Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.0% → 83.3%

Time: 37.7s

Alternatives: 30

Speedup: 0.5×

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

Specification

Math

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

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: 73.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 83.3% accurate, 0.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 91.9%

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

   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 y around -inf 18.5%

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

   5. Simplified 25.9%

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

      1. associate--l+ 25.9%

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

      2. fma-def 35.2%

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

      3. fma-neg 35.2%

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

   7. Applied egg-rr 35.2%

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

   8. Taylor expanded in c around 0 40.7%

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

   10. Simplified 59.3%

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

4. Final simplification 85.0%

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

Alternative 2: 80.9% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (+ (* j (- (* t c) (* y i))) (+ t_1 (* b (- (* a i) (* z c)))))))
   (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 = (j * ((t * c) - (y * i))) + (t_1 + (b * ((a * i) - (z * c))));
	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 = (j * ((t * c) - (y * i))) + (t_1 + (b * ((a * i) - (z * c))));
	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 = (j * ((t * c) - (y * i))) + (t_1 + (b * ((a * i) - (z * c))))
	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(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(t_1 + Float64(b * Float64(Float64(a * i) - Float64(z * c)))))
	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 = (j * ((t * c) - (y * i))) + (t_1 + (b * ((a * i) - (z * c))));
	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[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $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 91.9%

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

   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 52.0%

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

      1. *-commutative 52.0%

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

   5. Simplified 52.0%

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

4. Final simplification 83.5%

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

Alternative 3: 54.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := t_1 - z \cdot \left(b \cdot c\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -1.4 \cdot 10^{+194}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{+110}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{+58}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-8}:\\ \;\;\;\;t_1 + z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-175}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) - z \cdot \left(b \cdot c - x \cdot y\right)\\ \mathbf{elif}\;x \leq -8.4 \cdot 10^{-278}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-25}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+85}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i))))
        (t_2 (- t_1 (* z (* b c))))
        (t_3 (* x (- (* y z) (* t a)))))
   (if (<= x -1.4e+194)
     t_3
     (if (<= x -1.6e+110)
       t_2
       (if (<= x -4.5e+58)
         t_3
         (if (<= x -3.4e-8)
           (+ t_1 (* z (* x y)))
           (if (<= x -3.2e-175)
             (- (* c (* t j)) (* z (- (* b c) (* x y))))
             (if (<= x -8.4e-278)
               (* b (- (* a i) (* z c)))
               (if (<= x 5.8e-25)
                 t_2
                 (if (<= x 3.2e+85) (* 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 = j * ((t * c) - (y * i));
	double t_2 = t_1 - (z * (b * c));
	double t_3 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.4e+194) {
		tmp = t_3;
	} else if (x <= -1.6e+110) {
		tmp = t_2;
	} else if (x <= -4.5e+58) {
		tmp = t_3;
	} else if (x <= -3.4e-8) {
		tmp = t_1 + (z * (x * y));
	} else if (x <= -3.2e-175) {
		tmp = (c * (t * j)) - (z * ((b * c) - (x * y)));
	} else if (x <= -8.4e-278) {
		tmp = b * ((a * i) - (z * c));
	} else if (x <= 5.8e-25) {
		tmp = t_2;
	} else if (x <= 3.2e+85) {
		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 = j * ((t * c) - (y * i))
    t_2 = t_1 - (z * (b * c))
    t_3 = x * ((y * z) - (t * a))
    if (x <= (-1.4d+194)) then
        tmp = t_3
    else if (x <= (-1.6d+110)) then
        tmp = t_2
    else if (x <= (-4.5d+58)) then
        tmp = t_3
    else if (x <= (-3.4d-8)) then
        tmp = t_1 + (z * (x * y))
    else if (x <= (-3.2d-175)) then
        tmp = (c * (t * j)) - (z * ((b * c) - (x * y)))
    else if (x <= (-8.4d-278)) then
        tmp = b * ((a * i) - (z * c))
    else if (x <= 5.8d-25) then
        tmp = t_2
    else if (x <= 3.2d+85) 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 = j * ((t * c) - (y * i));
	double t_2 = t_1 - (z * (b * c));
	double t_3 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.4e+194) {
		tmp = t_3;
	} else if (x <= -1.6e+110) {
		tmp = t_2;
	} else if (x <= -4.5e+58) {
		tmp = t_3;
	} else if (x <= -3.4e-8) {
		tmp = t_1 + (z * (x * y));
	} else if (x <= -3.2e-175) {
		tmp = (c * (t * j)) - (z * ((b * c) - (x * y)));
	} else if (x <= -8.4e-278) {
		tmp = b * ((a * i) - (z * c));
	} else if (x <= 5.8e-25) {
		tmp = t_2;
	} else if (x <= 3.2e+85) {
		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 = j * ((t * c) - (y * i))
	t_2 = t_1 - (z * (b * c))
	t_3 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -1.4e+194:
		tmp = t_3
	elif x <= -1.6e+110:
		tmp = t_2
	elif x <= -4.5e+58:
		tmp = t_3
	elif x <= -3.4e-8:
		tmp = t_1 + (z * (x * y))
	elif x <= -3.2e-175:
		tmp = (c * (t * j)) - (z * ((b * c) - (x * y)))
	elif x <= -8.4e-278:
		tmp = b * ((a * i) - (z * c))
	elif x <= 5.8e-25:
		tmp = t_2
	elif x <= 3.2e+85:
		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(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(t_1 - Float64(z * Float64(b * c)))
	t_3 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -1.4e+194)
		tmp = t_3;
	elseif (x <= -1.6e+110)
		tmp = t_2;
	elseif (x <= -4.5e+58)
		tmp = t_3;
	elseif (x <= -3.4e-8)
		tmp = Float64(t_1 + Float64(z * Float64(x * y)));
	elseif (x <= -3.2e-175)
		tmp = Float64(Float64(c * Float64(t * j)) - Float64(z * Float64(Float64(b * c) - Float64(x * y))));
	elseif (x <= -8.4e-278)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (x <= 5.8e-25)
		tmp = t_2;
	elseif (x <= 3.2e+85)
		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 = j * ((t * c) - (y * i));
	t_2 = t_1 - (z * (b * c));
	t_3 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -1.4e+194)
		tmp = t_3;
	elseif (x <= -1.6e+110)
		tmp = t_2;
	elseif (x <= -4.5e+58)
		tmp = t_3;
	elseif (x <= -3.4e-8)
		tmp = t_1 + (z * (x * y));
	elseif (x <= -3.2e-175)
		tmp = (c * (t * j)) - (z * ((b * c) - (x * y)));
	elseif (x <= -8.4e-278)
		tmp = b * ((a * i) - (z * c));
	elseif (x <= 5.8e-25)
		tmp = t_2;
	elseif (x <= 3.2e+85)
		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[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.4e+194], t$95$3, If[LessEqual[x, -1.6e+110], t$95$2, If[LessEqual[x, -4.5e+58], t$95$3, If[LessEqual[x, -3.4e-8], N[(t$95$1 + N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.2e-175], N[(N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision] - N[(z * N[(N[(b * c), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -8.4e-278], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.8e-25], t$95$2, If[LessEqual[x, 3.2e+85], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -1.40000000000000005e194 or -1.59999999999999997e110 < x < -4.4999999999999998e58 or 3.20000000000000018e85 < x

   1. Initial program 70.0%

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

   3. Taylor expanded in x around inf 80.7%

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

      1. *-commutative 80.7%

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

   5. Simplified 80.7%

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

   if -1.40000000000000005e194 < x < -1.59999999999999997e110 or -8.40000000000000054e-278 < x < 5.8000000000000001e-25

   1. Initial program 74.0%

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

   3. Taylor expanded in i around 0 67.5%

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

      1. *-commutative 67.5%

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

      2. *-commutative 67.5%

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

      3. *-commutative 67.5%

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

      4. *-commutative 67.5%

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

      5. associate-*l* 66.3%

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

      6. *-commutative 66.3%

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

   5. Simplified 66.3%

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

   6. Taylor expanded in x around 0 65.4%

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

      1. sub-neg 65.4%

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

      2. sub-neg 65.4%

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

      3. *-commutative 65.4%

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

      4. *-commutative 65.4%

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

      5. associate-*r* 64.4%

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

      6. *-commutative 64.4%

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

   8. Simplified 64.4%

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

   if -4.4999999999999998e58 < x < -3.4e-8

   1. Initial program 78.5%

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

   3. Taylor expanded in y around inf 79.1%

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

      1. *-commutative 79.1%

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

      2. *-commutative 79.1%

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

      3. associate-*l* 79.1%

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

   5. Simplified 79.1%

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

   if -3.4e-8 < x < -3.2e-175

   1. Initial program 84.3%

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

   3. Taylor expanded in y around -inf 90.5%

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

   5. Simplified 87.3%

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

   6. Taylor expanded in i around 0 68.1%

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

      1. sub-neg 68.1%

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

      2. associate-+r+ 68.1%

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

      3. sub-neg 68.1%

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

      4. associate-*r* 68.1%

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

      5. associate-*r* 71.0%

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

      6. distribute-rgt-out-- 74.1%

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

      7. +-commutative 74.1%

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

      8. fma-def 74.1%

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

   8. Simplified 74.1%

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

   9. Taylor expanded in a around 0 77.5%

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

   if -3.2e-175 < x < -8.40000000000000054e-278

   1. Initial program 54.0%

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

   3. Taylor expanded in b around inf 62.1%

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

   if 5.8000000000000001e-25 < x < 3.20000000000000018e85

   1. Initial program 67.7%

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

   3. Taylor expanded in y around -inf 50.6%

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

   5. Simplified 51.2%

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

   6. Taylor expanded in i around inf 67.4%

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

      1. mul-1-neg 67.4%

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

      2. neg-sub0 67.4%

         \[\leadsto i \cdot \left(\color{blue}{\left(0 - j \cdot y\right)} - -1 \cdot \left(a \cdot b\right)\right) \]

      3. mul-1-neg 67.4%

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

      4. *-commutative 67.4%

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

      5. associate--r+ 67.4%

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

      6. +-commutative 67.4%

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

      7. associate--r+ 67.4%

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

      8. neg-sub0 67.4%

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

      9. remove-double-neg 67.4%

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

      10. *-commutative 67.4%

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

   8. Simplified 67.4%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+194}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{+110}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{+58}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-8}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-175}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) - z \cdot \left(b \cdot c - x \cdot y\right)\\ \mathbf{elif}\;x \leq -8.4 \cdot 10^{-278}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-25}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+85}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 70.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -4.2 \cdot 10^{+120} \lor \neg \left(i \leq 2.2 \cdot 10^{+141}\right):\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - c \cdot \left(z \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -4.2e+120) (not (<= i 2.2e+141)))
   (* i (- (* a b) (* y j)))
   (+ (* j (- (* t c) (* y i))) (- (* x (- (* y z) (* t a))) (* c (* z b))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -4.2e+120) || !(i <= 2.2e+141)) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = (j * ((t * c) - (y * i))) + ((x * ((y * z) - (t * a))) - (c * (z * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((i <= (-4.2d+120)) .or. (.not. (i <= 2.2d+141))) then
        tmp = i * ((a * b) - (y * j))
    else
        tmp = (j * ((t * c) - (y * i))) + ((x * ((y * z) - (t * a))) - (c * (z * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -4.2e+120) || !(i <= 2.2e+141)) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = (j * ((t * c) - (y * i))) + ((x * ((y * z) - (t * a))) - (c * (z * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (i <= -4.2e+120) or not (i <= 2.2e+141):
		tmp = i * ((a * b) - (y * j))
	else:
		tmp = (j * ((t * c) - (y * i))) + ((x * ((y * z) - (t * a))) - (c * (z * b)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((i <= -4.2e+120) || !(i <= 2.2e+141))
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	else
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(c * Float64(z * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((i <= -4.2e+120) || ~((i <= 2.2e+141)))
		tmp = i * ((a * b) - (y * j));
	else
		tmp = (j * ((t * c) - (y * i))) + ((x * ((y * z) - (t * a))) - (c * (z * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[i, -4.2e+120], N[Not[LessEqual[i, 2.2e+141]], $MachinePrecision]], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -4.2000000000000001e120 or 2.2e141 < i

   1. Initial program 57.1%

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

   3. Taylor expanded in y around -inf 57.1%

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

   5. Simplified 57.0%

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

   6. Taylor expanded in i around inf 71.2%

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

      1. mul-1-neg 71.2%

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

      2. neg-sub0 71.2%

         \[\leadsto i \cdot \left(\color{blue}{\left(0 - j \cdot y\right)} - -1 \cdot \left(a \cdot b\right)\right) \]

      3. mul-1-neg 71.2%

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

      4. *-commutative 71.2%

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

      5. associate--r+ 71.2%

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

      6. +-commutative 71.2%

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

      7. associate--r+ 71.2%

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

      8. neg-sub0 71.2%

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

      9. remove-double-neg 71.2%

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

      10. *-commutative 71.2%

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

   8. Simplified 71.2%

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

   if -4.2000000000000001e120 < i < 2.2e141

   1. Initial program 79.4%

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

   3. Taylor expanded in i around 0 73.8%

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

      1. *-commutative 73.8%

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

      2. *-commutative 73.8%

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

      3. *-commutative 73.8%

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

      4. *-commutative 73.8%

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

      5. associate-*l* 73.8%

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

      6. *-commutative 73.8%

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

   5. Simplified 73.8%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4.2 \cdot 10^{+120} \lor \neg \left(i \leq 2.2 \cdot 10^{+141}\right):\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - c \cdot \left(z \cdot b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_2 := c \cdot \left(t \cdot j\right) - z \cdot \left(b \cdot c - x \cdot y\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -1.15 \cdot 10^{+194}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-181}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -4.9 \cdot 10^{-297}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-218}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-199}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-110}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-67}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-30}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* a b) (* y j))))
        (t_2 (- (* c (* t j)) (* z (- (* b c) (* x y)))))
        (t_3 (* x (- (* y z) (* t a)))))
   (if (<= x -1.15e+194)
     t_3
     (if (<= x -2.3e-181)
       t_2
       (if (<= x -4.9e-297)
         (* b (- (* a i) (* z c)))
         (if (<= x 8.2e-218)
           (* j (- (* t c) (* y i)))
           (if (<= x 2.9e-199)
             t_1
             (if (<= x 1.65e-110)
               t_2
               (if (<= x 8.5e-67)
                 (* a (- (* b i) (* x t)))
                 (if (<= x 2.2e-30)
                   (* c (- (* t j) (* z b)))
                   (if (<= x 7.4e+85) t_1 t_3)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double t_2 = (c * (t * j)) - (z * ((b * c) - (x * y)));
	double t_3 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.15e+194) {
		tmp = t_3;
	} else if (x <= -2.3e-181) {
		tmp = t_2;
	} else if (x <= -4.9e-297) {
		tmp = b * ((a * i) - (z * c));
	} else if (x <= 8.2e-218) {
		tmp = j * ((t * c) - (y * i));
	} else if (x <= 2.9e-199) {
		tmp = t_1;
	} else if (x <= 1.65e-110) {
		tmp = t_2;
	} else if (x <= 8.5e-67) {
		tmp = a * ((b * i) - (x * t));
	} else if (x <= 2.2e-30) {
		tmp = c * ((t * j) - (z * b));
	} else if (x <= 7.4e+85) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = i * ((a * b) - (y * j))
    t_2 = (c * (t * j)) - (z * ((b * c) - (x * y)))
    t_3 = x * ((y * z) - (t * a))
    if (x <= (-1.15d+194)) then
        tmp = t_3
    else if (x <= (-2.3d-181)) then
        tmp = t_2
    else if (x <= (-4.9d-297)) then
        tmp = b * ((a * i) - (z * c))
    else if (x <= 8.2d-218) then
        tmp = j * ((t * c) - (y * i))
    else if (x <= 2.9d-199) then
        tmp = t_1
    else if (x <= 1.65d-110) then
        tmp = t_2
    else if (x <= 8.5d-67) then
        tmp = a * ((b * i) - (x * t))
    else if (x <= 2.2d-30) then
        tmp = c * ((t * j) - (z * b))
    else if (x <= 7.4d+85) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double t_2 = (c * (t * j)) - (z * ((b * c) - (x * y)));
	double t_3 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.15e+194) {
		tmp = t_3;
	} else if (x <= -2.3e-181) {
		tmp = t_2;
	} else if (x <= -4.9e-297) {
		tmp = b * ((a * i) - (z * c));
	} else if (x <= 8.2e-218) {
		tmp = j * ((t * c) - (y * i));
	} else if (x <= 2.9e-199) {
		tmp = t_1;
	} else if (x <= 1.65e-110) {
		tmp = t_2;
	} else if (x <= 8.5e-67) {
		tmp = a * ((b * i) - (x * t));
	} else if (x <= 2.2e-30) {
		tmp = c * ((t * j) - (z * b));
	} else if (x <= 7.4e+85) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((a * b) - (y * j))
	t_2 = (c * (t * j)) - (z * ((b * c) - (x * y)))
	t_3 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -1.15e+194:
		tmp = t_3
	elif x <= -2.3e-181:
		tmp = t_2
	elif x <= -4.9e-297:
		tmp = b * ((a * i) - (z * c))
	elif x <= 8.2e-218:
		tmp = j * ((t * c) - (y * i))
	elif x <= 2.9e-199:
		tmp = t_1
	elif x <= 1.65e-110:
		tmp = t_2
	elif x <= 8.5e-67:
		tmp = a * ((b * i) - (x * t))
	elif x <= 2.2e-30:
		tmp = c * ((t * j) - (z * b))
	elif x <= 7.4e+85:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	t_2 = Float64(Float64(c * Float64(t * j)) - Float64(z * Float64(Float64(b * c) - Float64(x * y))))
	t_3 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -1.15e+194)
		tmp = t_3;
	elseif (x <= -2.3e-181)
		tmp = t_2;
	elseif (x <= -4.9e-297)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (x <= 8.2e-218)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (x <= 2.9e-199)
		tmp = t_1;
	elseif (x <= 1.65e-110)
		tmp = t_2;
	elseif (x <= 8.5e-67)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (x <= 2.2e-30)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (x <= 7.4e+85)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((a * b) - (y * j));
	t_2 = (c * (t * j)) - (z * ((b * c) - (x * y)));
	t_3 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -1.15e+194)
		tmp = t_3;
	elseif (x <= -2.3e-181)
		tmp = t_2;
	elseif (x <= -4.9e-297)
		tmp = b * ((a * i) - (z * c));
	elseif (x <= 8.2e-218)
		tmp = j * ((t * c) - (y * i));
	elseif (x <= 2.9e-199)
		tmp = t_1;
	elseif (x <= 1.65e-110)
		tmp = t_2;
	elseif (x <= 8.5e-67)
		tmp = a * ((b * i) - (x * t));
	elseif (x <= 2.2e-30)
		tmp = c * ((t * j) - (z * b));
	elseif (x <= 7.4e+85)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision] - N[(z * N[(N[(b * c), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.15e+194], t$95$3, If[LessEqual[x, -2.3e-181], t$95$2, If[LessEqual[x, -4.9e-297], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.2e-218], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.9e-199], t$95$1, If[LessEqual[x, 1.65e-110], t$95$2, If[LessEqual[x, 8.5e-67], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.2e-30], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.4e+85], t$95$1, t$95$3]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if x < -1.15000000000000003e194 or 7.4000000000000004e85 < x

   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 inf 80.8%

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

      1. *-commutative 80.8%

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

   5. Simplified 80.8%

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

   if -1.15000000000000003e194 < x < -2.29999999999999991e-181 or 2.9e-199 < x < 1.65e-110

   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 y around -inf 77.5%

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

   5. Simplified 74.3%

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

   6. Taylor expanded in i around 0 61.6%

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

      1. sub-neg 61.6%

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

      2. associate-+r+ 61.6%

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

      3. sub-neg 61.6%

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

      4. associate-*r* 59.6%

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

      5. associate-*r* 60.9%

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

      6. distribute-rgt-out-- 63.1%

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

      7. +-commutative 63.1%

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

      8. fma-def 63.1%

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

   8. Simplified 63.1%

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

   9. Taylor expanded in a around 0 66.9%

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

   if -2.29999999999999991e-181 < x < -4.89999999999999997e-297

   1. Initial program 58.7%

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

   3. Taylor expanded in b around inf 64.8%

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

   if -4.89999999999999997e-297 < x < 8.1999999999999995e-218

   1. Initial program 84.6%

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

   3. Taylor expanded in j around inf 69.0%

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

   if 8.1999999999999995e-218 < x < 2.9e-199 or 2.19999999999999983e-30 < x < 7.4000000000000004e85

   1. Initial program 69.3%

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

   3. Taylor expanded in y around -inf 59.6%

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

   5. Simplified 60.1%

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

   6. Taylor expanded in i around inf 73.3%

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

      1. mul-1-neg 73.3%

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

      2. neg-sub0 73.3%

         \[\leadsto i \cdot \left(\color{blue}{\left(0 - j \cdot y\right)} - -1 \cdot \left(a \cdot b\right)\right) \]

      3. mul-1-neg 73.3%

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

      4. *-commutative 73.3%

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

      5. associate--r+ 73.3%

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

      6. +-commutative 73.3%

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

      7. associate--r+ 73.3%

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

      8. neg-sub0 73.3%

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

      9. remove-double-neg 73.3%

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

      10. *-commutative 73.3%

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

   8. Simplified 73.3%

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

   if 1.65e-110 < x < 8.49999999999999993e-67

   1. Initial program 67.0%

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

   3. Taylor expanded in y around -inf 89.2%

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

   5. Simplified 89.3%

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

      1. associate--l+ 89.3%

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

      2. fma-def 89.3%

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

      3. fma-neg 89.3%

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

   7. Applied egg-rr 89.3%

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

   8. Taylor expanded in a around inf 70.1%

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

      1. mul-1-neg 70.1%

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

      2. *-commutative 70.1%

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

      3. neg-sub0 70.1%

         \[\leadsto a \cdot \left(\color{blue}{\left(0 - x \cdot t\right)} - -1 \cdot \left(b \cdot i\right)\right) \]

      4. mul-1-neg 70.1%

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

      5. distribute-lft-neg-out 70.1%

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

      6. associate--r+ 70.1%

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

      7. +-commutative 70.1%

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

      8. associate--r+ 70.1%

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

      9. neg-sub0 70.1%

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

      10. *-commutative 70.1%

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

      11. distribute-rgt-neg-in 70.1%

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

      12. remove-double-neg 70.1%

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

      13. *-commutative 70.1%

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

      14. *-commutative 70.1%

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

   10. Simplified 70.1%

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

   if 8.49999999999999993e-67 < x < 2.19999999999999983e-30

   1. Initial program 74.6%

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

   3. Taylor expanded in c around inf 63.6%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+194}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-181}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) - z \cdot \left(b \cdot c - x \cdot y\right)\\ \mathbf{elif}\;x \leq -4.9 \cdot 10^{-297}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-218}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-199}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-110}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) - z \cdot \left(b \cdot c - x \cdot y\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-67}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-30}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{+85}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_3 := j \cdot \left(t \cdot c - y \cdot i\right) + t_1\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{+161}:\\ \;\;\;\;t \cdot \left(c \cdot j\right) + t_2\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-69}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-239}:\\ \;\;\;\;t_1 - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+194}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (* y (- (* x z) (* i j))))
        (t_3 (+ (* j (- (* t c) (* y i))) t_1)))
   (if (<= y -2.5e+161)
     (+ (* t (* c j)) t_2)
     (if (<= y -2.05e-69)
       t_3
       (if (<= y 4.3e-239)
         (- t_1 (* b (* z c)))
         (if (<= y 4.5e+194) t_3 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = (j * ((t * c) - (y * i))) + t_1;
	double tmp;
	if (y <= -2.5e+161) {
		tmp = (t * (c * j)) + t_2;
	} else if (y <= -2.05e-69) {
		tmp = t_3;
	} else if (y <= 4.3e-239) {
		tmp = t_1 - (b * (z * c));
	} else if (y <= 4.5e+194) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = y * ((x * z) - (i * j))
    t_3 = (j * ((t * c) - (y * i))) + t_1
    if (y <= (-2.5d+161)) then
        tmp = (t * (c * j)) + t_2
    else if (y <= (-2.05d-69)) then
        tmp = t_3
    else if (y <= 4.3d-239) then
        tmp = t_1 - (b * (z * c))
    else if (y <= 4.5d+194) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = (j * ((t * c) - (y * i))) + t_1;
	double tmp;
	if (y <= -2.5e+161) {
		tmp = (t * (c * j)) + t_2;
	} else if (y <= -2.05e-69) {
		tmp = t_3;
	} else if (y <= 4.3e-239) {
		tmp = t_1 - (b * (z * c));
	} else if (y <= 4.5e+194) {
		tmp = t_3;
	} 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))
	t_2 = y * ((x * z) - (i * j))
	t_3 = (j * ((t * c) - (y * i))) + t_1
	tmp = 0
	if y <= -2.5e+161:
		tmp = (t * (c * j)) + t_2
	elif y <= -2.05e-69:
		tmp = t_3
	elif y <= 4.3e-239:
		tmp = t_1 - (b * (z * c))
	elif y <= 4.5e+194:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_3 = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + t_1)
	tmp = 0.0
	if (y <= -2.5e+161)
		tmp = Float64(Float64(t * Float64(c * j)) + t_2);
	elseif (y <= -2.05e-69)
		tmp = t_3;
	elseif (y <= 4.3e-239)
		tmp = Float64(t_1 - Float64(b * Float64(z * c)));
	elseif (y <= 4.5e+194)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = y * ((x * z) - (i * j));
	t_3 = (j * ((t * c) - (y * i))) + t_1;
	tmp = 0.0;
	if (y <= -2.5e+161)
		tmp = (t * (c * j)) + t_2;
	elseif (y <= -2.05e-69)
		tmp = t_3;
	elseif (y <= 4.3e-239)
		tmp = t_1 - (b * (z * c));
	elseif (y <= 4.5e+194)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[y, -2.5e+161], N[(N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[y, -2.05e-69], t$95$3, If[LessEqual[y, 4.3e-239], N[(t$95$1 - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.5e+194], t$95$3, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.4999999999999998e161

   1. Initial program 68.8%

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

   3. Taylor expanded in y around -inf 76.5%

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

   5. Simplified 84.2%

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

   6. Taylor expanded in b around 0 84.4%

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

   7. Taylor expanded in c around inf 87.0%

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

      1. *-commutative 87.0%

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

   9. Simplified 87.0%

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

   if -2.4999999999999998e161 < y < -2.04999999999999995e-69 or 4.3e-239 < y < 4.4999999999999998e194

   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 0 72.5%

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

   if -2.04999999999999995e-69 < y < 4.3e-239

   1. Initial program 79.1%

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

   3. Taylor expanded in j around 0 76.9%

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

      1. *-commutative 76.9%

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

   5. Simplified 76.9%

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

   6. Taylor expanded in c around inf 65.8%

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

   if 4.4999999999999998e194 < y

   1. Initial program 42.2%

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

   3. Taylor expanded in y around -inf 79.4%

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

      1. mul-1-neg 79.4%

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

      2. *-commutative 79.4%

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

      3. distribute-rgt-neg-in 79.4%

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

      4. +-commutative 79.4%

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

      5. mul-1-neg 79.4%

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

      6. unsub-neg 79.4%

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

      7. *-commutative 79.4%

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

   5. Simplified 79.4%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+161}:\\ \;\;\;\;t \cdot \left(c \cdot j\right) + y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-69}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-239}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+194}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 64.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_3 := j \cdot \left(t \cdot c - y \cdot i\right) + t_1\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{+161}:\\ \;\;\;\;t \cdot \left(c \cdot j\right) + t_2\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-69}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-209}:\\ \;\;\;\;t_1 + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+194}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (* y (- (* x z) (* i j))))
        (t_3 (+ (* j (- (* t c) (* y i))) t_1)))
   (if (<= y -2.5e+161)
     (+ (* t (* c j)) t_2)
     (if (<= y -8.5e-69)
       t_3
       (if (<= y 8e-209)
         (+ t_1 (* b (- (* a i) (* z c))))
         (if (<= y 2e+194) t_3 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = (j * ((t * c) - (y * i))) + t_1;
	double tmp;
	if (y <= -2.5e+161) {
		tmp = (t * (c * j)) + t_2;
	} else if (y <= -8.5e-69) {
		tmp = t_3;
	} else if (y <= 8e-209) {
		tmp = t_1 + (b * ((a * i) - (z * c)));
	} else if (y <= 2e+194) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = y * ((x * z) - (i * j))
    t_3 = (j * ((t * c) - (y * i))) + t_1
    if (y <= (-2.5d+161)) then
        tmp = (t * (c * j)) + t_2
    else if (y <= (-8.5d-69)) then
        tmp = t_3
    else if (y <= 8d-209) then
        tmp = t_1 + (b * ((a * i) - (z * c)))
    else if (y <= 2d+194) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = (j * ((t * c) - (y * i))) + t_1;
	double tmp;
	if (y <= -2.5e+161) {
		tmp = (t * (c * j)) + t_2;
	} else if (y <= -8.5e-69) {
		tmp = t_3;
	} else if (y <= 8e-209) {
		tmp = t_1 + (b * ((a * i) - (z * c)));
	} else if (y <= 2e+194) {
		tmp = t_3;
	} 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))
	t_2 = y * ((x * z) - (i * j))
	t_3 = (j * ((t * c) - (y * i))) + t_1
	tmp = 0
	if y <= -2.5e+161:
		tmp = (t * (c * j)) + t_2
	elif y <= -8.5e-69:
		tmp = t_3
	elif y <= 8e-209:
		tmp = t_1 + (b * ((a * i) - (z * c)))
	elif y <= 2e+194:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_3 = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + t_1)
	tmp = 0.0
	if (y <= -2.5e+161)
		tmp = Float64(Float64(t * Float64(c * j)) + t_2);
	elseif (y <= -8.5e-69)
		tmp = t_3;
	elseif (y <= 8e-209)
		tmp = Float64(t_1 + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (y <= 2e+194)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = y * ((x * z) - (i * j));
	t_3 = (j * ((t * c) - (y * i))) + t_1;
	tmp = 0.0;
	if (y <= -2.5e+161)
		tmp = (t * (c * j)) + t_2;
	elseif (y <= -8.5e-69)
		tmp = t_3;
	elseif (y <= 8e-209)
		tmp = t_1 + (b * ((a * i) - (z * c)));
	elseif (y <= 2e+194)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[y, -2.5e+161], N[(N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[y, -8.5e-69], t$95$3, If[LessEqual[y, 8e-209], N[(t$95$1 + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e+194], t$95$3, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.4999999999999998e161

   1. Initial program 68.8%

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

   3. Taylor expanded in y around -inf 76.5%

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

   5. Simplified 84.2%

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

   6. Taylor expanded in b around 0 84.4%

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

   7. Taylor expanded in c around inf 87.0%

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

      1. *-commutative 87.0%

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

   9. Simplified 87.0%

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

   if -2.4999999999999998e161 < y < -8.50000000000000046e-69 or 8.0000000000000004e-209 < y < 1.99999999999999989e194

   1. Initial program 74.6%

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

   3. Taylor expanded in b around 0 72.6%

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

   if -8.50000000000000046e-69 < y < 8.0000000000000004e-209

   1. Initial program 81.2%

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

   3. Taylor expanded in j around 0 76.4%

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

      1. *-commutative 76.4%

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

   5. Simplified 76.4%

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

   if 1.99999999999999989e194 < y

   1. Initial program 42.2%

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

   3. Taylor expanded in y around -inf 79.4%

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

      1. mul-1-neg 79.4%

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

      2. *-commutative 79.4%

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

      3. distribute-rgt-neg-in 79.4%

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

      4. +-commutative 79.4%

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

      5. mul-1-neg 79.4%

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

      6. unsub-neg 79.4%

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

      7. *-commutative 79.4%

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

   5. Simplified 79.4%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+161}:\\ \;\;\;\;t \cdot \left(c \cdot j\right) + y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-69}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-209}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+194}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 54.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := t_1 - i \cdot \left(y \cdot j\right)\\ \mathbf{if}\;y \leq -1.55 \cdot 10^{+157}:\\ \;\;\;\;t \cdot \left(c \cdot j\right) + y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-89}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-240}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{-256}:\\ \;\;\;\;t_1 - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-11}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (- t_1 (* i (* y j)))))
   (if (<= y -1.55e+157)
     (+ (* t (* c j)) (* y (- (* x z) (* i j))))
     (if (<= y -1.35e-89)
       t_2
       (if (<= y -8.2e-240)
         (* b (- (* a i) (* z c)))
         (if (<= y 1.26e-256)
           (- t_1 (* b (* z c)))
           (if (<= y 6.2e-11)
             (- (* t (- (* c j) (* x a))) (* y (* i j)))
             t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = t_1 - (i * (y * j));
	double tmp;
	if (y <= -1.55e+157) {
		tmp = (t * (c * j)) + (y * ((x * z) - (i * j)));
	} else if (y <= -1.35e-89) {
		tmp = t_2;
	} else if (y <= -8.2e-240) {
		tmp = b * ((a * i) - (z * c));
	} else if (y <= 1.26e-256) {
		tmp = t_1 - (b * (z * c));
	} else if (y <= 6.2e-11) {
		tmp = (t * ((c * j) - (x * a))) - (y * (i * j));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = t_1 - (i * (y * j))
    if (y <= (-1.55d+157)) then
        tmp = (t * (c * j)) + (y * ((x * z) - (i * j)))
    else if (y <= (-1.35d-89)) then
        tmp = t_2
    else if (y <= (-8.2d-240)) then
        tmp = b * ((a * i) - (z * c))
    else if (y <= 1.26d-256) then
        tmp = t_1 - (b * (z * c))
    else if (y <= 6.2d-11) then
        tmp = (t * ((c * j) - (x * a))) - (y * (i * j))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = t_1 - (i * (y * j));
	double tmp;
	if (y <= -1.55e+157) {
		tmp = (t * (c * j)) + (y * ((x * z) - (i * j)));
	} else if (y <= -1.35e-89) {
		tmp = t_2;
	} else if (y <= -8.2e-240) {
		tmp = b * ((a * i) - (z * c));
	} else if (y <= 1.26e-256) {
		tmp = t_1 - (b * (z * c));
	} else if (y <= 6.2e-11) {
		tmp = (t * ((c * j) - (x * a))) - (y * (i * j));
	} 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))
	t_2 = t_1 - (i * (y * j))
	tmp = 0
	if y <= -1.55e+157:
		tmp = (t * (c * j)) + (y * ((x * z) - (i * j)))
	elif y <= -1.35e-89:
		tmp = t_2
	elif y <= -8.2e-240:
		tmp = b * ((a * i) - (z * c))
	elif y <= 1.26e-256:
		tmp = t_1 - (b * (z * c))
	elif y <= 6.2e-11:
		tmp = (t * ((c * j) - (x * a))) - (y * (i * j))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(t_1 - Float64(i * Float64(y * j)))
	tmp = 0.0
	if (y <= -1.55e+157)
		tmp = Float64(Float64(t * Float64(c * j)) + Float64(y * Float64(Float64(x * z) - Float64(i * j))));
	elseif (y <= -1.35e-89)
		tmp = t_2;
	elseif (y <= -8.2e-240)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (y <= 1.26e-256)
		tmp = Float64(t_1 - Float64(b * Float64(z * c)));
	elseif (y <= 6.2e-11)
		tmp = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) - Float64(y * Float64(i * j)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = t_1 - (i * (y * j));
	tmp = 0.0;
	if (y <= -1.55e+157)
		tmp = (t * (c * j)) + (y * ((x * z) - (i * j)));
	elseif (y <= -1.35e-89)
		tmp = t_2;
	elseif (y <= -8.2e-240)
		tmp = b * ((a * i) - (z * c));
	elseif (y <= 1.26e-256)
		tmp = t_1 - (b * (z * c));
	elseif (y <= 6.2e-11)
		tmp = (t * ((c * j) - (x * a))) - (y * (i * j));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.55e+157], N[(N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.35e-89], t$95$2, If[LessEqual[y, -8.2e-240], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.26e-256], N[(t$95$1 - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.2e-11], N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.5499999999999999e157

   1. Initial program 70.4%

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

   3. Taylor expanded in y around -inf 77.7%

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

   5. Simplified 85.0%

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

   6. Taylor expanded in b around 0 85.2%

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

   7. Taylor expanded in c around inf 87.6%

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

      1. *-commutative 87.6%

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

   9. Simplified 87.6%

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

   if -1.5499999999999999e157 < y < -1.34999999999999994e-89 or 6.20000000000000056e-11 < y

   1. Initial program 67.1%

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

   3. Taylor expanded in i around 0 65.4%

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

      1. *-commutative 65.4%

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

      2. *-commutative 65.4%

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

      3. *-commutative 65.4%

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

      4. *-commutative 65.4%

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

      5. associate-*l* 66.4%

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

      6. *-commutative 66.4%

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

   5. Simplified 66.4%

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

   6. Taylor expanded in c around 0 69.5%

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

   if -1.34999999999999994e-89 < y < -8.2000000000000003e-240

   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 b around inf 68.3%

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

   if -8.2000000000000003e-240 < y < 1.25999999999999999e-256

   1. Initial program 85.4%

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

   3. Taylor expanded in j around 0 85.6%

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

      1. *-commutative 85.6%

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

   5. Simplified 85.6%

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

   6. Taylor expanded in c around inf 71.1%

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

   if 1.25999999999999999e-256 < y < 6.20000000000000056e-11

   1. Initial program 78.1%

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

   3. Taylor expanded in y around -inf 67.5%

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

   5. Simplified 72.8%

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

   6. Taylor expanded in b around 0 65.8%

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

   7. Taylor expanded in z around 0 70.9%

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

      1. +-commutative 70.9%

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

      2. *-commutative 70.9%

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

      3. *-commutative 70.9%

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

      4. mul-1-neg 70.9%

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

      5. associate-*r* 67.0%

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

      6. unsub-neg 67.0%

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

      7. *-commutative 67.0%

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

   9. Simplified 67.0%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+157}:\\ \;\;\;\;t \cdot \left(c \cdot j\right) + y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-89}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-240}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{-256}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-11}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -2.1 \cdot 10^{+116}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -6.2 \cdot 10^{-272}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;i \leq 1.35 \cdot 10^{+89}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* a b) (* y j)))))
   (if (<= i -2.1e+116)
     t_1
     (if (<= i -6.2e-272)
       (+ (* t (- (* c j) (* x a))) (* y (- (* x z) (* i j))))
       (if (<= i 1.35e+89)
         (+ (* x (- (* y z) (* t a))) (* b (- (* a i) (* z c))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -2.1e+116) {
		tmp = t_1;
	} else if (i <= -6.2e-272) {
		tmp = (t * ((c * j) - (x * a))) + (y * ((x * z) - (i * j)));
	} else if (i <= 1.35e+89) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * ((a * b) - (y * j))
    if (i <= (-2.1d+116)) then
        tmp = t_1
    else if (i <= (-6.2d-272)) then
        tmp = (t * ((c * j) - (x * a))) + (y * ((x * z) - (i * j)))
    else if (i <= 1.35d+89) then
        tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -2.1e+116) {
		tmp = t_1;
	} else if (i <= -6.2e-272) {
		tmp = (t * ((c * j) - (x * a))) + (y * ((x * z) - (i * j)));
	} else if (i <= 1.35e+89) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((a * b) - (y * j))
	tmp = 0
	if i <= -2.1e+116:
		tmp = t_1
	elif i <= -6.2e-272:
		tmp = (t * ((c * j) - (x * a))) + (y * ((x * z) - (i * j)))
	elif i <= 1.35e+89:
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -2.1e+116)
		tmp = t_1;
	elseif (i <= -6.2e-272)
		tmp = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) + Float64(y * Float64(Float64(x * z) - Float64(i * j))));
	elseif (i <= 1.35e+89)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((a * b) - (y * j));
	tmp = 0.0;
	if (i <= -2.1e+116)
		tmp = t_1;
	elseif (i <= -6.2e-272)
		tmp = (t * ((c * j) - (x * a))) + (y * ((x * z) - (i * j)));
	elseif (i <= 1.35e+89)
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.1e+116], t$95$1, If[LessEqual[i, -6.2e-272], N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.35e+89], 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], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if i < -2.1000000000000001e116 or 1.35e89 < i

   1. Initial program 59.8%

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

   3. Taylor expanded in y around -inf 58.7%

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

   5. Simplified 58.7%

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

   6. Taylor expanded in i around inf 70.7%

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

      1. mul-1-neg 70.7%

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

      2. neg-sub0 70.7%

         \[\leadsto i \cdot \left(\color{blue}{\left(0 - j \cdot y\right)} - -1 \cdot \left(a \cdot b\right)\right) \]

      3. mul-1-neg 70.7%

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

      4. *-commutative 70.7%

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

      5. associate--r+ 70.7%

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

      6. +-commutative 70.7%

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

      7. associate--r+ 70.7%

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

      8. neg-sub0 70.7%

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

      9. remove-double-neg 70.7%

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

      10. *-commutative 70.7%

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

   8. Simplified 70.7%

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

   if -2.1000000000000001e116 < i < -6.20000000000000059e-272

   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 y around -inf 75.4%

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

   5. Simplified 80.7%

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

   6. Taylor expanded in b around 0 76.3%

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

   if -6.20000000000000059e-272 < i < 1.35e89

   1. Initial program 83.7%

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

   3. Taylor expanded in j around 0 71.8%

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

      1. *-commutative 71.8%

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

   5. Simplified 71.8%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.1 \cdot 10^{+116}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -6.2 \cdot 10^{-272}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;i \leq 1.35 \cdot 10^{+89}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 44.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_3 := j \cdot \left(t \cdot c\right)\\ \mathbf{if}\;a \leq -3.4 \cdot 10^{+45}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.35 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{-107}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-239}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-300}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-193}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{+94}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z)))
        (t_2 (* a (- (* b i) (* x t))))
        (t_3 (* j (* t c))))
   (if (<= a -3.4e+45)
     t_2
     (if (<= a -3.35e-56)
       t_1
       (if (<= a -1.95e-107)
         t_3
         (if (<= a -4.5e-239)
           t_1
           (if (<= a 3.2e-300)
             t_3
             (if (<= a 1.2e-193)
               t_1
               (if (<= a 4.7e+94) (* b (- (* a i) (* z c))) t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double t_2 = a * ((b * i) - (x * t));
	double t_3 = j * (t * c);
	double tmp;
	if (a <= -3.4e+45) {
		tmp = t_2;
	} else if (a <= -3.35e-56) {
		tmp = t_1;
	} else if (a <= -1.95e-107) {
		tmp = t_3;
	} else if (a <= -4.5e-239) {
		tmp = t_1;
	} else if (a <= 3.2e-300) {
		tmp = t_3;
	} else if (a <= 1.2e-193) {
		tmp = t_1;
	} else if (a <= 4.7e+94) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * (y * z)
    t_2 = a * ((b * i) - (x * t))
    t_3 = j * (t * c)
    if (a <= (-3.4d+45)) then
        tmp = t_2
    else if (a <= (-3.35d-56)) then
        tmp = t_1
    else if (a <= (-1.95d-107)) then
        tmp = t_3
    else if (a <= (-4.5d-239)) then
        tmp = t_1
    else if (a <= 3.2d-300) then
        tmp = t_3
    else if (a <= 1.2d-193) then
        tmp = t_1
    else if (a <= 4.7d+94) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double t_2 = a * ((b * i) - (x * t));
	double t_3 = j * (t * c);
	double tmp;
	if (a <= -3.4e+45) {
		tmp = t_2;
	} else if (a <= -3.35e-56) {
		tmp = t_1;
	} else if (a <= -1.95e-107) {
		tmp = t_3;
	} else if (a <= -4.5e-239) {
		tmp = t_1;
	} else if (a <= 3.2e-300) {
		tmp = t_3;
	} else if (a <= 1.2e-193) {
		tmp = t_1;
	} else if (a <= 4.7e+94) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	t_2 = a * ((b * i) - (x * t))
	t_3 = j * (t * c)
	tmp = 0
	if a <= -3.4e+45:
		tmp = t_2
	elif a <= -3.35e-56:
		tmp = t_1
	elif a <= -1.95e-107:
		tmp = t_3
	elif a <= -4.5e-239:
		tmp = t_1
	elif a <= 3.2e-300:
		tmp = t_3
	elif a <= 1.2e-193:
		tmp = t_1
	elif a <= 4.7e+94:
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(y * z))
	t_2 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	t_3 = Float64(j * Float64(t * c))
	tmp = 0.0
	if (a <= -3.4e+45)
		tmp = t_2;
	elseif (a <= -3.35e-56)
		tmp = t_1;
	elseif (a <= -1.95e-107)
		tmp = t_3;
	elseif (a <= -4.5e-239)
		tmp = t_1;
	elseif (a <= 3.2e-300)
		tmp = t_3;
	elseif (a <= 1.2e-193)
		tmp = t_1;
	elseif (a <= 4.7e+94)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (y * z);
	t_2 = a * ((b * i) - (x * t));
	t_3 = j * (t * c);
	tmp = 0.0;
	if (a <= -3.4e+45)
		tmp = t_2;
	elseif (a <= -3.35e-56)
		tmp = t_1;
	elseif (a <= -1.95e-107)
		tmp = t_3;
	elseif (a <= -4.5e-239)
		tmp = t_1;
	elseif (a <= 3.2e-300)
		tmp = t_3;
	elseif (a <= 1.2e-193)
		tmp = t_1;
	elseif (a <= 4.7e+94)
		tmp = b * ((a * i) - (z * c));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.4e+45], t$95$2, If[LessEqual[a, -3.35e-56], t$95$1, If[LessEqual[a, -1.95e-107], t$95$3, If[LessEqual[a, -4.5e-239], t$95$1, If[LessEqual[a, 3.2e-300], t$95$3, If[LessEqual[a, 1.2e-193], t$95$1, If[LessEqual[a, 4.7e+94], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.4e45 or 4.70000000000000017e94 < a

   1. Initial program 63.5%

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

   3. Taylor expanded in y around -inf 67.2%

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

   5. Simplified 65.5%

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

      1. associate--l+ 65.5%

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

      2. fma-def 67.4%

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

      3. fma-neg 67.4%

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

   7. Applied egg-rr 67.4%

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

   8. Taylor expanded in a around inf 70.7%

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

      1. mul-1-neg 70.7%

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

      2. *-commutative 70.7%

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

      3. neg-sub0 70.7%

         \[\leadsto a \cdot \left(\color{blue}{\left(0 - x \cdot t\right)} - -1 \cdot \left(b \cdot i\right)\right) \]

      4. mul-1-neg 70.7%

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

      5. distribute-lft-neg-out 70.7%

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

      6. associate--r+ 70.7%

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

      7. +-commutative 70.7%

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

      8. associate--r+ 70.7%

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

      9. neg-sub0 70.7%

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

      10. *-commutative 70.7%

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

      11. distribute-rgt-neg-in 70.7%

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

      12. remove-double-neg 70.7%

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

      13. *-commutative 70.7%

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

      14. *-commutative 70.7%

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

   10. Simplified 70.7%

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

   if -3.4e45 < a < -3.3499999999999998e-56 or -1.95e-107 < a < -4.50000000000000013e-239 or 3.20000000000000021e-300 < a < 1.2e-193

   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 56.6%

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

      1. *-commutative 56.6%

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

   5. Simplified 56.6%

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

   6. Taylor expanded in z around inf 46.7%

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

      1. *-commutative 46.7%

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

   8. Simplified 46.7%

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

   if -3.3499999999999998e-56 < a < -1.95e-107 or -4.50000000000000013e-239 < a < 3.20000000000000021e-300

   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 y around -inf 69.6%

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

   5. Simplified 72.7%

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

   6. Taylor expanded in b around 0 69.3%

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

   7. Taylor expanded in c around inf 50.1%

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

      1. *-commutative 50.1%

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

      2. associate-*r* 53.1%

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

   9. Simplified 53.1%

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

   if 1.2e-193 < a < 4.70000000000000017e94

   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 b around inf 41.6%

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

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+45}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -3.35 \cdot 10^{-56}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{-107}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-239}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-300}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-193}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{+94}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;i \leq -1.1 \cdot 10^{+112}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -8.5 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -1.6 \cdot 10^{-24}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq -2.35 \cdot 10^{-271}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 3.3 \cdot 10^{-6}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 9.5 \cdot 10^{+49}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq 4.1 \cdot 10^{+86}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a))))
        (t_2 (* i (- (* a b) (* y j))))
        (t_3 (* x (- (* y z) (* t a)))))
   (if (<= i -1.1e+112)
     t_2
     (if (<= i -8.5e+46)
       t_1
       (if (<= i -1.6e-24)
         (* z (- (* x y) (* b c)))
         (if (<= i -2.35e-271)
           t_1
           (if (<= i 3.3e-6)
             t_3
             (if (<= i 9.5e+49)
               (* b (- (* a i) (* z c)))
               (if (<= i 4.1e+86) t_3 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double t_2 = i * ((a * b) - (y * j));
	double t_3 = x * ((y * z) - (t * a));
	double tmp;
	if (i <= -1.1e+112) {
		tmp = t_2;
	} else if (i <= -8.5e+46) {
		tmp = t_1;
	} else if (i <= -1.6e-24) {
		tmp = z * ((x * y) - (b * c));
	} else if (i <= -2.35e-271) {
		tmp = t_1;
	} else if (i <= 3.3e-6) {
		tmp = t_3;
	} else if (i <= 9.5e+49) {
		tmp = b * ((a * i) - (z * c));
	} else if (i <= 4.1e+86) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = t * ((c * j) - (x * a))
    t_2 = i * ((a * b) - (y * j))
    t_3 = x * ((y * z) - (t * a))
    if (i <= (-1.1d+112)) then
        tmp = t_2
    else if (i <= (-8.5d+46)) then
        tmp = t_1
    else if (i <= (-1.6d-24)) then
        tmp = z * ((x * y) - (b * c))
    else if (i <= (-2.35d-271)) then
        tmp = t_1
    else if (i <= 3.3d-6) then
        tmp = t_3
    else if (i <= 9.5d+49) then
        tmp = b * ((a * i) - (z * c))
    else if (i <= 4.1d+86) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double t_2 = i * ((a * b) - (y * j));
	double t_3 = x * ((y * z) - (t * a));
	double tmp;
	if (i <= -1.1e+112) {
		tmp = t_2;
	} else if (i <= -8.5e+46) {
		tmp = t_1;
	} else if (i <= -1.6e-24) {
		tmp = z * ((x * y) - (b * c));
	} else if (i <= -2.35e-271) {
		tmp = t_1;
	} else if (i <= 3.3e-6) {
		tmp = t_3;
	} else if (i <= 9.5e+49) {
		tmp = b * ((a * i) - (z * c));
	} else if (i <= 4.1e+86) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	t_2 = i * ((a * b) - (y * j))
	t_3 = x * ((y * z) - (t * a))
	tmp = 0
	if i <= -1.1e+112:
		tmp = t_2
	elif i <= -8.5e+46:
		tmp = t_1
	elif i <= -1.6e-24:
		tmp = z * ((x * y) - (b * c))
	elif i <= -2.35e-271:
		tmp = t_1
	elif i <= 3.3e-6:
		tmp = t_3
	elif i <= 9.5e+49:
		tmp = b * ((a * i) - (z * c))
	elif i <= 4.1e+86:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_2 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	t_3 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (i <= -1.1e+112)
		tmp = t_2;
	elseif (i <= -8.5e+46)
		tmp = t_1;
	elseif (i <= -1.6e-24)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (i <= -2.35e-271)
		tmp = t_1;
	elseif (i <= 3.3e-6)
		tmp = t_3;
	elseif (i <= 9.5e+49)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (i <= 4.1e+86)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((c * j) - (x * a));
	t_2 = i * ((a * b) - (y * j));
	t_3 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (i <= -1.1e+112)
		tmp = t_2;
	elseif (i <= -8.5e+46)
		tmp = t_1;
	elseif (i <= -1.6e-24)
		tmp = z * ((x * y) - (b * c));
	elseif (i <= -2.35e-271)
		tmp = t_1;
	elseif (i <= 3.3e-6)
		tmp = t_3;
	elseif (i <= 9.5e+49)
		tmp = b * ((a * i) - (z * c));
	elseif (i <= 4.1e+86)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.1e+112], t$95$2, If[LessEqual[i, -8.5e+46], t$95$1, If[LessEqual[i, -1.6e-24], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -2.35e-271], t$95$1, If[LessEqual[i, 3.3e-6], t$95$3, If[LessEqual[i, 9.5e+49], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4.1e+86], t$95$3, t$95$2]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -1.1e112 or 4.0999999999999999e86 < i

   1. Initial program 59.8%

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

   3. Taylor expanded in y around -inf 58.7%

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

   5. Simplified 58.7%

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

   6. Taylor expanded in i around inf 70.7%

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

      1. mul-1-neg 70.7%

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

      2. neg-sub0 70.7%

         \[\leadsto i \cdot \left(\color{blue}{\left(0 - j \cdot y\right)} - -1 \cdot \left(a \cdot b\right)\right) \]

      3. mul-1-neg 70.7%

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

      4. *-commutative 70.7%

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

      5. associate--r+ 70.7%

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

      6. +-commutative 70.7%

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

      7. associate--r+ 70.7%

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

      8. neg-sub0 70.7%

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

      9. remove-double-neg 70.7%

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

      10. *-commutative 70.7%

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

   8. Simplified 70.7%

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

   if -1.1e112 < i < -8.4999999999999996e46 or -1.60000000000000006e-24 < i < -2.35000000000000002e-271

   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 t around inf 62.4%

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

      1. +-commutative 62.4%

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

      2. mul-1-neg 62.4%

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

      3. unsub-neg 62.4%

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

   5. Simplified 62.4%

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

   if -8.4999999999999996e46 < i < -1.60000000000000006e-24

   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 z around inf 100.0%

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

   if -2.35000000000000002e-271 < i < 3.30000000000000017e-6 or 9.49999999999999969e49 < i < 4.0999999999999999e86

   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 x around inf 62.6%

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

      1. *-commutative 62.6%

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

   5. Simplified 62.6%

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

   if 3.30000000000000017e-6 < i < 9.49999999999999969e49

   1. Initial program 93.5%

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

   3. Taylor expanded in b around inf 63.2%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.1 \cdot 10^{+112}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -8.5 \cdot 10^{+46}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;i \leq -1.6 \cdot 10^{-24}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq -2.35 \cdot 10^{-271}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;i \leq 3.3 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq 9.5 \cdot 10^{+49}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq 4.1 \cdot 10^{+86}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 52.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;y \leq -4.1 \cdot 10^{-49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.063 \cdot 10^{-265}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5500000:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+132}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+178}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* j (- (* t c) (* y i))) (* z (* x y))))
        (t_2 (* a (- (* b i) (* x t)))))
   (if (<= y -4.1e-49)
     t_1
     (if (<= y 4.063e-265)
       t_2
       (if (<= y 5500000.0)
         (* t (- (* c j) (* x a)))
         (if (<= y 1.5e+132)
           t_1
           (if (<= y 4.6e+178) t_2 (* y (- (* x z) (* i j))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((t * c) - (y * i))) + (z * (x * y));
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (y <= -4.1e-49) {
		tmp = t_1;
	} else if (y <= 4.063e-265) {
		tmp = t_2;
	} else if (y <= 5500000.0) {
		tmp = t * ((c * j) - (x * a));
	} else if (y <= 1.5e+132) {
		tmp = t_1;
	} else if (y <= 4.6e+178) {
		tmp = t_2;
	} else {
		tmp = y * ((x * z) - (i * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (j * ((t * c) - (y * i))) + (z * (x * y))
    t_2 = a * ((b * i) - (x * t))
    if (y <= (-4.1d-49)) then
        tmp = t_1
    else if (y <= 4.063d-265) then
        tmp = t_2
    else if (y <= 5500000.0d0) then
        tmp = t * ((c * j) - (x * a))
    else if (y <= 1.5d+132) then
        tmp = t_1
    else if (y <= 4.6d+178) then
        tmp = t_2
    else
        tmp = y * ((x * z) - (i * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((t * c) - (y * i))) + (z * (x * y));
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (y <= -4.1e-49) {
		tmp = t_1;
	} else if (y <= 4.063e-265) {
		tmp = t_2;
	} else if (y <= 5500000.0) {
		tmp = t * ((c * j) - (x * a));
	} else if (y <= 1.5e+132) {
		tmp = t_1;
	} else if (y <= 4.6e+178) {
		tmp = t_2;
	} else {
		tmp = y * ((x * z) - (i * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((t * c) - (y * i))) + (z * (x * y))
	t_2 = a * ((b * i) - (x * t))
	tmp = 0
	if y <= -4.1e-49:
		tmp = t_1
	elif y <= 4.063e-265:
		tmp = t_2
	elif y <= 5500000.0:
		tmp = t * ((c * j) - (x * a))
	elif y <= 1.5e+132:
		tmp = t_1
	elif y <= 4.6e+178:
		tmp = t_2
	else:
		tmp = y * ((x * z) - (i * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(z * Float64(x * y)))
	t_2 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (y <= -4.1e-49)
		tmp = t_1;
	elseif (y <= 4.063e-265)
		tmp = t_2;
	elseif (y <= 5500000.0)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (y <= 1.5e+132)
		tmp = t_1;
	elseif (y <= 4.6e+178)
		tmp = t_2;
	else
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (j * ((t * c) - (y * i))) + (z * (x * y));
	t_2 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (y <= -4.1e-49)
		tmp = t_1;
	elseif (y <= 4.063e-265)
		tmp = t_2;
	elseif (y <= 5500000.0)
		tmp = t * ((c * j) - (x * a));
	elseif (y <= 1.5e+132)
		tmp = t_1;
	elseif (y <= 4.6e+178)
		tmp = t_2;
	else
		tmp = y * ((x * z) - (i * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.1e-49], t$95$1, If[LessEqual[y, 4.063e-265], t$95$2, If[LessEqual[y, 5500000.0], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.5e+132], t$95$1, If[LessEqual[y, 4.6e+178], t$95$2, N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.1000000000000001e-49 or 5.5e6 < y < 1.4999999999999999e132

   1. Initial program 72.7%

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

   3. Taylor expanded in y around inf 69.7%

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

      1. *-commutative 69.7%

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

      2. *-commutative 69.7%

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

      3. associate-*l* 67.9%

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

   5. Simplified 67.9%

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

   if -4.1000000000000001e-49 < y < 4.06299999999999987e-265 or 1.4999999999999999e132 < y < 4.6000000000000002e178

   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 y around -inf 73.1%

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

   5. Simplified 71.8%

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

      1. associate--l+ 71.8%

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

      2. fma-def 71.8%

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

      3. fma-neg 71.8%

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

   7. Applied egg-rr 71.8%

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

   8. Taylor expanded in a around inf 66.1%

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

      1. mul-1-neg 66.1%

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

      2. *-commutative 66.1%

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

      3. neg-sub0 66.1%

         \[\leadsto a \cdot \left(\color{blue}{\left(0 - x \cdot t\right)} - -1 \cdot \left(b \cdot i\right)\right) \]

      4. mul-1-neg 66.1%

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

      5. distribute-lft-neg-out 66.1%

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

      6. associate--r+ 66.1%

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

      7. +-commutative 66.1%

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

      8. associate--r+ 66.1%

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

      9. neg-sub0 66.1%

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

      10. *-commutative 66.1%

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

      11. distribute-rgt-neg-in 66.1%

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

      12. remove-double-neg 66.1%

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

      13. *-commutative 66.1%

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

      14. *-commutative 66.1%

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

   10. Simplified 66.1%

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

   if 4.06299999999999987e-265 < y < 5.5e6

   1. Initial program 80.0%

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

   3. Taylor expanded in t around inf 60.9%

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

      1. +-commutative 60.9%

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

      2. mul-1-neg 60.9%

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

      3. unsub-neg 60.9%

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

   5. Simplified 60.9%

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

   if 4.6000000000000002e178 < y

   1. Initial program 44.5%

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

   3. Taylor expanded in y around -inf 76.6%

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

      1. mul-1-neg 76.6%

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

      2. *-commutative 76.6%

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

      3. distribute-rgt-neg-in 76.6%

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

      4. +-commutative 76.6%

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

      5. mul-1-neg 76.6%

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

      6. unsub-neg 76.6%

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

      7. *-commutative 76.6%

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

   5. Simplified 76.6%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{-49}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 4.063 \cdot 10^{-265}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq 5500000:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+132}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+178}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 59.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-56}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) - z \cdot \left(b \cdot c - x \cdot y\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-88}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+33}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -1.15e-56)
   (- (* c (* t j)) (* z (- (* b c) (* x y))))
   (if (<= z 4.2e-88)
     (- (* t (- (* c j) (* x a))) (* y (* i j)))
     (if (<= z 2.05e+33)
       (- (* j (- (* t c) (* y i))) (* z (* b c)))
       (* z (- (* x y) (* b c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -1.15e-56) {
		tmp = (c * (t * j)) - (z * ((b * c) - (x * y)));
	} else if (z <= 4.2e-88) {
		tmp = (t * ((c * j) - (x * a))) - (y * (i * j));
	} else if (z <= 2.05e+33) {
		tmp = (j * ((t * c) - (y * i))) - (z * (b * c));
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-1.15d-56)) then
        tmp = (c * (t * j)) - (z * ((b * c) - (x * y)))
    else if (z <= 4.2d-88) then
        tmp = (t * ((c * j) - (x * a))) - (y * (i * j))
    else if (z <= 2.05d+33) then
        tmp = (j * ((t * c) - (y * i))) - (z * (b * c))
    else
        tmp = z * ((x * y) - (b * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -1.15e-56) {
		tmp = (c * (t * j)) - (z * ((b * c) - (x * y)));
	} else if (z <= 4.2e-88) {
		tmp = (t * ((c * j) - (x * a))) - (y * (i * j));
	} else if (z <= 2.05e+33) {
		tmp = (j * ((t * c) - (y * i))) - (z * (b * c));
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -1.15e-56:
		tmp = (c * (t * j)) - (z * ((b * c) - (x * y)))
	elif z <= 4.2e-88:
		tmp = (t * ((c * j) - (x * a))) - (y * (i * j))
	elif z <= 2.05e+33:
		tmp = (j * ((t * c) - (y * i))) - (z * (b * c))
	else:
		tmp = z * ((x * y) - (b * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -1.15e-56)
		tmp = Float64(Float64(c * Float64(t * j)) - Float64(z * Float64(Float64(b * c) - Float64(x * y))));
	elseif (z <= 4.2e-88)
		tmp = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) - Float64(y * Float64(i * j)));
	elseif (z <= 2.05e+33)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) - Float64(z * Float64(b * c)));
	else
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -1.15e-56)
		tmp = (c * (t * j)) - (z * ((b * c) - (x * y)));
	elseif (z <= 4.2e-88)
		tmp = (t * ((c * j) - (x * a))) - (y * (i * j));
	elseif (z <= 2.05e+33)
		tmp = (j * ((t * c) - (y * i))) - (z * (b * c));
	else
		tmp = z * ((x * y) - (b * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -1.15e-56], N[(N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision] - N[(z * N[(N[(b * c), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e-88], N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.05e+33], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.15000000000000001e-56

   1. Initial program 68.1%

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

   3. Taylor expanded in y around -inf 66.8%

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

   5. Simplified 60.8%

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

   6. Taylor expanded in i around 0 59.0%

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

      1. sub-neg 59.0%

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

      2. associate-+r+ 59.0%

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

      3. sub-neg 59.0%

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

      4. associate-*r* 57.6%

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

      5. associate-*r* 56.2%

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

      6. distribute-rgt-out-- 60.8%

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

      7. +-commutative 60.8%

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

      8. fma-def 62.3%

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

   8. Simplified 62.3%

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

   9. Taylor expanded in a around 0 63.9%

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

   if -1.15000000000000001e-56 < z < 4.1999999999999999e-88

   1. Initial program 76.6%

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

   3. Taylor expanded in y around -inf 75.7%

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

   5. Simplified 79.6%

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

   6. Taylor expanded in b around 0 76.3%

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

   7. Taylor expanded in z around 0 71.0%

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

      1. +-commutative 71.0%

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

      2. *-commutative 71.0%

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

      3. *-commutative 71.0%

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

      4. mul-1-neg 71.0%

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

      5. associate-*r* 70.0%

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

      6. unsub-neg 70.0%

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

      7. *-commutative 70.0%

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

   9. Simplified 70.0%

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

   if 4.1999999999999999e-88 < z < 2.04999999999999997e33

   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 i around 0 80.0%

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

      1. *-commutative 80.0%

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

      2. *-commutative 80.0%

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

      3. *-commutative 80.0%

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

      4. *-commutative 80.0%

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

      5. associate-*l* 80.1%

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

      6. *-commutative 80.1%

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

   5. Simplified 80.1%

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

   6. Taylor expanded in x around 0 65.2%

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

      1. sub-neg 65.2%

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

      2. sub-neg 65.2%

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

      3. *-commutative 65.2%

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

      4. *-commutative 65.2%

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

      5. associate-*r* 69.0%

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

      6. *-commutative 69.0%

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

   8. Simplified 69.0%

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

   if 2.04999999999999997e33 < z

   1. Initial program 64.6%

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

   3. Taylor expanded in z around inf 65.7%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-56}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) - z \cdot \left(b \cdot c - x \cdot y\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-88}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+33}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 54.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := t_1 - i \cdot \left(y \cdot j\right)\\ \mathbf{if}\;y \leq -2.95 \cdot 10^{-62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-255}:\\ \;\;\;\;t_1 - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-11}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (- t_1 (* i (* y j)))))
   (if (<= y -2.95e-62)
     t_2
     (if (<= y 2.25e-255)
       (- t_1 (* b (* z c)))
       (if (<= y 7.4e-11) (- (* t (- (* c j) (* x a))) (* y (* i j))) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = t_1 - (i * (y * j));
	double tmp;
	if (y <= -2.95e-62) {
		tmp = t_2;
	} else if (y <= 2.25e-255) {
		tmp = t_1 - (b * (z * c));
	} else if (y <= 7.4e-11) {
		tmp = (t * ((c * j) - (x * a))) - (y * (i * j));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = t_1 - (i * (y * j))
    if (y <= (-2.95d-62)) then
        tmp = t_2
    else if (y <= 2.25d-255) then
        tmp = t_1 - (b * (z * c))
    else if (y <= 7.4d-11) then
        tmp = (t * ((c * j) - (x * a))) - (y * (i * j))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = t_1 - (i * (y * j));
	double tmp;
	if (y <= -2.95e-62) {
		tmp = t_2;
	} else if (y <= 2.25e-255) {
		tmp = t_1 - (b * (z * c));
	} else if (y <= 7.4e-11) {
		tmp = (t * ((c * j) - (x * a))) - (y * (i * j));
	} 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))
	t_2 = t_1 - (i * (y * j))
	tmp = 0
	if y <= -2.95e-62:
		tmp = t_2
	elif y <= 2.25e-255:
		tmp = t_1 - (b * (z * c))
	elif y <= 7.4e-11:
		tmp = (t * ((c * j) - (x * a))) - (y * (i * j))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(t_1 - Float64(i * Float64(y * j)))
	tmp = 0.0
	if (y <= -2.95e-62)
		tmp = t_2;
	elseif (y <= 2.25e-255)
		tmp = Float64(t_1 - Float64(b * Float64(z * c)));
	elseif (y <= 7.4e-11)
		tmp = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) - Float64(y * Float64(i * j)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = t_1 - (i * (y * j));
	tmp = 0.0;
	if (y <= -2.95e-62)
		tmp = t_2;
	elseif (y <= 2.25e-255)
		tmp = t_1 - (b * (z * c));
	elseif (y <= 7.4e-11)
		tmp = (t * ((c * j) - (x * a))) - (y * (i * j));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.95e-62], t$95$2, If[LessEqual[y, 2.25e-255], N[(t$95$1 - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.4e-11], N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.9500000000000002e-62 or 7.4000000000000003e-11 < y

   1. Initial program 67.4%

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

   3. Taylor expanded in i around 0 65.4%

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

      1. *-commutative 65.4%

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

      2. *-commutative 65.4%

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

      3. *-commutative 65.4%

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

      4. *-commutative 65.4%

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

      5. associate-*l* 65.3%

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

      6. *-commutative 65.3%

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

   5. Simplified 65.3%

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

   6. Taylor expanded in c around 0 70.5%

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

   if -2.9500000000000002e-62 < y < 2.2499999999999999e-255

   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 77.4%

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

      1. *-commutative 77.4%

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

   5. Simplified 77.4%

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

   6. Taylor expanded in c around inf 65.7%

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

   if 2.2499999999999999e-255 < y < 7.4000000000000003e-11

   1. Initial program 78.1%

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

   3. Taylor expanded in y around -inf 67.5%

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

   5. Simplified 72.8%

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

   6. Taylor expanded in b around 0 65.8%

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

   7. Taylor expanded in z around 0 70.9%

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

      1. +-commutative 70.9%

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

      2. *-commutative 70.9%

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

      3. *-commutative 70.9%

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

      4. mul-1-neg 70.9%

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

      5. associate-*r* 67.0%

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

      6. unsub-neg 67.0%

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

      7. *-commutative 67.0%

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

   9. Simplified 67.0%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.95 \cdot 10^{-62}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-255}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-11}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 30.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(z \cdot \left(-b\right)\right)\\ t_2 := j \cdot \left(i \cdot \left(-y\right)\right)\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{+88}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -1300:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-81}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.063 \cdot 10^{-265}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-239}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-56}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* z (- b)))) (t_2 (* j (* i (- y)))))
   (if (<= y -1.8e+88)
     (* x (* y z))
     (if (<= y -1300.0)
       t_2
       (if (<= y -2.6e-81)
         (* j (* t c))
         (if (<= y -1.3e-152)
           t_1
           (if (<= y 4.063e-265)
             (* a (* b i))
             (if (<= y 1.35e-239)
               t_1
               (if (<= y 7.5e-56) (* c (* t j)) t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (z * -b);
	double t_2 = j * (i * -y);
	double tmp;
	if (y <= -1.8e+88) {
		tmp = x * (y * z);
	} else if (y <= -1300.0) {
		tmp = t_2;
	} else if (y <= -2.6e-81) {
		tmp = j * (t * c);
	} else if (y <= -1.3e-152) {
		tmp = t_1;
	} else if (y <= 4.063e-265) {
		tmp = a * (b * i);
	} else if (y <= 1.35e-239) {
		tmp = t_1;
	} else if (y <= 7.5e-56) {
		tmp = c * (t * j);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * (z * -b)
    t_2 = j * (i * -y)
    if (y <= (-1.8d+88)) then
        tmp = x * (y * z)
    else if (y <= (-1300.0d0)) then
        tmp = t_2
    else if (y <= (-2.6d-81)) then
        tmp = j * (t * c)
    else if (y <= (-1.3d-152)) then
        tmp = t_1
    else if (y <= 4.063d-265) then
        tmp = a * (b * i)
    else if (y <= 1.35d-239) then
        tmp = t_1
    else if (y <= 7.5d-56) then
        tmp = c * (t * j)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (z * -b);
	double t_2 = j * (i * -y);
	double tmp;
	if (y <= -1.8e+88) {
		tmp = x * (y * z);
	} else if (y <= -1300.0) {
		tmp = t_2;
	} else if (y <= -2.6e-81) {
		tmp = j * (t * c);
	} else if (y <= -1.3e-152) {
		tmp = t_1;
	} else if (y <= 4.063e-265) {
		tmp = a * (b * i);
	} else if (y <= 1.35e-239) {
		tmp = t_1;
	} else if (y <= 7.5e-56) {
		tmp = c * (t * j);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (z * -b)
	t_2 = j * (i * -y)
	tmp = 0
	if y <= -1.8e+88:
		tmp = x * (y * z)
	elif y <= -1300.0:
		tmp = t_2
	elif y <= -2.6e-81:
		tmp = j * (t * c)
	elif y <= -1.3e-152:
		tmp = t_1
	elif y <= 4.063e-265:
		tmp = a * (b * i)
	elif y <= 1.35e-239:
		tmp = t_1
	elif y <= 7.5e-56:
		tmp = c * (t * j)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(z * Float64(-b)))
	t_2 = Float64(j * Float64(i * Float64(-y)))
	tmp = 0.0
	if (y <= -1.8e+88)
		tmp = Float64(x * Float64(y * z));
	elseif (y <= -1300.0)
		tmp = t_2;
	elseif (y <= -2.6e-81)
		tmp = Float64(j * Float64(t * c));
	elseif (y <= -1.3e-152)
		tmp = t_1;
	elseif (y <= 4.063e-265)
		tmp = Float64(a * Float64(b * i));
	elseif (y <= 1.35e-239)
		tmp = t_1;
	elseif (y <= 7.5e-56)
		tmp = Float64(c * Float64(t * j));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (z * -b);
	t_2 = j * (i * -y);
	tmp = 0.0;
	if (y <= -1.8e+88)
		tmp = x * (y * z);
	elseif (y <= -1300.0)
		tmp = t_2;
	elseif (y <= -2.6e-81)
		tmp = j * (t * c);
	elseif (y <= -1.3e-152)
		tmp = t_1;
	elseif (y <= 4.063e-265)
		tmp = a * (b * i);
	elseif (y <= 1.35e-239)
		tmp = t_1;
	elseif (y <= 7.5e-56)
		tmp = c * (t * j);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(i * (-y)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.8e+88], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1300.0], t$95$2, If[LessEqual[y, -2.6e-81], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.3e-152], t$95$1, If[LessEqual[y, 4.063e-265], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.35e-239], t$95$1, If[LessEqual[y, 7.5e-56], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -1.8000000000000001e88

   1. Initial program 68.2%

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

   3. Taylor expanded in x around inf 63.1%

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

      1. *-commutative 63.1%

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

   5. Simplified 63.1%

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

   6. Taylor expanded in z around inf 55.9%

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

      1. *-commutative 55.9%

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

   8. Simplified 55.9%

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

   if -1.8000000000000001e88 < y < -1300 or 7.50000000000000041e-56 < y

   1. Initial program 64.7%

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

   3. Taylor expanded in i around 0 61.3%

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

      1. *-commutative 61.3%

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

      2. *-commutative 61.3%

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

      3. *-commutative 61.3%

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

      4. *-commutative 61.3%

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

      5. associate-*l* 63.6%

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

      6. *-commutative 63.6%

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

   5. Simplified 63.6%

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

   6. Taylor expanded in i around inf 44.0%

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

      1. mul-1-neg 44.0%

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

      2. *-commutative 44.0%

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

      3. associate-*r* 39.6%

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

      4. *-commutative 39.6%

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

      5. distribute-rgt-neg-out 39.6%

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

      6. *-commutative 39.6%

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

      7. distribute-rgt-neg-in 39.6%

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

   8. Simplified 39.6%

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

   if -1300 < y < -2.5999999999999999e-81

   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 y around -inf 72.4%

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

   5. Simplified 72.7%

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

   6. Taylor expanded in b around 0 78.6%

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

   7. Taylor expanded in c around inf 30.9%

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

      1. *-commutative 30.9%

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

      2. associate-*r* 36.7%

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

   9. Simplified 36.7%

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

   if -2.5999999999999999e-81 < y < -1.30000000000000006e-152 or 4.06299999999999987e-265 < y < 1.35e-239

   1. Initial program 71.8%

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

   3. Taylor expanded in y around -inf 64.9%

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

   5. Simplified 57.5%

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

   6. Taylor expanded in c around inf 71.8%

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

      1. *-commutative 71.8%

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

   8. Simplified 71.8%

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

   9. Taylor expanded in t around 0 68.4%

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

       1. mul-1-neg 68.4%

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

       2. distribute-lft-neg-out 68.4%

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

       3. *-commutative 68.4%

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

   11. Simplified 68.4%

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

   if -1.30000000000000006e-152 < y < 4.06299999999999987e-265

   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 b around inf 62.2%

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

   4. Taylor expanded in a around inf 37.3%

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

   if 1.35e-239 < y < 7.50000000000000041e-56

   1. Initial program 79.9%

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

   3. Taylor expanded in y around -inf 64.6%

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

   5. Simplified 73.4%

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

   6. Taylor expanded in c around inf 49.5%

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

      1. *-commutative 49.5%

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

   8. Simplified 49.5%

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

   9. Taylor expanded in t around inf 41.0%

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

       1. *-commutative 41.0%

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

   11. Simplified 41.0%

       \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+88}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -1300:\\ \;\;\;\;j \cdot \left(i \cdot \left(-y\right)\right)\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-81}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-152}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq 4.063 \cdot 10^{-265}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-239}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-56}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(i \cdot \left(-y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 30.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(i \cdot \left(-y\right)\right)\\ t_2 := \left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -1.02 \cdot 10^{+89}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -1450:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-88}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-144}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-242}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-134}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;y \leq 18000000:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (* i (- y)))) (t_2 (* (* t a) (- x))))
   (if (<= y -1.02e+89)
     (* x (* y z))
     (if (<= y -1450.0)
       t_1
       (if (<= y -1.45e-88)
         t_2
         (if (<= y -5.6e-144)
           (* c (* z (- b)))
           (if (<= y 4.2e-242)
             t_2
             (if (<= y 3.6e-134)
               (* c (* t j))
               (if (<= y 18000000.0) 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 = j * (i * -y);
	double t_2 = (t * a) * -x;
	double tmp;
	if (y <= -1.02e+89) {
		tmp = x * (y * z);
	} else if (y <= -1450.0) {
		tmp = t_1;
	} else if (y <= -1.45e-88) {
		tmp = t_2;
	} else if (y <= -5.6e-144) {
		tmp = c * (z * -b);
	} else if (y <= 4.2e-242) {
		tmp = t_2;
	} else if (y <= 3.6e-134) {
		tmp = c * (t * j);
	} else if (y <= 18000000.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (i * -y)
    t_2 = (t * a) * -x
    if (y <= (-1.02d+89)) then
        tmp = x * (y * z)
    else if (y <= (-1450.0d0)) then
        tmp = t_1
    else if (y <= (-1.45d-88)) then
        tmp = t_2
    else if (y <= (-5.6d-144)) then
        tmp = c * (z * -b)
    else if (y <= 4.2d-242) then
        tmp = t_2
    else if (y <= 3.6d-134) then
        tmp = c * (t * j)
    else if (y <= 18000000.0d0) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (i * -y);
	double t_2 = (t * a) * -x;
	double tmp;
	if (y <= -1.02e+89) {
		tmp = x * (y * z);
	} else if (y <= -1450.0) {
		tmp = t_1;
	} else if (y <= -1.45e-88) {
		tmp = t_2;
	} else if (y <= -5.6e-144) {
		tmp = c * (z * -b);
	} else if (y <= 4.2e-242) {
		tmp = t_2;
	} else if (y <= 3.6e-134) {
		tmp = c * (t * j);
	} else if (y <= 18000000.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * (i * -y)
	t_2 = (t * a) * -x
	tmp = 0
	if y <= -1.02e+89:
		tmp = x * (y * z)
	elif y <= -1450.0:
		tmp = t_1
	elif y <= -1.45e-88:
		tmp = t_2
	elif y <= -5.6e-144:
		tmp = c * (z * -b)
	elif y <= 4.2e-242:
		tmp = t_2
	elif y <= 3.6e-134:
		tmp = c * (t * j)
	elif y <= 18000000.0:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(i * Float64(-y)))
	t_2 = Float64(Float64(t * a) * Float64(-x))
	tmp = 0.0
	if (y <= -1.02e+89)
		tmp = Float64(x * Float64(y * z));
	elseif (y <= -1450.0)
		tmp = t_1;
	elseif (y <= -1.45e-88)
		tmp = t_2;
	elseif (y <= -5.6e-144)
		tmp = Float64(c * Float64(z * Float64(-b)));
	elseif (y <= 4.2e-242)
		tmp = t_2;
	elseif (y <= 3.6e-134)
		tmp = Float64(c * Float64(t * j));
	elseif (y <= 18000000.0)
		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 = j * (i * -y);
	t_2 = (t * a) * -x;
	tmp = 0.0;
	if (y <= -1.02e+89)
		tmp = x * (y * z);
	elseif (y <= -1450.0)
		tmp = t_1;
	elseif (y <= -1.45e-88)
		tmp = t_2;
	elseif (y <= -5.6e-144)
		tmp = c * (z * -b);
	elseif (y <= 4.2e-242)
		tmp = t_2;
	elseif (y <= 3.6e-134)
		tmp = c * (t * j);
	elseif (y <= 18000000.0)
		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[(j * N[(i * (-y)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * a), $MachinePrecision] * (-x)), $MachinePrecision]}, If[LessEqual[y, -1.02e+89], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1450.0], t$95$1, If[LessEqual[y, -1.45e-88], t$95$2, If[LessEqual[y, -5.6e-144], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e-242], t$95$2, If[LessEqual[y, 3.6e-134], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 18000000.0], t$95$2, t$95$1]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.0199999999999999e89

   1. Initial program 68.2%

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

   3. Taylor expanded in x around inf 63.1%

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

      1. *-commutative 63.1%

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

   5. Simplified 63.1%

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

   6. Taylor expanded in z around inf 55.9%

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

      1. *-commutative 55.9%

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

   8. Simplified 55.9%

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

   if -1.0199999999999999e89 < y < -1450 or 1.8e7 < y

   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 i around 0 60.8%

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

      1. *-commutative 60.8%

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

      2. *-commutative 60.8%

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

      3. *-commutative 60.8%

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

      4. *-commutative 60.8%

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

      5. associate-*l* 63.5%

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

      6. *-commutative 63.5%

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

   5. Simplified 63.5%

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

   6. Taylor expanded in i around inf 46.2%

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

      1. mul-1-neg 46.2%

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

      2. *-commutative 46.2%

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

      3. associate-*r* 41.2%

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

      4. *-commutative 41.2%

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

      5. distribute-rgt-neg-out 41.2%

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

      6. *-commutative 41.2%

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

      7. distribute-rgt-neg-in 41.2%

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

   8. Simplified 41.2%

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

   if -1450 < y < -1.4500000000000001e-88 or -5.59999999999999995e-144 < y < 4.20000000000000037e-242 or 3.5999999999999999e-134 < y < 1.8e7

   1. Initial program 80.2%

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

   3. Taylor expanded in x around inf 46.5%

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

      1. *-commutative 46.5%

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

   5. Simplified 46.5%

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

   6. Taylor expanded in z around 0 44.1%

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

      1. neg-mul-1 44.1%

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

      2. distribute-rgt-neg-in 44.1%

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

   8. Simplified 44.1%

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

   if -1.4500000000000001e-88 < y < -5.59999999999999995e-144

   1. Initial program 58.2%

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

   3. Taylor expanded in y around -inf 58.2%

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

   5. Simplified 44.0%

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

   6. Taylor expanded in c around inf 85.6%

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

      1. *-commutative 85.6%

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

   8. Simplified 85.6%

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

   9. Taylor expanded in t around 0 78.6%

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

       1. mul-1-neg 78.6%

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

       2. distribute-lft-neg-out 78.6%

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

       3. *-commutative 78.6%

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

   11. Simplified 78.6%

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

   if 4.20000000000000037e-242 < y < 3.5999999999999999e-134

   1. Initial program 82.1%

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

   3. Taylor expanded in y around -inf 68.7%

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

   5. Simplified 68.8%

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

   6. Taylor expanded in c around inf 52.2%

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

      1. *-commutative 52.2%

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

   8. Simplified 52.2%

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

   9. Taylor expanded in t around inf 42.0%

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

       1. *-commutative 42.0%

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

   11. Simplified 42.0%

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

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+89}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -1450:\\ \;\;\;\;j \cdot \left(i \cdot \left(-y\right)\right)\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-88}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-144}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-242}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-134}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;y \leq 18000000:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(i \cdot \left(-y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 30.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(y \cdot \left(-j\right)\right)\\ t_2 := \left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{+90}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -10500:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-90}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-146}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-249}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-133}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;y \leq 12500000:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* y (- j)))) (t_2 (* (* t a) (- x))))
   (if (<= y -2.7e+90)
     (* x (* y z))
     (if (<= y -10500.0)
       t_1
       (if (<= y -7.2e-90)
         t_2
         (if (<= y -1.6e-146)
           (* c (* z (- b)))
           (if (<= y 1.9e-249)
             t_2
             (if (<= y 1.5e-133)
               (* c (* t j))
               (if (<= y 12500000.0) 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 = i * (y * -j);
	double t_2 = (t * a) * -x;
	double tmp;
	if (y <= -2.7e+90) {
		tmp = x * (y * z);
	} else if (y <= -10500.0) {
		tmp = t_1;
	} else if (y <= -7.2e-90) {
		tmp = t_2;
	} else if (y <= -1.6e-146) {
		tmp = c * (z * -b);
	} else if (y <= 1.9e-249) {
		tmp = t_2;
	} else if (y <= 1.5e-133) {
		tmp = c * (t * j);
	} else if (y <= 12500000.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i * (y * -j)
    t_2 = (t * a) * -x
    if (y <= (-2.7d+90)) then
        tmp = x * (y * z)
    else if (y <= (-10500.0d0)) then
        tmp = t_1
    else if (y <= (-7.2d-90)) then
        tmp = t_2
    else if (y <= (-1.6d-146)) then
        tmp = c * (z * -b)
    else if (y <= 1.9d-249) then
        tmp = t_2
    else if (y <= 1.5d-133) then
        tmp = c * (t * j)
    else if (y <= 12500000.0d0) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (y * -j);
	double t_2 = (t * a) * -x;
	double tmp;
	if (y <= -2.7e+90) {
		tmp = x * (y * z);
	} else if (y <= -10500.0) {
		tmp = t_1;
	} else if (y <= -7.2e-90) {
		tmp = t_2;
	} else if (y <= -1.6e-146) {
		tmp = c * (z * -b);
	} else if (y <= 1.9e-249) {
		tmp = t_2;
	} else if (y <= 1.5e-133) {
		tmp = c * (t * j);
	} else if (y <= 12500000.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (y * -j)
	t_2 = (t * a) * -x
	tmp = 0
	if y <= -2.7e+90:
		tmp = x * (y * z)
	elif y <= -10500.0:
		tmp = t_1
	elif y <= -7.2e-90:
		tmp = t_2
	elif y <= -1.6e-146:
		tmp = c * (z * -b)
	elif y <= 1.9e-249:
		tmp = t_2
	elif y <= 1.5e-133:
		tmp = c * (t * j)
	elif y <= 12500000.0:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(y * Float64(-j)))
	t_2 = Float64(Float64(t * a) * Float64(-x))
	tmp = 0.0
	if (y <= -2.7e+90)
		tmp = Float64(x * Float64(y * z));
	elseif (y <= -10500.0)
		tmp = t_1;
	elseif (y <= -7.2e-90)
		tmp = t_2;
	elseif (y <= -1.6e-146)
		tmp = Float64(c * Float64(z * Float64(-b)));
	elseif (y <= 1.9e-249)
		tmp = t_2;
	elseif (y <= 1.5e-133)
		tmp = Float64(c * Float64(t * j));
	elseif (y <= 12500000.0)
		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 = i * (y * -j);
	t_2 = (t * a) * -x;
	tmp = 0.0;
	if (y <= -2.7e+90)
		tmp = x * (y * z);
	elseif (y <= -10500.0)
		tmp = t_1;
	elseif (y <= -7.2e-90)
		tmp = t_2;
	elseif (y <= -1.6e-146)
		tmp = c * (z * -b);
	elseif (y <= 1.9e-249)
		tmp = t_2;
	elseif (y <= 1.5e-133)
		tmp = c * (t * j);
	elseif (y <= 12500000.0)
		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[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * a), $MachinePrecision] * (-x)), $MachinePrecision]}, If[LessEqual[y, -2.7e+90], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -10500.0], t$95$1, If[LessEqual[y, -7.2e-90], t$95$2, If[LessEqual[y, -1.6e-146], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e-249], t$95$2, If[LessEqual[y, 1.5e-133], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 12500000.0], t$95$2, t$95$1]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.7e90

   1. Initial program 68.2%

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

   3. Taylor expanded in x around inf 63.1%

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

      1. *-commutative 63.1%

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

   5. Simplified 63.1%

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

   6. Taylor expanded in z around inf 55.9%

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

      1. *-commutative 55.9%

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

   8. Simplified 55.9%

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

   if -2.7e90 < y < -10500 or 1.25e7 < y

   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 i around 0 60.8%

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

      1. *-commutative 60.8%

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

      2. *-commutative 60.8%

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

      3. *-commutative 60.8%

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

      4. *-commutative 60.8%

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

      5. associate-*l* 63.5%

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

      6. *-commutative 63.5%

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

   5. Simplified 63.5%

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

   6. Taylor expanded in i around inf 46.2%

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

      1. associate-*r* 46.2%

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

      2. neg-mul-1 46.2%

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

   8. Simplified 46.2%

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

   if -10500 < y < -7.19999999999999961e-90 or -1.6e-146 < y < 1.9e-249 or 1.5000000000000001e-133 < y < 1.25e7

   1. Initial program 80.2%

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

   3. Taylor expanded in x around inf 46.5%

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

      1. *-commutative 46.5%

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

   5. Simplified 46.5%

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

   6. Taylor expanded in z around 0 44.1%

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

      1. neg-mul-1 44.1%

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

      2. distribute-rgt-neg-in 44.1%

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

   8. Simplified 44.1%

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

   if -7.19999999999999961e-90 < y < -1.6e-146

   1. Initial program 58.2%

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

   3. Taylor expanded in y around -inf 58.2%

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

   5. Simplified 44.0%

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

   6. Taylor expanded in c around inf 85.6%

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

      1. *-commutative 85.6%

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

   8. Simplified 85.6%

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

   9. Taylor expanded in t around 0 78.6%

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

       1. mul-1-neg 78.6%

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

       2. distribute-lft-neg-out 78.6%

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

       3. *-commutative 78.6%

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

   11. Simplified 78.6%

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

   if 1.9e-249 < y < 1.5000000000000001e-133

   1. Initial program 82.1%

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

   3. Taylor expanded in y around -inf 68.7%

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

   5. Simplified 68.8%

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

   6. Taylor expanded in c around inf 52.2%

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

      1. *-commutative 52.2%

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

   8. Simplified 52.2%

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

   9. Taylor expanded in t around inf 42.0%

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

       1. *-commutative 42.0%

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

   11. Simplified 42.0%

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

4. Final simplification 47.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+90}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -10500:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-90}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-146}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-249}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-133}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;y \leq 12500000:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 49.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -7.5 \cdot 10^{+111}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 3 \cdot 10^{-281}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 5.8 \cdot 10^{-172}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 4 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 5.6 \cdot 10^{+49}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a)))) (t_2 (* i (- (* a b) (* y j)))))
   (if (<= i -7.5e+111)
     t_2
     (if (<= i 3e-281)
       t_1
       (if (<= i 5.8e-172)
         (* x (* y z))
         (if (<= i 4e-18)
           t_1
           (if (<= i 5.6e+49) (* b (- (* a i) (* z c))) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double t_2 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -7.5e+111) {
		tmp = t_2;
	} else if (i <= 3e-281) {
		tmp = t_1;
	} else if (i <= 5.8e-172) {
		tmp = x * (y * z);
	} else if (i <= 4e-18) {
		tmp = t_1;
	} else if (i <= 5.6e+49) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((c * j) - (x * a))
    t_2 = i * ((a * b) - (y * j))
    if (i <= (-7.5d+111)) then
        tmp = t_2
    else if (i <= 3d-281) then
        tmp = t_1
    else if (i <= 5.8d-172) then
        tmp = x * (y * z)
    else if (i <= 4d-18) then
        tmp = t_1
    else if (i <= 5.6d+49) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double t_2 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -7.5e+111) {
		tmp = t_2;
	} else if (i <= 3e-281) {
		tmp = t_1;
	} else if (i <= 5.8e-172) {
		tmp = x * (y * z);
	} else if (i <= 4e-18) {
		tmp = t_1;
	} else if (i <= 5.6e+49) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	t_2 = i * ((a * b) - (y * j))
	tmp = 0
	if i <= -7.5e+111:
		tmp = t_2
	elif i <= 3e-281:
		tmp = t_1
	elif i <= 5.8e-172:
		tmp = x * (y * z)
	elif i <= 4e-18:
		tmp = t_1
	elif i <= 5.6e+49:
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_2 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -7.5e+111)
		tmp = t_2;
	elseif (i <= 3e-281)
		tmp = t_1;
	elseif (i <= 5.8e-172)
		tmp = Float64(x * Float64(y * z));
	elseif (i <= 4e-18)
		tmp = t_1;
	elseif (i <= 5.6e+49)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((c * j) - (x * a));
	t_2 = i * ((a * b) - (y * j));
	tmp = 0.0;
	if (i <= -7.5e+111)
		tmp = t_2;
	elseif (i <= 3e-281)
		tmp = t_1;
	elseif (i <= 5.8e-172)
		tmp = x * (y * z);
	elseif (i <= 4e-18)
		tmp = t_1;
	elseif (i <= 5.6e+49)
		tmp = b * ((a * i) - (z * c));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -7.5e+111], t$95$2, If[LessEqual[i, 3e-281], t$95$1, If[LessEqual[i, 5.8e-172], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4e-18], t$95$1, If[LessEqual[i, 5.6e+49], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -7.49999999999999948e111 or 5.5999999999999996e49 < i

   1. Initial program 59.9%

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

   3. Taylor expanded in y around -inf 58.8%

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

   5. Simplified 58.7%

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

   6. Taylor expanded in i around inf 69.2%

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

      1. mul-1-neg 69.2%

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

      2. neg-sub0 69.2%

         \[\leadsto i \cdot \left(\color{blue}{\left(0 - j \cdot y\right)} - -1 \cdot \left(a \cdot b\right)\right) \]

      3. mul-1-neg 69.2%

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

      4. *-commutative 69.2%

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

      5. associate--r+ 69.2%

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

      6. +-commutative 69.2%

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

      7. associate--r+ 69.2%

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

      8. neg-sub0 69.2%

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

      9. remove-double-neg 69.2%

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

      10. *-commutative 69.2%

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

   8. Simplified 69.2%

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

   if -7.49999999999999948e111 < i < 2.99999999999999975e-281 or 5.79999999999999995e-172 < i < 4.0000000000000003e-18

   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 t around inf 55.8%

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

      1. +-commutative 55.8%

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

      2. mul-1-neg 55.8%

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

      3. unsub-neg 55.8%

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

   5. Simplified 55.8%

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

   if 2.99999999999999975e-281 < i < 5.79999999999999995e-172

   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 x around inf 69.2%

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

      1. *-commutative 69.2%

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

   5. Simplified 69.2%

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

   6. Taylor expanded in z around inf 51.4%

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

      1. *-commutative 51.4%

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

   8. Simplified 51.4%

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

   if 4.0000000000000003e-18 < i < 5.5999999999999996e49

   1. Initial program 94.5%

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

   3. Taylor expanded in b around inf 64.0%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -7.5 \cdot 10^{+111}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq 3 \cdot 10^{-281}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;i \leq 5.8 \cdot 10^{-172}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 4 \cdot 10^{-18}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;i \leq 5.6 \cdot 10^{+49}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 51.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -1.05 \cdot 10^{+113}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -9 \cdot 10^{-271}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;i \leq 2.85 \cdot 10^{-6}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 1.75 \cdot 10^{+49}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq 1.05 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (* i (- (* a b) (* y j)))))
   (if (<= i -1.05e+113)
     t_2
     (if (<= i -9e-271)
       (* t (- (* c j) (* x a)))
       (if (<= i 2.85e-6)
         t_1
         (if (<= i 1.75e+49)
           (* b (- (* a i) (* z c)))
           (if (<= i 1.05e+75) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -1.05e+113) {
		tmp = t_2;
	} else if (i <= -9e-271) {
		tmp = t * ((c * j) - (x * a));
	} else if (i <= 2.85e-6) {
		tmp = t_1;
	} else if (i <= 1.75e+49) {
		tmp = b * ((a * i) - (z * c));
	} else if (i <= 1.05e+75) {
		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))
    t_2 = i * ((a * b) - (y * j))
    if (i <= (-1.05d+113)) then
        tmp = t_2
    else if (i <= (-9d-271)) then
        tmp = t * ((c * j) - (x * a))
    else if (i <= 2.85d-6) then
        tmp = t_1
    else if (i <= 1.75d+49) then
        tmp = b * ((a * i) - (z * c))
    else if (i <= 1.05d+75) 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));
	double t_2 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -1.05e+113) {
		tmp = t_2;
	} else if (i <= -9e-271) {
		tmp = t * ((c * j) - (x * a));
	} else if (i <= 2.85e-6) {
		tmp = t_1;
	} else if (i <= 1.75e+49) {
		tmp = b * ((a * i) - (z * c));
	} else if (i <= 1.05e+75) {
		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))
	t_2 = i * ((a * b) - (y * j))
	tmp = 0
	if i <= -1.05e+113:
		tmp = t_2
	elif i <= -9e-271:
		tmp = t * ((c * j) - (x * a))
	elif i <= 2.85e-6:
		tmp = t_1
	elif i <= 1.75e+49:
		tmp = b * ((a * i) - (z * c))
	elif i <= 1.05e+75:
		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(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -1.05e+113)
		tmp = t_2;
	elseif (i <= -9e-271)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (i <= 2.85e-6)
		tmp = t_1;
	elseif (i <= 1.75e+49)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (i <= 1.05e+75)
		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));
	t_2 = i * ((a * b) - (y * j));
	tmp = 0.0;
	if (i <= -1.05e+113)
		tmp = t_2;
	elseif (i <= -9e-271)
		tmp = t * ((c * j) - (x * a));
	elseif (i <= 2.85e-6)
		tmp = t_1;
	elseif (i <= 1.75e+49)
		tmp = b * ((a * i) - (z * c));
	elseif (i <= 1.05e+75)
		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[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.05e+113], t$95$2, If[LessEqual[i, -9e-271], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.85e-6], t$95$1, If[LessEqual[i, 1.75e+49], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.05e+75], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -1.0499999999999999e113 or 1.04999999999999999e75 < i

   1. Initial program 59.8%

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

   3. Taylor expanded in y around -inf 58.7%

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

   5. Simplified 58.7%

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

   6. Taylor expanded in i around inf 70.7%

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

      1. mul-1-neg 70.7%

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

      2. neg-sub0 70.7%

         \[\leadsto i \cdot \left(\color{blue}{\left(0 - j \cdot y\right)} - -1 \cdot \left(a \cdot b\right)\right) \]

      3. mul-1-neg 70.7%

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

      4. *-commutative 70.7%

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

      5. associate--r+ 70.7%

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

      6. +-commutative 70.7%

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

      7. associate--r+ 70.7%

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

      8. neg-sub0 70.7%

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

      9. remove-double-neg 70.7%

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

      10. *-commutative 70.7%

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

   8. Simplified 70.7%

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

   if -1.0499999999999999e113 < i < -8.9999999999999995e-271

   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 t around inf 59.9%

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

      1. +-commutative 59.9%

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

      2. mul-1-neg 59.9%

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

      3. unsub-neg 59.9%

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

   5. Simplified 59.9%

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

   if -8.9999999999999995e-271 < i < 2.8499999999999998e-6 or 1.74999999999999987e49 < i < 1.04999999999999999e75

   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 x around inf 62.6%

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

      1. *-commutative 62.6%

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

   5. Simplified 62.6%

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

   if 2.8499999999999998e-6 < i < 1.74999999999999987e49

   1. Initial program 93.5%

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

   3. Taylor expanded in b around inf 63.2%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.05 \cdot 10^{+113}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -9 \cdot 10^{-271}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;i \leq 2.85 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq 1.75 \cdot 10^{+49}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq 1.05 \cdot 10^{+75}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 52.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -31500:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -9.6 \cdot 10^{-87}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;y \leq -9.4 \cdot 10^{-269}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 4.063 \cdot 10^{-265}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq 19500000:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j)))))
   (if (<= y -31500.0)
     t_1
     (if (<= y -9.6e-87)
       (* x (- (* y z) (* t a)))
       (if (<= y -9.4e-269)
         (* b (- (* a i) (* z c)))
         (if (<= y 4.063e-265)
           (* a (- (* b i) (* x t)))
           (if (<= y 19500000.0) (* t (- (* c j) (* x a))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -31500.0) {
		tmp = t_1;
	} else if (y <= -9.6e-87) {
		tmp = x * ((y * z) - (t * a));
	} else if (y <= -9.4e-269) {
		tmp = b * ((a * i) - (z * c));
	} else if (y <= 4.063e-265) {
		tmp = a * ((b * i) - (x * t));
	} else if (y <= 19500000.0) {
		tmp = t * ((c * j) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((x * z) - (i * j))
    if (y <= (-31500.0d0)) then
        tmp = t_1
    else if (y <= (-9.6d-87)) then
        tmp = x * ((y * z) - (t * a))
    else if (y <= (-9.4d-269)) then
        tmp = b * ((a * i) - (z * c))
    else if (y <= 4.063d-265) then
        tmp = a * ((b * i) - (x * t))
    else if (y <= 19500000.0d0) then
        tmp = t * ((c * j) - (x * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -31500.0) {
		tmp = t_1;
	} else if (y <= -9.6e-87) {
		tmp = x * ((y * z) - (t * a));
	} else if (y <= -9.4e-269) {
		tmp = b * ((a * i) - (z * c));
	} else if (y <= 4.063e-265) {
		tmp = a * ((b * i) - (x * t));
	} else if (y <= 19500000.0) {
		tmp = t * ((c * j) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -31500.0:
		tmp = t_1
	elif y <= -9.6e-87:
		tmp = x * ((y * z) - (t * a))
	elif y <= -9.4e-269:
		tmp = b * ((a * i) - (z * c))
	elif y <= 4.063e-265:
		tmp = a * ((b * i) - (x * t))
	elif y <= 19500000.0:
		tmp = t * ((c * j) - (x * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -31500.0)
		tmp = t_1;
	elseif (y <= -9.6e-87)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (y <= -9.4e-269)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (y <= 4.063e-265)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (y <= 19500000.0)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * 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 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -31500.0)
		tmp = t_1;
	elseif (y <= -9.6e-87)
		tmp = x * ((y * z) - (t * a));
	elseif (y <= -9.4e-269)
		tmp = b * ((a * i) - (z * c));
	elseif (y <= 4.063e-265)
		tmp = a * ((b * i) - (x * t));
	elseif (y <= 19500000.0)
		tmp = t * ((c * j) - (x * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -31500.0], t$95$1, If[LessEqual[y, -9.6e-87], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -9.4e-269], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.063e-265], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 19500000.0], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -31500 or 1.95e7 < y

   1. Initial program 65.4%

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

   3. Taylor expanded in y around -inf 65.3%

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

      1. mul-1-neg 65.3%

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

      2. *-commutative 65.3%

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

      3. distribute-rgt-neg-in 65.3%

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

      4. +-commutative 65.3%

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

      5. mul-1-neg 65.3%

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

      6. unsub-neg 65.3%

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

      7. *-commutative 65.3%

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

   5. Simplified 65.3%

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

   if -31500 < y < -9.5999999999999998e-87

   1. Initial program 80.6%

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

   3. Taylor expanded in x around inf 63.7%

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

      1. *-commutative 63.7%

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

   5. Simplified 63.7%

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

   if -9.5999999999999998e-87 < y < -9.3999999999999995e-269

   1. Initial program 79.5%

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

   3. Taylor expanded in b around inf 67.3%

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

   if -9.3999999999999995e-269 < y < 4.06299999999999987e-265

   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 y around -inf 63.3%

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

   5. Simplified 75.8%

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

      1. associate--l+ 75.8%

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

      2. fma-def 75.8%

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

      3. fma-neg 75.8%

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

   7. Applied egg-rr 75.8%

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

   8. Taylor expanded in a around inf 72.9%

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

      1. mul-1-neg 72.9%

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

      2. *-commutative 72.9%

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

      3. neg-sub0 72.9%

         \[\leadsto a \cdot \left(\color{blue}{\left(0 - x \cdot t\right)} - -1 \cdot \left(b \cdot i\right)\right) \]

      4. mul-1-neg 72.9%

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

      5. distribute-lft-neg-out 72.9%

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

      6. associate--r+ 72.9%

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

      7. +-commutative 72.9%

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

      8. associate--r+ 72.9%

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

      9. neg-sub0 72.9%

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

      10. *-commutative 72.9%

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

      11. distribute-rgt-neg-in 72.9%

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

      12. remove-double-neg 72.9%

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

      13. *-commutative 72.9%

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

      14. *-commutative 72.9%

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

   10. Simplified 72.9%

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

   if 4.06299999999999987e-265 < y < 1.95e7

   1. Initial program 80.0%

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

   3. Taylor expanded in t around inf 60.9%

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

      1. +-commutative 60.9%

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

      2. mul-1-neg 60.9%

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

      3. unsub-neg 60.9%

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

   5. Simplified 60.9%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -31500:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -9.6 \cdot 10^{-87}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;y \leq -9.4 \cdot 10^{-269}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 4.063 \cdot 10^{-265}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq 19500000:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 59.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -2.1 \cdot 10^{-49} \lor \neg \left(j \leq 2.8 \cdot 10^{+90}\right):\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -2.1e-49) (not (<= j 2.8e+90)))
   (+ (* j (- (* t c) (* y i))) (* z (* x y)))
   (- (* x (- (* y z) (* t a))) (* b (* z c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -2.1e-49) || !(j <= 2.8e+90)) {
		tmp = (j * ((t * c) - (y * i))) + (z * (x * y));
	} else {
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((j <= (-2.1d-49)) .or. (.not. (j <= 2.8d+90))) then
        tmp = (j * ((t * c) - (y * i))) + (z * (x * y))
    else
        tmp = (x * ((y * z) - (t * a))) - (b * (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -2.1e-49) || !(j <= 2.8e+90)) {
		tmp = (j * ((t * c) - (y * i))) + (z * (x * y));
	} else {
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -2.1e-49) or not (j <= 2.8e+90):
		tmp = (j * ((t * c) - (y * i))) + (z * (x * y))
	else:
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -2.1e-49) || !(j <= 2.8e+90))
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(z * Float64(x * y)));
	else
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -2.1e-49) || ~((j <= 2.8e+90)))
		tmp = (j * ((t * c) - (y * i))) + (z * (x * y));
	else
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -2.1e-49], N[Not[LessEqual[j, 2.8e+90]], $MachinePrecision]], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -2.0999999999999999e-49 or 2.8e90 < j

   1. Initial program 69.3%

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

   3. Taylor expanded in y around inf 69.2%

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

      1. *-commutative 69.2%

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

      2. *-commutative 69.2%

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

      3. associate-*l* 69.1%

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

   5. Simplified 69.1%

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

   if -2.0999999999999999e-49 < j < 2.8e90

   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 j around 0 71.0%

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

      1. *-commutative 71.0%

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

   5. Simplified 71.0%

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

   6. Taylor expanded in c around inf 66.0%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.1 \cdot 10^{-49} \lor \neg \left(j \leq 2.8 \cdot 10^{+90}\right):\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 50.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -4.8 \cdot 10^{+121}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 6.5 \cdot 10^{-198}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 6 \cdot 10^{-165}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 6 \cdot 10^{+49}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* a b) (* y j)))))
   (if (<= i -4.8e+121)
     t_1
     (if (<= i 6.5e-198)
       (* c (- (* t j) (* z b)))
       (if (<= i 6e-165)
         (* x (* y z))
         (if (<= i 6e+49) (* b (- (* a i) (* z c))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -4.8e+121) {
		tmp = t_1;
	} else if (i <= 6.5e-198) {
		tmp = c * ((t * j) - (z * b));
	} else if (i <= 6e-165) {
		tmp = x * (y * z);
	} else if (i <= 6e+49) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * ((a * b) - (y * j))
    if (i <= (-4.8d+121)) then
        tmp = t_1
    else if (i <= 6.5d-198) then
        tmp = c * ((t * j) - (z * b))
    else if (i <= 6d-165) then
        tmp = x * (y * z)
    else if (i <= 6d+49) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -4.8e+121) {
		tmp = t_1;
	} else if (i <= 6.5e-198) {
		tmp = c * ((t * j) - (z * b));
	} else if (i <= 6e-165) {
		tmp = x * (y * z);
	} else if (i <= 6e+49) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((a * b) - (y * j))
	tmp = 0
	if i <= -4.8e+121:
		tmp = t_1
	elif i <= 6.5e-198:
		tmp = c * ((t * j) - (z * b))
	elif i <= 6e-165:
		tmp = x * (y * z)
	elif i <= 6e+49:
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -4.8e+121)
		tmp = t_1;
	elseif (i <= 6.5e-198)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (i <= 6e-165)
		tmp = Float64(x * Float64(y * z));
	elseif (i <= 6e+49)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((a * b) - (y * j));
	tmp = 0.0;
	if (i <= -4.8e+121)
		tmp = t_1;
	elseif (i <= 6.5e-198)
		tmp = c * ((t * j) - (z * b));
	elseif (i <= 6e-165)
		tmp = x * (y * z);
	elseif (i <= 6e+49)
		tmp = b * ((a * i) - (z * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -4.8e+121], t$95$1, If[LessEqual[i, 6.5e-198], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 6e-165], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 6e+49], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -4.8e121 or 6.0000000000000005e49 < i

   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 y around -inf 60.2%

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

   5. Simplified 60.2%

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

   6. Taylor expanded in i around inf 70.1%

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

      1. mul-1-neg 70.1%

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

      2. neg-sub0 70.1%

         \[\leadsto i \cdot \left(\color{blue}{\left(0 - j \cdot y\right)} - -1 \cdot \left(a \cdot b\right)\right) \]

      3. mul-1-neg 70.1%

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

      4. *-commutative 70.1%

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

      5. associate--r+ 70.1%

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

      6. +-commutative 70.1%

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

      7. associate--r+ 70.1%

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

      8. neg-sub0 70.1%

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

      9. remove-double-neg 70.1%

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

      10. *-commutative 70.1%

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

   8. Simplified 70.1%

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

   if -4.8e121 < i < 6.5000000000000004e-198

   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 c around inf 44.4%

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

   if 6.5000000000000004e-198 < i < 5.99999999999999958e-165

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf 99.6%

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

      1. *-commutative 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in z around inf 86.2%

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

      1. *-commutative 86.2%

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

   8. Simplified 86.2%

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

   if 5.99999999999999958e-165 < i < 6.0000000000000005e49

   1. Initial program 86.7%

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

   3. Taylor expanded in b around inf 46.0%

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

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4.8 \cdot 10^{+121}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq 6.5 \cdot 10^{-198}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 6 \cdot 10^{-165}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 6 \cdot 10^{+49}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 50.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.45 \cdot 10^{-35}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 1.02 \cdot 10^{-147}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 4.1 \cdot 10^{-59}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 5.4 \cdot 10^{+108}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))) (t_2 (* j (- (* t c) (* y i)))))
   (if (<= j -1.45e-35)
     t_2
     (if (<= j 1.02e-147)
       t_1
       (if (<= j 4.1e-59) (* x (* y z)) (if (<= j 5.4e+108) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -1.45e-35) {
		tmp = t_2;
	} else if (j <= 1.02e-147) {
		tmp = t_1;
	} else if (j <= 4.1e-59) {
		tmp = x * (y * z);
	} else if (j <= 5.4e+108) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((b * i) - (x * t))
    t_2 = j * ((t * c) - (y * i))
    if (j <= (-1.45d-35)) then
        tmp = t_2
    else if (j <= 1.02d-147) then
        tmp = t_1
    else if (j <= 4.1d-59) then
        tmp = x * (y * z)
    else if (j <= 5.4d+108) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -1.45e-35) {
		tmp = t_2;
	} else if (j <= 1.02e-147) {
		tmp = t_1;
	} else if (j <= 4.1e-59) {
		tmp = x * (y * z);
	} else if (j <= 5.4e+108) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	t_2 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -1.45e-35:
		tmp = t_2
	elif j <= 1.02e-147:
		tmp = t_1
	elif j <= 4.1e-59:
		tmp = x * (y * z)
	elif j <= 5.4e+108:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	t_2 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -1.45e-35)
		tmp = t_2;
	elseif (j <= 1.02e-147)
		tmp = t_1;
	elseif (j <= 4.1e-59)
		tmp = Float64(x * Float64(y * z));
	elseif (j <= 5.4e+108)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((b * i) - (x * t));
	t_2 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -1.45e-35)
		tmp = t_2;
	elseif (j <= 1.02e-147)
		tmp = t_1;
	elseif (j <= 4.1e-59)
		tmp = x * (y * z);
	elseif (j <= 5.4e+108)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.45e-35], t$95$2, If[LessEqual[j, 1.02e-147], t$95$1, If[LessEqual[j, 4.1e-59], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.4e+108], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.4500000000000001e-35 or 5.4e108 < j

   1. Initial program 70.2%

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

   3. Taylor expanded in j around inf 68.3%

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

   if -1.4500000000000001e-35 < j < 1.02e-147 or 4.0999999999999996e-59 < j < 5.4e108

   1. Initial program 73.8%

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

   3. Taylor expanded in y around -inf 77.6%

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

   5. Simplified 77.0%

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

      1. associate--l+ 77.0%

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

      2. fma-def 79.4%

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

      3. fma-neg 79.4%

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

   7. Applied egg-rr 79.4%

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

   8. Taylor expanded in a around inf 50.4%

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

      1. mul-1-neg 50.4%

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

      2. *-commutative 50.4%

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

      3. neg-sub0 50.4%

         \[\leadsto a \cdot \left(\color{blue}{\left(0 - x \cdot t\right)} - -1 \cdot \left(b \cdot i\right)\right) \]

      4. mul-1-neg 50.4%

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

      5. distribute-lft-neg-out 50.4%

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

      6. associate--r+ 50.4%

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

      7. +-commutative 50.4%

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

      8. associate--r+ 50.4%

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

      9. neg-sub0 50.4%

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

      10. *-commutative 50.4%

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

      11. distribute-rgt-neg-in 50.4%

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

      12. remove-double-neg 50.4%

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

      13. *-commutative 50.4%

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

      14. *-commutative 50.4%

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

   10. Simplified 50.4%

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

   if 1.02e-147 < j < 4.0999999999999996e-59

   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 x around inf 55.0%

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

      1. *-commutative 55.0%

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

   5. Simplified 55.0%

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

   6. Taylor expanded in z around inf 50.2%

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

      1. *-commutative 50.2%

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

   8. Simplified 50.2%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.45 \cdot 10^{-35}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 1.02 \cdot 10^{-147}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;j \leq 4.1 \cdot 10^{-59}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 5.4 \cdot 10^{+108}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 29.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(z \cdot \left(-b\right)\right)\\ t_2 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;y \leq -7.2 \cdot 10^{-69}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.063 \cdot 10^{-265}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-247}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-11}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* z (- b)))) (t_2 (* x (* y z))))
   (if (<= y -7.2e-69)
     t_2
     (if (<= y -1.85e-143)
       t_1
       (if (<= y 4.063e-265)
         (* a (* b i))
         (if (<= y 4.6e-247) t_1 (if (<= y 7.5e-11) (* c (* t j)) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (z * -b);
	double t_2 = x * (y * z);
	double tmp;
	if (y <= -7.2e-69) {
		tmp = t_2;
	} else if (y <= -1.85e-143) {
		tmp = t_1;
	} else if (y <= 4.063e-265) {
		tmp = a * (b * i);
	} else if (y <= 4.6e-247) {
		tmp = t_1;
	} else if (y <= 7.5e-11) {
		tmp = c * (t * j);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * (z * -b)
    t_2 = x * (y * z)
    if (y <= (-7.2d-69)) then
        tmp = t_2
    else if (y <= (-1.85d-143)) then
        tmp = t_1
    else if (y <= 4.063d-265) then
        tmp = a * (b * i)
    else if (y <= 4.6d-247) then
        tmp = t_1
    else if (y <= 7.5d-11) then
        tmp = c * (t * j)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (z * -b);
	double t_2 = x * (y * z);
	double tmp;
	if (y <= -7.2e-69) {
		tmp = t_2;
	} else if (y <= -1.85e-143) {
		tmp = t_1;
	} else if (y <= 4.063e-265) {
		tmp = a * (b * i);
	} else if (y <= 4.6e-247) {
		tmp = t_1;
	} else if (y <= 7.5e-11) {
		tmp = c * (t * j);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (z * -b)
	t_2 = x * (y * z)
	tmp = 0
	if y <= -7.2e-69:
		tmp = t_2
	elif y <= -1.85e-143:
		tmp = t_1
	elif y <= 4.063e-265:
		tmp = a * (b * i)
	elif y <= 4.6e-247:
		tmp = t_1
	elif y <= 7.5e-11:
		tmp = c * (t * j)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(z * Float64(-b)))
	t_2 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (y <= -7.2e-69)
		tmp = t_2;
	elseif (y <= -1.85e-143)
		tmp = t_1;
	elseif (y <= 4.063e-265)
		tmp = Float64(a * Float64(b * i));
	elseif (y <= 4.6e-247)
		tmp = t_1;
	elseif (y <= 7.5e-11)
		tmp = Float64(c * Float64(t * j));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (z * -b);
	t_2 = x * (y * z);
	tmp = 0.0;
	if (y <= -7.2e-69)
		tmp = t_2;
	elseif (y <= -1.85e-143)
		tmp = t_1;
	elseif (y <= 4.063e-265)
		tmp = a * (b * i);
	elseif (y <= 4.6e-247)
		tmp = t_1;
	elseif (y <= 7.5e-11)
		tmp = c * (t * j);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.2e-69], t$95$2, If[LessEqual[y, -1.85e-143], t$95$1, If[LessEqual[y, 4.063e-265], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.6e-247], t$95$1, If[LessEqual[y, 7.5e-11], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.20000000000000035e-69 or 7.5e-11 < y

   1. Initial program 67.4%

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

   3. Taylor expanded in x around inf 53.8%

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

      1. *-commutative 53.8%

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

   5. Simplified 53.8%

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

   6. Taylor expanded in z around inf 41.4%

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

      1. *-commutative 41.4%

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

   8. Simplified 41.4%

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

   if -7.20000000000000035e-69 < y < -1.85e-143 or 4.06299999999999987e-265 < y < 4.6e-247

   1. Initial program 76.7%

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

   3. Taylor expanded in y around -inf 71.1%

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

   5. Simplified 65.0%

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

   6. Taylor expanded in c around inf 70.9%

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

      1. *-commutative 70.9%

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

   8. Simplified 70.9%

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

   9. Taylor expanded in t around 0 62.3%

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

       1. mul-1-neg 62.3%

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

       2. distribute-lft-neg-out 62.3%

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

       3. *-commutative 62.3%

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

   11. Simplified 62.3%

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

   if -1.85e-143 < y < 4.06299999999999987e-265

   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 b around inf 62.2%

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

   4. Taylor expanded in a around inf 37.3%

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

   if 4.6e-247 < y < 7.5e-11

   1. Initial program 77.7%

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

   3. Taylor expanded in y around -inf 66.8%

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

   5. Simplified 72.3%

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

   6. Taylor expanded in c around inf 47.0%

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

      1. *-commutative 47.0%

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

   8. Simplified 47.0%

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

   9. Taylor expanded in t around inf 38.1%

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

       1. *-commutative 38.1%

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

   11. Simplified 38.1%

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

4. Final simplification 41.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{-69}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-143}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq 4.063 \cdot 10^{-265}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-247}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-11}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 40.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;y \leq -1.9 \cdot 10^{+88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -35000:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq 10^{+185}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))))
   (if (<= y -1.9e+88)
     t_1
     (if (<= y -35000.0)
       (* i (* y (- j)))
       (if (<= y 1e+185) (* a (- (* b i) (* x t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double tmp;
	if (y <= -1.9e+88) {
		tmp = t_1;
	} else if (y <= -35000.0) {
		tmp = i * (y * -j);
	} else if (y <= 1e+185) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y * z)
    if (y <= (-1.9d+88)) then
        tmp = t_1
    else if (y <= (-35000.0d0)) then
        tmp = i * (y * -j)
    else if (y <= 1d+185) then
        tmp = a * ((b * i) - (x * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double tmp;
	if (y <= -1.9e+88) {
		tmp = t_1;
	} else if (y <= -35000.0) {
		tmp = i * (y * -j);
	} else if (y <= 1e+185) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	tmp = 0
	if y <= -1.9e+88:
		tmp = t_1
	elif y <= -35000.0:
		tmp = i * (y * -j)
	elif y <= 1e+185:
		tmp = a * ((b * i) - (x * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (y <= -1.9e+88)
		tmp = t_1;
	elseif (y <= -35000.0)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (y <= 1e+185)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (y * z);
	tmp = 0.0;
	if (y <= -1.9e+88)
		tmp = t_1;
	elseif (y <= -35000.0)
		tmp = i * (y * -j);
	elseif (y <= 1e+185)
		tmp = a * ((b * i) - (x * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.9e+88], t$95$1, If[LessEqual[y, -35000.0], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e+185], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.8999999999999998e88 or 9.9999999999999998e184 < y

   1. Initial program 60.6%

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

   3. Taylor expanded in x around inf 58.6%

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

      1. *-commutative 58.6%

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

   5. Simplified 58.6%

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

   6. Taylor expanded in z around inf 53.7%

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

      1. *-commutative 53.7%

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

   8. Simplified 53.7%

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

   if -1.8999999999999998e88 < y < -35000

   1. Initial program 88.1%

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

   3. Taylor expanded in i around 0 77.2%

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

      1. *-commutative 77.2%

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

      2. *-commutative 77.2%

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

      3. *-commutative 77.2%

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

      4. *-commutative 77.2%

         \[\leadsto \left(x \cdot \left(z \cdot y - a \cdot t\right) - \color{blue}{\left(c \cdot z\right) \cdot b}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      5. associate-*l* 71.3%

         \[\leadsto \left(x \cdot \left(z \cdot y - a \cdot t\right) - \color{blue}{c \cdot \left(z \cdot b\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 71.3%

         \[\leadsto \left(x \cdot \left(z \cdot y - a \cdot t\right) - c \cdot \color{blue}{\left(b \cdot z\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 71.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(z \cdot y - a \cdot t\right) - c \cdot \left(b \cdot z\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   6. Taylor expanded in i around inf 54.0%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 54.0%

         \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(j \cdot y\right)} \]

      2. neg-mul-1 54.0%

         \[\leadsto \color{blue}{\left(-i\right)} \cdot \left(j \cdot y\right) \]

   8. Simplified 54.0%

      \[\leadsto \color{blue}{\left(-i\right) \cdot \left(j \cdot y\right)} \]

   if -35000 < y < 9.9999999999999998e184

   1. Initial program 76.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 70.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right)\right) + c \cdot \left(j \cdot t\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

   5. Simplified 71.8%

      \[\leadsto \color{blue}{\left(\left(i \cdot j - z \cdot x\right) \cdot \left(-y\right) + t \cdot \left(c \cdot j - a \cdot x\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate--l+ 71.8%

         \[\leadsto \color{blue}{\left(i \cdot j - z \cdot x\right) \cdot \left(-y\right) + \left(t \cdot \left(c \cdot j - a \cdot x\right) - b \cdot \left(c \cdot z - a \cdot i\right)\right)} \]

      2. fma-def 72.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(i \cdot j - z \cdot x, -y, t \cdot \left(c \cdot j - a \cdot x\right) - b \cdot \left(c \cdot z - a \cdot i\right)\right)} \]

      3. fma-neg 72.4%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(i, j, -z \cdot x\right)}, -y, t \cdot \left(c \cdot j - a \cdot x\right) - b \cdot \left(c \cdot z - a \cdot i\right)\right) \]

   7. Applied egg-rr 72.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(i, j, -z \cdot x\right), -y, t \cdot \left(c \cdot j - a \cdot x\right) - b \cdot \left(c \cdot z - a \cdot i\right)\right)} \]

   8. Taylor expanded in a around inf 51.7%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 51.7%

         \[\leadsto a \cdot \left(\color{blue}{\left(-t \cdot x\right)} - -1 \cdot \left(b \cdot i\right)\right) \]

      2. *-commutative 51.7%

         \[\leadsto a \cdot \left(\left(-\color{blue}{x \cdot t}\right) - -1 \cdot \left(b \cdot i\right)\right) \]

      3. neg-sub0 51.7%

         \[\leadsto a \cdot \left(\color{blue}{\left(0 - x \cdot t\right)} - -1 \cdot \left(b \cdot i\right)\right) \]

      4. mul-1-neg 51.7%

         \[\leadsto a \cdot \left(\left(0 - x \cdot t\right) - \color{blue}{\left(-b \cdot i\right)}\right) \]

      5. distribute-lft-neg-out 51.7%

         \[\leadsto a \cdot \left(\left(0 - x \cdot t\right) - \color{blue}{\left(-b\right) \cdot i}\right) \]

      6. associate--r+ 51.7%

         \[\leadsto a \cdot \color{blue}{\left(0 - \left(x \cdot t + \left(-b\right) \cdot i\right)\right)} \]

      7. +-commutative 51.7%

         \[\leadsto a \cdot \left(0 - \color{blue}{\left(\left(-b\right) \cdot i + x \cdot t\right)}\right) \]

      8. associate--r+ 51.7%

         \[\leadsto a \cdot \color{blue}{\left(\left(0 - \left(-b\right) \cdot i\right) - x \cdot t\right)} \]

      9. neg-sub0 51.7%

         \[\leadsto a \cdot \left(\color{blue}{\left(-\left(-b\right) \cdot i\right)} - x \cdot t\right) \]

      10. *-commutative 51.7%

          \[\leadsto a \cdot \left(\left(-\color{blue}{i \cdot \left(-b\right)}\right) - x \cdot t\right) \]

      11. distribute-rgt-neg-in 51.7%

          \[\leadsto a \cdot \left(\left(-\color{blue}{\left(-i \cdot b\right)}\right) - x \cdot t\right) \]

      12. remove-double-neg 51.7%

          \[\leadsto a \cdot \left(\color{blue}{i \cdot b} - x \cdot t\right) \]

      13. *-commutative 51.7%

          \[\leadsto a \cdot \left(\color{blue}{b \cdot i} - x \cdot t\right) \]

      14. *-commutative 51.7%

          \[\leadsto a \cdot \left(b \cdot i - \color{blue}{t \cdot x}\right) \]

   10. Simplified 51.7%

       \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+88}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -35000:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq 10^{+185}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 52.5% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3.55 \cdot 10^{+18} \lor \neg \left(c \leq 1.26 \cdot 10^{+116}\right):\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -3.55e+18) (not (<= c 1.26e+116)))
   (* c (- (* t j) (* z b)))
   (* a (- (* b i) (* x t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -3.55e+18) || !(c <= 1.26e+116)) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = a * ((b * i) - (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((c <= (-3.55d+18)) .or. (.not. (c <= 1.26d+116))) then
        tmp = c * ((t * j) - (z * b))
    else
        tmp = a * ((b * i) - (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -3.55e+18) || !(c <= 1.26e+116)) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = a * ((b * i) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -3.55e+18) or not (c <= 1.26e+116):
		tmp = c * ((t * j) - (z * b))
	else:
		tmp = a * ((b * i) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -3.55e+18) || !(c <= 1.26e+116))
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	else
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -3.55e+18) || ~((c <= 1.26e+116)))
		tmp = c * ((t * j) - (z * b));
	else
		tmp = a * ((b * i) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -3.55e+18], N[Not[LessEqual[c, 1.26e+116]], $MachinePrecision]], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -3.55e18 or 1.2599999999999999e116 < c

   1. Initial program 66.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 61.9%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]

   if -3.55e18 < c < 1.2599999999999999e116

   1. Initial program 77.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 74.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right)\right) + c \cdot \left(j \cdot t\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

   5. Simplified 80.4%

      \[\leadsto \color{blue}{\left(\left(i \cdot j - z \cdot x\right) \cdot \left(-y\right) + t \cdot \left(c \cdot j - a \cdot x\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate--l+ 80.4%

         \[\leadsto \color{blue}{\left(i \cdot j - z \cdot x\right) \cdot \left(-y\right) + \left(t \cdot \left(c \cdot j - a \cdot x\right) - b \cdot \left(c \cdot z - a \cdot i\right)\right)} \]

      2. fma-def 81.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(i \cdot j - z \cdot x, -y, t \cdot \left(c \cdot j - a \cdot x\right) - b \cdot \left(c \cdot z - a \cdot i\right)\right)} \]

      3. fma-neg 81.1%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(i, j, -z \cdot x\right)}, -y, t \cdot \left(c \cdot j - a \cdot x\right) - b \cdot \left(c \cdot z - a \cdot i\right)\right) \]

   7. Applied egg-rr 81.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(i, j, -z \cdot x\right), -y, t \cdot \left(c \cdot j - a \cdot x\right) - b \cdot \left(c \cdot z - a \cdot i\right)\right)} \]

   8. Taylor expanded in a around inf 46.7%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 46.7%

         \[\leadsto a \cdot \left(\color{blue}{\left(-t \cdot x\right)} - -1 \cdot \left(b \cdot i\right)\right) \]

      2. *-commutative 46.7%

         \[\leadsto a \cdot \left(\left(-\color{blue}{x \cdot t}\right) - -1 \cdot \left(b \cdot i\right)\right) \]

      3. neg-sub0 46.7%

         \[\leadsto a \cdot \left(\color{blue}{\left(0 - x \cdot t\right)} - -1 \cdot \left(b \cdot i\right)\right) \]

      4. mul-1-neg 46.7%

         \[\leadsto a \cdot \left(\left(0 - x \cdot t\right) - \color{blue}{\left(-b \cdot i\right)}\right) \]

      5. distribute-lft-neg-out 46.7%

         \[\leadsto a \cdot \left(\left(0 - x \cdot t\right) - \color{blue}{\left(-b\right) \cdot i}\right) \]

      6. associate--r+ 46.7%

         \[\leadsto a \cdot \color{blue}{\left(0 - \left(x \cdot t + \left(-b\right) \cdot i\right)\right)} \]

      7. +-commutative 46.7%

         \[\leadsto a \cdot \left(0 - \color{blue}{\left(\left(-b\right) \cdot i + x \cdot t\right)}\right) \]

      8. associate--r+ 46.7%

         \[\leadsto a \cdot \color{blue}{\left(\left(0 - \left(-b\right) \cdot i\right) - x \cdot t\right)} \]

      9. neg-sub0 46.7%

         \[\leadsto a \cdot \left(\color{blue}{\left(-\left(-b\right) \cdot i\right)} - x \cdot t\right) \]

      10. *-commutative 46.7%

          \[\leadsto a \cdot \left(\left(-\color{blue}{i \cdot \left(-b\right)}\right) - x \cdot t\right) \]

      11. distribute-rgt-neg-in 46.7%

          \[\leadsto a \cdot \left(\left(-\color{blue}{\left(-i \cdot b\right)}\right) - x \cdot t\right) \]

      12. remove-double-neg 46.7%

          \[\leadsto a \cdot \left(\color{blue}{i \cdot b} - x \cdot t\right) \]

      13. *-commutative 46.7%

          \[\leadsto a \cdot \left(\color{blue}{b \cdot i} - x \cdot t\right) \]

      14. *-commutative 46.7%

          \[\leadsto a \cdot \left(b \cdot i - \color{blue}{t \cdot x}\right) \]

   10. Simplified 46.7%

       \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.55 \cdot 10^{+18} \lor \neg \left(c \leq 1.26 \cdot 10^{+116}\right):\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 29.3% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;y \leq -1.25 \cdot 10^{-67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.063 \cdot 10^{-265}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-11}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))))
   (if (<= y -1.25e-67)
     t_1
     (if (<= y 4.063e-265)
       (* a (* b i))
       (if (<= y 8.6e-11) (* j (* t c)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double tmp;
	if (y <= -1.25e-67) {
		tmp = t_1;
	} else if (y <= 4.063e-265) {
		tmp = a * (b * i);
	} else if (y <= 8.6e-11) {
		tmp = j * (t * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y * z)
    if (y <= (-1.25d-67)) then
        tmp = t_1
    else if (y <= 4.063d-265) then
        tmp = a * (b * i)
    else if (y <= 8.6d-11) then
        tmp = j * (t * c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double tmp;
	if (y <= -1.25e-67) {
		tmp = t_1;
	} else if (y <= 4.063e-265) {
		tmp = a * (b * i);
	} else if (y <= 8.6e-11) {
		tmp = j * (t * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	tmp = 0
	if y <= -1.25e-67:
		tmp = t_1
	elif y <= 4.063e-265:
		tmp = a * (b * i)
	elif y <= 8.6e-11:
		tmp = j * (t * c)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (y <= -1.25e-67)
		tmp = t_1;
	elseif (y <= 4.063e-265)
		tmp = Float64(a * Float64(b * i));
	elseif (y <= 8.6e-11)
		tmp = Float64(j * Float64(t * c));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (y * z);
	tmp = 0.0;
	if (y <= -1.25e-67)
		tmp = t_1;
	elseif (y <= 4.063e-265)
		tmp = a * (b * i);
	elseif (y <= 8.6e-11)
		tmp = j * (t * c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.25e-67], t$95$1, If[LessEqual[y, 4.063e-265], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.6e-11], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.25e-67 or 8.60000000000000003e-11 < y

   1. Initial program 67.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 53.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   4. Step-by-step derivation

      1. *-commutative 53.8%

         \[\leadsto x \cdot \left(\color{blue}{z \cdot y} - a \cdot t\right) \]

   5. Simplified 53.8%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y - a \cdot t\right)} \]

   6. Taylor expanded in z around inf 41.4%

      \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-commutative 41.4%

         \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

   8. Simplified 41.4%

      \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

   if -1.25e-67 < y < 4.06299999999999987e-265

   1. Initial program 78.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 61.4%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]

   4. Taylor expanded in a around inf 34.3%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

   if 4.06299999999999987e-265 < y < 8.60000000000000003e-11

   1. Initial program 79.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 67.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right)\right) + c \cdot \left(j \cdot t\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

   5. Simplified 72.5%

      \[\leadsto \color{blue}{\left(\left(i \cdot j - z \cdot x\right) \cdot \left(-y\right) + t \cdot \left(c \cdot j - a \cdot x\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]

   6. Taylor expanded in b around 0 64.3%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(i \cdot j - x \cdot z\right)\right) + t \cdot \left(c \cdot j - a \cdot x\right)} \]

   7. Taylor expanded in c around inf 35.7%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   8. Step-by-step derivation

      1. *-commutative 35.7%

         \[\leadsto \color{blue}{\left(j \cdot t\right) \cdot c} \]

      2. associate-*r* 35.8%

         \[\leadsto \color{blue}{j \cdot \left(t \cdot c\right)} \]

   9. Simplified 35.8%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot c\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 38.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-67}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 4.063 \cdot 10^{-265}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-11}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 29.6% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.85 \cdot 10^{+19} \lor \neg \left(c \leq 3.4 \cdot 10^{-81}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -2.85e+19) (not (<= c 3.4e-81))) (* c (* t j)) (* a (* b i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -2.85e+19) || !(c <= 3.4e-81)) {
		tmp = c * (t * j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((c <= (-2.85d+19)) .or. (.not. (c <= 3.4d-81))) then
        tmp = c * (t * j)
    else
        tmp = a * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -2.85e+19) || !(c <= 3.4e-81)) {
		tmp = c * (t * j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -2.85e+19) or not (c <= 3.4e-81):
		tmp = c * (t * j)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -2.85e+19) || !(c <= 3.4e-81))
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -2.85e+19) || ~((c <= 3.4e-81)))
		tmp = c * (t * j);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -2.85e+19], N[Not[LessEqual[c, 3.4e-81]], $MachinePrecision]], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -2.85e19 or 3.3999999999999999e-81 < c

   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 y around -inf 70.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right)\right) + c \cdot \left(j \cdot t\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

   5. Simplified 66.7%

      \[\leadsto \color{blue}{\left(\left(i \cdot j - z \cdot x\right) \cdot \left(-y\right) + t \cdot \left(c \cdot j - a \cdot x\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]

   6. Taylor expanded in c around inf 54.3%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-commutative 54.3%

         \[\leadsto c \cdot \left(\color{blue}{t \cdot j} - b \cdot z\right) \]

   8. Simplified 54.3%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - b \cdot z\right)} \]

   9. Taylor expanded in t around inf 34.6%

      \[\leadsto c \cdot \color{blue}{\left(j \cdot t\right)} \]
   10. Step-by-step derivation

       1. *-commutative 34.6%

          \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

   11. Simplified 34.6%

       \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

   if -2.85e19 < c < 3.3999999999999999e-81

   1. Initial program 76.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 31.5%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]

   4. Taylor expanded in a around inf 25.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 30.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.85 \cdot 10^{+19} \lor \neg \left(c \leq 3.4 \cdot 10^{-81}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 29.9% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3 \cdot 10^{+17}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;c \leq 2.05 \cdot 10^{+88}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -3e+17)
   (* c (* t j))
   (if (<= c 2.05e+88) (* a (* b 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 (c <= -3e+17) {
		tmp = c * (t * j);
	} else if (c <= 2.05e+88) {
		tmp = a * (b * 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 (c <= (-3d+17)) then
        tmp = c * (t * j)
    else if (c <= 2.05d+88) then
        tmp = a * (b * 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 (c <= -3e+17) {
		tmp = c * (t * j);
	} else if (c <= 2.05e+88) {
		tmp = a * (b * i);
	} else {
		tmp = j * (t * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -3e+17:
		tmp = c * (t * j)
	elif c <= 2.05e+88:
		tmp = a * (b * i)
	else:
		tmp = j * (t * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -3e+17)
		tmp = Float64(c * Float64(t * j));
	elseif (c <= 2.05e+88)
		tmp = Float64(a * Float64(b * 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 (c <= -3e+17)
		tmp = c * (t * j);
	elseif (c <= 2.05e+88)
		tmp = a * (b * i);
	else
		tmp = j * (t * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -3e+17], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.05e+88], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -3e17

   1. Initial program 72.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 71.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right)\right) + c \cdot \left(j \cdot t\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

   5. Simplified 67.0%

      \[\leadsto \color{blue}{\left(\left(i \cdot j - z \cdot x\right) \cdot \left(-y\right) + t \cdot \left(c \cdot j - a \cdot x\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]

   6. Taylor expanded in c around inf 61.3%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-commutative 61.3%

         \[\leadsto c \cdot \left(\color{blue}{t \cdot j} - b \cdot z\right) \]

   8. Simplified 61.3%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - b \cdot z\right)} \]

   9. Taylor expanded in t around inf 35.5%

      \[\leadsto c \cdot \color{blue}{\left(j \cdot t\right)} \]
   10. Step-by-step derivation

       1. *-commutative 35.5%

          \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

   11. Simplified 35.5%

       \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

   if -3e17 < c < 2.05000000000000014e88

   1. Initial program 79.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 31.9%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]

   4. Taylor expanded in a around inf 24.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

   if 2.05000000000000014e88 < c

   1. Initial program 54.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 56.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right)\right) + c \cdot \left(j \cdot t\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

   5. Simplified 50.4%

      \[\leadsto \color{blue}{\left(\left(i \cdot j - z \cdot x\right) \cdot \left(-y\right) + t \cdot \left(c \cdot j - a \cdot x\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]

   6. Taylor expanded in b around 0 54.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(i \cdot j - x \cdot z\right)\right) + t \cdot \left(c \cdot j - a \cdot x\right)} \]

   7. Taylor expanded in c around inf 39.5%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   8. Step-by-step derivation

      1. *-commutative 39.5%

         \[\leadsto \color{blue}{\left(j \cdot t\right) \cdot c} \]

      2. associate-*r* 45.3%

         \[\leadsto \color{blue}{j \cdot \left(t \cdot c\right)} \]

   9. Simplified 45.3%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot c\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 31.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3 \cdot 10^{+17}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;c \leq 2.05 \cdot 10^{+88}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 22.3% 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 72.5%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
2. Add Preprocessing

3. Taylor expanded in b around inf 36.9%

   \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]

4. Taylor expanded in a around inf 19.0%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

5. Final simplification 19.0%

   \[\leadsto a \cdot \left(b \cdot i\right) \]
6. Add Preprocessing

Developer target: 69.1% 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 2024010 
(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)))))