elseif (y <= 3.3e+68)
		tmp = x * ((y * z) - (t * a));
	elseif (y <= 1.25e+72)
		tmp = a * (b * i);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.5e+121], t$95$2, If[LessEqual[y, -7.4e+33], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7e-264], t$95$1, If[LessEqual[y, 3.8e-264], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.1e+38], t$95$1, If[LessEqual[y, 3.3e+68], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.25e+72], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -6.50000000000000019e121 or 1.24999999999999998e72 < y

   1. Initial program 58.4%

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

      1. *-commutative 58.4%

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

      2. *-commutative 58.4%

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

      3. sub-neg 58.4%

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

      4. distribute-rgt-in 58.4%

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

      5. distribute-rgt-neg-in 58.4%

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

   4. Applied egg-rr 58.4%

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

   5. Taylor expanded in y around inf 65.9%

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

      1. mul-1-neg 65.9%

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

      2. distribute-lft-neg-out 65.9%

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

      3. +-commutative 65.9%

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

      4. distribute-lft-neg-out 65.9%

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

      5. unsub-neg 65.9%

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

      6. *-commutative 65.9%

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

   7. Simplified 65.9%

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

   if -6.50000000000000019e121 < y < -7.3999999999999997e33

   1. Initial program 74.8%

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

   3. Taylor expanded in j around 0 84.8%

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

      1. *-commutative 84.8%

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

      2. *-commutative 84.8%

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

   5. Simplified 84.8%

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

   6. Taylor expanded in z around 0 70.2%

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

      1. sub-neg 70.2%

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

      2. mul-1-neg 70.2%

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

      3. remove-double-neg 70.2%

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

      4. +-commutative 70.2%

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

      5. mul-1-neg 70.2%

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

      6. *-commutative 70.2%

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

      7. distribute-rgt-neg-in 70.2%

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

      8. distribute-lft-neg-in 70.2%

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

      9. distribute-lft-in 75.2%

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

      10. cancel-sign-sub-inv 75.2%

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

   8. Simplified 75.2%

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

   if -7.3999999999999997e33 < y < -7.0000000000000001e-264 or 3.80000000000000013e-264 < y < 1.10000000000000003e38

   1. Initial program 81.4%

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

   3. Taylor expanded in x around 0 70.5%

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

      1. *-commutative 70.5%

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

   5. Simplified 70.5%

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

   6. Taylor expanded in y around 0 66.6%

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

      1. *-commutative 66.6%

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

      2. *-commutative 66.6%

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

      3. *-commutative 66.6%

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

      4. *-commutative 66.6%

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

      5. sub-neg 66.6%

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

      6. +-commutative 66.6%

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

      7. +-commutative 66.6%

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

      8. sub-neg 66.6%

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

      9. *-commutative 66.6%

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

   8. Simplified 66.6%

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

   if -7.0000000000000001e-264 < y < 3.80000000000000013e-264

   1. Initial program 82.4%

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

   3. Taylor expanded in t around inf 65.3%

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

   if 1.10000000000000003e38 < y < 3.3e68

   1. Initial program 45.3%

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

   3. Taylor expanded in x around inf 57.0%

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

      1. *-commutative 57.0%

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

   5. Simplified 57.0%

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

   if 3.3e68 < y < 1.24999999999999998e72

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf 100.0%

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

      1. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in i around inf 100.0%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+121}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -7.4 \cdot 10^{+33}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-264}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-264}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+38}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+72}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.72 \cdot 10^{+56}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 8.8 \cdot 10^{-241}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{-200}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 1.06 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{+140} \lor \neg \left(b \leq 7.2 \cdot 10^{+174}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (* b (- (* a i) (* z c)))))
   (if (<= b -1.72e+56)
     t_2
     (if (<= b 8.8e-241)
       t_1
       (if (<= b 3.6e-200)
         (* c (- (* t j) (* z b)))
         (if (<= b 1.06e-39)
           t_1
           (if (or (<= b 3.6e+140) (not (<= b 7.2e+174)))
             t_2
             (* j (- (* t c) (* y i))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.72e+56) {
		tmp = t_2;
	} else if (b <= 8.8e-241) {
		tmp = t_1;
	} else if (b <= 3.6e-200) {
		tmp = c * ((t * j) - (z * b));
	} else if (b <= 1.06e-39) {
		tmp = t_1;
	} else if ((b <= 3.6e+140) || !(b <= 7.2e+174)) {
		tmp = t_2;
	} else {
		tmp = j * ((t * c) - (y * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = b * ((a * i) - (z * c))
    if (b <= (-1.72d+56)) then
        tmp = t_2
    else if (b <= 8.8d-241) then
        tmp = t_1
    else if (b <= 3.6d-200) then
        tmp = c * ((t * j) - (z * b))
    else if (b <= 1.06d-39) then
        tmp = t_1
    else if ((b <= 3.6d+140) .or. (.not. (b <= 7.2d+174))) then
        tmp = t_2
    else
        tmp = j * ((t * c) - (y * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.72e+56) {
		tmp = t_2;
	} else if (b <= 8.8e-241) {
		tmp = t_1;
	} else if (b <= 3.6e-200) {
		tmp = c * ((t * j) - (z * b));
	} else if (b <= 1.06e-39) {
		tmp = t_1;
	} else if ((b <= 3.6e+140) || !(b <= 7.2e+174)) {
		tmp = t_2;
	} else {
		tmp = j * ((t * c) - (y * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -1.72e+56:
		tmp = t_2
	elif b <= 8.8e-241:
		tmp = t_1
	elif b <= 3.6e-200:
		tmp = c * ((t * j) - (z * b))
	elif b <= 1.06e-39:
		tmp = t_1
	elif (b <= 3.6e+140) or not (b <= 7.2e+174):
		tmp = t_2
	else:
		tmp = j * ((t * c) - (y * i))
	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(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -1.72e+56)
		tmp = t_2;
	elseif (b <= 8.8e-241)
		tmp = t_1;
	elseif (b <= 3.6e-200)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (b <= 1.06e-39)
		tmp = t_1;
	elseif ((b <= 3.6e+140) || !(b <= 7.2e+174))
		tmp = t_2;
	else
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -1.72e+56)
		tmp = t_2;
	elseif (b <= 8.8e-241)
		tmp = t_1;
	elseif (b <= 3.6e-200)
		tmp = c * ((t * j) - (z * b));
	elseif (b <= 1.06e-39)
		tmp = t_1;
	elseif ((b <= 3.6e+140) || ~((b <= 7.2e+174)))
		tmp = t_2;
	else
		tmp = j * ((t * c) - (y * i));
	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[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.72e+56], t$95$2, If[LessEqual[b, 8.8e-241], t$95$1, If[LessEqual[b, 3.6e-200], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.06e-39], t$95$1, If[Or[LessEqual[b, 3.6e+140], N[Not[LessEqual[b, 7.2e+174]], $MachinePrecision]], t$95$2, N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.72e56 or 1.06000000000000004e-39 < b < 3.6e140 or 7.2000000000000003e174 < b

   1. Initial program 76.0%

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

   3. Taylor expanded in b around inf 65.6%

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

      1. *-commutative 65.6%

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

   5. Simplified 65.6%

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

   if -1.72e56 < b < 8.7999999999999997e-241 or 3.6000000000000002e-200 < b < 1.06000000000000004e-39

   1. Initial program 71.2%

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

   3. Taylor expanded in x around inf 53.6%

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

      1. *-commutative 53.6%

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

   5. Simplified 53.6%

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

   if 8.7999999999999997e-241 < b < 3.6000000000000002e-200

   1. Initial program 72.2%

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

   3. Taylor expanded in c around inf 85.9%

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

   if 3.6e140 < b < 7.2000000000000003e174

   1. Initial program 33.8%

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

   3. Taylor expanded in j around inf 59.2%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.72 \cdot 10^{+56}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 8.8 \cdot 10^{-241}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{-200}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 1.06 \cdot 10^{-39}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{+140} \lor \neg \left(b \leq 7.2 \cdot 10^{+174}\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 36.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;i \leq -1.15 \cdot 10^{+187}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;i \leq -1.32 \cdot 10^{+67}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;i \leq -8.8 \cdot 10^{-185}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq 1.85 \cdot 10^{-289}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 3.4 \cdot 10^{-205}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;i \leq 1.9 \cdot 10^{-91}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* x y))) (t_2 (* a (- (* b i) (* x t)))))
   (if (<= i -1.15e+187)
     (* b (* a i))
     (if (<= i -1.32e+67)
       (* i (* y (- j)))
       (if (<= i -8.8e-185)
         t_2
         (if (<= i 1.85e-289)
           t_1
           (if (<= i 3.4e-205)
             (* (* z c) (- b))
             (if (<= i 1.9e-91) 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 = z * (x * y);
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (i <= -1.15e+187) {
		tmp = b * (a * i);
	} else if (i <= -1.32e+67) {
		tmp = i * (y * -j);
	} else if (i <= -8.8e-185) {
		tmp = t_2;
	} else if (i <= 1.85e-289) {
		tmp = t_1;
	} else if (i <= 3.4e-205) {
		tmp = (z * c) * -b;
	} else if (i <= 1.9e-91) {
		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 = z * (x * y)
    t_2 = a * ((b * i) - (x * t))
    if (i <= (-1.15d+187)) then
        tmp = b * (a * i)
    else if (i <= (-1.32d+67)) then
        tmp = i * (y * -j)
    else if (i <= (-8.8d-185)) then
        tmp = t_2
    else if (i <= 1.85d-289) then
        tmp = t_1
    else if (i <= 3.4d-205) then
        tmp = (z * c) * -b
    else if (i <= 1.9d-91) 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 = z * (x * y);
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (i <= -1.15e+187) {
		tmp = b * (a * i);
	} else if (i <= -1.32e+67) {
		tmp = i * (y * -j);
	} else if (i <= -8.8e-185) {
		tmp = t_2;
	} else if (i <= 1.85e-289) {
		tmp = t_1;
	} else if (i <= 3.4e-205) {
		tmp = (z * c) * -b;
	} else if (i <= 1.9e-91) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (x * y)
	t_2 = a * ((b * i) - (x * t))
	tmp = 0
	if i <= -1.15e+187:
		tmp = b * (a * i)
	elif i <= -1.32e+67:
		tmp = i * (y * -j)
	elif i <= -8.8e-185:
		tmp = t_2
	elif i <= 1.85e-289:
		tmp = t_1
	elif i <= 3.4e-205:
		tmp = (z * c) * -b
	elif i <= 1.9e-91:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(x * y))
	t_2 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (i <= -1.15e+187)
		tmp = Float64(b * Float64(a * i));
	elseif (i <= -1.32e+67)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (i <= -8.8e-185)
		tmp = t_2;
	elseif (i <= 1.85e-289)
		tmp = t_1;
	elseif (i <= 3.4e-205)
		tmp = Float64(Float64(z * c) * Float64(-b));
	elseif (i <= 1.9e-91)
		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 = z * (x * y);
	t_2 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (i <= -1.15e+187)
		tmp = b * (a * i);
	elseif (i <= -1.32e+67)
		tmp = i * (y * -j);
	elseif (i <= -8.8e-185)
		tmp = t_2;
	elseif (i <= 1.85e-289)
		tmp = t_1;
	elseif (i <= 3.4e-205)
		tmp = (z * c) * -b;
	elseif (i <= 1.9e-91)
		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[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.15e+187], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.32e+67], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -8.8e-185], t$95$2, If[LessEqual[i, 1.85e-289], t$95$1, If[LessEqual[i, 3.4e-205], N[(N[(z * c), $MachinePrecision] * (-b)), $MachinePrecision], If[LessEqual[i, 1.9e-91], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -1.15000000000000002e187

   1. Initial program 55.0%

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

   3. Taylor expanded in b around inf 55.6%

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

      1. *-commutative 55.6%

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

   5. Simplified 55.6%

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

   6. Taylor expanded in i around inf 56.0%

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

      1. *-commutative 56.0%

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

   8. Simplified 56.0%

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

   if -1.15000000000000002e187 < i < -1.3200000000000001e67

   1. Initial program 63.4%

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

   3. Taylor expanded in x around 0 55.4%

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

      1. *-commutative 55.4%

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

   5. Simplified 55.4%

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

   6. Taylor expanded in c around 0 46.9%

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

   7. Taylor expanded in j around inf 46.9%

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

      1. neg-mul-1 46.9%

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

      2. *-commutative 46.9%

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

      3. distribute-rgt-neg-in 46.9%

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

      4. *-commutative 46.9%

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

   9. Simplified 46.9%

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

   if -1.3200000000000001e67 < i < -8.8000000000000002e-185 or 1.89999999999999989e-91 < i

   1. Initial program 73.1%

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

   3. Taylor expanded in j around 0 61.7%

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

      1. *-commutative 61.7%

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

      2. *-commutative 61.7%

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

   5. Simplified 61.7%

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

   6. Taylor expanded in z around 0 44.3%

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

      1. sub-neg 44.3%

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

      2. mul-1-neg 44.3%

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

      3. remove-double-neg 44.3%

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

      4. +-commutative 44.3%

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

      5. mul-1-neg 44.3%

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

      6. *-commutative 44.3%

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

      7. distribute-rgt-neg-in 44.3%

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

      8. distribute-lft-neg-in 44.3%

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

      9. distribute-lft-in 46.6%

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

      10. cancel-sign-sub-inv 46.6%

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

   8. Simplified 46.6%

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

   if -8.8000000000000002e-185 < i < 1.84999999999999994e-289 or 3.4000000000000002e-205 < i < 1.89999999999999989e-91

   1. Initial program 78.6%

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

   3. Taylor expanded in j around 0 72.4%

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

      1. *-commutative 72.4%

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

      2. *-commutative 72.4%

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

   5. Simplified 72.4%

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

   6. Taylor expanded in y around inf 43.7%

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

      1. associate-*r* 48.5%

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

      2. *-commutative 48.5%

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

   8. Simplified 48.5%

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

   if 1.84999999999999994e-289 < i < 3.4000000000000002e-205

   1. Initial program 82.2%

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

   3. Taylor expanded in b around inf 55.6%

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

      1. *-commutative 55.6%

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

   5. Simplified 55.6%

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

   6. Taylor expanded in i around 0 55.7%

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

      1. mul-1-neg 55.7%

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

      2. distribute-lft-neg-out 55.7%

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

      3. *-commutative 55.7%

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

   8. Simplified 55.7%

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

4. Final simplification 48.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.15 \cdot 10^{+187}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;i \leq -1.32 \cdot 10^{+67}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;i \leq -8.8 \cdot 10^{-185}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;i \leq 1.85 \cdot 10^{-289}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 3.4 \cdot 10^{-205}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;i \leq 1.9 \cdot 10^{-91}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 46.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.5 \cdot 10^{+143}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -3.3 \cdot 10^{-85}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-293}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-254}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{-52}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))) (t_2 (* a (- (* b i) (* x t)))))
   (if (<= a -1.5e+143)
     t_2
     (if (<= a -3.3e-85)
       (* b (- (* a i) (* z c)))
       (if (<= a 1.9e-293)
         t_1
         (if (<= a 1.35e-275)
           (* x (* y z))
           (if (<= a 6.8e-254)
             t_1
             (if (<= a 1.08e-52) (* z (* x y)) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -1.5e+143) {
		tmp = t_2;
	} else if (a <= -3.3e-85) {
		tmp = b * ((a * i) - (z * c));
	} else if (a <= 1.9e-293) {
		tmp = t_1;
	} else if (a <= 1.35e-275) {
		tmp = x * (y * z);
	} else if (a <= 6.8e-254) {
		tmp = t_1;
	} else if (a <= 1.08e-52) {
		tmp = z * (x * y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * ((t * j) - (z * b))
    t_2 = a * ((b * i) - (x * t))
    if (a <= (-1.5d+143)) then
        tmp = t_2
    else if (a <= (-3.3d-85)) then
        tmp = b * ((a * i) - (z * c))
    else if (a <= 1.9d-293) then
        tmp = t_1
    else if (a <= 1.35d-275) then
        tmp = x * (y * z)
    else if (a <= 6.8d-254) then
        tmp = t_1
    else if (a <= 1.08d-52) then
        tmp = z * (x * y)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -1.5e+143) {
		tmp = t_2;
	} else if (a <= -3.3e-85) {
		tmp = b * ((a * i) - (z * c));
	} else if (a <= 1.9e-293) {
		tmp = t_1;
	} else if (a <= 1.35e-275) {
		tmp = x * (y * z);
	} else if (a <= 6.8e-254) {
		tmp = t_1;
	} else if (a <= 1.08e-52) {
		tmp = z * (x * y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	t_2 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -1.5e+143:
		tmp = t_2
	elif a <= -3.3e-85:
		tmp = b * ((a * i) - (z * c))
	elif a <= 1.9e-293:
		tmp = t_1
	elif a <= 1.35e-275:
		tmp = x * (y * z)
	elif a <= 6.8e-254:
		tmp = t_1
	elif a <= 1.08e-52:
		tmp = z * (x * y)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	t_2 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -1.5e+143)
		tmp = t_2;
	elseif (a <= -3.3e-85)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (a <= 1.9e-293)
		tmp = t_1;
	elseif (a <= 1.35e-275)
		tmp = Float64(x * Float64(y * z));
	elseif (a <= 6.8e-254)
		tmp = t_1;
	elseif (a <= 1.08e-52)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((t * j) - (z * b));
	t_2 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -1.5e+143)
		tmp = t_2;
	elseif (a <= -3.3e-85)
		tmp = b * ((a * i) - (z * c));
	elseif (a <= 1.9e-293)
		tmp = t_1;
	elseif (a <= 1.35e-275)
		tmp = x * (y * z);
	elseif (a <= 6.8e-254)
		tmp = t_1;
	elseif (a <= 1.08e-52)
		tmp = z * (x * y);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.5e+143], t$95$2, If[LessEqual[a, -3.3e-85], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.9e-293], t$95$1, If[LessEqual[a, 1.35e-275], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.8e-254], t$95$1, If[LessEqual[a, 1.08e-52], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.5e143 or 1.08e-52 < a

   1. Initial program 65.8%

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

   3. Taylor expanded in j around 0 67.0%

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

      1. *-commutative 67.0%

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

      2. *-commutative 67.0%

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

   5. Simplified 67.0%

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

   6. Taylor expanded in z around 0 55.1%

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

      1. sub-neg 55.1%

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

      2. mul-1-neg 55.1%

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

      3. remove-double-neg 55.1%

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

      4. +-commutative 55.1%

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

      5. mul-1-neg 55.1%

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

      6. *-commutative 55.1%

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

      7. distribute-rgt-neg-in 55.1%

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

      8. distribute-lft-neg-in 55.1%

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

      9. distribute-lft-in 57.8%

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

      10. cancel-sign-sub-inv 57.8%

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

   8. Simplified 57.8%

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

   if -1.5e143 < a < -3.29999999999999973e-85

   1. Initial program 75.8%

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

   3. Taylor expanded in b around inf 52.3%

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

      1. *-commutative 52.3%

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

   5. Simplified 52.3%

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

   if -3.29999999999999973e-85 < a < 1.9e-293 or 1.34999999999999997e-275 < a < 6.79999999999999986e-254

   1. Initial program 72.8%

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

   3. Taylor expanded in c around inf 56.8%

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

   if 1.9e-293 < a < 1.34999999999999997e-275

   1. Initial program 79.7%

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

   3. Taylor expanded in x around inf 99.7%

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

      1. *-commutative 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in y around inf 99.7%

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

   if 6.79999999999999986e-254 < a < 1.08e-52

   1. Initial program 81.5%

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

   3. Taylor expanded in j around 0 54.4%

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

      1. *-commutative 54.4%

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

      2. *-commutative 54.4%

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

   5. Simplified 54.4%

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

   6. Taylor expanded in y around inf 33.4%

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

      1. associate-*r* 42.4%

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

      2. *-commutative 42.4%

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

   8. Simplified 42.4%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{+143}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -3.3 \cdot 10^{-85}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-293}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-254}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{-52}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 48.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.6 \cdot 10^{+96}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -4.8 \cdot 10^{-138}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;j \leq -7.8 \cdot 10^{-231}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq -1.02 \cdot 10^{-293}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{-266}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))) (t_2 (* j (- (* t c) (* y i)))))
   (if (<= j -1.6e+96)
     t_2
     (if (<= j -4.8e-138)
       (* a (- (* b i) (* x t)))
       (if (<= j -7.8e-231)
         (* y (* x z))
         (if (<= j -1.02e-293)
           t_1
           (if (<= j 2.6e-266) (* z (* x y)) (if (<= j 2.3e+25) 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 * ((a * i) - (z * c));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -1.6e+96) {
		tmp = t_2;
	} else if (j <= -4.8e-138) {
		tmp = a * ((b * i) - (x * t));
	} else if (j <= -7.8e-231) {
		tmp = y * (x * z);
	} else if (j <= -1.02e-293) {
		tmp = t_1;
	} else if (j <= 2.6e-266) {
		tmp = z * (x * y);
	} else if (j <= 2.3e+25) {
		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 * ((a * i) - (z * c))
    t_2 = j * ((t * c) - (y * i))
    if (j <= (-1.6d+96)) then
        tmp = t_2
    else if (j <= (-4.8d-138)) then
        tmp = a * ((b * i) - (x * t))
    else if (j <= (-7.8d-231)) then
        tmp = y * (x * z)
    else if (j <= (-1.02d-293)) then
        tmp = t_1
    else if (j <= 2.6d-266) then
        tmp = z * (x * y)
    else if (j <= 2.3d+25) 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 * ((a * i) - (z * c));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -1.6e+96) {
		tmp = t_2;
	} else if (j <= -4.8e-138) {
		tmp = a * ((b * i) - (x * t));
	} else if (j <= -7.8e-231) {
		tmp = y * (x * z);
	} else if (j <= -1.02e-293) {
		tmp = t_1;
	} else if (j <= 2.6e-266) {
		tmp = z * (x * y);
	} else if (j <= 2.3e+25) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -1.6e+96:
		tmp = t_2
	elif j <= -4.8e-138:
		tmp = a * ((b * i) - (x * t))
	elif j <= -7.8e-231:
		tmp = y * (x * z)
	elif j <= -1.02e-293:
		tmp = t_1
	elif j <= 2.6e-266:
		tmp = z * (x * y)
	elif j <= 2.3e+25:
		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(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -1.6e+96)
		tmp = t_2;
	elseif (j <= -4.8e-138)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (j <= -7.8e-231)
		tmp = Float64(y * Float64(x * z));
	elseif (j <= -1.02e-293)
		tmp = t_1;
	elseif (j <= 2.6e-266)
		tmp = Float64(z * Float64(x * y));
	elseif (j <= 2.3e+25)
		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 * ((a * i) - (z * c));
	t_2 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -1.6e+96)
		tmp = t_2;
	elseif (j <= -4.8e-138)
		tmp = a * ((b * i) - (x * t));
	elseif (j <= -7.8e-231)
		tmp = y * (x * z);
	elseif (j <= -1.02e-293)
		tmp = t_1;
	elseif (j <= 2.6e-266)
		tmp = z * (x * y);
	elseif (j <= 2.3e+25)
		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[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.6e+96], t$95$2, If[LessEqual[j, -4.8e-138], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -7.8e-231], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.02e-293], t$95$1, If[LessEqual[j, 2.6e-266], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.3e+25], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -1.60000000000000003e96 or 2.2999999999999998e25 < j

   1. Initial program 60.7%

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

   3. Taylor expanded in j around inf 58.5%

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

   if -1.60000000000000003e96 < j < -4.7999999999999998e-138

   1. Initial program 77.8%

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

   3. Taylor expanded in j around 0 72.3%

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

      1. *-commutative 72.3%

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

      2. *-commutative 72.3%

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

   5. Simplified 72.3%

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

   6. Taylor expanded in z around 0 46.7%

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

      1. sub-neg 46.7%

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

      2. mul-1-neg 46.7%

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

      3. remove-double-neg 46.7%

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

      4. +-commutative 46.7%

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

      5. mul-1-neg 46.7%

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

      6. *-commutative 46.7%

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

      7. distribute-rgt-neg-in 46.7%

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

      8. distribute-lft-neg-in 46.7%

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

      9. distribute-lft-in 46.7%

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

      10. cancel-sign-sub-inv 46.7%

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

   8. Simplified 46.7%

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

   if -4.7999999999999998e-138 < j < -7.7999999999999995e-231

   1. Initial program 67.5%

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

   3. Taylor expanded in x around inf 51.7%

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

      1. *-commutative 51.7%

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

   5. Simplified 51.7%

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

   6. Taylor expanded in y around inf 51.6%

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

      1. *-commutative 51.6%

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

      2. associate-*l* 60.2%

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

   8. Simplified 60.2%

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

   if -7.7999999999999995e-231 < j < -1.02000000000000001e-293 or 2.6e-266 < j < 2.2999999999999998e25

   1. Initial program 83.1%

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

   3. Taylor expanded in b around inf 56.7%

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

      1. *-commutative 56.7%

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

   5. Simplified 56.7%

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

   if -1.02000000000000001e-293 < j < 2.6e-266

   1. Initial program 70.1%

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

   3. Taylor expanded in j around 0 85.3%

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

      1. *-commutative 85.3%

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

      2. *-commutative 85.3%

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

   5. Simplified 85.3%

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

   6. Taylor expanded in y around inf 48.9%

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

      1. associate-*r* 63.3%

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

      2. *-commutative 63.3%

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

   8. Simplified 63.3%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.6 \cdot 10^{+96}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -4.8 \cdot 10^{-138}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;j \leq -7.8 \cdot 10^{-231}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq -1.02 \cdot 10^{-293}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{-266}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{+25}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -1.58 \cdot 10^{+119}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{+33}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+34}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + t\_1\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+89}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))) (t_2 (* y (- (* x z) (* i j)))))
   (if (<= y -1.58e+119)
     t_2
     (if (<= y -8.2e+33)
       (* a (- (* b i) (* x t)))
       (if (<= y 4.6e+34)
         (+ (* j (- (* t c) (* y i))) t_1)
         (if (<= y 1.55e+89) (+ (* y (* x z)) 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 * ((a * i) - (z * c));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.58e+119) {
		tmp = t_2;
	} else if (y <= -8.2e+33) {
		tmp = a * ((b * i) - (x * t));
	} else if (y <= 4.6e+34) {
		tmp = (j * ((t * c) - (y * i))) + t_1;
	} else if (y <= 1.55e+89) {
		tmp = (y * (x * z)) + 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 * ((a * i) - (z * c))
    t_2 = y * ((x * z) - (i * j))
    if (y <= (-1.58d+119)) then
        tmp = t_2
    else if (y <= (-8.2d+33)) then
        tmp = a * ((b * i) - (x * t))
    else if (y <= 4.6d+34) then
        tmp = (j * ((t * c) - (y * i))) + t_1
    else if (y <= 1.55d+89) then
        tmp = (y * (x * z)) + 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 * ((a * i) - (z * c));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.58e+119) {
		tmp = t_2;
	} else if (y <= -8.2e+33) {
		tmp = a * ((b * i) - (x * t));
	} else if (y <= 4.6e+34) {
		tmp = (j * ((t * c) - (y * i))) + t_1;
	} else if (y <= 1.55e+89) {
		tmp = (y * (x * z)) + t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -1.58e+119:
		tmp = t_2
	elif y <= -8.2e+33:
		tmp = a * ((b * i) - (x * t))
	elif y <= 4.6e+34:
		tmp = (j * ((t * c) - (y * i))) + t_1
	elif y <= 1.55e+89:
		tmp = (y * (x * z)) + 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(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -1.58e+119)
		tmp = t_2;
	elseif (y <= -8.2e+33)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (y <= 4.6e+34)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + t_1);
	elseif (y <= 1.55e+89)
		tmp = Float64(Float64(y * Float64(x * z)) + 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 * ((a * i) - (z * c));
	t_2 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -1.58e+119)
		tmp = t_2;
	elseif (y <= -8.2e+33)
		tmp = a * ((b * i) - (x * t));
	elseif (y <= 4.6e+34)
		tmp = (j * ((t * c) - (y * i))) + t_1;
	elseif (y <= 1.55e+89)
		tmp = (y * (x * z)) + 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[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.58e+119], t$95$2, If[LessEqual[y, -8.2e+33], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.6e+34], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[y, 1.55e+89], N[(N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.5800000000000001e119 or 1.55e89 < y

   1. Initial program 58.1%

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

      1. *-commutative 58.1%

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

      2. *-commutative 58.1%

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

      3. sub-neg 58.1%

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

      4. distribute-rgt-in 58.1%

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

      5. distribute-rgt-neg-in 58.1%

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

   4. Applied egg-rr 58.1%

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

   5. Taylor expanded in y around inf 66.6%

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

      1. mul-1-neg 66.6%

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

      2. distribute-lft-neg-out 66.6%

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

      3. +-commutative 66.6%

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

      4. distribute-lft-neg-out 66.6%

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

      5. unsub-neg 66.6%

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

      6. *-commutative 66.6%

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

   7. Simplified 66.6%

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

   if -1.5800000000000001e119 < y < -8.1999999999999999e33

   1. Initial program 74.8%

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

   3. Taylor expanded in j around 0 84.8%

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

      1. *-commutative 84.8%

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

      2. *-commutative 84.8%

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

   5. Simplified 84.8%

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

   6. Taylor expanded in z around 0 70.2%

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

      1. sub-neg 70.2%

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

      2. mul-1-neg 70.2%

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

      3. remove-double-neg 70.2%

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

      4. +-commutative 70.2%

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

      5. mul-1-neg 70.2%

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

      6. *-commutative 70.2%

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

      7. distribute-rgt-neg-in 70.2%

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

      8. distribute-lft-neg-in 70.2%

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

      9. distribute-lft-in 75.2%

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

      10. cancel-sign-sub-inv 75.2%

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

   8. Simplified 75.2%

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

   if -8.1999999999999999e33 < y < 4.5999999999999996e34

   1. Initial program 81.4%

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

   3. Taylor expanded in x around 0 67.5%

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

      1. *-commutative 67.5%

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

   5. Simplified 67.5%

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

   if 4.5999999999999996e34 < y < 1.55e89

   1. Initial program 60.4%

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

   3. Taylor expanded in j around 0 67.2%

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

      1. *-commutative 67.2%

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

      2. *-commutative 67.2%

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

   5. Simplified 67.2%

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

   6. Taylor expanded in y around inf 60.5%

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

      1. *-commutative 30.2%

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

      2. associate-*l* 30.2%

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

   8. Simplified 66.7%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.58 \cdot 10^{+119}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{+33}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+34}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+89}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 41.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;x \leq -1.95 \cdot 10^{-69}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-149}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{-84}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-43}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+180}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= x -1.95e-69)
     (* a (- (* b i) (* x t)))
     (if (<= x -2.4e-149)
       (* j (* t c))
       (if (<= x 2.25e-84)
         t_1
         (if (<= x 6.2e-43)
           (* y (* x z))
           (if (<= x 5.8e+180) t_1 (* z (* x y)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (x <= -1.95e-69) {
		tmp = a * ((b * i) - (x * t));
	} else if (x <= -2.4e-149) {
		tmp = j * (t * c);
	} else if (x <= 2.25e-84) {
		tmp = t_1;
	} else if (x <= 6.2e-43) {
		tmp = y * (x * z);
	} else if (x <= 5.8e+180) {
		tmp = t_1;
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    if (x <= (-1.95d-69)) then
        tmp = a * ((b * i) - (x * t))
    else if (x <= (-2.4d-149)) then
        tmp = j * (t * c)
    else if (x <= 2.25d-84) then
        tmp = t_1
    else if (x <= 6.2d-43) then
        tmp = y * (x * z)
    else if (x <= 5.8d+180) then
        tmp = t_1
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (x <= -1.95e-69) {
		tmp = a * ((b * i) - (x * t));
	} else if (x <= -2.4e-149) {
		tmp = j * (t * c);
	} else if (x <= 2.25e-84) {
		tmp = t_1;
	} else if (x <= 6.2e-43) {
		tmp = y * (x * z);
	} else if (x <= 5.8e+180) {
		tmp = t_1;
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	tmp = 0
	if x <= -1.95e-69:
		tmp = a * ((b * i) - (x * t))
	elif x <= -2.4e-149:
		tmp = j * (t * c)
	elif x <= 2.25e-84:
		tmp = t_1
	elif x <= 6.2e-43:
		tmp = y * (x * z)
	elif x <= 5.8e+180:
		tmp = t_1
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (x <= -1.95e-69)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (x <= -2.4e-149)
		tmp = Float64(j * Float64(t * c));
	elseif (x <= 2.25e-84)
		tmp = t_1;
	elseif (x <= 6.2e-43)
		tmp = Float64(y * Float64(x * z));
	elseif (x <= 5.8e+180)
		tmp = t_1;
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (x <= -1.95e-69)
		tmp = a * ((b * i) - (x * t));
	elseif (x <= -2.4e-149)
		tmp = j * (t * c);
	elseif (x <= 2.25e-84)
		tmp = t_1;
	elseif (x <= 6.2e-43)
		tmp = y * (x * z);
	elseif (x <= 5.8e+180)
		tmp = t_1;
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.95e-69], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.4e-149], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.25e-84], t$95$1, If[LessEqual[x, 6.2e-43], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.8e+180], t$95$1, N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.9499999999999999e-69

   1. Initial program 71.5%

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

   3. Taylor expanded in j around 0 65.3%

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

      1. *-commutative 65.3%

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

      2. *-commutative 65.3%

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

   5. Simplified 65.3%

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

   6. Taylor expanded in z around 0 47.1%

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

      1. sub-neg 47.1%

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

      2. mul-1-neg 47.1%

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

      3. remove-double-neg 47.1%

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

      4. +-commutative 47.1%

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

      5. mul-1-neg 47.1%

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

      6. *-commutative 47.1%

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

      7. distribute-rgt-neg-in 47.1%

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

      8. distribute-lft-neg-in 47.1%

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

      9. distribute-lft-in 49.6%

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

      10. cancel-sign-sub-inv 49.6%

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

   8. Simplified 49.6%

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

   if -1.9499999999999999e-69 < x < -2.4000000000000001e-149

   1. Initial program 63.7%

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

   3. Taylor expanded in x around 0 58.2%

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

      1. *-commutative 58.2%

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

   5. Simplified 58.2%

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

   6. Taylor expanded in t around inf 48.4%

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

      1. associate-*r* 53.4%

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

      2. *-commutative 53.4%

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

      3. associate-*r* 53.4%

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

   8. Simplified 53.4%

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

   if -2.4000000000000001e-149 < x < 2.25000000000000008e-84 or 6.1999999999999999e-43 < x < 5.80000000000000015e180

   1. Initial program 74.9%

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

   3. Taylor expanded in b around inf 54.5%

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

      1. *-commutative 54.5%

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

   5. Simplified 54.5%

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

   if 2.25000000000000008e-84 < x < 6.1999999999999999e-43

   1. Initial program 75.4%

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

   3. Taylor expanded in x around inf 52.0%

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

      1. *-commutative 52.0%

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

   5. Simplified 52.0%

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

   6. Taylor expanded in y around inf 43.8%

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

      1. *-commutative 43.8%

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

      2. associate-*l* 51.9%

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

   8. Simplified 51.9%

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

   if 5.80000000000000015e180 < x

   1. Initial program 62.0%

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

   3. Taylor expanded in j around 0 65.7%

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

      1. *-commutative 65.7%

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

      2. *-commutative 65.7%

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

   5. Simplified 65.7%

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

   6. Taylor expanded in y around inf 36.2%

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

      1. associate-*r* 46.0%

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

      2. *-commutative 46.0%

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

   8. Simplified 46.0%

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

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{-69}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-149}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{-84}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-43}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+180}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -5.5 \cdot 10^{+55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{+28}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{-240}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-200}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{-37}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= b -5.5e+55)
     t_1
     (if (<= b -1.75e+28)
       (* t (- (* c j) (* x a)))
       (if (<= b 1.85e-240)
         (* y (- (* x z) (* i j)))
         (if (<= b 4.5e-200)
           (* c (- (* t j) (* z b)))
           (if (<= b 4.6e-37) (* x (- (* y z) (* t 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 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -5.5e+55) {
		tmp = t_1;
	} else if (b <= -1.75e+28) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= 1.85e-240) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 4.5e-200) {
		tmp = c * ((t * j) - (z * b));
	} else if (b <= 4.6e-37) {
		tmp = x * ((y * z) - (t * 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 = b * ((a * i) - (z * c))
    if (b <= (-5.5d+55)) then
        tmp = t_1
    else if (b <= (-1.75d+28)) then
        tmp = t * ((c * j) - (x * a))
    else if (b <= 1.85d-240) then
        tmp = y * ((x * z) - (i * j))
    else if (b <= 4.5d-200) then
        tmp = c * ((t * j) - (z * b))
    else if (b <= 4.6d-37) then
        tmp = x * ((y * z) - (t * 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 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -5.5e+55) {
		tmp = t_1;
	} else if (b <= -1.75e+28) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= 1.85e-240) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 4.5e-200) {
		tmp = c * ((t * j) - (z * b));
	} else if (b <= 4.6e-37) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -5.5e+55:
		tmp = t_1
	elif b <= -1.75e+28:
		tmp = t * ((c * j) - (x * a))
	elif b <= 1.85e-240:
		tmp = y * ((x * z) - (i * j))
	elif b <= 4.5e-200:
		tmp = c * ((t * j) - (z * b))
	elif b <= 4.6e-37:
		tmp = x * ((y * z) - (t * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -5.5e+55)
		tmp = t_1;
	elseif (b <= -1.75e+28)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (b <= 1.85e-240)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (b <= 4.5e-200)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (b <= 4.6e-37)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * 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 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -5.5e+55)
		tmp = t_1;
	elseif (b <= -1.75e+28)
		tmp = t * ((c * j) - (x * a));
	elseif (b <= 1.85e-240)
		tmp = y * ((x * z) - (i * j));
	elseif (b <= 4.5e-200)
		tmp = c * ((t * j) - (z * b));
	elseif (b <= 4.6e-37)
		tmp = x * ((y * z) - (t * 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[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.5e+55], t$95$1, If[LessEqual[b, -1.75e+28], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.85e-240], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.5e-200], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.6e-37], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -5.5000000000000004e55 or 4.5999999999999999e-37 < b

   1. Initial program 71.9%

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

   3. Taylor expanded in b around inf 61.1%

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

      1. *-commutative 61.1%

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

   5. Simplified 61.1%

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

   if -5.5000000000000004e55 < b < -1.75e28

   1. Initial program 74.8%

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

   3. Taylor expanded in t around inf 76.0%

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

   if -1.75e28 < b < 1.8500000000000001e-240

   1. Initial program 68.9%

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

      1. *-commutative 68.9%

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

      2. *-commutative 68.9%

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

      3. sub-neg 68.9%

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

      4. distribute-rgt-in 68.9%

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

      5. distribute-rgt-neg-in 68.9%

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

   4. Applied egg-rr 68.9%

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

   5. Taylor expanded in y around inf 61.2%

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

      1. mul-1-neg 61.2%

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

      2. distribute-lft-neg-out 61.2%

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

      3. +-commutative 61.2%

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

      4. distribute-lft-neg-out 61.2%

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

      5. unsub-neg 61.2%

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

      6. *-commutative 61.2%

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

   7. Simplified 61.2%

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

   if 1.8500000000000001e-240 < b < 4.5000000000000002e-200

   1. Initial program 72.2%

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

   3. Taylor expanded in c around inf 85.9%

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

   if 4.5000000000000002e-200 < b < 4.5999999999999999e-37

   1. Initial program 75.6%

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

   3. Taylor expanded in x around inf 52.3%

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

      1. *-commutative 52.3%

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

   5. Simplified 52.3%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{+55}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{+28}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{-240}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-200}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{-37}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 29.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t \cdot \left(-a\right)\right)\\ t_2 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq -1.02 \cdot 10^{+49}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-109}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-188}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-262}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-67}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* t (- a)))) (t_2 (* z (* x y))))
   (if (<= y -1.02e+49)
     t_2
     (if (<= y -3.2e-109)
       t_1
       (if (<= y -1.55e-188)
         (* (* z c) (- b))
         (if (<= y -1.02e-262) (* b (* a i)) (if (<= y 4.4e-67) 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 * (t * -a);
	double t_2 = z * (x * y);
	double tmp;
	if (y <= -1.02e+49) {
		tmp = t_2;
	} else if (y <= -3.2e-109) {
		tmp = t_1;
	} else if (y <= -1.55e-188) {
		tmp = (z * c) * -b;
	} else if (y <= -1.02e-262) {
		tmp = b * (a * i);
	} else if (y <= 4.4e-67) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (t * -a)
    t_2 = z * (x * y)
    if (y <= (-1.02d+49)) then
        tmp = t_2
    else if (y <= (-3.2d-109)) then
        tmp = t_1
    else if (y <= (-1.55d-188)) then
        tmp = (z * c) * -b
    else if (y <= (-1.02d-262)) then
        tmp = b * (a * i)
    else if (y <= 4.4d-67) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (t * -a);
	double t_2 = z * (x * y);
	double tmp;
	if (y <= -1.02e+49) {
		tmp = t_2;
	} else if (y <= -3.2e-109) {
		tmp = t_1;
	} else if (y <= -1.55e-188) {
		tmp = (z * c) * -b;
	} else if (y <= -1.02e-262) {
		tmp = b * (a * i);
	} else if (y <= 4.4e-67) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (t * -a)
	t_2 = z * (x * y)
	tmp = 0
	if y <= -1.02e+49:
		tmp = t_2
	elif y <= -3.2e-109:
		tmp = t_1
	elif y <= -1.55e-188:
		tmp = (z * c) * -b
	elif y <= -1.02e-262:
		tmp = b * (a * i)
	elif y <= 4.4e-67:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(t * Float64(-a)))
	t_2 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (y <= -1.02e+49)
		tmp = t_2;
	elseif (y <= -3.2e-109)
		tmp = t_1;
	elseif (y <= -1.55e-188)
		tmp = Float64(Float64(z * c) * Float64(-b));
	elseif (y <= -1.02e-262)
		tmp = Float64(b * Float64(a * i));
	elseif (y <= 4.4e-67)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (t * -a);
	t_2 = z * (x * y);
	tmp = 0.0;
	if (y <= -1.02e+49)
		tmp = t_2;
	elseif (y <= -3.2e-109)
		tmp = t_1;
	elseif (y <= -1.55e-188)
		tmp = (z * c) * -b;
	elseif (y <= -1.02e-262)
		tmp = b * (a * i);
	elseif (y <= 4.4e-67)
		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[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.02e+49], t$95$2, If[LessEqual[y, -3.2e-109], t$95$1, If[LessEqual[y, -1.55e-188], N[(N[(z * c), $MachinePrecision] * (-b)), $MachinePrecision], If[LessEqual[y, -1.02e-262], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.4e-67], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.02e49 or 4.4000000000000002e-67 < y

   1. Initial program 64.1%

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

   3. Taylor expanded in j around 0 54.7%

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

      1. *-commutative 54.7%

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

      2. *-commutative 54.7%

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

   5. Simplified 54.7%

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

   6. Taylor expanded in y around inf 37.4%

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

      1. associate-*r* 40.7%

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

      2. *-commutative 40.7%

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

   8. Simplified 40.7%

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

   if -1.02e49 < y < -3.2000000000000002e-109 or -1.01999999999999994e-262 < y < 4.4000000000000002e-67

   1. Initial program 80.5%

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

   3. Taylor expanded in x around inf 38.4%

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

      1. *-commutative 38.4%

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

   5. Simplified 38.4%

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

   6. Taylor expanded in y around 0 35.2%

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

      1. mul-1-neg 35.2%

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

      2. *-commutative 35.2%

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

      3. distribute-rgt-neg-in 35.2%

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

   8. Simplified 35.2%

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

   if -3.2000000000000002e-109 < y < -1.5500000000000001e-188

   1. Initial program 91.8%

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

   3. Taylor expanded in b around inf 67.8%

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

      1. *-commutative 67.8%

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

   5. Simplified 67.8%

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

   6. Taylor expanded in i around 0 51.5%

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

      1. mul-1-neg 51.5%

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

      2. distribute-lft-neg-out 51.5%

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

      3. *-commutative 51.5%

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

   8. Simplified 51.5%

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

   if -1.5500000000000001e-188 < y < -1.01999999999999994e-262

   1. Initial program 72.8%

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

   3. Taylor expanded in b around inf 65.3%

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

      1. *-commutative 65.3%

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

   5. Simplified 65.3%

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

   6. Taylor expanded in i around inf 59.2%

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

      1. *-commutative 59.2%

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

   8. Simplified 59.2%

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

4. Final simplification 40.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+49}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-109}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-188}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-262}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-67}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 29.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+112}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-22}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-154}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;y \leq -2.65 \cdot 10^{-263}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-66}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -2.8e+112)
   (* x (* y z))
   (if (<= y -8.2e-22)
     (* a (* t (- x)))
     (if (<= y -8e-154)
       (* (* z c) (- b))
       (if (<= y -2.65e-263)
         (* b (* a i))
         (if (<= y 6e-66) (* x (* t (- a))) (* z (* x y))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -2.8e+112) {
		tmp = x * (y * z);
	} else if (y <= -8.2e-22) {
		tmp = a * (t * -x);
	} else if (y <= -8e-154) {
		tmp = (z * c) * -b;
	} else if (y <= -2.65e-263) {
		tmp = b * (a * i);
	} else if (y <= 6e-66) {
		tmp = x * (t * -a);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-2.8d+112)) then
        tmp = x * (y * z)
    else if (y <= (-8.2d-22)) then
        tmp = a * (t * -x)
    else if (y <= (-8d-154)) then
        tmp = (z * c) * -b
    else if (y <= (-2.65d-263)) then
        tmp = b * (a * i)
    else if (y <= 6d-66) then
        tmp = x * (t * -a)
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -2.8e+112) {
		tmp = x * (y * z);
	} else if (y <= -8.2e-22) {
		tmp = a * (t * -x);
	} else if (y <= -8e-154) {
		tmp = (z * c) * -b;
	} else if (y <= -2.65e-263) {
		tmp = b * (a * i);
	} else if (y <= 6e-66) {
		tmp = x * (t * -a);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -2.8e+112:
		tmp = x * (y * z)
	elif y <= -8.2e-22:
		tmp = a * (t * -x)
	elif y <= -8e-154:
		tmp = (z * c) * -b
	elif y <= -2.65e-263:
		tmp = b * (a * i)
	elif y <= 6e-66:
		tmp = x * (t * -a)
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -2.8e+112)
		tmp = Float64(x * Float64(y * z));
	elseif (y <= -8.2e-22)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (y <= -8e-154)
		tmp = Float64(Float64(z * c) * Float64(-b));
	elseif (y <= -2.65e-263)
		tmp = Float64(b * Float64(a * i));
	elseif (y <= 6e-66)
		tmp = Float64(x * Float64(t * Float64(-a)));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -2.8e+112)
		tmp = x * (y * z);
	elseif (y <= -8.2e-22)
		tmp = a * (t * -x);
	elseif (y <= -8e-154)
		tmp = (z * c) * -b;
	elseif (y <= -2.65e-263)
		tmp = b * (a * i);
	elseif (y <= 6e-66)
		tmp = x * (t * -a);
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -2.8e+112], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8.2e-22], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8e-154], N[(N[(z * c), $MachinePrecision] * (-b)), $MachinePrecision], If[LessEqual[y, -2.65e-263], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e-66], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -2.8000000000000001e112

   1. Initial program 58.8%

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

   3. Taylor expanded in x around inf 57.4%

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

      1. *-commutative 57.4%

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

   5. Simplified 57.4%

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

   6. Taylor expanded in y around inf 55.0%

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

   if -2.8000000000000001e112 < y < -8.1999999999999999e-22

   1. Initial program 78.3%

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

   3. Taylor expanded in a around inf 68.6%

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

      1. distribute-lft-out-- 68.6%

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

      2. *-commutative 68.6%

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

   5. Simplified 68.6%

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

   6. Taylor expanded in t around inf 44.2%

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

      1. associate-*r* 44.2%

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

      2. neg-mul-1 44.2%

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

   8. Simplified 44.2%

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

   if -8.1999999999999999e-22 < y < -7.9999999999999998e-154

   1. Initial program 87.8%

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

   3. Taylor expanded in b around inf 63.1%

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

      1. *-commutative 63.1%

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

   5. Simplified 63.1%

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

   6. Taylor expanded in i around 0 45.0%

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

      1. mul-1-neg 45.0%

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

      2. distribute-lft-neg-out 45.0%

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

      3. *-commutative 45.0%

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

   8. Simplified 45.0%

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

   if -7.9999999999999998e-154 < y < -2.6499999999999999e-263

   1. Initial program 78.8%

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

   3. Taylor expanded in b around inf 64.6%

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

      1. *-commutative 64.6%

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

   5. Simplified 64.6%

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

   6. Taylor expanded in i around inf 55.3%

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

      1. *-commutative 55.3%

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

   8. Simplified 55.3%

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

   if -2.6499999999999999e-263 < y < 6.0000000000000004e-66

   1. Initial program 79.8%

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

   3. Taylor expanded in x around inf 37.6%

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

      1. *-commutative 37.6%

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

   5. Simplified 37.6%

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

   6. Taylor expanded in y around 0 34.6%

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

      1. mul-1-neg 34.6%

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

      2. *-commutative 34.6%

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

      3. distribute-rgt-neg-in 34.6%

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

   8. Simplified 34.6%

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

   if 6.0000000000000004e-66 < y

   1. Initial program 64.4%

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

   3. Taylor expanded in j around 0 50.9%

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

      1. *-commutative 50.9%

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

      2. *-commutative 50.9%

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

   5. Simplified 50.9%

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

   6. Taylor expanded in y around inf 29.9%

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

      1. associate-*r* 34.3%

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

      2. *-commutative 34.3%

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

   8. Simplified 34.3%

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

4. Final simplification 41.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+112}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-22}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-154}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;y \leq -2.65 \cdot 10^{-263}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-66}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 68.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;b \leq -1.06 \cdot 10^{-82} \lor \neg \left(b \leq 5 \cdot 10^{-19}\right):\\ \;\;\;\;t\_1 + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t\_1 + c \cdot \left(t \cdot j\right)\right) - i \cdot \left(y \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (or (<= b -1.06e-82) (not (<= b 5e-19)))
     (+ t_1 (* b (- (* a i) (* z c))))
     (- (+ t_1 (* c (* t j))) (* i (* y j))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if ((b <= -1.06e-82) || !(b <= 5e-19)) {
		tmp = t_1 + (b * ((a * i) - (z * c)));
	} else {
		tmp = (t_1 + (c * (t * j))) - (i * (y * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if ((b <= (-1.06d-82)) .or. (.not. (b <= 5d-19))) then
        tmp = t_1 + (b * ((a * i) - (z * c)))
    else
        tmp = (t_1 + (c * (t * j))) - (i * (y * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if ((b <= -1.06e-82) || !(b <= 5e-19)) {
		tmp = t_1 + (b * ((a * i) - (z * c)));
	} else {
		tmp = (t_1 + (c * (t * j))) - (i * (y * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if (b <= -1.06e-82) or not (b <= 5e-19):
		tmp = t_1 + (b * ((a * i) - (z * c)))
	else:
		tmp = (t_1 + (c * (t * j))) - (i * (y * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if ((b <= -1.06e-82) || !(b <= 5e-19))
		tmp = Float64(t_1 + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	else
		tmp = Float64(Float64(t_1 + Float64(c * Float64(t * j))) - Float64(i * Float64(y * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if ((b <= -1.06e-82) || ~((b <= 5e-19)))
		tmp = t_1 + (b * ((a * i) - (z * c)));
	else
		tmp = (t_1 + (c * (t * j))) - (i * (y * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[b, -1.06e-82], N[Not[LessEqual[b, 5e-19]], $MachinePrecision]], N[(t$95$1 + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 + N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.06e-82 or 5.0000000000000004e-19 < b

   1. Initial program 71.7%

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

   3. Taylor expanded in j around 0 71.4%

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

      1. *-commutative 71.4%

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

      2. *-commutative 71.4%

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

   5. Simplified 71.4%

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

   if -1.06e-82 < b < 5.0000000000000004e-19

   1. Initial program 71.3%

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

      1. *-commutative 71.3%

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

      2. *-commutative 71.3%

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

      3. sub-neg 71.3%

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

      4. distribute-rgt-in 71.3%

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

      5. distribute-rgt-neg-in 71.3%

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

   4. Applied egg-rr 71.3%

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

   5. Taylor expanded in b around 0 78.4%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + \left(c \cdot \left(j \cdot t\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.06 \cdot 10^{-82} \lor \neg \left(b \leq 5 \cdot 10^{-19}\right):\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + c \cdot \left(t \cdot j\right)\right) - i \cdot \left(y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 68.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;b \leq -6.6 \cdot 10^{-83}:\\ \;\;\;\;t\_3 + t\_2\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-48}:\\ \;\;\;\;\left(t\_3 + t\_1\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t\_1 - a \cdot \left(x \cdot t\right)\right) + t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j)))
        (t_2 (* b (- (* a i) (* z c))))
        (t_3 (* x (- (* y z) (* t a)))))
   (if (<= b -6.6e-83)
     (+ t_3 t_2)
     (if (<= b 2e-48)
       (- (+ t_3 t_1) (* i (* y j)))
       (+ (- t_1 (* a (* x t))) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = x * ((y * z) - (t * a));
	double tmp;
	if (b <= -6.6e-83) {
		tmp = t_3 + t_2;
	} else if (b <= 2e-48) {
		tmp = (t_3 + t_1) - (i * (y * j));
	} else {
		tmp = (t_1 - (a * (x * t))) + t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = c * (t * j)
    t_2 = b * ((a * i) - (z * c))
    t_3 = x * ((y * z) - (t * a))
    if (b <= (-6.6d-83)) then
        tmp = t_3 + t_2
    else if (b <= 2d-48) then
        tmp = (t_3 + t_1) - (i * (y * j))
    else
        tmp = (t_1 - (a * (x * t))) + t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = x * ((y * z) - (t * a));
	double tmp;
	if (b <= -6.6e-83) {
		tmp = t_3 + t_2;
	} else if (b <= 2e-48) {
		tmp = (t_3 + t_1) - (i * (y * j));
	} else {
		tmp = (t_1 - (a * (x * t))) + t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (t * j)
	t_2 = b * ((a * i) - (z * c))
	t_3 = x * ((y * z) - (t * a))
	tmp = 0
	if b <= -6.6e-83:
		tmp = t_3 + t_2
	elif b <= 2e-48:
		tmp = (t_3 + t_1) - (i * (y * j))
	else:
		tmp = (t_1 - (a * (x * t))) + t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(t * j))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_3 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (b <= -6.6e-83)
		tmp = Float64(t_3 + t_2);
	elseif (b <= 2e-48)
		tmp = Float64(Float64(t_3 + t_1) - Float64(i * Float64(y * j)));
	else
		tmp = Float64(Float64(t_1 - Float64(a * Float64(x * t))) + t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (t * j);
	t_2 = b * ((a * i) - (z * c));
	t_3 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (b <= -6.6e-83)
		tmp = t_3 + t_2;
	elseif (b <= 2e-48)
		tmp = (t_3 + t_1) - (i * (y * j));
	else
		tmp = (t_1 - (a * (x * t))) + t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.6e-83], N[(t$95$3 + t$95$2), $MachinePrecision], If[LessEqual[b, 2e-48], N[(N[(t$95$3 + t$95$1), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.5999999999999999e-83

   1. Initial program 73.2%

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

   3. Taylor expanded in j around 0 74.8%

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

      1. *-commutative 74.8%

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

      2. *-commutative 74.8%

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

   5. Simplified 74.8%

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

   if -6.5999999999999999e-83 < b < 1.9999999999999999e-48

   1. Initial program 70.9%

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

      1. *-commutative 70.9%

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

      2. *-commutative 70.9%

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

      3. sub-neg 70.9%

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

      4. distribute-rgt-in 70.9%

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

      5. distribute-rgt-neg-in 70.9%

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

   4. Applied egg-rr 70.9%

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

   5. Taylor expanded in b around 0 78.3%

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

   if 1.9999999999999999e-48 < b

   1. Initial program 70.7%

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

   3. Taylor expanded in y around 0 70.7%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.6 \cdot 10^{-83}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-48}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + c \cdot \left(t \cdot j\right)\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot \left(t \cdot j\right) - a \cdot \left(x \cdot t\right)\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 62.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.7 \cdot 10^{-97} \lor \neg \left(b \leq 2.85 \cdot 10^{-141}\right):\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot \left(t \cdot j\right) + x \cdot \left(y \cdot z\right)\right) - i \cdot \left(y \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -4.7e-97) (not (<= b 2.85e-141)))
   (+ (* x (- (* y z) (* t a))) (* b (- (* a i) (* z c))))
   (- (+ (* c (* t j)) (* x (* y z))) (* i (* y j)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -4.7e-97) || !(b <= 2.85e-141)) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	} else {
		tmp = ((c * (t * j)) + (x * (y * z))) - (i * (y * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-4.7d-97)) .or. (.not. (b <= 2.85d-141))) then
        tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))
    else
        tmp = ((c * (t * j)) + (x * (y * z))) - (i * (y * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -4.7e-97) || !(b <= 2.85e-141)) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	} else {
		tmp = ((c * (t * j)) + (x * (y * z))) - (i * (y * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -4.7e-97) or not (b <= 2.85e-141):
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))
	else:
		tmp = ((c * (t * j)) + (x * (y * z))) - (i * (y * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -4.7e-97) || !(b <= 2.85e-141))
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	else
		tmp = Float64(Float64(Float64(c * Float64(t * j)) + Float64(x * Float64(y * z))) - Float64(i * Float64(y * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -4.7e-97) || ~((b <= 2.85e-141)))
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	else
		tmp = ((c * (t * j)) + (x * (y * z))) - (i * (y * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -4.7e-97], N[Not[LessEqual[b, 2.85e-141]], $MachinePrecision]], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.7000000000000002e-97 or 2.84999999999999975e-141 < b

   1. Initial program 72.2%

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

   3. Taylor expanded in j around 0 69.9%

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

      1. *-commutative 69.9%

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

      2. *-commutative 69.9%

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

   5. Simplified 69.9%

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

   if -4.7000000000000002e-97 < b < 2.84999999999999975e-141

   1. Initial program 70.0%

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

      1. *-commutative 70.0%

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

      2. *-commutative 70.0%

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

      3. sub-neg 70.0%

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

      4. distribute-rgt-in 70.0%

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

      5. distribute-rgt-neg-in 70.0%

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

   4. Applied egg-rr 70.0%

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

   5. Taylor expanded in b around 0 81.0%

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

   6. Taylor expanded in y around inf 71.1%

      \[\leadsto -1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + \left(c \cdot \left(j \cdot t\right) + \color{blue}{x \cdot \left(y \cdot z\right)}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.7 \cdot 10^{-97} \lor \neg \left(b \leq 2.85 \cdot 10^{-141}\right):\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot \left(t \cdot j\right) + x \cdot \left(y \cdot z\right)\right) - i \cdot \left(y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 28.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i\right)\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{+76}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-299}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-147}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-66}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* a i))))
   (if (<= y -2.4e+76)
     (* x (* y z))
     (if (<= y -2e-299)
       t_1
       (if (<= y 9.5e-147)
         (* j (* t c))
         (if (<= y 7.2e-66) t_1 (* 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 t_1 = b * (a * i);
	double tmp;
	if (y <= -2.4e+76) {
		tmp = x * (y * z);
	} else if (y <= -2e-299) {
		tmp = t_1;
	} else if (y <= 9.5e-147) {
		tmp = j * (t * c);
	} else if (y <= 7.2e-66) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = b * (a * i)
    if (y <= (-2.4d+76)) then
        tmp = x * (y * z)
    else if (y <= (-2d-299)) then
        tmp = t_1
    else if (y <= 9.5d-147) then
        tmp = j * (t * c)
    else if (y <= 7.2d-66) then
        tmp = t_1
    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 t_1 = b * (a * i);
	double tmp;
	if (y <= -2.4e+76) {
		tmp = x * (y * z);
	} else if (y <= -2e-299) {
		tmp = t_1;
	} else if (y <= 9.5e-147) {
		tmp = j * (t * c);
	} else if (y <= 7.2e-66) {
		tmp = t_1;
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (a * i)
	tmp = 0
	if y <= -2.4e+76:
		tmp = x * (y * z)
	elif y <= -2e-299:
		tmp = t_1
	elif y <= 9.5e-147:
		tmp = j * (t * c)
	elif y <= 7.2e-66:
		tmp = t_1
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(a * i))
	tmp = 0.0
	if (y <= -2.4e+76)
		tmp = Float64(x * Float64(y * z));
	elseif (y <= -2e-299)
		tmp = t_1;
	elseif (y <= 9.5e-147)
		tmp = Float64(j * Float64(t * c));
	elseif (y <= 7.2e-66)
		tmp = t_1;
	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)
	t_1 = b * (a * i);
	tmp = 0.0;
	if (y <= -2.4e+76)
		tmp = x * (y * z);
	elseif (y <= -2e-299)
		tmp = t_1;
	elseif (y <= 9.5e-147)
		tmp = j * (t * c);
	elseif (y <= 7.2e-66)
		tmp = t_1;
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.4e+76], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2e-299], t$95$1, If[LessEqual[y, 9.5e-147], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.2e-66], t$95$1, N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.4e76

   1. Initial program 61.1%

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

   3. Taylor expanded in x around inf 62.1%

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

      1. *-commutative 62.1%

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

   5. Simplified 62.1%

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

   6. Taylor expanded in y around inf 53.7%

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

   if -2.4e76 < y < -1.99999999999999998e-299 or 9.49999999999999986e-147 < y < 7.20000000000000025e-66

   1. Initial program 83.0%

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

   3. Taylor expanded in b around inf 53.0%

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

      1. *-commutative 53.0%

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

   5. Simplified 53.0%

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

   6. Taylor expanded in i around inf 36.0%

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

      1. *-commutative 36.0%

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

   8. Simplified 36.0%

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

   if -1.99999999999999998e-299 < y < 9.49999999999999986e-147

   1. Initial program 72.8%

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

   3. Taylor expanded in x around 0 64.8%

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

      1. *-commutative 64.8%

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

   5. Simplified 64.8%

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

   6. Taylor expanded in t around inf 33.1%

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

      1. associate-*r* 36.0%

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

      2. *-commutative 36.0%

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

      3. associate-*r* 41.3%

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

   8. Simplified 41.3%

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

   if 7.20000000000000025e-66 < y

   1. Initial program 64.4%

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

   3. Taylor expanded in x around inf 40.1%

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

      1. *-commutative 40.1%

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

   5. Simplified 40.1%

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

   6. Taylor expanded in y around inf 29.9%

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

      1. *-commutative 29.9%

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

      2. associate-*l* 34.1%

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

   8. Simplified 34.1%

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

4. Final simplification 39.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+76}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-299}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-147}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-66}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 29.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i\right)\\ t_2 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq -1.4 \cdot 10^{+74}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-300}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-150}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-24}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* a i))) (t_2 (* z (* x y))))
   (if (<= y -1.4e+74)
     t_2
     (if (<= y -4.2e-300)
       t_1
       (if (<= y 6e-150) (* j (* t c)) (if (<= y 8.6e-24) 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 * (a * i);
	double t_2 = z * (x * y);
	double tmp;
	if (y <= -1.4e+74) {
		tmp = t_2;
	} else if (y <= -4.2e-300) {
		tmp = t_1;
	} else if (y <= 6e-150) {
		tmp = j * (t * c);
	} else if (y <= 8.6e-24) {
		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 * (a * i)
    t_2 = z * (x * y)
    if (y <= (-1.4d+74)) then
        tmp = t_2
    else if (y <= (-4.2d-300)) then
        tmp = t_1
    else if (y <= 6d-150) then
        tmp = j * (t * c)
    else if (y <= 8.6d-24) 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 * (a * i);
	double t_2 = z * (x * y);
	double tmp;
	if (y <= -1.4e+74) {
		tmp = t_2;
	} else if (y <= -4.2e-300) {
		tmp = t_1;
	} else if (y <= 6e-150) {
		tmp = j * (t * c);
	} else if (y <= 8.6e-24) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (a * i)
	t_2 = z * (x * y)
	tmp = 0
	if y <= -1.4e+74:
		tmp = t_2
	elif y <= -4.2e-300:
		tmp = t_1
	elif y <= 6e-150:
		tmp = j * (t * c)
	elif y <= 8.6e-24:
		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(a * i))
	t_2 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (y <= -1.4e+74)
		tmp = t_2;
	elseif (y <= -4.2e-300)
		tmp = t_1;
	elseif (y <= 6e-150)
		tmp = Float64(j * Float64(t * c));
	elseif (y <= 8.6e-24)
		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 * (a * i);
	t_2 = z * (x * y);
	tmp = 0.0;
	if (y <= -1.4e+74)
		tmp = t_2;
	elseif (y <= -4.2e-300)
		tmp = t_1;
	elseif (y <= 6e-150)
		tmp = j * (t * c);
	elseif (y <= 8.6e-24)
		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[(a * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.4e+74], t$95$2, If[LessEqual[y, -4.2e-300], t$95$1, If[LessEqual[y, 6e-150], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.6e-24], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.40000000000000001e74 or 8.6000000000000006e-24 < y

   1. Initial program 61.6%

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

   3. Taylor expanded in j around 0 51.7%

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

      1. *-commutative 51.7%

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

      2. *-commutative 51.7%

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

   5. Simplified 51.7%

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

   6. Taylor expanded in y around inf 38.9%

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

      1. associate-*r* 42.6%

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

      2. *-commutative 42.6%

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

   8. Simplified 42.6%

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

   if -1.40000000000000001e74 < y < -4.20000000000000007e-300 or 6.0000000000000003e-150 < y < 8.6000000000000006e-24

   1. Initial program 83.3%

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

   3. Taylor expanded in b around inf 52.8%

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

      1. *-commutative 52.8%

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

   5. Simplified 52.8%

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

   6. Taylor expanded in i around inf 36.0%

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

      1. *-commutative 36.0%

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

   8. Simplified 36.0%

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

   if -4.20000000000000007e-300 < y < 6.0000000000000003e-150

   1. Initial program 72.8%

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

   3. Taylor expanded in x around 0 64.8%

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

      1. *-commutative 64.8%

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

   5. Simplified 64.8%

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

   6. Taylor expanded in t around inf 33.1%

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

      1. associate-*r* 36.0%

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

      2. *-commutative 36.0%

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

      3. associate-*r* 41.3%

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

   8. Simplified 41.3%

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

4. Final simplification 39.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+74}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-300}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-150}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-24}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 29.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i\right)\\ \mathbf{if}\;i \leq -0.000125:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -4.8 \cdot 10^{-165}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;i \leq 8.2 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* a i))))
   (if (<= i -0.000125)
     t_1
     (if (<= i -4.8e-165)
       (* c (* t j))
       (if (<= i 8.2e+17) (* x (* y z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (a * i);
	double tmp;
	if (i <= -0.000125) {
		tmp = t_1;
	} else if (i <= -4.8e-165) {
		tmp = c * (t * j);
	} else if (i <= 8.2e+17) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a * i)
    if (i <= (-0.000125d0)) then
        tmp = t_1
    else if (i <= (-4.8d-165)) then
        tmp = c * (t * j)
    else if (i <= 8.2d+17) then
        tmp = x * (y * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (a * i);
	double tmp;
	if (i <= -0.000125) {
		tmp = t_1;
	} else if (i <= -4.8e-165) {
		tmp = c * (t * j);
	} else if (i <= 8.2e+17) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (a * i)
	tmp = 0
	if i <= -0.000125:
		tmp = t_1
	elif i <= -4.8e-165:
		tmp = c * (t * j)
	elif i <= 8.2e+17:
		tmp = x * (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(a * i))
	tmp = 0.0
	if (i <= -0.000125)
		tmp = t_1;
	elseif (i <= -4.8e-165)
		tmp = Float64(c * Float64(t * j));
	elseif (i <= 8.2e+17)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (a * i);
	tmp = 0.0;
	if (i <= -0.000125)
		tmp = t_1;
	elseif (i <= -4.8e-165)
		tmp = c * (t * j);
	elseif (i <= 8.2e+17)
		tmp = x * (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -0.000125], t$95$1, If[LessEqual[i, -4.8e-165], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 8.2e+17], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if i < -1.25e-4 or 8.2e17 < i

   1. Initial program 61.1%

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

   3. Taylor expanded in b around inf 45.7%

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

      1. *-commutative 45.7%

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

   5. Simplified 45.7%

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

   6. Taylor expanded in i around inf 41.0%

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

      1. *-commutative 41.0%

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

   8. Simplified 41.0%

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

   if -1.25e-4 < i < -4.8000000000000004e-165

   1. Initial program 82.4%

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

   3. Taylor expanded in x around 0 57.9%

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

      1. *-commutative 57.9%

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

   5. Simplified 57.9%

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

   6. Taylor expanded in t around inf 31.7%

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

   if -4.8000000000000004e-165 < i < 8.2e17

   1. Initial program 81.7%

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

   3. Taylor expanded in x around inf 53.3%

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

      1. *-commutative 53.3%

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

   5. Simplified 53.3%

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

   6. Taylor expanded in y around inf 34.5%

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

4. Final simplification 37.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -0.000125:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;i \leq -4.8 \cdot 10^{-165}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;i \leq 8.2 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 28.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{+106} \lor \neg \left(t \leq 1.9 \cdot 10^{+131}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -1.85e+106) (not (<= t 1.9e+131))) (* c (* t j)) (* b (* a i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -1.85e+106) || !(t <= 1.9e+131)) {
		tmp = c * (t * j);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((t <= (-1.85d+106)) .or. (.not. (t <= 1.9d+131))) then
        tmp = c * (t * j)
    else
        tmp = b * (a * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -1.85e+106) || !(t <= 1.9e+131)) {
		tmp = c * (t * j);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -1.85e+106) or not (t <= 1.9e+131):
		tmp = c * (t * j)
	else:
		tmp = b * (a * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -1.85e+106) || !(t <= 1.9e+131))
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(b * Float64(a * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -1.85e+106) || ~((t <= 1.9e+131)))
		tmp = c * (t * j);
	else
		tmp = b * (a * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -1.85e+106], N[Not[LessEqual[t, 1.9e+131]], $MachinePrecision]], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.84999999999999997e106 or 1.9000000000000002e131 < t

   1. Initial program 58.8%

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

   3. Taylor expanded in x around 0 47.7%

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

      1. *-commutative 47.7%

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

   5. Simplified 47.7%

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

   6. Taylor expanded in t around inf 43.3%

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

   if -1.84999999999999997e106 < t < 1.9000000000000002e131

   1. Initial program 77.3%

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

   3. Taylor expanded in b around inf 42.6%

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

      1. *-commutative 42.6%

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

   5. Simplified 42.6%

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

   6. Taylor expanded in i around inf 27.5%

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

      1. *-commutative 27.5%

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

   8. Simplified 27.5%

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

4. Final simplification 32.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{+106} \lor \neg \left(t \leq 1.9 \cdot 10^{+131}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 28.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{+110}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq 450:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -1.85e+110)
   (* c (* t j))
   (if (<= t 450.0) (* b (* a i)) (* j (* t c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -1.85e+110) {
		tmp = c * (t * j);
	} else if (t <= 450.0) {
		tmp = b * (a * i);
	} else {
		tmp = j * (t * c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (t <= (-1.85d+110)) then
        tmp = c * (t * j)
    else if (t <= 450.0d0) then
        tmp = b * (a * i)
    else
        tmp = j * (t * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -1.85e+110) {
		tmp = c * (t * j);
	} else if (t <= 450.0) {
		tmp = b * (a * i);
	} else {
		tmp = j * (t * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -1.85e+110:
		tmp = c * (t * j)
	elif t <= 450.0:
		tmp = b * (a * i)
	else:
		tmp = j * (t * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -1.85e+110)
		tmp = Float64(c * Float64(t * j));
	elseif (t <= 450.0)
		tmp = Float64(b * Float64(a * i));
	else
		tmp = Float64(j * Float64(t * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -1.85e+110)
		tmp = c * (t * j);
	elseif (t <= 450.0)
		tmp = b * (a * i);
	else
		tmp = j * (t * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -1.85e+110], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 450.0], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.85000000000000006e110

   1. Initial program 58.9%

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

   3. Taylor expanded in x around 0 48.4%

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

      1. *-commutative 48.4%

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

   5. Simplified 48.4%

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

   6. Taylor expanded in t around inf 49.4%

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

   if -1.85000000000000006e110 < t < 450

   1. Initial program 76.2%

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

   3. Taylor expanded in b around inf 43.8%

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

      1. *-commutative 43.8%

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

   5. Simplified 43.8%

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

   6. Taylor expanded in i around inf 28.4%

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

      1. *-commutative 28.4%

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

   8. Simplified 28.4%

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

   if 450 < t

   1. Initial program 69.9%

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

   3. Taylor expanded in x around 0 51.1%

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

      1. *-commutative 51.1%

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

   5. Simplified 51.1%

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

   6. Taylor expanded in t around inf 28.7%

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

      1. associate-*r* 30.1%

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

      2. *-commutative 30.1%

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

      3. associate-*r* 30.1%

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

   8. Simplified 30.1%

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

4. Final simplification 32.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{+110}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq 450:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 22.4% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(b \cdot i\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 71.6%

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

3. Taylor expanded in b around inf 38.0%

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

   1. *-commutative 38.0%

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

5. Simplified 38.0%

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

6. Taylor expanded in i around inf 22.0%

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

7. Final simplification 22.0%

   \[\leadsto a \cdot \left(b \cdot i\right) \]
8. Add Preprocessing

Alternative 24: 21.9% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ b \cdot \left(a \cdot i\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 71.6%

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

3. Taylor expanded in b around inf 38.0%

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

   1. *-commutative 38.0%

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

5. Simplified 38.0%

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

6. Taylor expanded in i around inf 24.5%

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

   1. *-commutative 24.5%

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

8. Simplified 24.5%

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

9. Final simplification 24.5%

   \[\leadsto b \cdot \left(a \cdot i\right) \]
10. Add Preprocessing

Developer target: 68.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ t_2 := x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{if}\;t < -8.120978919195912 \cdot 10^{-33}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < -4.712553818218485 \cdot 10^{-169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t < -7.633533346031584 \cdot 10^{-308}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 1.0535888557455487 \cdot 10^{-139}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
          (/
           (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0)))
           (+ (* c t) (* i y)))))
        (t_2
         (-
          (* x (- (* z y) (* a t)))
          (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))
   (if (< t -8.120978919195912e-33)
     t_2
     (if (< t -4.712553818218485e-169)
       t_1
       (if (< t -7.633533346031584e-308)
         t_2
         (if (< t 1.0535888557455487e-139) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (pow((c * t), 2.0) - pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ** 2.0d0) - ((i * y) ** 2.0d0))) / ((c * t) + (i * y)))
    t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
    if (t < (-8.120978919195912d-33)) then
        tmp = t_2
    else if (t < (-4.712553818218485d-169)) then
        tmp = t_1
    else if (t < (-7.633533346031584d-308)) then
        tmp = t_2
    else if (t < 1.0535888557455487d-139) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (Math.pow((c * t), 2.0) - Math.pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (math.pow((c * t), 2.0) - math.pow((i * y), 2.0))) / ((c * t) + (i * y)))
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
	tmp = 0
	if t < -8.120978919195912e-33:
		tmp = t_2
	elif t < -4.712553818218485e-169:
		tmp = t_1
	elif t < -7.633533346031584e-308:
		tmp = t_2
	elif t < 1.0535888557455487e-139:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(Float64(j * Float64((Float64(c * t) ^ 2.0) - (Float64(i * y) ^ 2.0))) / Float64(Float64(c * t) + Float64(i * y))))
	t_2 = Float64(Float64(x * Float64(Float64(z * y) - Float64(a * t))) - Float64(Float64(b * Float64(Float64(z * c) - Float64(a * i))) - Float64(Float64(Float64(c * t) - Float64(y * i)) * j)))
	tmp = 0.0
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ^ 2.0) - ((i * y) ^ 2.0))) / ((c * t) + (i * y)));
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	tmp = 0.0;
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[Power[N[(c * t), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(i * y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * t), $MachinePrecision] + N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(c * t), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -8.120978919195912e-33], t$95$2, If[Less[t, -4.712553818218485e-169], t$95$1, If[Less[t, -7.633533346031584e-308], t$95$2, If[Less[t, 1.0535888557455487e-139], t$95$1, t$95$2]]]]]]

Reproduce

herbie shell --seed 2024039 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< t -8.120978919195912e-33) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -4.712553818218485e-169) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (if (< t -7.633533346031584e-308) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 1.0535888557455487e-139) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))))

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