Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.2% → 80.8%

Time: 22.9s

Alternatives: 26

Speedup: 0.5×

• 57.1% 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: 73.2% accurate, 1.0× speedup

Math

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

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: 80.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((t * c) - (y * i))) - ((b * ((z * c) - (a * i))) - (x * ((y * z) - (t * a))))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = b * ((a * i) - (z * c))
	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(b * Float64(Float64(z * c) - Float64(a * i))) - Float64(x * Float64(Float64(y * z) - Float64(t * a)))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	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))) - ((b * ((z * c) - (a * i))) - (x * ((y * z) - (t * a))));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = b * ((a * i) - (z * c));
	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[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $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 90.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   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 b around inf 57.7%

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

      1. *-commutative 57.7%

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

   5. Simplified 57.7%

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

4. Final simplification 84.9%

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

Alternative 2: 66.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ t_4 := i \cdot \left(\frac{t\_1}{i} + \left(a \cdot b - y \cdot j\right)\right)\\ \mathbf{if}\;b \leq -1.42 \cdot 10^{+169}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{+130}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{+77}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-79}:\\ \;\;\;\;\left(t\_1 + c \cdot \left(t \cdot j\right)\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{+63}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+181}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c))))
        (t_2 (* b (- (* a i) (* z c))))
        (t_3 (- (* x (- (* y z) (* t a))) (* j (- (* y i) (* t c)))))
        (t_4 (* i (+ (/ t_1 i) (- (* a b) (* y j))))))
   (if (<= b -1.42e+169)
     t_2
     (if (<= b -1.75e+130)
       t_3
       (if (<= b -3.6e+77)
         t_4
         (if (<= b -2.4e-79)
           (- (+ t_1 (* c (* t j))) (* a (* x t)))
           (if (<= b 1.45e+63) t_3 (if (<= b 9.5e+181) t_4 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = (x * ((y * z) - (t * a))) - (j * ((y * i) - (t * c)));
	double t_4 = i * ((t_1 / i) + ((a * b) - (y * j)));
	double tmp;
	if (b <= -1.42e+169) {
		tmp = t_2;
	} else if (b <= -1.75e+130) {
		tmp = t_3;
	} else if (b <= -3.6e+77) {
		tmp = t_4;
	} else if (b <= -2.4e-79) {
		tmp = (t_1 + (c * (t * j))) - (a * (x * t));
	} else if (b <= 1.45e+63) {
		tmp = t_3;
	} else if (b <= 9.5e+181) {
		tmp = t_4;
	} 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) :: t_4
    real(8) :: tmp
    t_1 = z * ((x * y) - (b * c))
    t_2 = b * ((a * i) - (z * c))
    t_3 = (x * ((y * z) - (t * a))) - (j * ((y * i) - (t * c)))
    t_4 = i * ((t_1 / i) + ((a * b) - (y * j)))
    if (b <= (-1.42d+169)) then
        tmp = t_2
    else if (b <= (-1.75d+130)) then
        tmp = t_3
    else if (b <= (-3.6d+77)) then
        tmp = t_4
    else if (b <= (-2.4d-79)) then
        tmp = (t_1 + (c * (t * j))) - (a * (x * t))
    else if (b <= 1.45d+63) then
        tmp = t_3
    else if (b <= 9.5d+181) then
        tmp = t_4
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = (x * ((y * z) - (t * a))) - (j * ((y * i) - (t * c)));
	double t_4 = i * ((t_1 / i) + ((a * b) - (y * j)));
	double tmp;
	if (b <= -1.42e+169) {
		tmp = t_2;
	} else if (b <= -1.75e+130) {
		tmp = t_3;
	} else if (b <= -3.6e+77) {
		tmp = t_4;
	} else if (b <= -2.4e-79) {
		tmp = (t_1 + (c * (t * j))) - (a * (x * t));
	} else if (b <= 1.45e+63) {
		tmp = t_3;
	} else if (b <= 9.5e+181) {
		tmp = t_4;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * ((x * y) - (b * c))
	t_2 = b * ((a * i) - (z * c))
	t_3 = (x * ((y * z) - (t * a))) - (j * ((y * i) - (t * c)))
	t_4 = i * ((t_1 / i) + ((a * b) - (y * j)))
	tmp = 0
	if b <= -1.42e+169:
		tmp = t_2
	elif b <= -1.75e+130:
		tmp = t_3
	elif b <= -3.6e+77:
		tmp = t_4
	elif b <= -2.4e-79:
		tmp = (t_1 + (c * (t * j))) - (a * (x * t))
	elif b <= 1.45e+63:
		tmp = t_3
	elif b <= 9.5e+181:
		tmp = t_4
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_3 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(j * Float64(Float64(y * i) - Float64(t * c))))
	t_4 = Float64(i * Float64(Float64(t_1 / i) + Float64(Float64(a * b) - Float64(y * j))))
	tmp = 0.0
	if (b <= -1.42e+169)
		tmp = t_2;
	elseif (b <= -1.75e+130)
		tmp = t_3;
	elseif (b <= -3.6e+77)
		tmp = t_4;
	elseif (b <= -2.4e-79)
		tmp = Float64(Float64(t_1 + Float64(c * Float64(t * j))) - Float64(a * Float64(x * t)));
	elseif (b <= 1.45e+63)
		tmp = t_3;
	elseif (b <= 9.5e+181)
		tmp = t_4;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * ((x * y) - (b * c));
	t_2 = b * ((a * i) - (z * c));
	t_3 = (x * ((y * z) - (t * a))) - (j * ((y * i) - (t * c)));
	t_4 = i * ((t_1 / i) + ((a * b) - (y * j)));
	tmp = 0.0;
	if (b <= -1.42e+169)
		tmp = t_2;
	elseif (b <= -1.75e+130)
		tmp = t_3;
	elseif (b <= -3.6e+77)
		tmp = t_4;
	elseif (b <= -2.4e-79)
		tmp = (t_1 + (c * (t * j))) - (a * (x * t));
	elseif (b <= 1.45e+63)
		tmp = t_3;
	elseif (b <= 9.5e+181)
		tmp = t_4;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(y * i), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(i * N[(N[(t$95$1 / i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.42e+169], t$95$2, If[LessEqual[b, -1.75e+130], t$95$3, If[LessEqual[b, -3.6e+77], t$95$4, If[LessEqual[b, -2.4e-79], N[(N[(t$95$1 + N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.45e+63], t$95$3, If[LessEqual[b, 9.5e+181], t$95$4, t$95$2]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.42000000000000002e169 or 9.50000000000000032e181 < b

   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 b around inf 76.9%

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

      1. *-commutative 76.9%

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

   5. Simplified 76.9%

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

   if -1.42000000000000002e169 < b < -1.75e130 or -2.40000000000000006e-79 < b < 1.45e63

   1. Initial program 77.9%

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

   3. Taylor expanded in b around 0 81.2%

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

   if -1.75e130 < b < -3.5999999999999998e77 or 1.45e63 < b < 9.50000000000000032e181

   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 i around inf 71.8%

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

   5. Simplified 74.1%

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

   6. Taylor expanded in t around 0 82.8%

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

   if -3.5999999999999998e77 < b < -2.40000000000000006e-79

   1. Initial program 71.1%

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

   3. Taylor expanded in i around inf 58.9%

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

   5. Simplified 63.1%

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

   6. Taylor expanded in i around 0 79.1%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.42 \cdot 10^{+169}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{+130}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{+77}:\\ \;\;\;\;i \cdot \left(\frac{z \cdot \left(x \cdot y - b \cdot c\right)}{i} + \left(a \cdot b - y \cdot j\right)\right)\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-79}:\\ \;\;\;\;\left(z \cdot \left(x \cdot y - b \cdot c\right) + c \cdot \left(t \cdot j\right)\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{+63}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+181}:\\ \;\;\;\;i \cdot \left(\frac{z \cdot \left(x \cdot y - b \cdot c\right)}{i} + \left(a \cdot b - y \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;b \leq -4.5 \cdot 10^{+232}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.25 \cdot 10^{+162}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq -6.4 \cdot 10^{-56} \lor \neg \left(b \leq 7.2 \cdot 10^{+34}\right):\\ \;\;\;\;b \cdot \left(\left(a \cdot i + \left(c \cdot \left(j \cdot \frac{t}{b}\right) + \frac{t\_1}{b}\right)\right) - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 - j \cdot \left(y \cdot i - t \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= b -4.5e+232)
     (* b (- (* a i) (* z c)))
     (if (<= b -1.25e+162)
       (* i (- (* a b) (* y j)))
       (if (or (<= b -6.4e-56) (not (<= b 7.2e+34)))
         (* b (- (+ (* a i) (+ (* c (* j (/ t b))) (/ t_1 b))) (* z c)))
         (- t_1 (* j (- (* y i) (* t c)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (b <= -4.5e+232) {
		tmp = b * ((a * i) - (z * c));
	} else if (b <= -1.25e+162) {
		tmp = i * ((a * b) - (y * j));
	} else if ((b <= -6.4e-56) || !(b <= 7.2e+34)) {
		tmp = b * (((a * i) + ((c * (j * (t / b))) + (t_1 / b))) - (z * c));
	} else {
		tmp = t_1 - (j * ((y * i) - (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) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (b <= (-4.5d+232)) then
        tmp = b * ((a * i) - (z * c))
    else if (b <= (-1.25d+162)) then
        tmp = i * ((a * b) - (y * j))
    else if ((b <= (-6.4d-56)) .or. (.not. (b <= 7.2d+34))) then
        tmp = b * (((a * i) + ((c * (j * (t / b))) + (t_1 / b))) - (z * c))
    else
        tmp = t_1 - (j * ((y * i) - (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 t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (b <= -4.5e+232) {
		tmp = b * ((a * i) - (z * c));
	} else if (b <= -1.25e+162) {
		tmp = i * ((a * b) - (y * j));
	} else if ((b <= -6.4e-56) || !(b <= 7.2e+34)) {
		tmp = b * (((a * i) + ((c * (j * (t / b))) + (t_1 / b))) - (z * c));
	} else {
		tmp = t_1 - (j * ((y * i) - (t * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if b <= -4.5e+232:
		tmp = b * ((a * i) - (z * c))
	elif b <= -1.25e+162:
		tmp = i * ((a * b) - (y * j))
	elif (b <= -6.4e-56) or not (b <= 7.2e+34):
		tmp = b * (((a * i) + ((c * (j * (t / b))) + (t_1 / b))) - (z * c))
	else:
		tmp = t_1 - (j * ((y * i) - (t * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (b <= -4.5e+232)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (b <= -1.25e+162)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif ((b <= -6.4e-56) || !(b <= 7.2e+34))
		tmp = Float64(b * Float64(Float64(Float64(a * i) + Float64(Float64(c * Float64(j * Float64(t / b))) + Float64(t_1 / b))) - Float64(z * c)));
	else
		tmp = Float64(t_1 - Float64(j * Float64(Float64(y * i) - Float64(t * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (b <= -4.5e+232)
		tmp = b * ((a * i) - (z * c));
	elseif (b <= -1.25e+162)
		tmp = i * ((a * b) - (y * j));
	elseif ((b <= -6.4e-56) || ~((b <= 7.2e+34)))
		tmp = b * (((a * i) + ((c * (j * (t / b))) + (t_1 / b))) - (z * c));
	else
		tmp = t_1 - (j * ((y * i) - (t * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.5e+232], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.25e+162], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, -6.4e-56], N[Not[LessEqual[b, 7.2e+34]], $MachinePrecision]], N[(b * N[(N[(N[(a * i), $MachinePrecision] + N[(N[(c * N[(j * N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(j * N[(N[(y * i), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -4.4999999999999998e232

   1. Initial program 69.4%

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

   3. Taylor expanded in b around inf 94.3%

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

      1. *-commutative 94.3%

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

   5. Simplified 94.3%

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

   if -4.4999999999999998e232 < b < -1.2499999999999999e162

   1. Initial program 68.7%

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

   3. Taylor expanded in i around inf 37.4%

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

   5. Simplified 43.7%

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

   6. Taylor expanded in i around inf 81.2%

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

      1. mul-1-neg 81.2%

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

      2. distribute-rgt-neg-in 81.2%

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

      3. mul-1-neg 81.2%

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

      4. distribute-rgt-neg-out 81.2%

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

      5. distribute-neg-in 81.2%

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

      6. neg-mul-1 81.2%

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

      7. unsub-neg 81.2%

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

      8. neg-mul-1 81.2%

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

      9. distribute-rgt-neg-out 81.2%

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

      10. remove-double-neg 81.2%

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

      11. *-commutative 81.2%

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

   8. Simplified 81.2%

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

   if -1.2499999999999999e162 < b < -6.39999999999999971e-56 or 7.2000000000000001e34 < b

   1. Initial program 72.6%

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

   3. Taylor expanded in b around inf 74.4%

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

   4. Taylor expanded in c around inf 71.2%

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

      1. associate-/l* 73.8%

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

      2. associate-/l* 74.7%

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

   6. Simplified 74.7%

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

   if -6.39999999999999971e-56 < b < 7.2000000000000001e34

   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 b around 0 80.9%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{+232}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.25 \cdot 10^{+162}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq -6.4 \cdot 10^{-56} \lor \neg \left(b \leq 7.2 \cdot 10^{+34}\right):\\ \;\;\;\;b \cdot \left(\left(a \cdot i + \left(c \cdot \left(j \cdot \frac{t}{b}\right) + \frac{x \cdot \left(y \cdot z - t \cdot a\right)}{b}\right)\right) - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 47.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := z \cdot \left(c \cdot \left(\frac{x \cdot y}{c} - b\right)\right)\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{+137}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-110}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.24 \cdot 10^{-238}:\\ \;\;\;\;i \cdot \left(j \cdot \left(\frac{t \cdot c}{i} - y\right)\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-148}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-83}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+107}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a)))) (t_2 (* z (* c (- (/ (* x y) c) b)))))
   (if (<= z -2.3e+137)
     t_2
     (if (<= z -9e-110)
       t_1
       (if (<= z -1.24e-238)
         (* i (* j (- (/ (* t c) i) y)))
         (if (<= z 4.2e-148)
           (- (* c (* t j)) (* a (* x t)))
           (if (<= z 9.6e-83)
             (* y (- (* x z) (* i j)))
             (if (<= z 7e-22)
               t_1
               (if (<= z 2.3e+107) (* 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 = z * (c * (((x * y) / c) - b));
	double tmp;
	if (z <= -2.3e+137) {
		tmp = t_2;
	} else if (z <= -9e-110) {
		tmp = t_1;
	} else if (z <= -1.24e-238) {
		tmp = i * (j * (((t * c) / i) - y));
	} else if (z <= 4.2e-148) {
		tmp = (c * (t * j)) - (a * (x * t));
	} else if (z <= 9.6e-83) {
		tmp = y * ((x * z) - (i * j));
	} else if (z <= 7e-22) {
		tmp = t_1;
	} else if (z <= 2.3e+107) {
		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 = z * (c * (((x * y) / c) - b))
    if (z <= (-2.3d+137)) then
        tmp = t_2
    else if (z <= (-9d-110)) then
        tmp = t_1
    else if (z <= (-1.24d-238)) then
        tmp = i * (j * (((t * c) / i) - y))
    else if (z <= 4.2d-148) then
        tmp = (c * (t * j)) - (a * (x * t))
    else if (z <= 9.6d-83) then
        tmp = y * ((x * z) - (i * j))
    else if (z <= 7d-22) then
        tmp = t_1
    else if (z <= 2.3d+107) 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 = z * (c * (((x * y) / c) - b));
	double tmp;
	if (z <= -2.3e+137) {
		tmp = t_2;
	} else if (z <= -9e-110) {
		tmp = t_1;
	} else if (z <= -1.24e-238) {
		tmp = i * (j * (((t * c) / i) - y));
	} else if (z <= 4.2e-148) {
		tmp = (c * (t * j)) - (a * (x * t));
	} else if (z <= 9.6e-83) {
		tmp = y * ((x * z) - (i * j));
	} else if (z <= 7e-22) {
		tmp = t_1;
	} else if (z <= 2.3e+107) {
		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 = z * (c * (((x * y) / c) - b))
	tmp = 0
	if z <= -2.3e+137:
		tmp = t_2
	elif z <= -9e-110:
		tmp = t_1
	elif z <= -1.24e-238:
		tmp = i * (j * (((t * c) / i) - y))
	elif z <= 4.2e-148:
		tmp = (c * (t * j)) - (a * (x * t))
	elif z <= 9.6e-83:
		tmp = y * ((x * z) - (i * j))
	elif z <= 7e-22:
		tmp = t_1
	elif z <= 2.3e+107:
		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(z * Float64(c * Float64(Float64(Float64(x * y) / c) - b)))
	tmp = 0.0
	if (z <= -2.3e+137)
		tmp = t_2;
	elseif (z <= -9e-110)
		tmp = t_1;
	elseif (z <= -1.24e-238)
		tmp = Float64(i * Float64(j * Float64(Float64(Float64(t * c) / i) - y)));
	elseif (z <= 4.2e-148)
		tmp = Float64(Float64(c * Float64(t * j)) - Float64(a * Float64(x * t)));
	elseif (z <= 9.6e-83)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (z <= 7e-22)
		tmp = t_1;
	elseif (z <= 2.3e+107)
		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 = z * (c * (((x * y) / c) - b));
	tmp = 0.0;
	if (z <= -2.3e+137)
		tmp = t_2;
	elseif (z <= -9e-110)
		tmp = t_1;
	elseif (z <= -1.24e-238)
		tmp = i * (j * (((t * c) / i) - y));
	elseif (z <= 4.2e-148)
		tmp = (c * (t * j)) - (a * (x * t));
	elseif (z <= 9.6e-83)
		tmp = y * ((x * z) - (i * j));
	elseif (z <= 7e-22)
		tmp = t_1;
	elseif (z <= 2.3e+107)
		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[(z * N[(c * N[(N[(N[(x * y), $MachinePrecision] / c), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.3e+137], t$95$2, If[LessEqual[z, -9e-110], t$95$1, If[LessEqual[z, -1.24e-238], N[(i * N[(j * N[(N[(N[(t * c), $MachinePrecision] / i), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e-148], N[(N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.6e-83], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7e-22], t$95$1, If[LessEqual[z, 2.3e+107], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -2.29999999999999999e137 or 2.3e107 < z

   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. Step-by-step derivation

      1. *-commutative 54.2%

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

      2. *-commutative 54.2%

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

      3. *-commutative 54.2%

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

      4. add-cube-cbrt 54.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(t \cdot c - y \cdot i\right) \cdot \color{blue}{\left(\left(\sqrt[3]{j} \cdot \sqrt[3]{j}\right) \cdot \sqrt[3]{j}\right)} \]

      5. associate-*r* 54.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{\left(\left(t \cdot c - y \cdot i\right) \cdot \left(\sqrt[3]{j} \cdot \sqrt[3]{j}\right)\right) \cdot \sqrt[3]{j}} \]

      6. pow2 54.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(t \cdot c - y \cdot i\right) \cdot \color{blue}{{\left(\sqrt[3]{j}\right)}^{2}}\right) \cdot \sqrt[3]{j} \]

   4. Applied egg-rr 54.2%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{\left(\left(t \cdot c - y \cdot i\right) \cdot {\left(\sqrt[3]{j}\right)}^{2}\right) \cdot \sqrt[3]{j}} \]

   5. Taylor expanded in z around inf 77.2%

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

      1. *-commutative 77.2%

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

      2. *-commutative 77.2%

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

   7. Simplified 77.2%

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

   8. Taylor expanded in c around inf 78.6%

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

   if -2.29999999999999999e137 < z < -9.0000000000000002e-110 or 9.6000000000000003e-83 < z < 7.00000000000000011e-22

   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 t around inf 59.0%

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

      1. +-commutative 59.0%

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

      2. mul-1-neg 59.0%

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

      3. unsub-neg 59.0%

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

      4. *-commutative 59.0%

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

      5. *-commutative 59.0%

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

   5. Simplified 59.0%

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

   if -9.0000000000000002e-110 < z < -1.23999999999999994e-238

   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 i around inf 75.6%

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

   5. Simplified 76.1%

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

   6. Taylor expanded in j around inf 69.8%

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

   if -1.23999999999999994e-238 < z < 4.2e-148

   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 b around 0 72.4%

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

   4. Taylor expanded in y around 0 62.1%

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

      1. +-commutative 62.1%

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

      2. mul-1-neg 62.1%

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

      3. unsub-neg 62.1%

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

   6. Simplified 62.1%

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

   if 4.2e-148 < z < 9.6000000000000003e-83

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 69.3%

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

      1. +-commutative 69.3%

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

      2. mul-1-neg 69.3%

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

      3. unsub-neg 69.3%

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

   5. Simplified 69.3%

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

   if 7.00000000000000011e-22 < z < 2.3e107

   1. Initial program 86.4%

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

   3. Taylor expanded in b around inf 63.1%

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

      1. *-commutative 63.1%

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

   5. Simplified 63.1%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+137}:\\ \;\;\;\;z \cdot \left(c \cdot \left(\frac{x \cdot y}{c} - b\right)\right)\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-110}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq -1.24 \cdot 10^{-238}:\\ \;\;\;\;i \cdot \left(j \cdot \left(\frac{t \cdot c}{i} - y\right)\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-148}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-83}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-22}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+107}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(c \cdot \left(\frac{x \cdot y}{c} - b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := z \cdot \left(c \cdot \left(\frac{x \cdot y}{c} - b\right)\right)\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{+138}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-107}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-223}:\\ \;\;\;\;i \cdot \left(j \cdot \left(\frac{t \cdot c}{i} - y\right)\right)\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-297}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-82}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+110}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a)))) (t_2 (* z (* c (- (/ (* x y) c) b)))))
   (if (<= z -7.2e+138)
     t_2
     (if (<= z -1.15e-107)
       t_1
       (if (<= z -5.6e-223)
         (* i (* j (- (/ (* t c) i) y)))
         (if (<= z 9.6e-297)
           t_1
           (if (<= z 5.2e-82)
             (* j (- (* t c) (* y i)))
             (if (<= z 4.5e-22)
               t_1
               (if (<= z 2.7e+110) (* 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 = z * (c * (((x * y) / c) - b));
	double tmp;
	if (z <= -7.2e+138) {
		tmp = t_2;
	} else if (z <= -1.15e-107) {
		tmp = t_1;
	} else if (z <= -5.6e-223) {
		tmp = i * (j * (((t * c) / i) - y));
	} else if (z <= 9.6e-297) {
		tmp = t_1;
	} else if (z <= 5.2e-82) {
		tmp = j * ((t * c) - (y * i));
	} else if (z <= 4.5e-22) {
		tmp = t_1;
	} else if (z <= 2.7e+110) {
		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 = z * (c * (((x * y) / c) - b))
    if (z <= (-7.2d+138)) then
        tmp = t_2
    else if (z <= (-1.15d-107)) then
        tmp = t_1
    else if (z <= (-5.6d-223)) then
        tmp = i * (j * (((t * c) / i) - y))
    else if (z <= 9.6d-297) then
        tmp = t_1
    else if (z <= 5.2d-82) then
        tmp = j * ((t * c) - (y * i))
    else if (z <= 4.5d-22) then
        tmp = t_1
    else if (z <= 2.7d+110) 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 = z * (c * (((x * y) / c) - b));
	double tmp;
	if (z <= -7.2e+138) {
		tmp = t_2;
	} else if (z <= -1.15e-107) {
		tmp = t_1;
	} else if (z <= -5.6e-223) {
		tmp = i * (j * (((t * c) / i) - y));
	} else if (z <= 9.6e-297) {
		tmp = t_1;
	} else if (z <= 5.2e-82) {
		tmp = j * ((t * c) - (y * i));
	} else if (z <= 4.5e-22) {
		tmp = t_1;
	} else if (z <= 2.7e+110) {
		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 = z * (c * (((x * y) / c) - b))
	tmp = 0
	if z <= -7.2e+138:
		tmp = t_2
	elif z <= -1.15e-107:
		tmp = t_1
	elif z <= -5.6e-223:
		tmp = i * (j * (((t * c) / i) - y))
	elif z <= 9.6e-297:
		tmp = t_1
	elif z <= 5.2e-82:
		tmp = j * ((t * c) - (y * i))
	elif z <= 4.5e-22:
		tmp = t_1
	elif z <= 2.7e+110:
		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(z * Float64(c * Float64(Float64(Float64(x * y) / c) - b)))
	tmp = 0.0
	if (z <= -7.2e+138)
		tmp = t_2;
	elseif (z <= -1.15e-107)
		tmp = t_1;
	elseif (z <= -5.6e-223)
		tmp = Float64(i * Float64(j * Float64(Float64(Float64(t * c) / i) - y)));
	elseif (z <= 9.6e-297)
		tmp = t_1;
	elseif (z <= 5.2e-82)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (z <= 4.5e-22)
		tmp = t_1;
	elseif (z <= 2.7e+110)
		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 = z * (c * (((x * y) / c) - b));
	tmp = 0.0;
	if (z <= -7.2e+138)
		tmp = t_2;
	elseif (z <= -1.15e-107)
		tmp = t_1;
	elseif (z <= -5.6e-223)
		tmp = i * (j * (((t * c) / i) - y));
	elseif (z <= 9.6e-297)
		tmp = t_1;
	elseif (z <= 5.2e-82)
		tmp = j * ((t * c) - (y * i));
	elseif (z <= 4.5e-22)
		tmp = t_1;
	elseif (z <= 2.7e+110)
		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[(z * N[(c * N[(N[(N[(x * y), $MachinePrecision] / c), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.2e+138], t$95$2, If[LessEqual[z, -1.15e-107], t$95$1, If[LessEqual[z, -5.6e-223], N[(i * N[(j * N[(N[(N[(t * c), $MachinePrecision] / i), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.6e-297], t$95$1, If[LessEqual[z, 5.2e-82], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e-22], t$95$1, If[LessEqual[z, 2.7e+110], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -7.2000000000000002e138 or 2.7000000000000001e110 < z

   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. Step-by-step derivation

      1. *-commutative 54.2%

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

      2. *-commutative 54.2%

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

      3. *-commutative 54.2%

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

      4. add-cube-cbrt 54.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(t \cdot c - y \cdot i\right) \cdot \color{blue}{\left(\left(\sqrt[3]{j} \cdot \sqrt[3]{j}\right) \cdot \sqrt[3]{j}\right)} \]

      5. associate-*r* 54.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{\left(\left(t \cdot c - y \cdot i\right) \cdot \left(\sqrt[3]{j} \cdot \sqrt[3]{j}\right)\right) \cdot \sqrt[3]{j}} \]

      6. pow2 54.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(t \cdot c - y \cdot i\right) \cdot \color{blue}{{\left(\sqrt[3]{j}\right)}^{2}}\right) \cdot \sqrt[3]{j} \]

   4. Applied egg-rr 54.2%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{\left(\left(t \cdot c - y \cdot i\right) \cdot {\left(\sqrt[3]{j}\right)}^{2}\right) \cdot \sqrt[3]{j}} \]

   5. Taylor expanded in z around inf 77.2%

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

      1. *-commutative 77.2%

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

      2. *-commutative 77.2%

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

   7. Simplified 77.2%

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

   8. Taylor expanded in c around inf 78.6%

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

   if -7.2000000000000002e138 < z < -1.15000000000000002e-107 or -5.6000000000000003e-223 < z < 9.5999999999999998e-297 or 5.2e-82 < z < 4.49999999999999987e-22

   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 t around inf 60.2%

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

      1. +-commutative 60.2%

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

      2. mul-1-neg 60.2%

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

      3. unsub-neg 60.2%

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

      4. *-commutative 60.2%

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

      5. *-commutative 60.2%

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

   5. Simplified 60.2%

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

   if -1.15000000000000002e-107 < z < -5.6000000000000003e-223

   1. Initial program 83.0%

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

   3. Taylor expanded in i around inf 77.1%

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

   5. Simplified 77.7%

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

   6. Taylor expanded in j around inf 70.9%

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

   if 9.5999999999999998e-297 < z < 5.2e-82

   1. Initial program 88.4%

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

   3. Taylor expanded in j around inf 62.8%

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

   if 4.49999999999999987e-22 < z < 2.7000000000000001e110

   1. Initial program 86.4%

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

   3. Taylor expanded in b around inf 63.1%

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

      1. *-commutative 63.1%

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

   5. Simplified 63.1%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+138}:\\ \;\;\;\;z \cdot \left(c \cdot \left(\frac{x \cdot y}{c} - b\right)\right)\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-107}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-223}:\\ \;\;\;\;i \cdot \left(j \cdot \left(\frac{t \cdot c}{i} - y\right)\right)\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-297}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-82}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-22}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+110}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(c \cdot \left(\frac{x \cdot y}{c} - b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 49.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{+137}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-102}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-270}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-296}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-80}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+106}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a)))) (t_2 (* z (- (* x y) (* b c)))))
   (if (<= z -2.9e+137)
     t_2
     (if (<= z -5e-102)
       t_1
       (if (<= z -9.5e-270)
         (* i (- (* a b) (* y j)))
         (if (<= z 1.22e-296)
           t_1
           (if (<= z 2.6e-80)
             (* j (- (* t c) (* y i)))
             (if (<= z 3.2e-25)
               t_1
               (if (<= z 5e+106) (* 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 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -2.9e+137) {
		tmp = t_2;
	} else if (z <= -5e-102) {
		tmp = t_1;
	} else if (z <= -9.5e-270) {
		tmp = i * ((a * b) - (y * j));
	} else if (z <= 1.22e-296) {
		tmp = t_1;
	} else if (z <= 2.6e-80) {
		tmp = j * ((t * c) - (y * i));
	} else if (z <= 3.2e-25) {
		tmp = t_1;
	} else if (z <= 5e+106) {
		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 = z * ((x * y) - (b * c))
    if (z <= (-2.9d+137)) then
        tmp = t_2
    else if (z <= (-5d-102)) then
        tmp = t_1
    else if (z <= (-9.5d-270)) then
        tmp = i * ((a * b) - (y * j))
    else if (z <= 1.22d-296) then
        tmp = t_1
    else if (z <= 2.6d-80) then
        tmp = j * ((t * c) - (y * i))
    else if (z <= 3.2d-25) then
        tmp = t_1
    else if (z <= 5d+106) 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 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -2.9e+137) {
		tmp = t_2;
	} else if (z <= -5e-102) {
		tmp = t_1;
	} else if (z <= -9.5e-270) {
		tmp = i * ((a * b) - (y * j));
	} else if (z <= 1.22e-296) {
		tmp = t_1;
	} else if (z <= 2.6e-80) {
		tmp = j * ((t * c) - (y * i));
	} else if (z <= 3.2e-25) {
		tmp = t_1;
	} else if (z <= 5e+106) {
		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 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -2.9e+137:
		tmp = t_2
	elif z <= -5e-102:
		tmp = t_1
	elif z <= -9.5e-270:
		tmp = i * ((a * b) - (y * j))
	elif z <= 1.22e-296:
		tmp = t_1
	elif z <= 2.6e-80:
		tmp = j * ((t * c) - (y * i))
	elif z <= 3.2e-25:
		tmp = t_1
	elif z <= 5e+106:
		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(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (z <= -2.9e+137)
		tmp = t_2;
	elseif (z <= -5e-102)
		tmp = t_1;
	elseif (z <= -9.5e-270)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (z <= 1.22e-296)
		tmp = t_1;
	elseif (z <= 2.6e-80)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (z <= 3.2e-25)
		tmp = t_1;
	elseif (z <= 5e+106)
		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 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -2.9e+137)
		tmp = t_2;
	elseif (z <= -5e-102)
		tmp = t_1;
	elseif (z <= -9.5e-270)
		tmp = i * ((a * b) - (y * j));
	elseif (z <= 1.22e-296)
		tmp = t_1;
	elseif (z <= 2.6e-80)
		tmp = j * ((t * c) - (y * i));
	elseif (z <= 3.2e-25)
		tmp = t_1;
	elseif (z <= 5e+106)
		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[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.9e+137], t$95$2, If[LessEqual[z, -5e-102], t$95$1, If[LessEqual[z, -9.5e-270], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.22e-296], t$95$1, If[LessEqual[z, 2.6e-80], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e-25], t$95$1, If[LessEqual[z, 5e+106], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.89999999999999985e137 or 4.9999999999999998e106 < z

   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 z around inf 77.2%

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

      1. *-commutative 77.2%

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

   5. Simplified 77.2%

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

   if -2.89999999999999985e137 < z < -5.00000000000000026e-102 or -9.5000000000000006e-270 < z < 1.22e-296 or 2.6000000000000001e-80 < z < 3.2000000000000001e-25

   1. Initial program 77.9%

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

   3. Taylor expanded in t around inf 61.4%

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

      1. +-commutative 61.4%

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

      2. mul-1-neg 61.4%

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

      3. unsub-neg 61.4%

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

      4. *-commutative 61.4%

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

      5. *-commutative 61.4%

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

   5. Simplified 61.4%

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

   if -5.00000000000000026e-102 < z < -9.5000000000000006e-270

   1. Initial program 81.0%

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

   3. Taylor expanded in i around inf 78.2%

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

   5. Simplified 78.6%

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

   6. Taylor expanded in i around inf 65.4%

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

      1. mul-1-neg 65.4%

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

      2. distribute-rgt-neg-in 65.4%

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

      3. mul-1-neg 65.4%

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

      4. distribute-rgt-neg-out 65.4%

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

      5. distribute-neg-in 65.4%

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

      6. neg-mul-1 65.4%

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

      7. unsub-neg 65.4%

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

      8. neg-mul-1 65.4%

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

      9. distribute-rgt-neg-out 65.4%

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

      10. remove-double-neg 65.4%

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

      11. *-commutative 65.4%

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

   8. Simplified 65.4%

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

   if 1.22e-296 < z < 2.6000000000000001e-80

   1. Initial program 88.4%

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

   3. Taylor expanded in j around inf 62.8%

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

   if 3.2000000000000001e-25 < z < 4.9999999999999998e106

   1. Initial program 86.4%

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

   3. Taylor expanded in b around inf 63.1%

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

      1. *-commutative 63.1%

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

   5. Simplified 63.1%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+137}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-102}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-270}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-296}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-80}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-25}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+106}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 49.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -4.5 \cdot 10^{+232}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{+132}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{-53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{-160}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{+27}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{+108}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+132}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= b -4.5e+232)
     t_1
     (if (<= b -1.05e+132)
       (* i (- (* a b) (* y j)))
       (if (<= b -8.5e-53)
         t_1
         (if (<= b 2.9e-160)
           (* x (- (* y z) (* t a)))
           (if (<= b 2.05e+27)
             (* t (- (* c j) (* x a)))
             (if (<= b 2.15e+108)
               (* y (- (* x z) (* i j)))
               (if (<= b 2.5e+132) (* c (- (* t j) (* z b))) t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -4.5e+232) {
		tmp = t_1;
	} else if (b <= -1.05e+132) {
		tmp = i * ((a * b) - (y * j));
	} else if (b <= -8.5e-53) {
		tmp = t_1;
	} else if (b <= 2.9e-160) {
		tmp = x * ((y * z) - (t * a));
	} else if (b <= 2.05e+27) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= 2.15e+108) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 2.5e+132) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    if (b <= (-4.5d+232)) then
        tmp = t_1
    else if (b <= (-1.05d+132)) then
        tmp = i * ((a * b) - (y * j))
    else if (b <= (-8.5d-53)) then
        tmp = t_1
    else if (b <= 2.9d-160) then
        tmp = x * ((y * z) - (t * a))
    else if (b <= 2.05d+27) then
        tmp = t * ((c * j) - (x * a))
    else if (b <= 2.15d+108) then
        tmp = y * ((x * z) - (i * j))
    else if (b <= 2.5d+132) then
        tmp = c * ((t * j) - (z * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -4.5e+232) {
		tmp = t_1;
	} else if (b <= -1.05e+132) {
		tmp = i * ((a * b) - (y * j));
	} else if (b <= -8.5e-53) {
		tmp = t_1;
	} else if (b <= 2.9e-160) {
		tmp = x * ((y * z) - (t * a));
	} else if (b <= 2.05e+27) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= 2.15e+108) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 2.5e+132) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -4.5e+232:
		tmp = t_1
	elif b <= -1.05e+132:
		tmp = i * ((a * b) - (y * j))
	elif b <= -8.5e-53:
		tmp = t_1
	elif b <= 2.9e-160:
		tmp = x * ((y * z) - (t * a))
	elif b <= 2.05e+27:
		tmp = t * ((c * j) - (x * a))
	elif b <= 2.15e+108:
		tmp = y * ((x * z) - (i * j))
	elif b <= 2.5e+132:
		tmp = c * ((t * j) - (z * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -4.5e+232)
		tmp = t_1;
	elseif (b <= -1.05e+132)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (b <= -8.5e-53)
		tmp = t_1;
	elseif (b <= 2.9e-160)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (b <= 2.05e+27)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (b <= 2.15e+108)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (b <= 2.5e+132)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -4.5e+232)
		tmp = t_1;
	elseif (b <= -1.05e+132)
		tmp = i * ((a * b) - (y * j));
	elseif (b <= -8.5e-53)
		tmp = t_1;
	elseif (b <= 2.9e-160)
		tmp = x * ((y * z) - (t * a));
	elseif (b <= 2.05e+27)
		tmp = t * ((c * j) - (x * a));
	elseif (b <= 2.15e+108)
		tmp = y * ((x * z) - (i * j));
	elseif (b <= 2.5e+132)
		tmp = c * ((t * j) - (z * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.5e+232], t$95$1, If[LessEqual[b, -1.05e+132], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -8.5e-53], t$95$1, If[LessEqual[b, 2.9e-160], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.05e+27], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.15e+108], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.5e+132], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -4.4999999999999998e232 or -1.04999999999999997e132 < b < -8.50000000000000044e-53 or 2.5000000000000001e132 < b

   1. Initial program 71.1%

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

   3. Taylor expanded in b around inf 69.0%

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

      1. *-commutative 69.0%

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

   5. Simplified 69.0%

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

   if -4.4999999999999998e232 < b < -1.04999999999999997e132

   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 i around inf 36.7%

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

   5. Simplified 45.8%

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

   6. Taylor expanded in i around inf 68.6%

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

      1. mul-1-neg 68.6%

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

      2. distribute-rgt-neg-in 68.6%

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

      3. mul-1-neg 68.6%

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

      4. distribute-rgt-neg-out 68.6%

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

      5. distribute-neg-in 68.6%

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

      6. neg-mul-1 68.6%

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

      7. unsub-neg 68.6%

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

      8. neg-mul-1 68.6%

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

      9. distribute-rgt-neg-out 68.6%

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

      10. remove-double-neg 68.6%

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

      11. *-commutative 68.6%

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

   8. Simplified 68.6%

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

   if -8.50000000000000044e-53 < b < 2.8999999999999999e-160

   1. Initial program 73.6%

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

      1. *-commutative 73.6%

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

      2. *-commutative 73.6%

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

      3. *-commutative 73.6%

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

      4. add-cube-cbrt 73.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(t \cdot c - y \cdot i\right) \cdot \color{blue}{\left(\left(\sqrt[3]{j} \cdot \sqrt[3]{j}\right) \cdot \sqrt[3]{j}\right)} \]

      5. associate-*r* 73.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{\left(\left(t \cdot c - y \cdot i\right) \cdot \left(\sqrt[3]{j} \cdot \sqrt[3]{j}\right)\right) \cdot \sqrt[3]{j}} \]

      6. pow2 73.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(t \cdot c - y \cdot i\right) \cdot \color{blue}{{\left(\sqrt[3]{j}\right)}^{2}}\right) \cdot \sqrt[3]{j} \]

   4. Applied egg-rr 73.4%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{\left(\left(t \cdot c - y \cdot i\right) \cdot {\left(\sqrt[3]{j}\right)}^{2}\right) \cdot \sqrt[3]{j}} \]

   5. Taylor expanded in x around inf 57.9%

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

      1. *-commutative 57.9%

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

   7. Simplified 57.9%

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

   if 2.8999999999999999e-160 < b < 2.0500000000000001e27

   1. Initial program 86.1%

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

   3. Taylor expanded in t around inf 63.6%

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

      1. +-commutative 63.6%

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

      2. mul-1-neg 63.6%

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

      3. unsub-neg 63.6%

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

      4. *-commutative 63.6%

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

      5. *-commutative 63.6%

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

   5. Simplified 63.6%

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

   if 2.0500000000000001e27 < b < 2.14999999999999998e108

   1. Initial program 73.9%

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

   3. Taylor expanded in y around inf 66.3%

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

      1. +-commutative 66.3%

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

      2. mul-1-neg 66.3%

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

      3. unsub-neg 66.3%

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

   5. Simplified 66.3%

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

   if 2.14999999999999998e108 < b < 2.5000000000000001e132

   1. Initial program 83.3%

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

   3. Taylor expanded in c around inf 100.0%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{+232}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{+132}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{-53}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{-160}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{+27}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{+108}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+132}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 49.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -3.05 \cdot 10^{+234}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{+131}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -7 \cdot 10^{-53}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 2.55 \cdot 10^{-160}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{+53}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+132}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* a b) (* y j)))) (t_2 (* b (- (* a i) (* z c)))))
   (if (<= b -3.05e+234)
     t_2
     (if (<= b -1.15e+131)
       t_1
       (if (<= b -7e-53)
         t_2
         (if (<= b 2.55e-160)
           (* x (- (* y z) (* t a)))
           (if (<= b 2.3e+53)
             (* t (- (* c j) (* x a)))
             (if (<= b 4.5e+96)
               t_1
               (if (<= b 1.5e+132) (* c (- (* t j) (* z b))) t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -3.05e+234) {
		tmp = t_2;
	} else if (b <= -1.15e+131) {
		tmp = t_1;
	} else if (b <= -7e-53) {
		tmp = t_2;
	} else if (b <= 2.55e-160) {
		tmp = x * ((y * z) - (t * a));
	} else if (b <= 2.3e+53) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= 4.5e+96) {
		tmp = t_1;
	} else if (b <= 1.5e+132) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i * ((a * b) - (y * j))
    t_2 = b * ((a * i) - (z * c))
    if (b <= (-3.05d+234)) then
        tmp = t_2
    else if (b <= (-1.15d+131)) then
        tmp = t_1
    else if (b <= (-7d-53)) then
        tmp = t_2
    else if (b <= 2.55d-160) then
        tmp = x * ((y * z) - (t * a))
    else if (b <= 2.3d+53) then
        tmp = t * ((c * j) - (x * a))
    else if (b <= 4.5d+96) then
        tmp = t_1
    else if (b <= 1.5d+132) then
        tmp = c * ((t * j) - (z * b))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -3.05e+234) {
		tmp = t_2;
	} else if (b <= -1.15e+131) {
		tmp = t_1;
	} else if (b <= -7e-53) {
		tmp = t_2;
	} else if (b <= 2.55e-160) {
		tmp = x * ((y * z) - (t * a));
	} else if (b <= 2.3e+53) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= 4.5e+96) {
		tmp = t_1;
	} else if (b <= 1.5e+132) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((a * b) - (y * j))
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -3.05e+234:
		tmp = t_2
	elif b <= -1.15e+131:
		tmp = t_1
	elif b <= -7e-53:
		tmp = t_2
	elif b <= 2.55e-160:
		tmp = x * ((y * z) - (t * a))
	elif b <= 2.3e+53:
		tmp = t * ((c * j) - (x * a))
	elif b <= 4.5e+96:
		tmp = t_1
	elif b <= 1.5e+132:
		tmp = c * ((t * j) - (z * b))
	else:
		tmp = t_2
	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(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -3.05e+234)
		tmp = t_2;
	elseif (b <= -1.15e+131)
		tmp = t_1;
	elseif (b <= -7e-53)
		tmp = t_2;
	elseif (b <= 2.55e-160)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (b <= 2.3e+53)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (b <= 4.5e+96)
		tmp = t_1;
	elseif (b <= 1.5e+132)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((a * b) - (y * j));
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -3.05e+234)
		tmp = t_2;
	elseif (b <= -1.15e+131)
		tmp = t_1;
	elseif (b <= -7e-53)
		tmp = t_2;
	elseif (b <= 2.55e-160)
		tmp = x * ((y * z) - (t * a));
	elseif (b <= 2.3e+53)
		tmp = t * ((c * j) - (x * a));
	elseif (b <= 4.5e+96)
		tmp = t_1;
	elseif (b <= 1.5e+132)
		tmp = c * ((t * j) - (z * b));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.05e+234], t$95$2, If[LessEqual[b, -1.15e+131], t$95$1, If[LessEqual[b, -7e-53], t$95$2, If[LessEqual[b, 2.55e-160], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.3e+53], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.5e+96], t$95$1, If[LessEqual[b, 1.5e+132], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -3.05000000000000006e234 or -1.14999999999999996e131 < b < -6.99999999999999987e-53 or 1.4999999999999999e132 < b

   1. Initial program 71.1%

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

   3. Taylor expanded in b around inf 69.0%

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

      1. *-commutative 69.0%

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

   5. Simplified 69.0%

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

   if -3.05000000000000006e234 < b < -1.14999999999999996e131 or 2.3000000000000002e53 < b < 4.49999999999999957e96

   1. Initial program 73.6%

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

   3. Taylor expanded in i around inf 53.0%

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

   5. Simplified 58.9%

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

   6. Taylor expanded in i around inf 73.7%

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

      1. mul-1-neg 73.7%

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

      2. distribute-rgt-neg-in 73.7%

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

      3. mul-1-neg 73.7%

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

      4. distribute-rgt-neg-out 73.7%

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

      5. distribute-neg-in 73.7%

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

      6. neg-mul-1 73.7%

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

      7. unsub-neg 73.7%

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

      8. neg-mul-1 73.7%

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

      9. distribute-rgt-neg-out 73.7%

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

      10. remove-double-neg 73.7%

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

      11. *-commutative 73.7%

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

   8. Simplified 73.7%

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

   if -6.99999999999999987e-53 < b < 2.55e-160

   1. Initial program 73.6%

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

      1. *-commutative 73.6%

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

      2. *-commutative 73.6%

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

      3. *-commutative 73.6%

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

      4. add-cube-cbrt 73.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(t \cdot c - y \cdot i\right) \cdot \color{blue}{\left(\left(\sqrt[3]{j} \cdot \sqrt[3]{j}\right) \cdot \sqrt[3]{j}\right)} \]

      5. associate-*r* 73.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{\left(\left(t \cdot c - y \cdot i\right) \cdot \left(\sqrt[3]{j} \cdot \sqrt[3]{j}\right)\right) \cdot \sqrt[3]{j}} \]

      6. pow2 73.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(t \cdot c - y \cdot i\right) \cdot \color{blue}{{\left(\sqrt[3]{j}\right)}^{2}}\right) \cdot \sqrt[3]{j} \]

   4. Applied egg-rr 73.4%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{\left(\left(t \cdot c - y \cdot i\right) \cdot {\left(\sqrt[3]{j}\right)}^{2}\right) \cdot \sqrt[3]{j}} \]

   5. Taylor expanded in x around inf 57.9%

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

      1. *-commutative 57.9%

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

   7. Simplified 57.9%

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

   if 2.55e-160 < b < 2.3000000000000002e53

   1. Initial program 86.0%

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

   3. Taylor expanded in t around inf 60.5%

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

      1. +-commutative 60.5%

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

      2. mul-1-neg 60.5%

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

      3. unsub-neg 60.5%

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

      4. *-commutative 60.5%

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

      5. *-commutative 60.5%

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

   5. Simplified 60.5%

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

   if 4.49999999999999957e96 < b < 1.4999999999999999e132

   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 c around inf 80.4%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.05 \cdot 10^{+234}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{+131}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq -7 \cdot 10^{-53}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 2.55 \cdot 10^{-160}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{+53}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+96}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+132}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 37.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(y \cdot \left(-j\right)\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;x \leq -4 \cdot 10^{+192}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq -3.75 \cdot 10^{-47}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-301}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-237}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-8}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+150}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* y (- j))))
        (t_2 (* b (- (* a i) (* z c))))
        (t_3 (* z (* x y))))
   (if (<= x -4e+192)
     t_3
     (if (<= x -3.75e-47)
       (* t (* x (- a)))
       (if (<= x 5.8e-301)
         t_2
         (if (<= x 9.5e-237)
           t_1
           (if (<= x 7.8e-8)
             t_2
             (if (<= x 1.3e+79) t_1 (if (<= x 3.2e+150) t_2 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 * (y * -j);
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = z * (x * y);
	double tmp;
	if (x <= -4e+192) {
		tmp = t_3;
	} else if (x <= -3.75e-47) {
		tmp = t * (x * -a);
	} else if (x <= 5.8e-301) {
		tmp = t_2;
	} else if (x <= 9.5e-237) {
		tmp = t_1;
	} else if (x <= 7.8e-8) {
		tmp = t_2;
	} else if (x <= 1.3e+79) {
		tmp = t_1;
	} else if (x <= 3.2e+150) {
		tmp = t_2;
	} 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 * (y * -j)
    t_2 = b * ((a * i) - (z * c))
    t_3 = z * (x * y)
    if (x <= (-4d+192)) then
        tmp = t_3
    else if (x <= (-3.75d-47)) then
        tmp = t * (x * -a)
    else if (x <= 5.8d-301) then
        tmp = t_2
    else if (x <= 9.5d-237) then
        tmp = t_1
    else if (x <= 7.8d-8) then
        tmp = t_2
    else if (x <= 1.3d+79) then
        tmp = t_1
    else if (x <= 3.2d+150) then
        tmp = t_2
    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 * (y * -j);
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = z * (x * y);
	double tmp;
	if (x <= -4e+192) {
		tmp = t_3;
	} else if (x <= -3.75e-47) {
		tmp = t * (x * -a);
	} else if (x <= 5.8e-301) {
		tmp = t_2;
	} else if (x <= 9.5e-237) {
		tmp = t_1;
	} else if (x <= 7.8e-8) {
		tmp = t_2;
	} else if (x <= 1.3e+79) {
		tmp = t_1;
	} else if (x <= 3.2e+150) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (y * -j)
	t_2 = b * ((a * i) - (z * c))
	t_3 = z * (x * y)
	tmp = 0
	if x <= -4e+192:
		tmp = t_3
	elif x <= -3.75e-47:
		tmp = t * (x * -a)
	elif x <= 5.8e-301:
		tmp = t_2
	elif x <= 9.5e-237:
		tmp = t_1
	elif x <= 7.8e-8:
		tmp = t_2
	elif x <= 1.3e+79:
		tmp = t_1
	elif x <= 3.2e+150:
		tmp = t_2
	else:
		tmp = t_3
	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(b * Float64(Float64(a * i) - Float64(z * c)))
	t_3 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (x <= -4e+192)
		tmp = t_3;
	elseif (x <= -3.75e-47)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (x <= 5.8e-301)
		tmp = t_2;
	elseif (x <= 9.5e-237)
		tmp = t_1;
	elseif (x <= 7.8e-8)
		tmp = t_2;
	elseif (x <= 1.3e+79)
		tmp = t_1;
	elseif (x <= 3.2e+150)
		tmp = t_2;
	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 * (y * -j);
	t_2 = b * ((a * i) - (z * c));
	t_3 = z * (x * y);
	tmp = 0.0;
	if (x <= -4e+192)
		tmp = t_3;
	elseif (x <= -3.75e-47)
		tmp = t * (x * -a);
	elseif (x <= 5.8e-301)
		tmp = t_2;
	elseif (x <= 9.5e-237)
		tmp = t_1;
	elseif (x <= 7.8e-8)
		tmp = t_2;
	elseif (x <= 1.3e+79)
		tmp = t_1;
	elseif (x <= 3.2e+150)
		tmp = t_2;
	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[(y * (-j)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4e+192], t$95$3, If[LessEqual[x, -3.75e-47], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.8e-301], t$95$2, If[LessEqual[x, 9.5e-237], t$95$1, If[LessEqual[x, 7.8e-8], t$95$2, If[LessEqual[x, 1.3e+79], t$95$1, If[LessEqual[x, 3.2e+150], t$95$2, t$95$3]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.00000000000000016e192 or 3.20000000000000016e150 < x

   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. Step-by-step derivation

      1. *-commutative 79.8%

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

      2. *-commutative 79.8%

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

      3. *-commutative 79.8%

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

      4. add-cube-cbrt 79.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(t \cdot c - y \cdot i\right) \cdot \color{blue}{\left(\left(\sqrt[3]{j} \cdot \sqrt[3]{j}\right) \cdot \sqrt[3]{j}\right)} \]

      5. associate-*r* 79.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{\left(\left(t \cdot c - y \cdot i\right) \cdot \left(\sqrt[3]{j} \cdot \sqrt[3]{j}\right)\right) \cdot \sqrt[3]{j}} \]

      6. pow2 79.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(t \cdot c - y \cdot i\right) \cdot \color{blue}{{\left(\sqrt[3]{j}\right)}^{2}}\right) \cdot \sqrt[3]{j} \]

   4. Applied egg-rr 79.7%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{\left(\left(t \cdot c - y \cdot i\right) \cdot {\left(\sqrt[3]{j}\right)}^{2}\right) \cdot \sqrt[3]{j}} \]

   5. Taylor expanded in z around inf 65.5%

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

      1. *-commutative 65.5%

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

      2. *-commutative 65.5%

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

   7. Simplified 65.5%

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

   8. Taylor expanded in y around inf 65.5%

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

   if -4.00000000000000016e192 < x < -3.74999999999999984e-47

   1. Initial program 72.8%

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

   3. Taylor expanded in t around inf 64.7%

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

      1. +-commutative 64.7%

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

      2. mul-1-neg 64.7%

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

      3. unsub-neg 64.7%

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

      4. *-commutative 64.7%

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

      5. *-commutative 64.7%

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

   5. Simplified 64.7%

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

   6. Taylor expanded in j around 0 47.7%

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

      1. mul-1-neg 47.7%

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

      2. *-commutative 47.7%

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

      3. distribute-rgt-neg-in 47.7%

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

   8. Simplified 47.7%

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

   if -3.74999999999999984e-47 < x < 5.79999999999999968e-301 or 9.4999999999999998e-237 < x < 7.7999999999999997e-8 or 1.30000000000000007e79 < x < 3.20000000000000016e150

   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 55.5%

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

      1. *-commutative 55.5%

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

   5. Simplified 55.5%

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

   if 5.79999999999999968e-301 < x < 9.4999999999999998e-237 or 7.7999999999999997e-8 < x < 1.30000000000000007e79

   1. Initial program 76.8%

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

   3. Taylor expanded in y around inf 57.2%

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

      1. +-commutative 57.2%

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

      2. mul-1-neg 57.2%

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

      3. unsub-neg 57.2%

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

   5. Simplified 57.2%

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

   6. Taylor expanded in x around 0 56.9%

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

      1. mul-1-neg 56.9%

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

      2. distribute-rgt-neg-in 56.9%

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

      3. *-commutative 56.9%

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

      4. distribute-rgt-neg-in 56.9%

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

   8. Simplified 56.9%

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

Alternative 10: 63.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := z \cdot \left(c \cdot \left(\frac{x \cdot y}{c} - b\right)\right)\\ t_3 := t\_1 - j \cdot \left(y \cdot i - t \cdot c\right)\\ t_4 := b \cdot \left(a \cdot i - z \cdot c\right) + t\_1\\ \mathbf{if}\;z \leq -1.32 \cdot 10^{+138}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -3700000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-111}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-20}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+153}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (* z (* c (- (/ (* x y) c) b))))
        (t_3 (- t_1 (* j (- (* y i) (* t c)))))
        (t_4 (+ (* b (- (* a i) (* z c))) t_1)))
   (if (<= z -1.32e+138)
     t_2
     (if (<= z -3700000.0)
       t_3
       (if (<= z -6.6e-111)
         t_4
         (if (<= z 1.25e-20) t_3 (if (<= z 4.9e+153) t_4 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 = z * (c * (((x * y) / c) - b));
	double t_3 = t_1 - (j * ((y * i) - (t * c)));
	double t_4 = (b * ((a * i) - (z * c))) + t_1;
	double tmp;
	if (z <= -1.32e+138) {
		tmp = t_2;
	} else if (z <= -3700000.0) {
		tmp = t_3;
	} else if (z <= -6.6e-111) {
		tmp = t_4;
	} else if (z <= 1.25e-20) {
		tmp = t_3;
	} else if (z <= 4.9e+153) {
		tmp = t_4;
	} 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) :: t_4
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = z * (c * (((x * y) / c) - b))
    t_3 = t_1 - (j * ((y * i) - (t * c)))
    t_4 = (b * ((a * i) - (z * c))) + t_1
    if (z <= (-1.32d+138)) then
        tmp = t_2
    else if (z <= (-3700000.0d0)) then
        tmp = t_3
    else if (z <= (-6.6d-111)) then
        tmp = t_4
    else if (z <= 1.25d-20) then
        tmp = t_3
    else if (z <= 4.9d+153) then
        tmp = t_4
    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 = z * (c * (((x * y) / c) - b));
	double t_3 = t_1 - (j * ((y * i) - (t * c)));
	double t_4 = (b * ((a * i) - (z * c))) + t_1;
	double tmp;
	if (z <= -1.32e+138) {
		tmp = t_2;
	} else if (z <= -3700000.0) {
		tmp = t_3;
	} else if (z <= -6.6e-111) {
		tmp = t_4;
	} else if (z <= 1.25e-20) {
		tmp = t_3;
	} else if (z <= 4.9e+153) {
		tmp = t_4;
	} 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 = z * (c * (((x * y) / c) - b))
	t_3 = t_1 - (j * ((y * i) - (t * c)))
	t_4 = (b * ((a * i) - (z * c))) + t_1
	tmp = 0
	if z <= -1.32e+138:
		tmp = t_2
	elif z <= -3700000.0:
		tmp = t_3
	elif z <= -6.6e-111:
		tmp = t_4
	elif z <= 1.25e-20:
		tmp = t_3
	elif z <= 4.9e+153:
		tmp = t_4
	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(z * Float64(c * Float64(Float64(Float64(x * y) / c) - b)))
	t_3 = Float64(t_1 - Float64(j * Float64(Float64(y * i) - Float64(t * c))))
	t_4 = Float64(Float64(b * Float64(Float64(a * i) - Float64(z * c))) + t_1)
	tmp = 0.0
	if (z <= -1.32e+138)
		tmp = t_2;
	elseif (z <= -3700000.0)
		tmp = t_3;
	elseif (z <= -6.6e-111)
		tmp = t_4;
	elseif (z <= 1.25e-20)
		tmp = t_3;
	elseif (z <= 4.9e+153)
		tmp = t_4;
	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 = z * (c * (((x * y) / c) - b));
	t_3 = t_1 - (j * ((y * i) - (t * c)));
	t_4 = (b * ((a * i) - (z * c))) + t_1;
	tmp = 0.0;
	if (z <= -1.32e+138)
		tmp = t_2;
	elseif (z <= -3700000.0)
		tmp = t_3;
	elseif (z <= -6.6e-111)
		tmp = t_4;
	elseif (z <= 1.25e-20)
		tmp = t_3;
	elseif (z <= 4.9e+153)
		tmp = t_4;
	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[(z * N[(c * N[(N[(N[(x * y), $MachinePrecision] / c), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 - N[(j * N[(N[(y * i), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[z, -1.32e+138], t$95$2, If[LessEqual[z, -3700000.0], t$95$3, If[LessEqual[z, -6.6e-111], t$95$4, If[LessEqual[z, 1.25e-20], t$95$3, If[LessEqual[z, 4.9e+153], t$95$4, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.32000000000000001e138 or 4.90000000000000002e153 < z

   1. Initial program 52.1%

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

      1. *-commutative 52.1%

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

      2. *-commutative 52.1%

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

      3. *-commutative 52.1%

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

      4. add-cube-cbrt 52.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(t \cdot c - y \cdot i\right) \cdot \color{blue}{\left(\left(\sqrt[3]{j} \cdot \sqrt[3]{j}\right) \cdot \sqrt[3]{j}\right)} \]

      5. associate-*r* 52.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{\left(\left(t \cdot c - y \cdot i\right) \cdot \left(\sqrt[3]{j} \cdot \sqrt[3]{j}\right)\right) \cdot \sqrt[3]{j}} \]

      6. pow2 52.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(t \cdot c - y \cdot i\right) \cdot \color{blue}{{\left(\sqrt[3]{j}\right)}^{2}}\right) \cdot \sqrt[3]{j} \]

   4. Applied egg-rr 52.1%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{\left(\left(t \cdot c - y \cdot i\right) \cdot {\left(\sqrt[3]{j}\right)}^{2}\right) \cdot \sqrt[3]{j}} \]

   5. Taylor expanded in z around inf 77.0%

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

      1. *-commutative 77.0%

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

      2. *-commutative 77.0%

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

   7. Simplified 77.0%

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

   8. Taylor expanded in c around inf 78.5%

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

   if -1.32000000000000001e138 < z < -3.7e6 or -6.6e-111 < z < 1.25e-20

   1. Initial program 78.3%

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

   3. Taylor expanded in b around 0 72.4%

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

   if -3.7e6 < z < -6.6e-111 or 1.25e-20 < z < 4.90000000000000002e153

   1. Initial program 90.6%

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

   3. Taylor expanded in j around 0 79.7%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{+138}:\\ \;\;\;\;z \cdot \left(c \cdot \left(\frac{x \cdot y}{c} - b\right)\right)\\ \mathbf{elif}\;z \leq -3700000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-111}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-20}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+153}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(c \cdot \left(\frac{x \cdot y}{c} - b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 49.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -6.7 \cdot 10^{+232}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -2.25 \cdot 10^{+132}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{-79}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+51}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{+135}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* a b) (* y j)))) (t_2 (* b (- (* a i) (* z c)))))
   (if (<= b -6.7e+232)
     t_2
     (if (<= b -2.25e+132)
       t_1
       (if (<= b -1.05e-79)
         t_2
         (if (<= b 4.5e+51)
           (* t (- (* c j) (* x a)))
           (if (<= b 4.5e+96)
             t_1
             (if (<= b 3.6e+135) (* c (- (* t j) (* z b))) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -6.7e+232) {
		tmp = t_2;
	} else if (b <= -2.25e+132) {
		tmp = t_1;
	} else if (b <= -1.05e-79) {
		tmp = t_2;
	} else if (b <= 4.5e+51) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= 4.5e+96) {
		tmp = t_1;
	} else if (b <= 3.6e+135) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i * ((a * b) - (y * j))
    t_2 = b * ((a * i) - (z * c))
    if (b <= (-6.7d+232)) then
        tmp = t_2
    else if (b <= (-2.25d+132)) then
        tmp = t_1
    else if (b <= (-1.05d-79)) then
        tmp = t_2
    else if (b <= 4.5d+51) then
        tmp = t * ((c * j) - (x * a))
    else if (b <= 4.5d+96) then
        tmp = t_1
    else if (b <= 3.6d+135) then
        tmp = c * ((t * j) - (z * b))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -6.7e+232) {
		tmp = t_2;
	} else if (b <= -2.25e+132) {
		tmp = t_1;
	} else if (b <= -1.05e-79) {
		tmp = t_2;
	} else if (b <= 4.5e+51) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= 4.5e+96) {
		tmp = t_1;
	} else if (b <= 3.6e+135) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((a * b) - (y * j))
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -6.7e+232:
		tmp = t_2
	elif b <= -2.25e+132:
		tmp = t_1
	elif b <= -1.05e-79:
		tmp = t_2
	elif b <= 4.5e+51:
		tmp = t * ((c * j) - (x * a))
	elif b <= 4.5e+96:
		tmp = t_1
	elif b <= 3.6e+135:
		tmp = c * ((t * j) - (z * b))
	else:
		tmp = t_2
	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(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -6.7e+232)
		tmp = t_2;
	elseif (b <= -2.25e+132)
		tmp = t_1;
	elseif (b <= -1.05e-79)
		tmp = t_2;
	elseif (b <= 4.5e+51)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (b <= 4.5e+96)
		tmp = t_1;
	elseif (b <= 3.6e+135)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((a * b) - (y * j));
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -6.7e+232)
		tmp = t_2;
	elseif (b <= -2.25e+132)
		tmp = t_1;
	elseif (b <= -1.05e-79)
		tmp = t_2;
	elseif (b <= 4.5e+51)
		tmp = t * ((c * j) - (x * a));
	elseif (b <= 4.5e+96)
		tmp = t_1;
	elseif (b <= 3.6e+135)
		tmp = c * ((t * j) - (z * b));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.7e+232], t$95$2, If[LessEqual[b, -2.25e+132], t$95$1, If[LessEqual[b, -1.05e-79], t$95$2, If[LessEqual[b, 4.5e+51], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.5e+96], t$95$1, If[LessEqual[b, 3.6e+135], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -6.69999999999999976e232 or -2.24999999999999986e132 < b < -1.05e-79 or 3.5999999999999998e135 < b

   1. Initial program 70.3%

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

   3. Taylor expanded in b around inf 67.4%

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

      1. *-commutative 67.4%

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

   5. Simplified 67.4%

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

   if -6.69999999999999976e232 < b < -2.24999999999999986e132 or 4.5e51 < b < 4.49999999999999957e96

   1. Initial program 73.6%

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

   3. Taylor expanded in i around inf 53.0%

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

   5. Simplified 58.9%

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

   6. Taylor expanded in i around inf 73.7%

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

      1. mul-1-neg 73.7%

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

      2. distribute-rgt-neg-in 73.7%

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

      3. mul-1-neg 73.7%

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

      4. distribute-rgt-neg-out 73.7%

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

      5. distribute-neg-in 73.7%

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

      6. neg-mul-1 73.7%

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

      7. unsub-neg 73.7%

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

      8. neg-mul-1 73.7%

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

      9. distribute-rgt-neg-out 73.7%

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

      10. remove-double-neg 73.7%

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

      11. *-commutative 73.7%

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

   8. Simplified 73.7%

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

   if -1.05e-79 < b < 4.5e51

   1. Initial program 78.9%

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

   3. Taylor expanded in t around inf 55.9%

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

      1. +-commutative 55.9%

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

      2. mul-1-neg 55.9%

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

      3. unsub-neg 55.9%

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

      4. *-commutative 55.9%

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

      5. *-commutative 55.9%

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

   5. Simplified 55.9%

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

   if 4.49999999999999957e96 < b < 3.5999999999999998e135

   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 c around inf 80.4%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.7 \cdot 10^{+232}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2.25 \cdot 10^{+132}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{-79}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+51}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+96}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{+135}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 29.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ t_2 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;x \leq -8.4 \cdot 10^{+186}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-46}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-265}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-170}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-117}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+88}:\\ \;\;\;\;y \cdot \left(j \cdot \left(-i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j))) (t_2 (* z (* x y))))
   (if (<= x -8.4e+186)
     t_2
     (if (<= x -1.45e-46)
       (* t (* x (- a)))
       (if (<= x 2.4e-265)
         t_1
         (if (<= x 1.25e-170)
           (* i (* y (- j)))
           (if (<= x 2.9e-117)
             t_1
             (if (<= x 9e+88) (* y (* j (- i))) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double t_2 = z * (x * y);
	double tmp;
	if (x <= -8.4e+186) {
		tmp = t_2;
	} else if (x <= -1.45e-46) {
		tmp = t * (x * -a);
	} else if (x <= 2.4e-265) {
		tmp = t_1;
	} else if (x <= 1.25e-170) {
		tmp = i * (y * -j);
	} else if (x <= 2.9e-117) {
		tmp = t_1;
	} else if (x <= 9e+88) {
		tmp = y * (j * -i);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * (t * j)
    t_2 = z * (x * y)
    if (x <= (-8.4d+186)) then
        tmp = t_2
    else if (x <= (-1.45d-46)) then
        tmp = t * (x * -a)
    else if (x <= 2.4d-265) then
        tmp = t_1
    else if (x <= 1.25d-170) then
        tmp = i * (y * -j)
    else if (x <= 2.9d-117) then
        tmp = t_1
    else if (x <= 9d+88) then
        tmp = y * (j * -i)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double t_2 = z * (x * y);
	double tmp;
	if (x <= -8.4e+186) {
		tmp = t_2;
	} else if (x <= -1.45e-46) {
		tmp = t * (x * -a);
	} else if (x <= 2.4e-265) {
		tmp = t_1;
	} else if (x <= 1.25e-170) {
		tmp = i * (y * -j);
	} else if (x <= 2.9e-117) {
		tmp = t_1;
	} else if (x <= 9e+88) {
		tmp = y * (j * -i);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (t * j)
	t_2 = z * (x * y)
	tmp = 0
	if x <= -8.4e+186:
		tmp = t_2
	elif x <= -1.45e-46:
		tmp = t * (x * -a)
	elif x <= 2.4e-265:
		tmp = t_1
	elif x <= 1.25e-170:
		tmp = i * (y * -j)
	elif x <= 2.9e-117:
		tmp = t_1
	elif x <= 9e+88:
		tmp = y * (j * -i)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(t * j))
	t_2 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (x <= -8.4e+186)
		tmp = t_2;
	elseif (x <= -1.45e-46)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (x <= 2.4e-265)
		tmp = t_1;
	elseif (x <= 1.25e-170)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (x <= 2.9e-117)
		tmp = t_1;
	elseif (x <= 9e+88)
		tmp = Float64(y * Float64(j * Float64(-i)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (t * j);
	t_2 = z * (x * y);
	tmp = 0.0;
	if (x <= -8.4e+186)
		tmp = t_2;
	elseif (x <= -1.45e-46)
		tmp = t * (x * -a);
	elseif (x <= 2.4e-265)
		tmp = t_1;
	elseif (x <= 1.25e-170)
		tmp = i * (y * -j);
	elseif (x <= 2.9e-117)
		tmp = t_1;
	elseif (x <= 9e+88)
		tmp = y * (j * -i);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8.4e+186], t$95$2, If[LessEqual[x, -1.45e-46], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.4e-265], t$95$1, If[LessEqual[x, 1.25e-170], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.9e-117], t$95$1, If[LessEqual[x, 9e+88], N[(y * N[(j * (-i)), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -8.4000000000000001e186 or 9e88 < x

   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. Step-by-step derivation

      1. *-commutative 75.6%

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

      2. *-commutative 75.6%

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

      3. *-commutative 75.6%

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

      4. add-cube-cbrt 75.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(t \cdot c - y \cdot i\right) \cdot \color{blue}{\left(\left(\sqrt[3]{j} \cdot \sqrt[3]{j}\right) \cdot \sqrt[3]{j}\right)} \]

      5. associate-*r* 75.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{\left(\left(t \cdot c - y \cdot i\right) \cdot \left(\sqrt[3]{j} \cdot \sqrt[3]{j}\right)\right) \cdot \sqrt[3]{j}} \]

      6. pow2 75.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(t \cdot c - y \cdot i\right) \cdot \color{blue}{{\left(\sqrt[3]{j}\right)}^{2}}\right) \cdot \sqrt[3]{j} \]

   4. Applied egg-rr 75.5%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{\left(\left(t \cdot c - y \cdot i\right) \cdot {\left(\sqrt[3]{j}\right)}^{2}\right) \cdot \sqrt[3]{j}} \]

   5. Taylor expanded in z around inf 62.6%

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

      1. *-commutative 62.6%

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

      2. *-commutative 62.6%

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

   7. Simplified 62.6%

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

   8. Taylor expanded in y around inf 57.7%

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

   if -8.4000000000000001e186 < x < -1.45000000000000002e-46

   1. Initial program 72.8%

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

   3. Taylor expanded in t around inf 64.7%

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

      1. +-commutative 64.7%

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

      2. mul-1-neg 64.7%

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

      3. unsub-neg 64.7%

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

      4. *-commutative 64.7%

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

      5. *-commutative 64.7%

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

   5. Simplified 64.7%

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

   6. Taylor expanded in j around 0 47.7%

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

      1. mul-1-neg 47.7%

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

      2. *-commutative 47.7%

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

      3. distribute-rgt-neg-in 47.7%

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

   8. Simplified 47.7%

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

   if -1.45000000000000002e-46 < x < 2.4e-265 or 1.25000000000000003e-170 < x < 2.9000000000000001e-117

   1. Initial program 72.2%

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

   3. Taylor expanded in b around 0 50.9%

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

   4. Taylor expanded in c around inf 39.7%

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

   if 2.4e-265 < x < 1.25000000000000003e-170

   1. Initial program 71.4%

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

   3. Taylor expanded in y around inf 48.5%

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

      1. +-commutative 48.5%

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

      2. mul-1-neg 48.5%

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

      3. unsub-neg 48.5%

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

   5. Simplified 48.5%

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

   6. Taylor expanded in x around 0 51.4%

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

      1. mul-1-neg 51.4%

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

      2. distribute-rgt-neg-in 51.4%

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

      3. *-commutative 51.4%

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

      4. distribute-rgt-neg-in 51.4%

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

   8. Simplified 51.4%

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

   if 2.9000000000000001e-117 < x < 9e88

   1. Initial program 79.6%

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

   3. Taylor expanded in y around inf 42.2%

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

      1. +-commutative 42.2%

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

      2. mul-1-neg 42.2%

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

      3. unsub-neg 42.2%

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

   5. Simplified 42.2%

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

   6. Taylor expanded in x around 0 38.7%

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

      1. neg-mul-1 38.7%

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

      2. distribute-rgt-neg-in 38.7%

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

   8. Simplified 38.7%

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

4. Final simplification 46.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.4 \cdot 10^{+186}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-46}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-265}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-170}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-117}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+88}:\\ \;\;\;\;y \cdot \left(j \cdot \left(-i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 29.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(y \cdot \left(-j\right)\right)\\ t_2 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;x \leq -1 \cdot 10^{+199}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -4.05 \cdot 10^{-44}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-264}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-170}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-60}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+88}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* y (- j)))) (t_2 (* z (* x y))))
   (if (<= x -1e+199)
     t_2
     (if (<= x -4.05e-44)
       (* t (* x (- a)))
       (if (<= x 1.85e-264)
         (* c (* t j))
         (if (<= x 2.1e-170)
           t_1
           (if (<= x 9.5e-60) (* b (* a i)) (if (<= x 4.8e+88) 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 = i * (y * -j);
	double t_2 = z * (x * y);
	double tmp;
	if (x <= -1e+199) {
		tmp = t_2;
	} else if (x <= -4.05e-44) {
		tmp = t * (x * -a);
	} else if (x <= 1.85e-264) {
		tmp = c * (t * j);
	} else if (x <= 2.1e-170) {
		tmp = t_1;
	} else if (x <= 9.5e-60) {
		tmp = b * (a * i);
	} else if (x <= 4.8e+88) {
		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 = i * (y * -j)
    t_2 = z * (x * y)
    if (x <= (-1d+199)) then
        tmp = t_2
    else if (x <= (-4.05d-44)) then
        tmp = t * (x * -a)
    else if (x <= 1.85d-264) then
        tmp = c * (t * j)
    else if (x <= 2.1d-170) then
        tmp = t_1
    else if (x <= 9.5d-60) then
        tmp = b * (a * i)
    else if (x <= 4.8d+88) 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 = i * (y * -j);
	double t_2 = z * (x * y);
	double tmp;
	if (x <= -1e+199) {
		tmp = t_2;
	} else if (x <= -4.05e-44) {
		tmp = t * (x * -a);
	} else if (x <= 1.85e-264) {
		tmp = c * (t * j);
	} else if (x <= 2.1e-170) {
		tmp = t_1;
	} else if (x <= 9.5e-60) {
		tmp = b * (a * i);
	} else if (x <= 4.8e+88) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (y * -j)
	t_2 = z * (x * y)
	tmp = 0
	if x <= -1e+199:
		tmp = t_2
	elif x <= -4.05e-44:
		tmp = t * (x * -a)
	elif x <= 1.85e-264:
		tmp = c * (t * j)
	elif x <= 2.1e-170:
		tmp = t_1
	elif x <= 9.5e-60:
		tmp = b * (a * i)
	elif x <= 4.8e+88:
		tmp = t_1
	else:
		tmp = t_2
	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(z * Float64(x * y))
	tmp = 0.0
	if (x <= -1e+199)
		tmp = t_2;
	elseif (x <= -4.05e-44)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (x <= 1.85e-264)
		tmp = Float64(c * Float64(t * j));
	elseif (x <= 2.1e-170)
		tmp = t_1;
	elseif (x <= 9.5e-60)
		tmp = Float64(b * Float64(a * i));
	elseif (x <= 4.8e+88)
		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 = i * (y * -j);
	t_2 = z * (x * y);
	tmp = 0.0;
	if (x <= -1e+199)
		tmp = t_2;
	elseif (x <= -4.05e-44)
		tmp = t * (x * -a);
	elseif (x <= 1.85e-264)
		tmp = c * (t * j);
	elseif (x <= 2.1e-170)
		tmp = t_1;
	elseif (x <= 9.5e-60)
		tmp = b * (a * i);
	elseif (x <= 4.8e+88)
		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[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1e+199], t$95$2, If[LessEqual[x, -4.05e-44], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.85e-264], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.1e-170], t$95$1, If[LessEqual[x, 9.5e-60], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.8e+88], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.0000000000000001e199 or 4.7999999999999998e88 < x

   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. Step-by-step derivation

      1. *-commutative 75.6%

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

      2. *-commutative 75.6%

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

      3. *-commutative 75.6%

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

      4. add-cube-cbrt 75.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(t \cdot c - y \cdot i\right) \cdot \color{blue}{\left(\left(\sqrt[3]{j} \cdot \sqrt[3]{j}\right) \cdot \sqrt[3]{j}\right)} \]

      5. associate-*r* 75.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{\left(\left(t \cdot c - y \cdot i\right) \cdot \left(\sqrt[3]{j} \cdot \sqrt[3]{j}\right)\right) \cdot \sqrt[3]{j}} \]

      6. pow2 75.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(t \cdot c - y \cdot i\right) \cdot \color{blue}{{\left(\sqrt[3]{j}\right)}^{2}}\right) \cdot \sqrt[3]{j} \]

   4. Applied egg-rr 75.5%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{\left(\left(t \cdot c - y \cdot i\right) \cdot {\left(\sqrt[3]{j}\right)}^{2}\right) \cdot \sqrt[3]{j}} \]

   5. Taylor expanded in z around inf 62.6%

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

      1. *-commutative 62.6%

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

      2. *-commutative 62.6%

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

   7. Simplified 62.6%

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

   8. Taylor expanded in y around inf 57.7%

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

   if -1.0000000000000001e199 < x < -4.0499999999999999e-44

   1. Initial program 72.8%

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

   3. Taylor expanded in t around inf 64.7%

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

      1. +-commutative 64.7%

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

      2. mul-1-neg 64.7%

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

      3. unsub-neg 64.7%

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

      4. *-commutative 64.7%

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

      5. *-commutative 64.7%

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

   5. Simplified 64.7%

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

   6. Taylor expanded in j around 0 47.7%

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

      1. mul-1-neg 47.7%

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

      2. *-commutative 47.7%

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

      3. distribute-rgt-neg-in 47.7%

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

   8. Simplified 47.7%

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

   if -4.0499999999999999e-44 < x < 1.84999999999999998e-264

   1. Initial program 73.4%

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

   3. Taylor expanded in b around 0 48.3%

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

   4. Taylor expanded in c around inf 35.9%

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

   if 1.84999999999999998e-264 < x < 2.1000000000000001e-170 or 9.49999999999999958e-60 < x < 4.7999999999999998e88

   1. Initial program 76.4%

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

   3. Taylor expanded in y around inf 44.7%

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

      1. +-commutative 44.7%

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

      2. mul-1-neg 44.7%

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

      3. unsub-neg 44.7%

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

   5. Simplified 44.7%

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

   6. Taylor expanded in x around 0 44.4%

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

      1. mul-1-neg 44.4%

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

      2. distribute-rgt-neg-in 44.4%

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

      3. *-commutative 44.4%

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

      4. distribute-rgt-neg-in 44.4%

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

   8. Simplified 44.4%

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

   if 2.1000000000000001e-170 < x < 9.49999999999999958e-60

   1. Initial program 73.7%

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

   3. Taylor expanded in b around inf 54.6%

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

      1. *-commutative 54.6%

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

   5. Simplified 54.6%

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

   6. Taylor expanded in a around inf 44.5%

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

      1. *-commutative 44.5%

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

   8. Simplified 44.5%

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

4. Final simplification 46.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+199}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq -4.05 \cdot 10^{-44}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-264}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-170}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-60}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+88}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -9.2 \cdot 10^{+51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -130:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;c \leq -8.2 \cdot 10^{-147}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{-67}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 9.4 \cdot 10^{+38}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))))
   (if (<= c -9.2e+51)
     t_1
     (if (<= c -130.0)
       (* t (- (* c j) (* x a)))
       (if (<= c -8.2e-147)
         (* y (- (* x z) (* i j)))
         (if (<= c 3.2e-67)
           (* a (- (* b i) (* x t)))
           (if (<= c 9.4e+38) (* i (- (* a b) (* y j))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -9.2e+51) {
		tmp = t_1;
	} else if (c <= -130.0) {
		tmp = t * ((c * j) - (x * a));
	} else if (c <= -8.2e-147) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 3.2e-67) {
		tmp = a * ((b * i) - (x * t));
	} else if (c <= 9.4e+38) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((t * j) - (z * b))
    if (c <= (-9.2d+51)) then
        tmp = t_1
    else if (c <= (-130.0d0)) then
        tmp = t * ((c * j) - (x * a))
    else if (c <= (-8.2d-147)) then
        tmp = y * ((x * z) - (i * j))
    else if (c <= 3.2d-67) then
        tmp = a * ((b * i) - (x * t))
    else if (c <= 9.4d+38) then
        tmp = i * ((a * b) - (y * j))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -9.2e+51) {
		tmp = t_1;
	} else if (c <= -130.0) {
		tmp = t * ((c * j) - (x * a));
	} else if (c <= -8.2e-147) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 3.2e-67) {
		tmp = a * ((b * i) - (x * t));
	} else if (c <= 9.4e+38) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -9.2e+51:
		tmp = t_1
	elif c <= -130.0:
		tmp = t * ((c * j) - (x * a))
	elif c <= -8.2e-147:
		tmp = y * ((x * z) - (i * j))
	elif c <= 3.2e-67:
		tmp = a * ((b * i) - (x * t))
	elif c <= 9.4e+38:
		tmp = i * ((a * b) - (y * j))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -9.2e+51)
		tmp = t_1;
	elseif (c <= -130.0)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (c <= -8.2e-147)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (c <= 3.2e-67)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (c <= 9.4e+38)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -9.2e+51)
		tmp = t_1;
	elseif (c <= -130.0)
		tmp = t * ((c * j) - (x * a));
	elseif (c <= -8.2e-147)
		tmp = y * ((x * z) - (i * j));
	elseif (c <= 3.2e-67)
		tmp = a * ((b * i) - (x * t));
	elseif (c <= 9.4e+38)
		tmp = i * ((a * b) - (y * j));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -9.2e+51], t$95$1, If[LessEqual[c, -130.0], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -8.2e-147], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.2e-67], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 9.4e+38], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -9.2000000000000002e51 or 9.3999999999999998e38 < c

   1. Initial program 67.3%

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

   3. Taylor expanded in c around inf 66.4%

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

   if -9.2000000000000002e51 < c < -130

   1. Initial program 78.3%

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

   3. Taylor expanded in t around inf 66.1%

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

      1. +-commutative 66.1%

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

      2. mul-1-neg 66.1%

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

      3. unsub-neg 66.1%

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

      4. *-commutative 66.1%

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

      5. *-commutative 66.1%

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

   5. Simplified 66.1%

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

   if -130 < c < -8.1999999999999999e-147

   1. Initial program 79.6%

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

   3. Taylor expanded in y around inf 70.6%

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

      1. +-commutative 70.6%

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

      2. mul-1-neg 70.6%

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

      3. unsub-neg 70.6%

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

   5. Simplified 70.6%

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

   if -8.1999999999999999e-147 < c < 3.20000000000000021e-67

   1. Initial program 77.4%

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

   3. Taylor expanded in a around -inf 59.8%

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

   if 3.20000000000000021e-67 < c < 9.3999999999999998e38

   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 inf 87.1%

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

   5. Simplified 83.1%

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

   6. Taylor expanded in i around inf 70.2%

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

      1. mul-1-neg 70.2%

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

      2. distribute-rgt-neg-in 70.2%

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

      3. mul-1-neg 70.2%

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

      4. distribute-rgt-neg-out 70.2%

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

      5. distribute-neg-in 70.2%

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

      6. neg-mul-1 70.2%

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

      7. unsub-neg 70.2%

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

      8. neg-mul-1 70.2%

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

      9. distribute-rgt-neg-out 70.2%

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

      10. remove-double-neg 70.2%

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

      11. *-commutative 70.2%

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

   8. Simplified 70.2%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -9.2 \cdot 10^{+51}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -130:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;c \leq -8.2 \cdot 10^{-147}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{-67}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 9.4 \cdot 10^{+38}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 29.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j\right)\\ \mathbf{if}\;c \leq -4.1 \cdot 10^{+138}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -2.85 \cdot 10^{-161}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 7.5 \cdot 10^{+65}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq 6.2 \cdot 10^{+209} \lor \neg \left(c \leq 1.55 \cdot 10^{+268}\right):\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (* c j))))
   (if (<= c -4.1e+138)
     t_1
     (if (<= c -2.85e-161)
       (* z (* x y))
       (if (<= c 7.5e+65)
         (* b (* a i))
         (if (or (<= c 6.2e+209) (not (<= c 1.55e+268)))
           (* b (* 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 = t * (c * j);
	double tmp;
	if (c <= -4.1e+138) {
		tmp = t_1;
	} else if (c <= -2.85e-161) {
		tmp = z * (x * y);
	} else if (c <= 7.5e+65) {
		tmp = b * (a * i);
	} else if ((c <= 6.2e+209) || !(c <= 1.55e+268)) {
		tmp = b * (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 = t * (c * j)
    if (c <= (-4.1d+138)) then
        tmp = t_1
    else if (c <= (-2.85d-161)) then
        tmp = z * (x * y)
    else if (c <= 7.5d+65) then
        tmp = b * (a * i)
    else if ((c <= 6.2d+209) .or. (.not. (c <= 1.55d+268))) then
        tmp = b * (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 = t * (c * j);
	double tmp;
	if (c <= -4.1e+138) {
		tmp = t_1;
	} else if (c <= -2.85e-161) {
		tmp = z * (x * y);
	} else if (c <= 7.5e+65) {
		tmp = b * (a * i);
	} else if ((c <= 6.2e+209) || !(c <= 1.55e+268)) {
		tmp = b * (z * -c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * (c * j)
	tmp = 0
	if c <= -4.1e+138:
		tmp = t_1
	elif c <= -2.85e-161:
		tmp = z * (x * y)
	elif c <= 7.5e+65:
		tmp = b * (a * i)
	elif (c <= 6.2e+209) or not (c <= 1.55e+268):
		tmp = b * (z * -c)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(c * j))
	tmp = 0.0
	if (c <= -4.1e+138)
		tmp = t_1;
	elseif (c <= -2.85e-161)
		tmp = Float64(z * Float64(x * y));
	elseif (c <= 7.5e+65)
		tmp = Float64(b * Float64(a * i));
	elseif ((c <= 6.2e+209) || !(c <= 1.55e+268))
		tmp = Float64(b * Float64(z * Float64(-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 = t * (c * j);
	tmp = 0.0;
	if (c <= -4.1e+138)
		tmp = t_1;
	elseif (c <= -2.85e-161)
		tmp = z * (x * y);
	elseif (c <= 7.5e+65)
		tmp = b * (a * i);
	elseif ((c <= 6.2e+209) || ~((c <= 1.55e+268)))
		tmp = b * (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[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4.1e+138], t$95$1, If[LessEqual[c, -2.85e-161], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 7.5e+65], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[c, 6.2e+209], N[Not[LessEqual[c, 1.55e+268]], $MachinePrecision]], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -4.0999999999999998e138 or 6.2000000000000002e209 < c < 1.55000000000000005e268

   1. Initial program 61.4%

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

   3. Taylor expanded in b around 0 63.6%

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

   4. Taylor expanded in c around inf 53.9%

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

      1. associate-*r* 57.9%

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

   6. Applied egg-rr 57.9%

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

   if -4.0999999999999998e138 < c < -2.85000000000000011e-161

   1. Initial program 80.1%

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

      1. *-commutative 80.1%

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

      2. *-commutative 80.1%

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

      3. *-commutative 80.1%

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

      4. add-cube-cbrt 79.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(t \cdot c - y \cdot i\right) \cdot \color{blue}{\left(\left(\sqrt[3]{j} \cdot \sqrt[3]{j}\right) \cdot \sqrt[3]{j}\right)} \]

      5. associate-*r* 79.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{\left(\left(t \cdot c - y \cdot i\right) \cdot \left(\sqrt[3]{j} \cdot \sqrt[3]{j}\right)\right) \cdot \sqrt[3]{j}} \]

      6. pow2 79.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(t \cdot c - y \cdot i\right) \cdot \color{blue}{{\left(\sqrt[3]{j}\right)}^{2}}\right) \cdot \sqrt[3]{j} \]

   4. Applied egg-rr 79.8%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{\left(\left(t \cdot c - y \cdot i\right) \cdot {\left(\sqrt[3]{j}\right)}^{2}\right) \cdot \sqrt[3]{j}} \]

   5. Taylor expanded in z around inf 46.8%

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

      1. *-commutative 46.8%

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

      2. *-commutative 46.8%

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

   7. Simplified 46.8%

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

   8. Taylor expanded in y around inf 32.4%

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

   if -2.85000000000000011e-161 < c < 7.50000000000000006e65

   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 b around inf 39.0%

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

      1. *-commutative 39.0%

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

   5. Simplified 39.0%

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

   6. Taylor expanded in a around inf 34.9%

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

      1. *-commutative 34.9%

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

   8. Simplified 34.9%

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

   if 7.50000000000000006e65 < c < 6.2000000000000002e209 or 1.55000000000000005e268 < c

   1. Initial program 66.9%

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

   3. Taylor expanded in b around inf 54.9%

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

      1. *-commutative 54.9%

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

   5. Simplified 54.9%

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

   6. Taylor expanded in a around 0 52.5%

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

      1. mul-1-neg 52.5%

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

      2. distribute-rgt-neg-in 52.5%

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

      3. distribute-rgt-neg-in 52.5%

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

   8. Simplified 52.5%

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

4. Final simplification 41.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.1 \cdot 10^{+138}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq -2.85 \cdot 10^{-161}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 7.5 \cdot 10^{+65}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq 6.2 \cdot 10^{+209} \lor \neg \left(c \leq 1.55 \cdot 10^{+268}\right):\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 30.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(y \cdot \left(-j\right)\right)\\ t_2 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;x \leq -7.8 \cdot 10^{-28}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-264}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-170}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-59}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+87}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* y (- j)))) (t_2 (* z (* x y))))
   (if (<= x -7.8e-28)
     t_2
     (if (<= x 1.85e-264)
       (* c (* t j))
       (if (<= x 3.2e-170)
         t_1
         (if (<= x 1.4e-59) (* b (* a i)) (if (<= x 4.5e+87) 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 = i * (y * -j);
	double t_2 = z * (x * y);
	double tmp;
	if (x <= -7.8e-28) {
		tmp = t_2;
	} else if (x <= 1.85e-264) {
		tmp = c * (t * j);
	} else if (x <= 3.2e-170) {
		tmp = t_1;
	} else if (x <= 1.4e-59) {
		tmp = b * (a * i);
	} else if (x <= 4.5e+87) {
		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 = i * (y * -j)
    t_2 = z * (x * y)
    if (x <= (-7.8d-28)) then
        tmp = t_2
    else if (x <= 1.85d-264) then
        tmp = c * (t * j)
    else if (x <= 3.2d-170) then
        tmp = t_1
    else if (x <= 1.4d-59) then
        tmp = b * (a * i)
    else if (x <= 4.5d+87) 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 = i * (y * -j);
	double t_2 = z * (x * y);
	double tmp;
	if (x <= -7.8e-28) {
		tmp = t_2;
	} else if (x <= 1.85e-264) {
		tmp = c * (t * j);
	} else if (x <= 3.2e-170) {
		tmp = t_1;
	} else if (x <= 1.4e-59) {
		tmp = b * (a * i);
	} else if (x <= 4.5e+87) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (y * -j)
	t_2 = z * (x * y)
	tmp = 0
	if x <= -7.8e-28:
		tmp = t_2
	elif x <= 1.85e-264:
		tmp = c * (t * j)
	elif x <= 3.2e-170:
		tmp = t_1
	elif x <= 1.4e-59:
		tmp = b * (a * i)
	elif x <= 4.5e+87:
		tmp = t_1
	else:
		tmp = t_2
	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(z * Float64(x * y))
	tmp = 0.0
	if (x <= -7.8e-28)
		tmp = t_2;
	elseif (x <= 1.85e-264)
		tmp = Float64(c * Float64(t * j));
	elseif (x <= 3.2e-170)
		tmp = t_1;
	elseif (x <= 1.4e-59)
		tmp = Float64(b * Float64(a * i));
	elseif (x <= 4.5e+87)
		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 = i * (y * -j);
	t_2 = z * (x * y);
	tmp = 0.0;
	if (x <= -7.8e-28)
		tmp = t_2;
	elseif (x <= 1.85e-264)
		tmp = c * (t * j);
	elseif (x <= 3.2e-170)
		tmp = t_1;
	elseif (x <= 1.4e-59)
		tmp = b * (a * i);
	elseif (x <= 4.5e+87)
		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[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7.8e-28], t$95$2, If[LessEqual[x, 1.85e-264], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.2e-170], t$95$1, If[LessEqual[x, 1.4e-59], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.5e+87], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -7.79999999999999998e-28 or 4.5000000000000003e87 < x

   1. Initial program 75.2%

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

      1. *-commutative 75.2%

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

      2. *-commutative 75.2%

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

      3. *-commutative 75.2%

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

      4. add-cube-cbrt 75.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(t \cdot c - y \cdot i\right) \cdot \color{blue}{\left(\left(\sqrt[3]{j} \cdot \sqrt[3]{j}\right) \cdot \sqrt[3]{j}\right)} \]

      5. associate-*r* 75.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{\left(\left(t \cdot c - y \cdot i\right) \cdot \left(\sqrt[3]{j} \cdot \sqrt[3]{j}\right)\right) \cdot \sqrt[3]{j}} \]

      6. pow2 75.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(t \cdot c - y \cdot i\right) \cdot \color{blue}{{\left(\sqrt[3]{j}\right)}^{2}}\right) \cdot \sqrt[3]{j} \]

   4. Applied egg-rr 75.1%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{\left(\left(t \cdot c - y \cdot i\right) \cdot {\left(\sqrt[3]{j}\right)}^{2}\right) \cdot \sqrt[3]{j}} \]

   5. Taylor expanded in z around inf 54.1%

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

      1. *-commutative 54.1%

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

      2. *-commutative 54.1%

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

   7. Simplified 54.1%

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

   8. Taylor expanded in y around inf 48.2%

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

   if -7.79999999999999998e-28 < x < 1.84999999999999998e-264

   1. Initial program 72.2%

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

   3. Taylor expanded in b around 0 48.7%

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

   4. Taylor expanded in c around inf 35.3%

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

   if 1.84999999999999998e-264 < x < 3.1999999999999999e-170 or 1.3999999999999999e-59 < x < 4.5000000000000003e87

   1. Initial program 76.4%

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

   3. Taylor expanded in y around inf 44.7%

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

      1. +-commutative 44.7%

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

      2. mul-1-neg 44.7%

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

      3. unsub-neg 44.7%

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

   5. Simplified 44.7%

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

   6. Taylor expanded in x around 0 44.4%

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

      1. mul-1-neg 44.4%

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

      2. distribute-rgt-neg-in 44.4%

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

      3. *-commutative 44.4%

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

      4. distribute-rgt-neg-in 44.4%

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

   8. Simplified 44.4%

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

   if 3.1999999999999999e-170 < x < 1.3999999999999999e-59

   1. Initial program 73.7%

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

   3. Taylor expanded in b around inf 54.6%

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

      1. *-commutative 54.6%

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

   5. Simplified 54.6%

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

   6. Taylor expanded in a around inf 44.5%

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

      1. *-commutative 44.5%

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

   8. Simplified 44.5%

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

4. Final simplification 43.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{-28}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-264}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-170}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-59}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+87}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 59.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(c \cdot \left(\frac{x \cdot y}{c} - b\right)\right)\\ \mathbf{if}\;z \leq -8.2 \cdot 10^{+139}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 220000000000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+146}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;z \leq 6.7 \cdot 10^{+273}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* c (- (/ (* x y) c) b)))))
   (if (<= z -8.2e+139)
     t_1
     (if (<= z 220000000000.0)
       (- (* x (- (* y z) (* t a))) (* j (- (* y i) (* t c))))
       (if (<= z 4.8e+146)
         (* b (- (* a i) (* z c)))
         (if (<= z 6.7e+273) (* y (- (* x z) (* i j))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (c * (((x * y) / c) - b));
	double tmp;
	if (z <= -8.2e+139) {
		tmp = t_1;
	} else if (z <= 220000000000.0) {
		tmp = (x * ((y * z) - (t * a))) - (j * ((y * i) - (t * c)));
	} else if (z <= 4.8e+146) {
		tmp = b * ((a * i) - (z * c));
	} else if (z <= 6.7e+273) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (c * (((x * y) / c) - b))
    if (z <= (-8.2d+139)) then
        tmp = t_1
    else if (z <= 220000000000.0d0) then
        tmp = (x * ((y * z) - (t * a))) - (j * ((y * i) - (t * c)))
    else if (z <= 4.8d+146) then
        tmp = b * ((a * i) - (z * c))
    else if (z <= 6.7d+273) then
        tmp = y * ((x * z) - (i * j))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (c * (((x * y) / c) - b));
	double tmp;
	if (z <= -8.2e+139) {
		tmp = t_1;
	} else if (z <= 220000000000.0) {
		tmp = (x * ((y * z) - (t * a))) - (j * ((y * i) - (t * c)));
	} else if (z <= 4.8e+146) {
		tmp = b * ((a * i) - (z * c));
	} else if (z <= 6.7e+273) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (c * (((x * y) / c) - b))
	tmp = 0
	if z <= -8.2e+139:
		tmp = t_1
	elif z <= 220000000000.0:
		tmp = (x * ((y * z) - (t * a))) - (j * ((y * i) - (t * c)))
	elif z <= 4.8e+146:
		tmp = b * ((a * i) - (z * c))
	elif z <= 6.7e+273:
		tmp = y * ((x * z) - (i * j))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(c * Float64(Float64(Float64(x * y) / c) - b)))
	tmp = 0.0
	if (z <= -8.2e+139)
		tmp = t_1;
	elseif (z <= 220000000000.0)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(j * Float64(Float64(y * i) - Float64(t * c))));
	elseif (z <= 4.8e+146)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (z <= 6.7e+273)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * (c * (((x * y) / c) - b));
	tmp = 0.0;
	if (z <= -8.2e+139)
		tmp = t_1;
	elseif (z <= 220000000000.0)
		tmp = (x * ((y * z) - (t * a))) - (j * ((y * i) - (t * c)));
	elseif (z <= 4.8e+146)
		tmp = b * ((a * i) - (z * c));
	elseif (z <= 6.7e+273)
		tmp = y * ((x * z) - (i * j));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(c * N[(N[(N[(x * y), $MachinePrecision] / c), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.2e+139], t$95$1, If[LessEqual[z, 220000000000.0], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(y * i), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.8e+146], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.7e+273], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.2000000000000004e139 or 6.6999999999999998e273 < z

   1. Initial program 58.3%

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

      1. *-commutative 58.3%

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

      2. *-commutative 58.3%

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

      3. *-commutative 58.3%

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

      4. add-cube-cbrt 58.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(t \cdot c - y \cdot i\right) \cdot \color{blue}{\left(\left(\sqrt[3]{j} \cdot \sqrt[3]{j}\right) \cdot \sqrt[3]{j}\right)} \]

      5. associate-*r* 58.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{\left(\left(t \cdot c - y \cdot i\right) \cdot \left(\sqrt[3]{j} \cdot \sqrt[3]{j}\right)\right) \cdot \sqrt[3]{j}} \]

      6. pow2 58.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(t \cdot c - y \cdot i\right) \cdot \color{blue}{{\left(\sqrt[3]{j}\right)}^{2}}\right) \cdot \sqrt[3]{j} \]

   4. Applied egg-rr 58.3%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{\left(\left(t \cdot c - y \cdot i\right) \cdot {\left(\sqrt[3]{j}\right)}^{2}\right) \cdot \sqrt[3]{j}} \]

   5. Taylor expanded in z around inf 85.8%

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

      1. *-commutative 85.8%

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

      2. *-commutative 85.8%

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

   7. Simplified 85.8%

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

   8. Taylor expanded in c around inf 88.1%

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

   if -8.2000000000000004e139 < z < 2.2e11

   1. Initial program 81.7%

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

   3. Taylor expanded in b around 0 69.2%

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

   if 2.2e11 < z < 4.8000000000000004e146

   1. Initial program 87.4%

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

   3. Taylor expanded in b around inf 74.6%

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

      1. *-commutative 74.6%

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

   5. Simplified 74.6%

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

   if 4.8000000000000004e146 < z < 6.6999999999999998e273

   1. Initial program 40.5%

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

   3. Taylor expanded in y around inf 69.3%

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

      1. +-commutative 69.3%

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

      2. mul-1-neg 69.3%

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

      3. unsub-neg 69.3%

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

   5. Simplified 69.3%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+139}:\\ \;\;\;\;z \cdot \left(c \cdot \left(\frac{x \cdot y}{c} - b\right)\right)\\ \mathbf{elif}\;z \leq 220000000000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+146}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;z \leq 6.7 \cdot 10^{+273}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(c \cdot \left(\frac{x \cdot y}{c} - b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 29.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ t_2 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;x \leq -1.2 \cdot 10^{-26}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-114}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+40}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{+140}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j))) (t_2 (* z (* x y))))
   (if (<= x -1.2e-26)
     t_2
     (if (<= x 4.6e-114)
       t_1
       (if (<= x 3.7e+40)
         (* a (* b i))
         (if (<= x 2.1e+72) t_1 (if (<= x 9.8e+140) (* b (* a i)) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double t_2 = z * (x * y);
	double tmp;
	if (x <= -1.2e-26) {
		tmp = t_2;
	} else if (x <= 4.6e-114) {
		tmp = t_1;
	} else if (x <= 3.7e+40) {
		tmp = a * (b * i);
	} else if (x <= 2.1e+72) {
		tmp = t_1;
	} else if (x <= 9.8e+140) {
		tmp = b * (a * i);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * (t * j)
    t_2 = z * (x * y)
    if (x <= (-1.2d-26)) then
        tmp = t_2
    else if (x <= 4.6d-114) then
        tmp = t_1
    else if (x <= 3.7d+40) then
        tmp = a * (b * i)
    else if (x <= 2.1d+72) then
        tmp = t_1
    else if (x <= 9.8d+140) then
        tmp = b * (a * i)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double t_2 = z * (x * y);
	double tmp;
	if (x <= -1.2e-26) {
		tmp = t_2;
	} else if (x <= 4.6e-114) {
		tmp = t_1;
	} else if (x <= 3.7e+40) {
		tmp = a * (b * i);
	} else if (x <= 2.1e+72) {
		tmp = t_1;
	} else if (x <= 9.8e+140) {
		tmp = b * (a * i);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (t * j)
	t_2 = z * (x * y)
	tmp = 0
	if x <= -1.2e-26:
		tmp = t_2
	elif x <= 4.6e-114:
		tmp = t_1
	elif x <= 3.7e+40:
		tmp = a * (b * i)
	elif x <= 2.1e+72:
		tmp = t_1
	elif x <= 9.8e+140:
		tmp = b * (a * i)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(t * j))
	t_2 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (x <= -1.2e-26)
		tmp = t_2;
	elseif (x <= 4.6e-114)
		tmp = t_1;
	elseif (x <= 3.7e+40)
		tmp = Float64(a * Float64(b * i));
	elseif (x <= 2.1e+72)
		tmp = t_1;
	elseif (x <= 9.8e+140)
		tmp = Float64(b * Float64(a * i));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (t * j);
	t_2 = z * (x * y);
	tmp = 0.0;
	if (x <= -1.2e-26)
		tmp = t_2;
	elseif (x <= 4.6e-114)
		tmp = t_1;
	elseif (x <= 3.7e+40)
		tmp = a * (b * i);
	elseif (x <= 2.1e+72)
		tmp = t_1;
	elseif (x <= 9.8e+140)
		tmp = b * (a * i);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.2e-26], t$95$2, If[LessEqual[x, 4.6e-114], t$95$1, If[LessEqual[x, 3.7e+40], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.1e+72], t$95$1, If[LessEqual[x, 9.8e+140], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.2e-26 or 9.79999999999999918e140 < x

   1. Initial program 76.9%

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

      1. *-commutative 76.9%

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

      2. *-commutative 76.9%

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

      3. *-commutative 76.9%

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

      4. add-cube-cbrt 76.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(t \cdot c - y \cdot i\right) \cdot \color{blue}{\left(\left(\sqrt[3]{j} \cdot \sqrt[3]{j}\right) \cdot \sqrt[3]{j}\right)} \]

      5. associate-*r* 76.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{\left(\left(t \cdot c - y \cdot i\right) \cdot \left(\sqrt[3]{j} \cdot \sqrt[3]{j}\right)\right) \cdot \sqrt[3]{j}} \]

      6. pow2 76.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(t \cdot c - y \cdot i\right) \cdot \color{blue}{{\left(\sqrt[3]{j}\right)}^{2}}\right) \cdot \sqrt[3]{j} \]

   4. Applied egg-rr 76.8%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{\left(\left(t \cdot c - y \cdot i\right) \cdot {\left(\sqrt[3]{j}\right)}^{2}\right) \cdot \sqrt[3]{j}} \]

   5. Taylor expanded in z around inf 54.4%

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

      1. *-commutative 54.4%

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

      2. *-commutative 54.4%

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

   7. Simplified 54.4%

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

   8. Taylor expanded in y around inf 51.1%

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

   if -1.2e-26 < x < 4.5999999999999999e-114 or 3.7e40 < x < 2.1000000000000001e72

   1. Initial program 71.3%

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

   3. Taylor expanded in b around 0 52.9%

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

   4. Taylor expanded in c around inf 35.1%

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

   if 4.5999999999999999e-114 < x < 3.7e40

   1. Initial program 83.2%

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

   3. Taylor expanded in b around inf 47.7%

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

      1. *-commutative 47.7%

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

   5. Simplified 47.7%

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

   6. Taylor expanded in a around inf 38.9%

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

      1. *-commutative 38.9%

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

   8. Simplified 38.9%

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

   if 2.1000000000000001e72 < x < 9.79999999999999918e140

   1. Initial program 66.6%

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

   3. Taylor expanded in b around inf 56.4%

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

      1. *-commutative 56.4%

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

   5. Simplified 56.4%

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

   6. Taylor expanded in a around inf 29.3%

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

      1. *-commutative 29.3%

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

   8. Simplified 29.3%

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

4. Final simplification 40.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{-26}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-114}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+40}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+72}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{+140}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 29.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ t_2 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;x \leq -4.55 \cdot 10^{-26}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-116}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+40}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+140}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j))) (t_2 (* x (* y z))))
   (if (<= x -4.55e-26)
     t_2
     (if (<= x 3.1e-116)
       t_1
       (if (<= x 1.85e+40)
         (* a (* b i))
         (if (<= x 2.1e+72) t_1 (if (<= x 5e+140) (* b (* a i)) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double t_2 = x * (y * z);
	double tmp;
	if (x <= -4.55e-26) {
		tmp = t_2;
	} else if (x <= 3.1e-116) {
		tmp = t_1;
	} else if (x <= 1.85e+40) {
		tmp = a * (b * i);
	} else if (x <= 2.1e+72) {
		tmp = t_1;
	} else if (x <= 5e+140) {
		tmp = b * (a * i);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * (t * j)
    t_2 = x * (y * z)
    if (x <= (-4.55d-26)) then
        tmp = t_2
    else if (x <= 3.1d-116) then
        tmp = t_1
    else if (x <= 1.85d+40) then
        tmp = a * (b * i)
    else if (x <= 2.1d+72) then
        tmp = t_1
    else if (x <= 5d+140) then
        tmp = b * (a * i)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double t_2 = x * (y * z);
	double tmp;
	if (x <= -4.55e-26) {
		tmp = t_2;
	} else if (x <= 3.1e-116) {
		tmp = t_1;
	} else if (x <= 1.85e+40) {
		tmp = a * (b * i);
	} else if (x <= 2.1e+72) {
		tmp = t_1;
	} else if (x <= 5e+140) {
		tmp = b * (a * i);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (t * j)
	t_2 = x * (y * z)
	tmp = 0
	if x <= -4.55e-26:
		tmp = t_2
	elif x <= 3.1e-116:
		tmp = t_1
	elif x <= 1.85e+40:
		tmp = a * (b * i)
	elif x <= 2.1e+72:
		tmp = t_1
	elif x <= 5e+140:
		tmp = b * (a * i)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(t * j))
	t_2 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (x <= -4.55e-26)
		tmp = t_2;
	elseif (x <= 3.1e-116)
		tmp = t_1;
	elseif (x <= 1.85e+40)
		tmp = Float64(a * Float64(b * i));
	elseif (x <= 2.1e+72)
		tmp = t_1;
	elseif (x <= 5e+140)
		tmp = Float64(b * Float64(a * i));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (t * j);
	t_2 = x * (y * z);
	tmp = 0.0;
	if (x <= -4.55e-26)
		tmp = t_2;
	elseif (x <= 3.1e-116)
		tmp = t_1;
	elseif (x <= 1.85e+40)
		tmp = a * (b * i);
	elseif (x <= 2.1e+72)
		tmp = t_1;
	elseif (x <= 5e+140)
		tmp = b * (a * i);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.55e-26], t$95$2, If[LessEqual[x, 3.1e-116], t$95$1, If[LessEqual[x, 1.85e+40], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.1e+72], t$95$1, If[LessEqual[x, 5e+140], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.5499999999999997e-26 or 5.00000000000000008e140 < x

   1. Initial program 76.9%

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

   3. Taylor expanded in y around inf 48.5%

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

      1. +-commutative 48.5%

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

      2. mul-1-neg 48.5%

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

      3. unsub-neg 48.5%

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

   5. Simplified 48.5%

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

   6. Taylor expanded in x around inf 46.9%

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

   if -4.5499999999999997e-26 < x < 3.10000000000000018e-116 or 1.85e40 < x < 2.1000000000000001e72

   1. Initial program 71.3%

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

   3. Taylor expanded in b around 0 52.9%

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

   4. Taylor expanded in c around inf 35.1%

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

   if 3.10000000000000018e-116 < x < 1.85e40

   1. Initial program 83.2%

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

   3. Taylor expanded in b around inf 47.7%

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

      1. *-commutative 47.7%

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

   5. Simplified 47.7%

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

   6. Taylor expanded in a around inf 38.9%

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

      1. *-commutative 38.9%

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

   8. Simplified 38.9%

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

   if 2.1000000000000001e72 < x < 5.00000000000000008e140

   1. Initial program 66.6%

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

   3. Taylor expanded in b around inf 56.4%

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

      1. *-commutative 56.4%

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

   5. Simplified 56.4%

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

   6. Taylor expanded in a around inf 29.3%

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

      1. *-commutative 29.3%

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

   8. Simplified 29.3%

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

4. Final simplification 39.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.55 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-116}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+40}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+72}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+140}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 51.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -3.3 \cdot 10^{+103} \lor \neg \left(i \leq -2.5 \cdot 10^{+55}\right) \land \left(i \leq -3.3 \cdot 10^{-34} \lor \neg \left(i \leq 1.15 \cdot 10^{+74}\right)\right):\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -3.3e+103)
         (and (not (<= i -2.5e+55))
              (or (<= i -3.3e-34) (not (<= i 1.15e+74)))))
   (* i (- (* a b) (* y j)))
   (* c (- (* t j) (* 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 <= -3.3e+103) || (!(i <= -2.5e+55) && ((i <= -3.3e-34) || !(i <= 1.15e+74)))) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = c * ((t * j) - (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 <= (-3.3d+103)) .or. (.not. (i <= (-2.5d+55))) .and. (i <= (-3.3d-34)) .or. (.not. (i <= 1.15d+74))) then
        tmp = i * ((a * b) - (y * j))
    else
        tmp = c * ((t * j) - (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 <= -3.3e+103) || (!(i <= -2.5e+55) && ((i <= -3.3e-34) || !(i <= 1.15e+74)))) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = c * ((t * j) - (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (i <= -3.3e+103) or (not (i <= -2.5e+55) and ((i <= -3.3e-34) or not (i <= 1.15e+74))):
		tmp = i * ((a * b) - (y * j))
	else:
		tmp = c * ((t * j) - (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((i <= -3.3e+103) || (!(i <= -2.5e+55) && ((i <= -3.3e-34) || !(i <= 1.15e+74))))
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	else
		tmp = Float64(c * Float64(Float64(t * j) - 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 <= -3.3e+103) || (~((i <= -2.5e+55)) && ((i <= -3.3e-34) || ~((i <= 1.15e+74)))))
		tmp = i * ((a * b) - (y * j));
	else
		tmp = c * ((t * j) - (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[i, -3.3e+103], And[N[Not[LessEqual[i, -2.5e+55]], $MachinePrecision], Or[LessEqual[i, -3.3e-34], N[Not[LessEqual[i, 1.15e+74]], $MachinePrecision]]]], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -3.30000000000000009e103 or -2.50000000000000023e55 < i < -3.29999999999999983e-34 or 1.1499999999999999e74 < i

   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 i around inf 68.7%

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

   5. Simplified 72.4%

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

   6. Taylor expanded in i around inf 64.7%

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

      1. mul-1-neg 64.7%

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

      2. distribute-rgt-neg-in 64.7%

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

      3. mul-1-neg 64.7%

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

      4. distribute-rgt-neg-out 64.7%

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

      5. distribute-neg-in 64.7%

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

      6. neg-mul-1 64.7%

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

      7. unsub-neg 64.7%

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

      8. neg-mul-1 64.7%

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

      9. distribute-rgt-neg-out 64.7%

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

      10. remove-double-neg 64.7%

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

      11. *-commutative 64.7%

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

   8. Simplified 64.7%

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

   if -3.30000000000000009e103 < i < -2.50000000000000023e55 or -3.29999999999999983e-34 < i < 1.1499999999999999e74

   1. Initial program 78.2%

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

   3. Taylor expanded in c around inf 50.9%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.3 \cdot 10^{+103} \lor \neg \left(i \leq -2.5 \cdot 10^{+55}\right) \land \left(i \leq -3.3 \cdot 10^{-34} \lor \neg \left(i \leq 1.15 \cdot 10^{+74}\right)\right):\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 43.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-101}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-264}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-22}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{+173}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -3.5e-101)
   (* c (- (* t j) (* z b)))
   (if (<= z -9.5e-264)
     (* i (- (* a b) (* y j)))
     (if (<= z 6.4e-22)
       (* j (- (* t c) (* y i)))
       (if (<= z 9.6e+173) (* b (- (* a i) (* z c))) (* z (* x y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -3.5e-101) {
		tmp = c * ((t * j) - (z * b));
	} else if (z <= -9.5e-264) {
		tmp = i * ((a * b) - (y * j));
	} else if (z <= 6.4e-22) {
		tmp = j * ((t * c) - (y * i));
	} else if (z <= 9.6e+173) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-3.5d-101)) then
        tmp = c * ((t * j) - (z * b))
    else if (z <= (-9.5d-264)) then
        tmp = i * ((a * b) - (y * j))
    else if (z <= 6.4d-22) then
        tmp = j * ((t * c) - (y * i))
    else if (z <= 9.6d+173) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -3.5e-101) {
		tmp = c * ((t * j) - (z * b));
	} else if (z <= -9.5e-264) {
		tmp = i * ((a * b) - (y * j));
	} else if (z <= 6.4e-22) {
		tmp = j * ((t * c) - (y * i));
	} else if (z <= 9.6e+173) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -3.5e-101:
		tmp = c * ((t * j) - (z * b))
	elif z <= -9.5e-264:
		tmp = i * ((a * b) - (y * j))
	elif z <= 6.4e-22:
		tmp = j * ((t * c) - (y * i))
	elif z <= 9.6e+173:
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -3.5e-101)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (z <= -9.5e-264)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (z <= 6.4e-22)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (z <= 9.6e+173)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -3.5e-101)
		tmp = c * ((t * j) - (z * b));
	elseif (z <= -9.5e-264)
		tmp = i * ((a * b) - (y * j));
	elseif (z <= 6.4e-22)
		tmp = j * ((t * c) - (y * i));
	elseif (z <= 9.6e+173)
		tmp = b * ((a * i) - (z * c));
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -3.5e-101], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9.5e-264], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.4e-22], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.6e+173], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.49999999999999994e-101

   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 c around inf 51.0%

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

   if -3.49999999999999994e-101 < z < -9.50000000000000012e-264

   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 i around inf 77.7%

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

   5. Simplified 78.2%

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

   6. Taylor expanded in i around inf 65.2%

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

      1. mul-1-neg 65.2%

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

      2. distribute-rgt-neg-in 65.2%

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

      3. mul-1-neg 65.2%

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

      4. distribute-rgt-neg-out 65.2%

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

      5. distribute-neg-in 65.2%

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

      6. neg-mul-1 65.2%

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

      7. unsub-neg 65.2%

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

      8. neg-mul-1 65.2%

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

      9. distribute-rgt-neg-out 65.2%

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

      10. remove-double-neg 65.2%

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

      11. *-commutative 65.2%

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

   8. Simplified 65.2%

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

   if -9.50000000000000012e-264 < z < 6.39999999999999975e-22

   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 inf 56.7%

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

   if 6.39999999999999975e-22 < z < 9.5999999999999997e173

   1. Initial program 76.8%

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

   3. Taylor expanded in b around inf 61.5%

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

      1. *-commutative 61.5%

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

   5. Simplified 61.5%

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

   if 9.5999999999999997e173 < z

   1. Initial program 52.6%

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

      1. *-commutative 52.6%

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

      2. *-commutative 52.6%

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

      3. *-commutative 52.6%

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

      4. add-cube-cbrt 52.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(t \cdot c - y \cdot i\right) \cdot \color{blue}{\left(\left(\sqrt[3]{j} \cdot \sqrt[3]{j}\right) \cdot \sqrt[3]{j}\right)} \]

      5. associate-*r* 52.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{\left(\left(t \cdot c - y \cdot i\right) \cdot \left(\sqrt[3]{j} \cdot \sqrt[3]{j}\right)\right) \cdot \sqrt[3]{j}} \]

      6. pow2 52.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(t \cdot c - y \cdot i\right) \cdot \color{blue}{{\left(\sqrt[3]{j}\right)}^{2}}\right) \cdot \sqrt[3]{j} \]

   4. Applied egg-rr 52.6%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{\left(\left(t \cdot c - y \cdot i\right) \cdot {\left(\sqrt[3]{j}\right)}^{2}\right) \cdot \sqrt[3]{j}} \]

   5. Taylor expanded in z around inf 72.3%

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

      1. *-commutative 72.3%

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

      2. *-commutative 72.3%

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

   7. Simplified 72.3%

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

   8. Taylor expanded in y around inf 54.9%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-101}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-264}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-22}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{+173}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 45.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -3.7 \cdot 10^{+179}:\\ \;\;\;\;y \cdot \left(j \cdot \left(-i\right)\right)\\ \mathbf{elif}\;i \leq -6.5 \cdot 10^{+24} \lor \neg \left(i \leq 3.8 \cdot 10^{+29}\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -3.7e+179)
   (* y (* j (- i)))
   (if (or (<= i -6.5e+24) (not (<= i 3.8e+29)))
     (* b (- (* a i) (* z c)))
     (* c (- (* t j) (* 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 <= -3.7e+179) {
		tmp = y * (j * -i);
	} else if ((i <= -6.5e+24) || !(i <= 3.8e+29)) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = c * ((t * j) - (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 <= (-3.7d+179)) then
        tmp = y * (j * -i)
    else if ((i <= (-6.5d+24)) .or. (.not. (i <= 3.8d+29))) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = c * ((t * j) - (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 <= -3.7e+179) {
		tmp = y * (j * -i);
	} else if ((i <= -6.5e+24) || !(i <= 3.8e+29)) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = c * ((t * j) - (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -3.7e+179:
		tmp = y * (j * -i)
	elif (i <= -6.5e+24) or not (i <= 3.8e+29):
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = c * ((t * j) - (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -3.7e+179)
		tmp = Float64(y * Float64(j * Float64(-i)));
	elseif ((i <= -6.5e+24) || !(i <= 3.8e+29))
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = Float64(c * Float64(Float64(t * j) - 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 <= -3.7e+179)
		tmp = y * (j * -i);
	elseif ((i <= -6.5e+24) || ~((i <= 3.8e+29)))
		tmp = b * ((a * i) - (z * c));
	else
		tmp = c * ((t * j) - (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -3.7e+179], N[(y * N[(j * (-i)), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[i, -6.5e+24], N[Not[LessEqual[i, 3.8e+29]], $MachinePrecision]], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if i < -3.6999999999999999e179

   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 65.7%

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

      1. +-commutative 65.7%

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

      2. mul-1-neg 65.7%

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

      3. unsub-neg 65.7%

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

   5. Simplified 65.7%

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

   6. Taylor expanded in x around 0 57.5%

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

      1. neg-mul-1 57.5%

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

      2. distribute-rgt-neg-in 57.5%

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

   8. Simplified 57.5%

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

   if -3.6999999999999999e179 < i < -6.4999999999999996e24 or 3.79999999999999971e29 < i

   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 b around inf 53.5%

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

      1. *-commutative 53.5%

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

   5. Simplified 53.5%

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

   if -6.4999999999999996e24 < i < 3.79999999999999971e29

   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 c around inf 48.5%

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

4. Final simplification 51.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.7 \cdot 10^{+179}:\\ \;\;\;\;y \cdot \left(j \cdot \left(-i\right)\right)\\ \mathbf{elif}\;i \leq -6.5 \cdot 10^{+24} \lor \neg \left(i \leq 3.8 \cdot 10^{+29}\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 30.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -7.5 \cdot 10^{-65} \lor \neg \left(c \leq 1.9 \cdot 10^{+33}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -7.5e-65) (not (<= c 1.9e+33))) (* c (* t j)) (* b (* a i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -7.5e-65) || !(c <= 1.9e+33)) {
		tmp = c * (t * j);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((c <= (-7.5d-65)) .or. (.not. (c <= 1.9d+33))) then
        tmp = c * (t * j)
    else
        tmp = b * (a * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -7.5e-65) || !(c <= 1.9e+33)) {
		tmp = c * (t * j);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -7.5e-65) or not (c <= 1.9e+33):
		tmp = c * (t * j)
	else:
		tmp = b * (a * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -7.5e-65) || !(c <= 1.9e+33))
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(b * Float64(a * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -7.5e-65) || ~((c <= 1.9e+33)))
		tmp = c * (t * j);
	else
		tmp = b * (a * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -7.5e-65], N[Not[LessEqual[c, 1.9e+33]], $MachinePrecision]], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -7.5000000000000002e-65 or 1.90000000000000001e33 < c

   1. Initial program 71.3%

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

   3. Taylor expanded in b around 0 64.7%

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

   4. Taylor expanded in c around inf 33.3%

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

   if -7.5000000000000002e-65 < c < 1.90000000000000001e33

   1. Initial program 77.8%

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

   3. Taylor expanded in b around inf 38.9%

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

      1. *-commutative 38.9%

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

   5. Simplified 38.9%

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

   6. Taylor expanded in a around inf 32.9%

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

      1. *-commutative 32.9%

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

   8. Simplified 32.9%

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

4. Final simplification 33.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -7.5 \cdot 10^{-65} \lor \neg \left(c \leq 1.9 \cdot 10^{+33}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 30.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3.2 \cdot 10^{-64}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;c \leq 3.3 \cdot 10^{+31}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -3.2e-64)
   (* c (* t j))
   (if (<= c 3.3e+31) (* b (* a i)) (* j (* t c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -3.2e-64) {
		tmp = c * (t * j);
	} else if (c <= 3.3e+31) {
		tmp = b * (a * i);
	} else {
		tmp = j * (t * c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (c <= (-3.2d-64)) then
        tmp = c * (t * j)
    else if (c <= 3.3d+31) then
        tmp = b * (a * i)
    else
        tmp = j * (t * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -3.2e-64) {
		tmp = c * (t * j);
	} else if (c <= 3.3e+31) {
		tmp = b * (a * i);
	} else {
		tmp = j * (t * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -3.2e-64:
		tmp = c * (t * j)
	elif c <= 3.3e+31:
		tmp = b * (a * i)
	else:
		tmp = j * (t * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -3.2e-64)
		tmp = Float64(c * Float64(t * j));
	elseif (c <= 3.3e+31)
		tmp = Float64(b * Float64(a * i));
	else
		tmp = Float64(j * Float64(t * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -3.2e-64)
		tmp = c * (t * j);
	elseif (c <= 3.3e+31)
		tmp = b * (a * i);
	else
		tmp = j * (t * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -3.2e-64], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.3e+31], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -3.19999999999999975e-64

   1. Initial program 71.5%

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

   3. Taylor expanded in b around 0 71.6%

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

   4. Taylor expanded in c around inf 34.9%

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

   if -3.19999999999999975e-64 < c < 3.29999999999999992e31

   1. Initial program 77.8%

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

   3. Taylor expanded in b around inf 38.9%

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

      1. *-commutative 38.9%

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

   5. Simplified 38.9%

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

   6. Taylor expanded in a around inf 32.9%

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

      1. *-commutative 32.9%

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

   8. Simplified 32.9%

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

   if 3.29999999999999992e31 < c

   1. Initial program 71.1%

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

   3. Taylor expanded in b around 0 55.5%

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

   4. Taylor expanded in y around 0 36.2%

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

      1. +-commutative 36.2%

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

      2. mul-1-neg 36.2%

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

      3. unsub-neg 36.2%

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

   6. Simplified 36.2%

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

   7. Taylor expanded in c around inf 31.0%

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

      1. *-commutative 31.0%

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

      2. associate-*r* 32.8%

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

      3. *-commutative 32.8%

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

      4. *-commutative 32.8%

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

   9. Simplified 32.8%

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

4. Final simplification 33.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.2 \cdot 10^{-64}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;c \leq 3.3 \cdot 10^{+31}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 23.2% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ b \cdot \left(a \cdot i\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 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 inf 39.3%

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

   1. *-commutative 39.3%

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

5. Simplified 39.3%

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

6. Taylor expanded in a around inf 22.1%

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

   1. *-commutative 22.1%

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

8. Simplified 22.1%

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

9. Final simplification 22.1%

   \[\leadsto b \cdot \left(a \cdot i\right) \]
10. Add Preprocessing

Alternative 26: 22.8% 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 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 inf 39.3%

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

   1. *-commutative 39.3%

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

5. Simplified 39.3%

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

6. Taylor expanded in a around inf 21.1%

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

   1. *-commutative 21.1%

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

8. Simplified 21.1%

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

9. Final simplification 21.1%

   \[\leadsto a \cdot \left(b \cdot i\right) \]
10. Add Preprocessing

Developer target: 68.7% 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 2024096 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :alt
  (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)))))