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

Percentage Accurate: 73.5% → 82.1%

Time: 34.3s

Alternatives: 24

Speedup: 0.5×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 82.1% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 94.2%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in t around inf 48.2%

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

      1. distribute-lft-out-- 48.2%

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

      2. *-commutative 48.2%

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

   5. Simplified 48.2%

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

4. Final simplification 83.6%

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

Alternative 2: 67.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_3 := \left(a \cdot \left(c \cdot j\right) + i \cdot \left(t \cdot b - y \cdot j\right)\right) - b \cdot \left(z \cdot c\right)\\ t_4 := t_2 + t_1\\ \mathbf{if}\;j \leq -3.7 \cdot 10^{+107}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -6.2 \cdot 10^{+42}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -1.25 \cdot 10^{-79}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;j \leq 0.00106:\\ \;\;\;\;t_1 + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 4.3 \cdot 10^{+108}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (* j (- (* a c) (* y i))))
        (t_3 (- (+ (* a (* c j)) (* i (- (* t b) (* y j)))) (* b (* z c))))
        (t_4 (+ t_2 t_1)))
   (if (<= j -3.7e+107)
     t_2
     (if (<= j -6.2e+42)
       t_3
       (if (<= j -1.25e-79)
         t_4
         (if (<= j 0.00106)
           (+ t_1 (* b (- (* t i) (* z c))))
           (if (<= j 4.3e+108) t_3 t_4)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = j * ((a * c) - (y * i));
	double t_3 = ((a * (c * j)) + (i * ((t * b) - (y * j)))) - (b * (z * c));
	double t_4 = t_2 + t_1;
	double tmp;
	if (j <= -3.7e+107) {
		tmp = t_2;
	} else if (j <= -6.2e+42) {
		tmp = t_3;
	} else if (j <= -1.25e-79) {
		tmp = t_4;
	} else if (j <= 0.00106) {
		tmp = t_1 + (b * ((t * i) - (z * c)));
	} else if (j <= 4.3e+108) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	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 = j * ((a * c) - (y * i))
    t_3 = ((a * (c * j)) + (i * ((t * b) - (y * j)))) - (b * (z * c))
    t_4 = t_2 + t_1
    if (j <= (-3.7d+107)) then
        tmp = t_2
    else if (j <= (-6.2d+42)) then
        tmp = t_3
    else if (j <= (-1.25d-79)) then
        tmp = t_4
    else if (j <= 0.00106d0) then
        tmp = t_1 + (b * ((t * i) - (z * c)))
    else if (j <= 4.3d+108) then
        tmp = t_3
    else
        tmp = t_4
    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 = j * ((a * c) - (y * i));
	double t_3 = ((a * (c * j)) + (i * ((t * b) - (y * j)))) - (b * (z * c));
	double t_4 = t_2 + t_1;
	double tmp;
	if (j <= -3.7e+107) {
		tmp = t_2;
	} else if (j <= -6.2e+42) {
		tmp = t_3;
	} else if (j <= -1.25e-79) {
		tmp = t_4;
	} else if (j <= 0.00106) {
		tmp = t_1 + (b * ((t * i) - (z * c)));
	} else if (j <= 4.3e+108) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = j * ((a * c) - (y * i))
	t_3 = ((a * (c * j)) + (i * ((t * b) - (y * j)))) - (b * (z * c))
	t_4 = t_2 + t_1
	tmp = 0
	if j <= -3.7e+107:
		tmp = t_2
	elif j <= -6.2e+42:
		tmp = t_3
	elif j <= -1.25e-79:
		tmp = t_4
	elif j <= 0.00106:
		tmp = t_1 + (b * ((t * i) - (z * c)))
	elif j <= 4.3e+108:
		tmp = t_3
	else:
		tmp = t_4
	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(j * Float64(Float64(a * c) - Float64(y * i)))
	t_3 = Float64(Float64(Float64(a * Float64(c * j)) + Float64(i * Float64(Float64(t * b) - Float64(y * j)))) - Float64(b * Float64(z * c)))
	t_4 = Float64(t_2 + t_1)
	tmp = 0.0
	if (j <= -3.7e+107)
		tmp = t_2;
	elseif (j <= -6.2e+42)
		tmp = t_3;
	elseif (j <= -1.25e-79)
		tmp = t_4;
	elseif (j <= 0.00106)
		tmp = Float64(t_1 + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	elseif (j <= 4.3e+108)
		tmp = t_3;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = j * ((a * c) - (y * i));
	t_3 = ((a * (c * j)) + (i * ((t * b) - (y * j)))) - (b * (z * c));
	t_4 = t_2 + t_1;
	tmp = 0.0;
	if (j <= -3.7e+107)
		tmp = t_2;
	elseif (j <= -6.2e+42)
		tmp = t_3;
	elseif (j <= -1.25e-79)
		tmp = t_4;
	elseif (j <= 0.00106)
		tmp = t_1 + (b * ((t * i) - (z * c)));
	elseif (j <= 4.3e+108)
		tmp = t_3;
	else
		tmp = t_4;
	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[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision] + N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$2 + t$95$1), $MachinePrecision]}, If[LessEqual[j, -3.7e+107], t$95$2, If[LessEqual[j, -6.2e+42], t$95$3, If[LessEqual[j, -1.25e-79], t$95$4, If[LessEqual[j, 0.00106], N[(t$95$1 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.3e+108], t$95$3, t$95$4]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -3.7e107

   1. Initial program 66.5%

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

   3. Taylor expanded in b around 0 69.2%

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

   4. Taylor expanded in j around inf 72.1%

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

   if -3.7e107 < j < -6.2000000000000003e42 or 0.00105999999999999996 < j < 4.29999999999999996e108

   1. Initial program 62.6%

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

   3. Taylor expanded in i around -inf 65.8%

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

   4. Taylor expanded in x around 0 81.2%

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

      1. neg-mul-1 81.2%

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

      2. +-commutative 81.2%

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

      3. unsub-neg 81.2%

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

      4. *-commutative 81.2%

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

   6. Simplified 81.2%

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

   if -6.2000000000000003e42 < j < -1.25e-79 or 4.29999999999999996e108 < j

   1. Initial program 74.9%

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

   3. Taylor expanded in b around 0 72.6%

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

   if -1.25e-79 < j < 0.00105999999999999996

   1. Initial program 75.6%

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

   3. Taylor expanded in j around 0 78.4%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.7 \cdot 10^{+107}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -6.2 \cdot 10^{+42}:\\ \;\;\;\;\left(a \cdot \left(c \cdot j\right) + i \cdot \left(t \cdot b - y \cdot j\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;j \leq -1.25 \cdot 10^{-79}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 0.00106:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 4.3 \cdot 10^{+108}:\\ \;\;\;\;\left(a \cdot \left(c \cdot j\right) + i \cdot \left(t \cdot b - y \cdot j\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 59.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ t_3 := b \cdot \left(t \cdot i - z \cdot c\right) + t_1\\ \mathbf{if}\;j \leq -1.05 \cdot 10^{+135}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -3.8 \cdot 10^{+42}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -5 \cdot 10^{-88}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 1.9 \cdot 10^{-53}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{+73}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 1.05 \cdot 10^{+100}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 - j \cdot \left(y \cdot i - a \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z)))
        (t_2 (- (* x (- (* y z) (* t a))) (* i (* y j))))
        (t_3 (+ (* b (- (* t i) (* z c))) t_1)))
   (if (<= j -1.05e+135)
     (* j (- (* a c) (* y i)))
     (if (<= j -3.8e+42)
       t_3
       (if (<= j -5e-88)
         t_2
         (if (<= j 1.9e-53)
           t_3
           (if (<= j 4.5e+73)
             t_2
             (if (<= j 1.05e+100)
               (* c (- (* a j) (* z b)))
               (- t_1 (* j (- (* y i) (* a 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);
	double t_2 = (x * ((y * z) - (t * a))) - (i * (y * j));
	double t_3 = (b * ((t * i) - (z * c))) + t_1;
	double tmp;
	if (j <= -1.05e+135) {
		tmp = j * ((a * c) - (y * i));
	} else if (j <= -3.8e+42) {
		tmp = t_3;
	} else if (j <= -5e-88) {
		tmp = t_2;
	} else if (j <= 1.9e-53) {
		tmp = t_3;
	} else if (j <= 4.5e+73) {
		tmp = t_2;
	} else if (j <= 1.05e+100) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = t_1 - (j * ((y * i) - (a * 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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * (y * z)
    t_2 = (x * ((y * z) - (t * a))) - (i * (y * j))
    t_3 = (b * ((t * i) - (z * c))) + t_1
    if (j <= (-1.05d+135)) then
        tmp = j * ((a * c) - (y * i))
    else if (j <= (-3.8d+42)) then
        tmp = t_3
    else if (j <= (-5d-88)) then
        tmp = t_2
    else if (j <= 1.9d-53) then
        tmp = t_3
    else if (j <= 4.5d+73) then
        tmp = t_2
    else if (j <= 1.05d+100) then
        tmp = c * ((a * j) - (z * b))
    else
        tmp = t_1 - (j * ((y * i) - (a * 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);
	double t_2 = (x * ((y * z) - (t * a))) - (i * (y * j));
	double t_3 = (b * ((t * i) - (z * c))) + t_1;
	double tmp;
	if (j <= -1.05e+135) {
		tmp = j * ((a * c) - (y * i));
	} else if (j <= -3.8e+42) {
		tmp = t_3;
	} else if (j <= -5e-88) {
		tmp = t_2;
	} else if (j <= 1.9e-53) {
		tmp = t_3;
	} else if (j <= 4.5e+73) {
		tmp = t_2;
	} else if (j <= 1.05e+100) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = t_1 - (j * ((y * i) - (a * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	t_2 = (x * ((y * z) - (t * a))) - (i * (y * j))
	t_3 = (b * ((t * i) - (z * c))) + t_1
	tmp = 0
	if j <= -1.05e+135:
		tmp = j * ((a * c) - (y * i))
	elif j <= -3.8e+42:
		tmp = t_3
	elif j <= -5e-88:
		tmp = t_2
	elif j <= 1.9e-53:
		tmp = t_3
	elif j <= 4.5e+73:
		tmp = t_2
	elif j <= 1.05e+100:
		tmp = c * ((a * j) - (z * b))
	else:
		tmp = t_1 - (j * ((y * i) - (a * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(y * z))
	t_2 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(i * Float64(y * j)))
	t_3 = Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) + t_1)
	tmp = 0.0
	if (j <= -1.05e+135)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (j <= -3.8e+42)
		tmp = t_3;
	elseif (j <= -5e-88)
		tmp = t_2;
	elseif (j <= 1.9e-53)
		tmp = t_3;
	elseif (j <= 4.5e+73)
		tmp = t_2;
	elseif (j <= 1.05e+100)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	else
		tmp = Float64(t_1 - Float64(j * Float64(Float64(y * i) - Float64(a * 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_2 = (x * ((y * z) - (t * a))) - (i * (y * j));
	t_3 = (b * ((t * i) - (z * c))) + t_1;
	tmp = 0.0;
	if (j <= -1.05e+135)
		tmp = j * ((a * c) - (y * i));
	elseif (j <= -3.8e+42)
		tmp = t_3;
	elseif (j <= -5e-88)
		tmp = t_2;
	elseif (j <= 1.9e-53)
		tmp = t_3;
	elseif (j <= 4.5e+73)
		tmp = t_2;
	elseif (j <= 1.05e+100)
		tmp = c * ((a * j) - (z * b));
	else
		tmp = t_1 - (j * ((y * i) - (a * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[j, -1.05e+135], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3.8e+42], t$95$3, If[LessEqual[j, -5e-88], t$95$2, If[LessEqual[j, 1.9e-53], t$95$3, If[LessEqual[j, 4.5e+73], t$95$2, If[LessEqual[j, 1.05e+100], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(j * N[(N[(y * i), $MachinePrecision] - N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -1.05000000000000005e135

   1. Initial program 71.3%

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

   3. Taylor expanded in b around 0 77.3%

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

   4. Taylor expanded in j around inf 77.9%

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

   if -1.05000000000000005e135 < j < -3.7999999999999998e42 or -5.00000000000000009e-88 < j < 1.8999999999999999e-53

   1. Initial program 72.1%

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

   3. Taylor expanded in j around 0 74.7%

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

   4. Taylor expanded in a around 0 67.1%

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

   if -3.7999999999999998e42 < j < -5.00000000000000009e-88 or 1.8999999999999999e-53 < j < 4.49999999999999985e73

   1. Initial program 75.7%

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

   3. Taylor expanded in b around 0 70.6%

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

   4. Taylor expanded in a around 0 68.0%

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

      1. associate-*r* 68.0%

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

      2. neg-mul-1 68.0%

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

   6. Simplified 68.0%

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

   if 4.49999999999999985e73 < j < 1.0499999999999999e100

   1. Initial program 75.0%

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

   3. Taylor expanded in c around inf 99.6%

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

   if 1.0499999999999999e100 < j

   1. Initial program 71.6%

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

   3. Taylor expanded in b around 0 68.5%

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

   4. Taylor expanded in t around 0 69.2%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.05 \cdot 10^{+135}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -3.8 \cdot 10^{+42}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq -5 \cdot 10^{-88}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;j \leq 1.9 \cdot 10^{-53}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{+73}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;j \leq 1.05 \cdot 10^{+100}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 49.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_3 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;y \leq -3.3 \cdot 10^{+33}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-82}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-123}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-239}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-252}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-70}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+26}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t))))
        (t_2 (* b (- (* t i) (* z c))))
        (t_3 (* c (- (* a j) (* z b)))))
   (if (<= y -3.3e+33)
     (* y (- (* x z) (* i j)))
     (if (<= y -4e-82)
       t_2
       (if (<= y -6.5e-123)
         t_1
         (if (<= y -3.3e-239)
           t_3
           (if (<= y 1.15e-252)
             t_1
             (if (<= y 6.8e-70)
               t_2
               (if (<= y 9.5e+26) t_3 (* i (- (* t b) (* y j))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double t_3 = c * ((a * j) - (z * b));
	double tmp;
	if (y <= -3.3e+33) {
		tmp = y * ((x * z) - (i * j));
	} else if (y <= -4e-82) {
		tmp = t_2;
	} else if (y <= -6.5e-123) {
		tmp = t_1;
	} else if (y <= -3.3e-239) {
		tmp = t_3;
	} else if (y <= 1.15e-252) {
		tmp = t_1;
	} else if (y <= 6.8e-70) {
		tmp = t_2;
	} else if (y <= 9.5e+26) {
		tmp = t_3;
	} else {
		tmp = i * ((t * b) - (y * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    t_2 = b * ((t * i) - (z * c))
    t_3 = c * ((a * j) - (z * b))
    if (y <= (-3.3d+33)) then
        tmp = y * ((x * z) - (i * j))
    else if (y <= (-4d-82)) then
        tmp = t_2
    else if (y <= (-6.5d-123)) then
        tmp = t_1
    else if (y <= (-3.3d-239)) then
        tmp = t_3
    else if (y <= 1.15d-252) then
        tmp = t_1
    else if (y <= 6.8d-70) then
        tmp = t_2
    else if (y <= 9.5d+26) then
        tmp = t_3
    else
        tmp = i * ((t * b) - (y * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double t_3 = c * ((a * j) - (z * b));
	double tmp;
	if (y <= -3.3e+33) {
		tmp = y * ((x * z) - (i * j));
	} else if (y <= -4e-82) {
		tmp = t_2;
	} else if (y <= -6.5e-123) {
		tmp = t_1;
	} else if (y <= -3.3e-239) {
		tmp = t_3;
	} else if (y <= 1.15e-252) {
		tmp = t_1;
	} else if (y <= 6.8e-70) {
		tmp = t_2;
	} else if (y <= 9.5e+26) {
		tmp = t_3;
	} else {
		tmp = i * ((t * b) - (y * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = b * ((t * i) - (z * c))
	t_3 = c * ((a * j) - (z * b))
	tmp = 0
	if y <= -3.3e+33:
		tmp = y * ((x * z) - (i * j))
	elif y <= -4e-82:
		tmp = t_2
	elif y <= -6.5e-123:
		tmp = t_1
	elif y <= -3.3e-239:
		tmp = t_3
	elif y <= 1.15e-252:
		tmp = t_1
	elif y <= 6.8e-70:
		tmp = t_2
	elif y <= 9.5e+26:
		tmp = t_3
	else:
		tmp = i * ((t * b) - (y * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_3 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (y <= -3.3e+33)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (y <= -4e-82)
		tmp = t_2;
	elseif (y <= -6.5e-123)
		tmp = t_1;
	elseif (y <= -3.3e-239)
		tmp = t_3;
	elseif (y <= 1.15e-252)
		tmp = t_1;
	elseif (y <= 6.8e-70)
		tmp = t_2;
	elseif (y <= 9.5e+26)
		tmp = t_3;
	else
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	t_2 = b * ((t * i) - (z * c));
	t_3 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (y <= -3.3e+33)
		tmp = y * ((x * z) - (i * j));
	elseif (y <= -4e-82)
		tmp = t_2;
	elseif (y <= -6.5e-123)
		tmp = t_1;
	elseif (y <= -3.3e-239)
		tmp = t_3;
	elseif (y <= 1.15e-252)
		tmp = t_1;
	elseif (y <= 6.8e-70)
		tmp = t_2;
	elseif (y <= 9.5e+26)
		tmp = t_3;
	else
		tmp = i * ((t * b) - (y * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.3e+33], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4e-82], t$95$2, If[LessEqual[y, -6.5e-123], t$95$1, If[LessEqual[y, -3.3e-239], t$95$3, If[LessEqual[y, 1.15e-252], t$95$1, If[LessEqual[y, 6.8e-70], t$95$2, If[LessEqual[y, 9.5e+26], t$95$3, N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.29999999999999976e33

   1. Initial program 61.1%

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

   3. Taylor expanded in y around inf 66.7%

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

      1. +-commutative 66.7%

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

      2. mul-1-neg 66.7%

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

      3. unsub-neg 66.7%

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

      4. *-commutative 66.7%

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

   5. Simplified 66.7%

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

   if -3.29999999999999976e33 < y < -4e-82 or 1.1499999999999999e-252 < y < 6.79999999999999991e-70

   1. Initial program 83.5%

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

   3. Taylor expanded in b around inf 64.5%

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

   if -4e-82 < y < -6.49999999999999938e-123 or -3.29999999999999995e-239 < y < 1.1499999999999999e-252

   1. Initial program 69.4%

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

   3. Taylor expanded in a around inf 77.4%

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

      1. expm1-log1p-u 38.0%

         \[\leadsto a \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)\right)} \]

      2. expm1-udef 36.4%

         \[\leadsto a \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} - 1\right)} \]

      3. +-commutative 36.4%

         \[\leadsto a \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{c \cdot j + -1 \cdot \left(t \cdot x\right)}\right)} - 1\right) \]

      4. *-commutative 36.4%

         \[\leadsto a \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{j \cdot c} + -1 \cdot \left(t \cdot x\right)\right)} - 1\right) \]

      5. fma-def 36.4%

         \[\leadsto a \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\mathsf{fma}\left(j, c, -1 \cdot \left(t \cdot x\right)\right)}\right)} - 1\right) \]

      6. mul-1-neg 36.4%

         \[\leadsto a \cdot \left(e^{\mathsf{log1p}\left(\mathsf{fma}\left(j, c, \color{blue}{-t \cdot x}\right)\right)} - 1\right) \]

   5. Applied egg-rr 36.4%

      \[\leadsto a \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\mathsf{fma}\left(j, c, -t \cdot x\right)\right)} - 1\right)} \]
   6. Step-by-step derivation

      1. expm1-def 38.0%

         \[\leadsto a \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\mathsf{fma}\left(j, c, -t \cdot x\right)\right)\right)} \]

      2. expm1-log1p 77.4%

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

      3. fma-neg 77.4%

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

      4. *-commutative 77.4%

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

      5. *-commutative 77.4%

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

   7. Simplified 77.4%

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

   if -6.49999999999999938e-123 < y < -3.29999999999999995e-239 or 6.79999999999999991e-70 < y < 9.50000000000000054e26

   1. Initial program 79.9%

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

   3. Taylor expanded in c around inf 61.6%

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

   if 9.50000000000000054e26 < y

   1. Initial program 68.2%

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

   3. Taylor expanded in i around -inf 64.6%

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

   4. Taylor expanded in x around 0 59.3%

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

      1. neg-mul-1 59.3%

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

      2. +-commutative 59.3%

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

      3. unsub-neg 59.3%

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

      4. *-commutative 59.3%

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

   6. Simplified 59.3%

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

   7. Taylor expanded in i around inf 59.2%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+33}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-82}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-123}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-239}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-252}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-70}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+26}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -7.2 \cdot 10^{+72}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-18}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-244}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.46 \cdot 10^{-192}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-23}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+78}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+141}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))) (t_2 (* a (- (* c j) (* x t)))))
   (if (<= a -7.2e+72)
     t_2
     (if (<= a -1.1e-18)
       (* y (- (* x z) (* i j)))
       (if (<= a 4.8e-244)
         (* b (- (* t i) (* z c)))
         (if (<= a 1.46e-192)
           t_1
           (if (<= a 4.5e-23)
             (- (* x (* y z)) (* b (* z c)))
             (if (<= a 7e+78)
               t_1
               (if (<= a 2e+141) (* z (- (* x y) (* b 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 = j * ((a * c) - (y * i));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -7.2e+72) {
		tmp = t_2;
	} else if (a <= -1.1e-18) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= 4.8e-244) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 1.46e-192) {
		tmp = t_1;
	} else if (a <= 4.5e-23) {
		tmp = (x * (y * z)) - (b * (z * c));
	} else if (a <= 7e+78) {
		tmp = t_1;
	} else if (a <= 2e+141) {
		tmp = z * ((x * y) - (b * 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 = j * ((a * c) - (y * i))
    t_2 = a * ((c * j) - (x * t))
    if (a <= (-7.2d+72)) then
        tmp = t_2
    else if (a <= (-1.1d-18)) then
        tmp = y * ((x * z) - (i * j))
    else if (a <= 4.8d-244) then
        tmp = b * ((t * i) - (z * c))
    else if (a <= 1.46d-192) then
        tmp = t_1
    else if (a <= 4.5d-23) then
        tmp = (x * (y * z)) - (b * (z * c))
    else if (a <= 7d+78) then
        tmp = t_1
    else if (a <= 2d+141) then
        tmp = z * ((x * y) - (b * 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 = j * ((a * c) - (y * i));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -7.2e+72) {
		tmp = t_2;
	} else if (a <= -1.1e-18) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= 4.8e-244) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 1.46e-192) {
		tmp = t_1;
	} else if (a <= 4.5e-23) {
		tmp = (x * (y * z)) - (b * (z * c));
	} else if (a <= 7e+78) {
		tmp = t_1;
	} else if (a <= 2e+141) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -7.2e+72:
		tmp = t_2
	elif a <= -1.1e-18:
		tmp = y * ((x * z) - (i * j))
	elif a <= 4.8e-244:
		tmp = b * ((t * i) - (z * c))
	elif a <= 1.46e-192:
		tmp = t_1
	elif a <= 4.5e-23:
		tmp = (x * (y * z)) - (b * (z * c))
	elif a <= 7e+78:
		tmp = t_1
	elif a <= 2e+141:
		tmp = z * ((x * y) - (b * c))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -7.2e+72)
		tmp = t_2;
	elseif (a <= -1.1e-18)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (a <= 4.8e-244)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (a <= 1.46e-192)
		tmp = t_1;
	elseif (a <= 4.5e-23)
		tmp = Float64(Float64(x * Float64(y * z)) - Float64(b * Float64(z * c)));
	elseif (a <= 7e+78)
		tmp = t_1;
	elseif (a <= 2e+141)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * 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 = j * ((a * c) - (y * i));
	t_2 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -7.2e+72)
		tmp = t_2;
	elseif (a <= -1.1e-18)
		tmp = y * ((x * z) - (i * j));
	elseif (a <= 4.8e-244)
		tmp = b * ((t * i) - (z * c));
	elseif (a <= 1.46e-192)
		tmp = t_1;
	elseif (a <= 4.5e-23)
		tmp = (x * (y * z)) - (b * (z * c));
	elseif (a <= 7e+78)
		tmp = t_1;
	elseif (a <= 2e+141)
		tmp = z * ((x * y) - (b * 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[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.2e+72], t$95$2, If[LessEqual[a, -1.1e-18], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.8e-244], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.46e-192], t$95$1, If[LessEqual[a, 4.5e-23], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7e+78], t$95$1, If[LessEqual[a, 2e+141], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -7.20000000000000069e72 or 2.00000000000000003e141 < a

   1. Initial program 60.0%

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

   3. Taylor expanded in a around inf 64.9%

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

      1. expm1-log1p-u 32.0%

         \[\leadsto a \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)\right)} \]

      2. expm1-udef 28.2%

         \[\leadsto a \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} - 1\right)} \]

      3. +-commutative 28.2%

         \[\leadsto a \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{c \cdot j + -1 \cdot \left(t \cdot x\right)}\right)} - 1\right) \]

      4. *-commutative 28.2%

         \[\leadsto a \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{j \cdot c} + -1 \cdot \left(t \cdot x\right)\right)} - 1\right) \]

      5. fma-def 28.2%

         \[\leadsto a \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\mathsf{fma}\left(j, c, -1 \cdot \left(t \cdot x\right)\right)}\right)} - 1\right) \]

      6. mul-1-neg 28.2%

         \[\leadsto a \cdot \left(e^{\mathsf{log1p}\left(\mathsf{fma}\left(j, c, \color{blue}{-t \cdot x}\right)\right)} - 1\right) \]

   5. Applied egg-rr 28.2%

      \[\leadsto a \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\mathsf{fma}\left(j, c, -t \cdot x\right)\right)} - 1\right)} \]
   6. Step-by-step derivation

      1. expm1-def 32.0%

         \[\leadsto a \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\mathsf{fma}\left(j, c, -t \cdot x\right)\right)\right)} \]

      2. expm1-log1p 64.9%

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

      3. fma-neg 64.9%

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

      4. *-commutative 64.9%

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

      5. *-commutative 64.9%

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

   7. Simplified 64.9%

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

   if -7.20000000000000069e72 < a < -1.0999999999999999e-18

   1. Initial program 79.0%

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

   3. Taylor expanded in y around inf 74.0%

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

      1. +-commutative 74.0%

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

      2. mul-1-neg 74.0%

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

      3. unsub-neg 74.0%

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

      4. *-commutative 74.0%

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

   5. Simplified 74.0%

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

   if -1.0999999999999999e-18 < a < 4.80000000000000032e-244

   1. Initial program 81.3%

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

   3. Taylor expanded in b around inf 66.6%

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

   if 4.80000000000000032e-244 < a < 1.46000000000000002e-192 or 4.49999999999999975e-23 < a < 7.0000000000000003e78

   1. Initial program 81.2%

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

   3. Taylor expanded in b around 0 80.6%

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

   4. Taylor expanded in j around inf 69.9%

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

   if 1.46000000000000002e-192 < a < 4.49999999999999975e-23

   1. Initial program 80.0%

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

   3. Taylor expanded in i around -inf 70.5%

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

   4. Taylor expanded in z around inf 54.4%

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

   if 7.0000000000000003e78 < a < 2.00000000000000003e141

   1. Initial program 70.2%

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

   3. Taylor expanded in z around inf 61.2%

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

      1. *-commutative 61.2%

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

      2. *-commutative 61.2%

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

   5. Simplified 61.2%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{+72}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-18}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-244}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.46 \cdot 10^{-192}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-23}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+78}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+141}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 28.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c\right)\\ \mathbf{if}\;b \leq -5.8 \cdot 10^{+120}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{-226}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 1.56 \cdot 10^{-285}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-199}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 3.05 \cdot 10^{-121}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 1.12 \cdot 10^{+119}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (* a c))))
   (if (<= b -5.8e+120)
     (* b (* t i))
     (if (<= b -8.5e-69)
       t_1
       (if (<= b -8.5e-226)
         (* x (* y z))
         (if (<= b 1.56e-285)
           t_1
           (if (<= b 4.5e-199)
             (* z (* x y))
             (if (<= b 3.05e-121)
               (* a (* c j))
               (if (<= b 1.12e+119) (* (* x t) (- a)) (* i (* t b)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (a * c);
	double tmp;
	if (b <= -5.8e+120) {
		tmp = b * (t * i);
	} else if (b <= -8.5e-69) {
		tmp = t_1;
	} else if (b <= -8.5e-226) {
		tmp = x * (y * z);
	} else if (b <= 1.56e-285) {
		tmp = t_1;
	} else if (b <= 4.5e-199) {
		tmp = z * (x * y);
	} else if (b <= 3.05e-121) {
		tmp = a * (c * j);
	} else if (b <= 1.12e+119) {
		tmp = (x * t) * -a;
	} else {
		tmp = i * (t * 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) :: t_1
    real(8) :: tmp
    t_1 = j * (a * c)
    if (b <= (-5.8d+120)) then
        tmp = b * (t * i)
    else if (b <= (-8.5d-69)) then
        tmp = t_1
    else if (b <= (-8.5d-226)) then
        tmp = x * (y * z)
    else if (b <= 1.56d-285) then
        tmp = t_1
    else if (b <= 4.5d-199) then
        tmp = z * (x * y)
    else if (b <= 3.05d-121) then
        tmp = a * (c * j)
    else if (b <= 1.12d+119) then
        tmp = (x * t) * -a
    else
        tmp = i * (t * 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 t_1 = j * (a * c);
	double tmp;
	if (b <= -5.8e+120) {
		tmp = b * (t * i);
	} else if (b <= -8.5e-69) {
		tmp = t_1;
	} else if (b <= -8.5e-226) {
		tmp = x * (y * z);
	} else if (b <= 1.56e-285) {
		tmp = t_1;
	} else if (b <= 4.5e-199) {
		tmp = z * (x * y);
	} else if (b <= 3.05e-121) {
		tmp = a * (c * j);
	} else if (b <= 1.12e+119) {
		tmp = (x * t) * -a;
	} else {
		tmp = i * (t * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * (a * c)
	tmp = 0
	if b <= -5.8e+120:
		tmp = b * (t * i)
	elif b <= -8.5e-69:
		tmp = t_1
	elif b <= -8.5e-226:
		tmp = x * (y * z)
	elif b <= 1.56e-285:
		tmp = t_1
	elif b <= 4.5e-199:
		tmp = z * (x * y)
	elif b <= 3.05e-121:
		tmp = a * (c * j)
	elif b <= 1.12e+119:
		tmp = (x * t) * -a
	else:
		tmp = i * (t * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(a * c))
	tmp = 0.0
	if (b <= -5.8e+120)
		tmp = Float64(b * Float64(t * i));
	elseif (b <= -8.5e-69)
		tmp = t_1;
	elseif (b <= -8.5e-226)
		tmp = Float64(x * Float64(y * z));
	elseif (b <= 1.56e-285)
		tmp = t_1;
	elseif (b <= 4.5e-199)
		tmp = Float64(z * Float64(x * y));
	elseif (b <= 3.05e-121)
		tmp = Float64(a * Float64(c * j));
	elseif (b <= 1.12e+119)
		tmp = Float64(Float64(x * t) * Float64(-a));
	else
		tmp = Float64(i * Float64(t * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * (a * c);
	tmp = 0.0;
	if (b <= -5.8e+120)
		tmp = b * (t * i);
	elseif (b <= -8.5e-69)
		tmp = t_1;
	elseif (b <= -8.5e-226)
		tmp = x * (y * z);
	elseif (b <= 1.56e-285)
		tmp = t_1;
	elseif (b <= 4.5e-199)
		tmp = z * (x * y);
	elseif (b <= 3.05e-121)
		tmp = a * (c * j);
	elseif (b <= 1.12e+119)
		tmp = (x * t) * -a;
	else
		tmp = i * (t * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.8e+120], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -8.5e-69], t$95$1, If[LessEqual[b, -8.5e-226], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.56e-285], t$95$1, If[LessEqual[b, 4.5e-199], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.05e-121], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.12e+119], N[(N[(x * t), $MachinePrecision] * (-a)), $MachinePrecision], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -5.8000000000000003e120

   1. Initial program 69.8%

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

   3. Taylor expanded in b around inf 72.6%

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

   4. Taylor expanded in i around inf 52.6%

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

   if -5.8000000000000003e120 < b < -8.50000000000000046e-69 or -8.4999999999999998e-226 < b < 1.55999999999999998e-285

   1. Initial program 76.0%

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

   3. Taylor expanded in i around -inf 69.6%

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

   4. Taylor expanded in x around 0 56.9%

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

      1. neg-mul-1 56.9%

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

      2. +-commutative 56.9%

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

      3. unsub-neg 56.9%

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

      4. *-commutative 56.9%

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

   6. Simplified 56.9%

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

   7. Taylor expanded in a around inf 34.5%

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

      1. *-commutative 34.5%

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

      2. *-commutative 34.5%

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

      3. associate-*l* 41.8%

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

   9. Simplified 41.8%

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

   if -8.50000000000000046e-69 < b < -8.4999999999999998e-226

   1. Initial program 73.8%

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

   3. Taylor expanded in z around inf 29.1%

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

      1. *-commutative 29.1%

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

      2. *-commutative 29.1%

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

   5. Simplified 29.1%

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

   6. Taylor expanded in y around inf 32.8%

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

      1. *-commutative 32.8%

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

   8. Simplified 32.8%

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

   if 1.55999999999999998e-285 < b < 4.49999999999999998e-199

   1. Initial program 75.4%

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

   3. Taylor expanded in z around inf 51.5%

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

      1. *-commutative 51.5%

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

      2. *-commutative 51.5%

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

   5. Simplified 51.5%

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

   6. Taylor expanded in y around inf 45.4%

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

      1. *-commutative 45.4%

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

      2. *-commutative 45.4%

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

      3. associate-*l* 51.2%

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

      4. *-commutative 51.2%

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

   8. Simplified 51.2%

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

   if 4.49999999999999998e-199 < b < 3.04999999999999989e-121

   1. Initial program 43.0%

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

   3. Taylor expanded in a around inf 59.3%

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

   4. Taylor expanded in t around 0 42.1%

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

   if 3.04999999999999989e-121 < b < 1.11999999999999994e119

   1. Initial program 76.6%

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

   3. Taylor expanded in t around inf 53.7%

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

      1. distribute-lft-out-- 53.7%

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

      2. *-commutative 53.7%

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

   5. Simplified 53.7%

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

   6. Taylor expanded in a around inf 35.4%

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

      1. mul-1-neg 35.4%

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

      2. distribute-rgt-neg-in 35.4%

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

      3. distribute-rgt-neg-in 35.4%

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

   8. Simplified 35.4%

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

   if 1.11999999999999994e119 < b

   1. Initial program 74.9%

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

   3. Taylor expanded in j around 0 63.9%

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

   4. Taylor expanded in i around inf 40.0%

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

      1. associate-*r* 37.9%

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

      2. *-commutative 37.9%

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

      3. associate-*l* 44.3%

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

   6. Simplified 44.3%

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

4. Final simplification 42.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.8 \cdot 10^{+120}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{-69}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{-226}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 1.56 \cdot 10^{-285}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-199}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 3.05 \cdot 10^{-121}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 1.12 \cdot 10^{+119}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 29.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c\right)\\ t_2 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;b \leq -9.2 \cdot 10^{+120}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq -9.6 \cdot 10^{-70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.26 \cdot 10^{-225}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-282}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-199}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-147}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-21}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (* a c))) (t_2 (* z (* x y))))
   (if (<= b -9.2e+120)
     (* b (* t i))
     (if (<= b -9.6e-70)
       t_1
       (if (<= b -1.26e-225)
         (* x (* y z))
         (if (<= b 9e-282)
           t_1
           (if (<= b 2e-199)
             t_2
             (if (<= b 3e-147)
               (* a (* c j))
               (if (<= b 9e-21) t_2 (* i (* t b)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (a * c);
	double t_2 = z * (x * y);
	double tmp;
	if (b <= -9.2e+120) {
		tmp = b * (t * i);
	} else if (b <= -9.6e-70) {
		tmp = t_1;
	} else if (b <= -1.26e-225) {
		tmp = x * (y * z);
	} else if (b <= 9e-282) {
		tmp = t_1;
	} else if (b <= 2e-199) {
		tmp = t_2;
	} else if (b <= 3e-147) {
		tmp = a * (c * j);
	} else if (b <= 9e-21) {
		tmp = t_2;
	} else {
		tmp = i * (t * 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (a * c)
    t_2 = z * (x * y)
    if (b <= (-9.2d+120)) then
        tmp = b * (t * i)
    else if (b <= (-9.6d-70)) then
        tmp = t_1
    else if (b <= (-1.26d-225)) then
        tmp = x * (y * z)
    else if (b <= 9d-282) then
        tmp = t_1
    else if (b <= 2d-199) then
        tmp = t_2
    else if (b <= 3d-147) then
        tmp = a * (c * j)
    else if (b <= 9d-21) then
        tmp = t_2
    else
        tmp = i * (t * 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 t_1 = j * (a * c);
	double t_2 = z * (x * y);
	double tmp;
	if (b <= -9.2e+120) {
		tmp = b * (t * i);
	} else if (b <= -9.6e-70) {
		tmp = t_1;
	} else if (b <= -1.26e-225) {
		tmp = x * (y * z);
	} else if (b <= 9e-282) {
		tmp = t_1;
	} else if (b <= 2e-199) {
		tmp = t_2;
	} else if (b <= 3e-147) {
		tmp = a * (c * j);
	} else if (b <= 9e-21) {
		tmp = t_2;
	} else {
		tmp = i * (t * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * (a * c)
	t_2 = z * (x * y)
	tmp = 0
	if b <= -9.2e+120:
		tmp = b * (t * i)
	elif b <= -9.6e-70:
		tmp = t_1
	elif b <= -1.26e-225:
		tmp = x * (y * z)
	elif b <= 9e-282:
		tmp = t_1
	elif b <= 2e-199:
		tmp = t_2
	elif b <= 3e-147:
		tmp = a * (c * j)
	elif b <= 9e-21:
		tmp = t_2
	else:
		tmp = i * (t * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(a * c))
	t_2 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (b <= -9.2e+120)
		tmp = Float64(b * Float64(t * i));
	elseif (b <= -9.6e-70)
		tmp = t_1;
	elseif (b <= -1.26e-225)
		tmp = Float64(x * Float64(y * z));
	elseif (b <= 9e-282)
		tmp = t_1;
	elseif (b <= 2e-199)
		tmp = t_2;
	elseif (b <= 3e-147)
		tmp = Float64(a * Float64(c * j));
	elseif (b <= 9e-21)
		tmp = t_2;
	else
		tmp = Float64(i * Float64(t * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * (a * c);
	t_2 = z * (x * y);
	tmp = 0.0;
	if (b <= -9.2e+120)
		tmp = b * (t * i);
	elseif (b <= -9.6e-70)
		tmp = t_1;
	elseif (b <= -1.26e-225)
		tmp = x * (y * z);
	elseif (b <= 9e-282)
		tmp = t_1;
	elseif (b <= 2e-199)
		tmp = t_2;
	elseif (b <= 3e-147)
		tmp = a * (c * j);
	elseif (b <= 9e-21)
		tmp = t_2;
	else
		tmp = i * (t * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9.2e+120], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -9.6e-70], t$95$1, If[LessEqual[b, -1.26e-225], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9e-282], t$95$1, If[LessEqual[b, 2e-199], t$95$2, If[LessEqual[b, 3e-147], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9e-21], t$95$2, N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -9.1999999999999997e120

   1. Initial program 69.8%

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

   3. Taylor expanded in b around inf 72.6%

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

   4. Taylor expanded in i around inf 52.6%

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

   if -9.1999999999999997e120 < b < -9.6000000000000005e-70 or -1.2599999999999999e-225 < b < 9.00000000000000017e-282

   1. Initial program 76.0%

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

   3. Taylor expanded in i around -inf 69.6%

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

   4. Taylor expanded in x around 0 56.9%

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

      1. neg-mul-1 56.9%

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

      2. +-commutative 56.9%

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

      3. unsub-neg 56.9%

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

      4. *-commutative 56.9%

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

   6. Simplified 56.9%

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

   7. Taylor expanded in a around inf 34.5%

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

      1. *-commutative 34.5%

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

      2. *-commutative 34.5%

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

      3. associate-*l* 41.8%

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

   9. Simplified 41.8%

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

   if -9.6000000000000005e-70 < b < -1.2599999999999999e-225

   1. Initial program 73.8%

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

   3. Taylor expanded in z around inf 29.1%

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

      1. *-commutative 29.1%

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

      2. *-commutative 29.1%

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

   5. Simplified 29.1%

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

   6. Taylor expanded in y around inf 32.8%

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

      1. *-commutative 32.8%

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

   8. Simplified 32.8%

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

   if 9.00000000000000017e-282 < b < 1.99999999999999996e-199 or 3.0000000000000002e-147 < b < 8.99999999999999936e-21

   1. Initial program 71.3%

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

   3. Taylor expanded in z around inf 44.6%

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

      1. *-commutative 44.6%

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

      2. *-commutative 44.6%

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

   5. Simplified 44.6%

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

   6. Taylor expanded in y around inf 35.7%

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

      1. *-commutative 35.7%

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

      2. *-commutative 35.7%

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

      3. associate-*l* 42.1%

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

      4. *-commutative 42.1%

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

   8. Simplified 42.1%

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

   if 1.99999999999999996e-199 < b < 3.0000000000000002e-147

   1. Initial program 45.8%

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

   3. Taylor expanded in a around inf 73.1%

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

   4. Taylor expanded in t around 0 55.0%

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

   if 8.99999999999999936e-21 < b

   1. Initial program 75.3%

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

   3. Taylor expanded in j around 0 66.1%

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

   4. Taylor expanded in i around inf 33.0%

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

      1. associate-*r* 31.7%

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

      2. *-commutative 31.7%

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

      3. associate-*l* 35.6%

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

   6. Simplified 35.6%

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

4. Final simplification 41.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.2 \cdot 10^{+120}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq -9.6 \cdot 10^{-70}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;b \leq -1.26 \cdot 10^{-225}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-282}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-199}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-147}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-21}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := t_1 - j \cdot \left(y \cdot i - a \cdot c\right)\\ t_3 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;j \leq -9.5 \cdot 10^{+143}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -1.6 \cdot 10^{+82}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq -8.2 \cdot 10^{-80}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -4.8 \cdot 10^{-135}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 940:\\ \;\;\;\;t_3 + t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z)))
        (t_2 (- t_1 (* j (- (* y i) (* a c)))))
        (t_3 (* b (- (* t i) (* z c)))))
   (if (<= j -9.5e+143)
     (* j (- (* a c) (* y i)))
     (if (<= j -1.6e+82)
       (* t (- (* b i) (* x a)))
       (if (<= j -8.2e-80)
         t_2
         (if (<= j -4.8e-135) t_3 (if (<= j 940.0) (+ t_3 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);
	double t_2 = t_1 - (j * ((y * i) - (a * c)));
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if (j <= -9.5e+143) {
		tmp = j * ((a * c) - (y * i));
	} else if (j <= -1.6e+82) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= -8.2e-80) {
		tmp = t_2;
	} else if (j <= -4.8e-135) {
		tmp = t_3;
	} else if (j <= 940.0) {
		tmp = t_3 + 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) :: t_3
    real(8) :: tmp
    t_1 = x * (y * z)
    t_2 = t_1 - (j * ((y * i) - (a * c)))
    t_3 = b * ((t * i) - (z * c))
    if (j <= (-9.5d+143)) then
        tmp = j * ((a * c) - (y * i))
    else if (j <= (-1.6d+82)) then
        tmp = t * ((b * i) - (x * a))
    else if (j <= (-8.2d-80)) then
        tmp = t_2
    else if (j <= (-4.8d-135)) then
        tmp = t_3
    else if (j <= 940.0d0) then
        tmp = t_3 + 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);
	double t_2 = t_1 - (j * ((y * i) - (a * c)));
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if (j <= -9.5e+143) {
		tmp = j * ((a * c) - (y * i));
	} else if (j <= -1.6e+82) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= -8.2e-80) {
		tmp = t_2;
	} else if (j <= -4.8e-135) {
		tmp = t_3;
	} else if (j <= 940.0) {
		tmp = t_3 + 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_2 = t_1 - (j * ((y * i) - (a * c)))
	t_3 = b * ((t * i) - (z * c))
	tmp = 0
	if j <= -9.5e+143:
		tmp = j * ((a * c) - (y * i))
	elif j <= -1.6e+82:
		tmp = t * ((b * i) - (x * a))
	elif j <= -8.2e-80:
		tmp = t_2
	elif j <= -4.8e-135:
		tmp = t_3
	elif j <= 940.0:
		tmp = t_3 + t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(y * z))
	t_2 = Float64(t_1 - Float64(j * Float64(Float64(y * i) - Float64(a * c))))
	t_3 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (j <= -9.5e+143)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (j <= -1.6e+82)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (j <= -8.2e-80)
		tmp = t_2;
	elseif (j <= -4.8e-135)
		tmp = t_3;
	elseif (j <= 940.0)
		tmp = Float64(t_3 + 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_2 = t_1 - (j * ((y * i) - (a * c)));
	t_3 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (j <= -9.5e+143)
		tmp = j * ((a * c) - (y * i));
	elseif (j <= -1.6e+82)
		tmp = t * ((b * i) - (x * a));
	elseif (j <= -8.2e-80)
		tmp = t_2;
	elseif (j <= -4.8e-135)
		tmp = t_3;
	elseif (j <= 940.0)
		tmp = t_3 + t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - N[(j * N[(N[(y * i), $MachinePrecision] - N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -9.5e+143], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.6e+82], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -8.2e-80], t$95$2, If[LessEqual[j, -4.8e-135], t$95$3, If[LessEqual[j, 940.0], N[(t$95$3 + t$95$1), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -9.50000000000000066e143

   1. Initial program 71.8%

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

   3. Taylor expanded in b around 0 78.4%

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

   4. Taylor expanded in j around inf 82.1%

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

   if -9.50000000000000066e143 < j < -1.59999999999999987e82

   1. Initial program 61.2%

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

   3. Taylor expanded in t around inf 69.6%

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

      1. distribute-lft-out-- 69.6%

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

      2. *-commutative 69.6%

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

   5. Simplified 69.6%

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

   if -1.59999999999999987e82 < j < -8.1999999999999999e-80 or 940 < j

   1. Initial program 70.3%

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

   3. Taylor expanded in b around 0 65.5%

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

   4. Taylor expanded in t around 0 65.7%

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

   if -8.1999999999999999e-80 < j < -4.7999999999999997e-135

   1. Initial program 78.5%

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

   3. Taylor expanded in b around inf 65.5%

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

   if -4.7999999999999997e-135 < j < 940

   1. Initial program 75.3%

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

   3. Taylor expanded in j around 0 78.4%

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

   4. Taylor expanded in a around 0 66.0%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -9.5 \cdot 10^{+143}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -1.6 \cdot 10^{+82}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq -8.2 \cdot 10^{-80}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{elif}\;j \leq -4.8 \cdot 10^{-135}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 940:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -3.7 \cdot 10^{+113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -3.3 \cdot 10^{+75}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq -4.4 \cdot 10^{+49}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 10^{+119}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))))
   (if (<= b -3.7e+113)
     t_1
     (if (<= b -3.3e+75)
       (* a (- (* c j) (* x t)))
       (if (<= b -4.4e+49)
         (* c (- (* a j) (* z b)))
         (if (<= b 1e+119)
           (+ (* j (- (* a c) (* y i))) (* x (- (* y z) (* t a))))
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -3.7e+113) {
		tmp = t_1;
	} else if (b <= -3.3e+75) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= -4.4e+49) {
		tmp = c * ((a * j) - (z * b));
	} else if (b <= 1e+119) {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    if (b <= (-3.7d+113)) then
        tmp = t_1
    else if (b <= (-3.3d+75)) then
        tmp = a * ((c * j) - (x * t))
    else if (b <= (-4.4d+49)) then
        tmp = c * ((a * j) - (z * b))
    else if (b <= 1d+119) then
        tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -3.7e+113) {
		tmp = t_1;
	} else if (b <= -3.3e+75) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= -4.4e+49) {
		tmp = c * ((a * j) - (z * b));
	} else if (b <= 1e+119) {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -3.7e+113:
		tmp = t_1
	elif b <= -3.3e+75:
		tmp = a * ((c * j) - (x * t))
	elif b <= -4.4e+49:
		tmp = c * ((a * j) - (z * b))
	elif b <= 1e+119:
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -3.7e+113)
		tmp = t_1;
	elseif (b <= -3.3e+75)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (b <= -4.4e+49)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (b <= 1e+119)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -3.7e+113)
		tmp = t_1;
	elseif (b <= -3.3e+75)
		tmp = a * ((c * j) - (x * t));
	elseif (b <= -4.4e+49)
		tmp = c * ((a * j) - (z * b));
	elseif (b <= 1e+119)
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.7e+113], t$95$1, If[LessEqual[b, -3.3e+75], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.4e+49], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1e+119], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.6999999999999998e113 or 9.99999999999999944e118 < b

   1. Initial program 71.6%

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

   3. Taylor expanded in b around inf 74.3%

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

   if -3.6999999999999998e113 < b < -3.29999999999999998e75

   1. Initial program 80.0%

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

   3. Taylor expanded in a around inf 80.3%

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

      1. expm1-log1p-u 40.2%

         \[\leadsto a \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)\right)} \]

      2. expm1-udef 40.2%

         \[\leadsto a \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} - 1\right)} \]

      3. +-commutative 40.2%

         \[\leadsto a \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{c \cdot j + -1 \cdot \left(t \cdot x\right)}\right)} - 1\right) \]

      4. *-commutative 40.2%

         \[\leadsto a \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{j \cdot c} + -1 \cdot \left(t \cdot x\right)\right)} - 1\right) \]

      5. fma-def 40.2%

         \[\leadsto a \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\mathsf{fma}\left(j, c, -1 \cdot \left(t \cdot x\right)\right)}\right)} - 1\right) \]

      6. mul-1-neg 40.2%

         \[\leadsto a \cdot \left(e^{\mathsf{log1p}\left(\mathsf{fma}\left(j, c, \color{blue}{-t \cdot x}\right)\right)} - 1\right) \]

   5. Applied egg-rr 40.2%

      \[\leadsto a \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\mathsf{fma}\left(j, c, -t \cdot x\right)\right)} - 1\right)} \]
   6. Step-by-step derivation

      1. expm1-def 40.2%

         \[\leadsto a \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\mathsf{fma}\left(j, c, -t \cdot x\right)\right)\right)} \]

      2. expm1-log1p 80.3%

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

      3. fma-neg 80.3%

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

      4. *-commutative 80.3%

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

      5. *-commutative 80.3%

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

   7. Simplified 80.3%

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

   if -3.29999999999999998e75 < b < -4.4000000000000001e49

   1. Initial program 69.8%

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

   3. Taylor expanded in c around inf 67.4%

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

   if -4.4000000000000001e49 < b < 9.99999999999999944e118

   1. Initial program 72.7%

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

   3. Taylor expanded in b around 0 68.1%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.7 \cdot 10^{+113}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -3.3 \cdot 10^{+75}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq -4.4 \cdot 10^{+49}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 10^{+119}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 67.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_3 := t_1 + t_2\\ \mathbf{if}\;b \leq -1.25 \cdot 10^{+115}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.9 \cdot 10^{-78}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-118}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + t_1\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{+118}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (* b (- (* t i) (* z c))))
        (t_3 (+ t_1 t_2)))
   (if (<= b -1.25e+115)
     t_2
     (if (<= b -1.9e-78)
       t_3
       (if (<= b 1.4e-118)
         (+ (* j (- (* a c) (* y i))) t_1)
         (if (<= b 1.75e+118) t_3 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = b * ((t * i) - (z * c));
	double t_3 = t_1 + t_2;
	double tmp;
	if (b <= -1.25e+115) {
		tmp = t_2;
	} else if (b <= -1.9e-78) {
		tmp = t_3;
	} else if (b <= 1.4e-118) {
		tmp = (j * ((a * c) - (y * i))) + t_1;
	} else if (b <= 1.75e+118) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = b * ((t * i) - (z * c))
    t_3 = t_1 + t_2
    if (b <= (-1.25d+115)) then
        tmp = t_2
    else if (b <= (-1.9d-78)) then
        tmp = t_3
    else if (b <= 1.4d-118) then
        tmp = (j * ((a * c) - (y * i))) + t_1
    else if (b <= 1.75d+118) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = b * ((t * i) - (z * c));
	double t_3 = t_1 + t_2;
	double tmp;
	if (b <= -1.25e+115) {
		tmp = t_2;
	} else if (b <= -1.9e-78) {
		tmp = t_3;
	} else if (b <= 1.4e-118) {
		tmp = (j * ((a * c) - (y * i))) + t_1;
	} else if (b <= 1.75e+118) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = b * ((t * i) - (z * c))
	t_3 = t_1 + t_2
	tmp = 0
	if b <= -1.25e+115:
		tmp = t_2
	elif b <= -1.9e-78:
		tmp = t_3
	elif b <= 1.4e-118:
		tmp = (j * ((a * c) - (y * i))) + t_1
	elif b <= 1.75e+118:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_3 = Float64(t_1 + t_2)
	tmp = 0.0
	if (b <= -1.25e+115)
		tmp = t_2;
	elseif (b <= -1.9e-78)
		tmp = t_3;
	elseif (b <= 1.4e-118)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + t_1);
	elseif (b <= 1.75e+118)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = b * ((t * i) - (z * c));
	t_3 = t_1 + t_2;
	tmp = 0.0;
	if (b <= -1.25e+115)
		tmp = t_2;
	elseif (b <= -1.9e-78)
		tmp = t_3;
	elseif (b <= 1.4e-118)
		tmp = (j * ((a * c) - (y * i))) + t_1;
	elseif (b <= 1.75e+118)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 + t$95$2), $MachinePrecision]}, If[LessEqual[b, -1.25e+115], t$95$2, If[LessEqual[b, -1.9e-78], t$95$3, If[LessEqual[b, 1.4e-118], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[b, 1.75e+118], t$95$3, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.25000000000000002e115 or 1.75000000000000008e118 < b

   1. Initial program 70.8%

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

   3. Taylor expanded in b around inf 73.5%

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

   if -1.25000000000000002e115 < b < -1.8999999999999999e-78 or 1.4e-118 < b < 1.75000000000000008e118

   1. Initial program 80.1%

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

   3. Taylor expanded in j around 0 71.0%

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

   if -1.8999999999999999e-78 < b < 1.4e-118

   1. Initial program 64.5%

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

   3. Taylor expanded in b around 0 74.0%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+115}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.9 \cdot 10^{-78}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-118}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{+118}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 66.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;b \leq -8.8 \cdot 10^{+115}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.95 \cdot 10^{-89}:\\ \;\;\;\;\left(a \cdot \left(c \cdot j\right) + t_2\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-119}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + t_2\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{+118}:\\ \;\;\;\;t_2 + t_1\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* x (- (* y z) (* t a)))))
   (if (<= b -8.8e+115)
     t_1
     (if (<= b -1.95e-89)
       (- (+ (* a (* c j)) t_2) (* b (* z c)))
       (if (<= b 3.8e-119)
         (+ (* j (- (* a c) (* y i))) t_2)
         (if (<= b 4.2e+118) (+ t_2 t_1) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (b <= -8.8e+115) {
		tmp = t_1;
	} else if (b <= -1.95e-89) {
		tmp = ((a * (c * j)) + t_2) - (b * (z * c));
	} else if (b <= 3.8e-119) {
		tmp = (j * ((a * c) - (y * i))) + t_2;
	} else if (b <= 4.2e+118) {
		tmp = t_2 + t_1;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = x * ((y * z) - (t * a))
    if (b <= (-8.8d+115)) then
        tmp = t_1
    else if (b <= (-1.95d-89)) then
        tmp = ((a * (c * j)) + t_2) - (b * (z * c))
    else if (b <= 3.8d-119) then
        tmp = (j * ((a * c) - (y * i))) + t_2
    else if (b <= 4.2d+118) then
        tmp = t_2 + t_1
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (b <= -8.8e+115) {
		tmp = t_1;
	} else if (b <= -1.95e-89) {
		tmp = ((a * (c * j)) + t_2) - (b * (z * c));
	} else if (b <= 3.8e-119) {
		tmp = (j * ((a * c) - (y * i))) + t_2;
	} else if (b <= 4.2e+118) {
		tmp = t_2 + t_1;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = x * ((y * z) - (t * a))
	tmp = 0
	if b <= -8.8e+115:
		tmp = t_1
	elif b <= -1.95e-89:
		tmp = ((a * (c * j)) + t_2) - (b * (z * c))
	elif b <= 3.8e-119:
		tmp = (j * ((a * c) - (y * i))) + t_2
	elif b <= 4.2e+118:
		tmp = t_2 + t_1
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (b <= -8.8e+115)
		tmp = t_1;
	elseif (b <= -1.95e-89)
		tmp = Float64(Float64(Float64(a * Float64(c * j)) + t_2) - Float64(b * Float64(z * c)));
	elseif (b <= 3.8e-119)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + t_2);
	elseif (b <= 4.2e+118)
		tmp = Float64(t_2 + t_1);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (b <= -8.8e+115)
		tmp = t_1;
	elseif (b <= -1.95e-89)
		tmp = ((a * (c * j)) + t_2) - (b * (z * c));
	elseif (b <= 3.8e-119)
		tmp = (j * ((a * c) - (y * i))) + t_2;
	elseif (b <= 4.2e+118)
		tmp = t_2 + t_1;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8.8e+115], t$95$1, If[LessEqual[b, -1.95e-89], N[(N[(N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.8e-119], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[b, 4.2e+118], N[(t$95$2 + t$95$1), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -8.8000000000000001e115 or 4.2e118 < b

   1. Initial program 70.8%

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

   3. Taylor expanded in b around inf 73.5%

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

   if -8.8000000000000001e115 < b < -1.94999999999999989e-89

   1. Initial program 80.5%

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

   3. Taylor expanded in i around 0 73.8%

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

   if -1.94999999999999989e-89 < b < 3.79999999999999975e-119

   1. Initial program 64.5%

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

   3. Taylor expanded in b around 0 74.0%

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

   if 3.79999999999999975e-119 < b < 4.2e118

   1. Initial program 79.7%

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

   3. Taylor expanded in j around 0 74.0%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.8 \cdot 10^{+115}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.95 \cdot 10^{-89}:\\ \;\;\;\;\left(a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-119}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{+118}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 28.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;b \leq -1.45 \cdot 10^{+119}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq -1.1 \cdot 10^{-67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2.15 \cdot 10^{-224}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.22 \cdot 10^{-285}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-199}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 9.6 \cdot 10^{-119}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (* a c))) (t_2 (* x (* y z))))
   (if (<= b -1.45e+119)
     (* b (* t i))
     (if (<= b -1.1e-67)
       t_1
       (if (<= b -2.15e-224)
         t_2
         (if (<= b 1.22e-285)
           t_1
           (if (<= b 4e-199) t_2 (if (<= b 9.6e-119) t_1 (* i (* t b))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (a * c);
	double t_2 = x * (y * z);
	double tmp;
	if (b <= -1.45e+119) {
		tmp = b * (t * i);
	} else if (b <= -1.1e-67) {
		tmp = t_1;
	} else if (b <= -2.15e-224) {
		tmp = t_2;
	} else if (b <= 1.22e-285) {
		tmp = t_1;
	} else if (b <= 4e-199) {
		tmp = t_2;
	} else if (b <= 9.6e-119) {
		tmp = t_1;
	} else {
		tmp = i * (t * 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (a * c)
    t_2 = x * (y * z)
    if (b <= (-1.45d+119)) then
        tmp = b * (t * i)
    else if (b <= (-1.1d-67)) then
        tmp = t_1
    else if (b <= (-2.15d-224)) then
        tmp = t_2
    else if (b <= 1.22d-285) then
        tmp = t_1
    else if (b <= 4d-199) then
        tmp = t_2
    else if (b <= 9.6d-119) then
        tmp = t_1
    else
        tmp = i * (t * 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 t_1 = j * (a * c);
	double t_2 = x * (y * z);
	double tmp;
	if (b <= -1.45e+119) {
		tmp = b * (t * i);
	} else if (b <= -1.1e-67) {
		tmp = t_1;
	} else if (b <= -2.15e-224) {
		tmp = t_2;
	} else if (b <= 1.22e-285) {
		tmp = t_1;
	} else if (b <= 4e-199) {
		tmp = t_2;
	} else if (b <= 9.6e-119) {
		tmp = t_1;
	} else {
		tmp = i * (t * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * (a * c)
	t_2 = x * (y * z)
	tmp = 0
	if b <= -1.45e+119:
		tmp = b * (t * i)
	elif b <= -1.1e-67:
		tmp = t_1
	elif b <= -2.15e-224:
		tmp = t_2
	elif b <= 1.22e-285:
		tmp = t_1
	elif b <= 4e-199:
		tmp = t_2
	elif b <= 9.6e-119:
		tmp = t_1
	else:
		tmp = i * (t * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(a * c))
	t_2 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (b <= -1.45e+119)
		tmp = Float64(b * Float64(t * i));
	elseif (b <= -1.1e-67)
		tmp = t_1;
	elseif (b <= -2.15e-224)
		tmp = t_2;
	elseif (b <= 1.22e-285)
		tmp = t_1;
	elseif (b <= 4e-199)
		tmp = t_2;
	elseif (b <= 9.6e-119)
		tmp = t_1;
	else
		tmp = Float64(i * Float64(t * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * (a * c);
	t_2 = x * (y * z);
	tmp = 0.0;
	if (b <= -1.45e+119)
		tmp = b * (t * i);
	elseif (b <= -1.1e-67)
		tmp = t_1;
	elseif (b <= -2.15e-224)
		tmp = t_2;
	elseif (b <= 1.22e-285)
		tmp = t_1;
	elseif (b <= 4e-199)
		tmp = t_2;
	elseif (b <= 9.6e-119)
		tmp = t_1;
	else
		tmp = i * (t * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.45e+119], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.1e-67], t$95$1, If[LessEqual[b, -2.15e-224], t$95$2, If[LessEqual[b, 1.22e-285], t$95$1, If[LessEqual[b, 4e-199], t$95$2, If[LessEqual[b, 9.6e-119], t$95$1, N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.45000000000000004e119

   1. Initial program 69.8%

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

   3. Taylor expanded in b around inf 72.6%

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

   4. Taylor expanded in i around inf 52.6%

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

   if -1.45000000000000004e119 < b < -1.1000000000000001e-67 or -2.15e-224 < b < 1.22000000000000006e-285 or 3.99999999999999993e-199 < b < 9.60000000000000034e-119

   1. Initial program 68.0%

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

   3. Taylor expanded in i around -inf 68.0%

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

   4. Taylor expanded in x around 0 57.8%

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

      1. neg-mul-1 57.8%

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

      2. +-commutative 57.8%

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

      3. unsub-neg 57.8%

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

      4. *-commutative 57.8%

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

   6. Simplified 57.8%

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

   7. Taylor expanded in a around inf 35.7%

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

      1. *-commutative 35.7%

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

      2. *-commutative 35.7%

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

      3. associate-*l* 41.4%

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

   9. Simplified 41.4%

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

   if -1.1000000000000001e-67 < b < -2.15e-224 or 1.22000000000000006e-285 < b < 3.99999999999999993e-199

   1. Initial program 74.5%

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

   3. Taylor expanded in z around inf 38.3%

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

      1. *-commutative 38.3%

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

      2. *-commutative 38.3%

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

   5. Simplified 38.3%

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

   6. Taylor expanded in y around inf 38.0%

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

      1. *-commutative 38.0%

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

   8. Simplified 38.0%

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

   if 9.60000000000000034e-119 < b

   1. Initial program 76.6%

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

   3. Taylor expanded in j around 0 68.5%

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

   4. Taylor expanded in i around inf 30.3%

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

      1. associate-*r* 29.3%

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

      2. *-commutative 29.3%

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

      3. associate-*l* 32.3%

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

   6. Simplified 32.3%

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

4. Final simplification 39.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.45 \cdot 10^{+119}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq -1.1 \cdot 10^{-67}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;b \leq -2.15 \cdot 10^{-224}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 1.22 \cdot 10^{-285}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-199}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 9.6 \cdot 10^{-119}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 57.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -3.1 \cdot 10^{+113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -4.8 \cdot 10^{+75}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq -4 \cdot 10^{+50}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{-81}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{+67}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))))
   (if (<= b -3.1e+113)
     t_1
     (if (<= b -4.8e+75)
       (* a (- (* c j) (* x t)))
       (if (<= b -4e+50)
         (* c (- (* a j) (* z b)))
         (if (<= b 1.3e-81)
           (- (* x (* y z)) (* j (- (* y i) (* a c))))
           (if (<= b 1.55e+67) (* t (- (* b i) (* x a))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -3.1e+113) {
		tmp = t_1;
	} else if (b <= -4.8e+75) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= -4e+50) {
		tmp = c * ((a * j) - (z * b));
	} else if (b <= 1.3e-81) {
		tmp = (x * (y * z)) - (j * ((y * i) - (a * c)));
	} else if (b <= 1.55e+67) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    if (b <= (-3.1d+113)) then
        tmp = t_1
    else if (b <= (-4.8d+75)) then
        tmp = a * ((c * j) - (x * t))
    else if (b <= (-4d+50)) then
        tmp = c * ((a * j) - (z * b))
    else if (b <= 1.3d-81) then
        tmp = (x * (y * z)) - (j * ((y * i) - (a * c)))
    else if (b <= 1.55d+67) then
        tmp = t * ((b * i) - (x * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -3.1e+113) {
		tmp = t_1;
	} else if (b <= -4.8e+75) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= -4e+50) {
		tmp = c * ((a * j) - (z * b));
	} else if (b <= 1.3e-81) {
		tmp = (x * (y * z)) - (j * ((y * i) - (a * c)));
	} else if (b <= 1.55e+67) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -3.1e+113:
		tmp = t_1
	elif b <= -4.8e+75:
		tmp = a * ((c * j) - (x * t))
	elif b <= -4e+50:
		tmp = c * ((a * j) - (z * b))
	elif b <= 1.3e-81:
		tmp = (x * (y * z)) - (j * ((y * i) - (a * c)))
	elif b <= 1.55e+67:
		tmp = t * ((b * i) - (x * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -3.1e+113)
		tmp = t_1;
	elseif (b <= -4.8e+75)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (b <= -4e+50)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (b <= 1.3e-81)
		tmp = Float64(Float64(x * Float64(y * z)) - Float64(j * Float64(Float64(y * i) - Float64(a * c))));
	elseif (b <= 1.55e+67)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -3.1e+113)
		tmp = t_1;
	elseif (b <= -4.8e+75)
		tmp = a * ((c * j) - (x * t));
	elseif (b <= -4e+50)
		tmp = c * ((a * j) - (z * b));
	elseif (b <= 1.3e-81)
		tmp = (x * (y * z)) - (j * ((y * i) - (a * c)));
	elseif (b <= 1.55e+67)
		tmp = t * ((b * i) - (x * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.1e+113], t$95$1, If[LessEqual[b, -4.8e+75], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4e+50], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.3e-81], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(y * i), $MachinePrecision] - N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.55e+67], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -3.09999999999999991e113 or 1.54999999999999998e67 < b

   1. Initial program 70.7%

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

   3. Taylor expanded in b around inf 69.3%

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

   if -3.09999999999999991e113 < b < -4.8e75

   1. Initial program 80.0%

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

   3. Taylor expanded in a around inf 80.3%

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

      1. expm1-log1p-u 40.2%

         \[\leadsto a \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)\right)} \]

      2. expm1-udef 40.2%

         \[\leadsto a \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} - 1\right)} \]

      3. +-commutative 40.2%

         \[\leadsto a \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{c \cdot j + -1 \cdot \left(t \cdot x\right)}\right)} - 1\right) \]

      4. *-commutative 40.2%

         \[\leadsto a \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{j \cdot c} + -1 \cdot \left(t \cdot x\right)\right)} - 1\right) \]

      5. fma-def 40.2%

         \[\leadsto a \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\mathsf{fma}\left(j, c, -1 \cdot \left(t \cdot x\right)\right)}\right)} - 1\right) \]

      6. mul-1-neg 40.2%

         \[\leadsto a \cdot \left(e^{\mathsf{log1p}\left(\mathsf{fma}\left(j, c, \color{blue}{-t \cdot x}\right)\right)} - 1\right) \]

   5. Applied egg-rr 40.2%

      \[\leadsto a \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\mathsf{fma}\left(j, c, -t \cdot x\right)\right)} - 1\right)} \]
   6. Step-by-step derivation

      1. expm1-def 40.2%

         \[\leadsto a \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\mathsf{fma}\left(j, c, -t \cdot x\right)\right)\right)} \]

      2. expm1-log1p 80.3%

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

      3. fma-neg 80.3%

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

      4. *-commutative 80.3%

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

      5. *-commutative 80.3%

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

   7. Simplified 80.3%

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

   if -4.8e75 < b < -4.0000000000000003e50

   1. Initial program 69.8%

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

   3. Taylor expanded in c around inf 67.4%

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

   if -4.0000000000000003e50 < b < 1.2999999999999999e-81

   1. Initial program 69.9%

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

   3. Taylor expanded in b around 0 71.1%

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

   4. Taylor expanded in t around 0 67.5%

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

   if 1.2999999999999999e-81 < b < 1.54999999999999998e67

   1. Initial program 84.5%

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

   3. Taylor expanded in t around inf 66.1%

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

      1. distribute-lft-out-- 66.1%

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

      2. *-commutative 66.1%

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

   5. Simplified 66.1%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.1 \cdot 10^{+113}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -4.8 \cdot 10^{+75}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq -4 \cdot 10^{+50}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{-81}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{+67}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 25.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+108}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-101}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-261}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-242}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+136}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -3.1e+108)
   (* z (* x y))
   (if (<= y -4.5e-101)
     (* b (* t i))
     (if (<= y -1e-261)
       (* j (* a c))
       (if (<= y 4e-242)
         (* (* x t) (- a))
         (if (<= y 1.95e+136) (* z (* c (- b))) (* i (* t 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 (y <= -3.1e+108) {
		tmp = z * (x * y);
	} else if (y <= -4.5e-101) {
		tmp = b * (t * i);
	} else if (y <= -1e-261) {
		tmp = j * (a * c);
	} else if (y <= 4e-242) {
		tmp = (x * t) * -a;
	} else if (y <= 1.95e+136) {
		tmp = z * (c * -b);
	} else {
		tmp = i * (t * 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 (y <= (-3.1d+108)) then
        tmp = z * (x * y)
    else if (y <= (-4.5d-101)) then
        tmp = b * (t * i)
    else if (y <= (-1d-261)) then
        tmp = j * (a * c)
    else if (y <= 4d-242) then
        tmp = (x * t) * -a
    else if (y <= 1.95d+136) then
        tmp = z * (c * -b)
    else
        tmp = i * (t * 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 (y <= -3.1e+108) {
		tmp = z * (x * y);
	} else if (y <= -4.5e-101) {
		tmp = b * (t * i);
	} else if (y <= -1e-261) {
		tmp = j * (a * c);
	} else if (y <= 4e-242) {
		tmp = (x * t) * -a;
	} else if (y <= 1.95e+136) {
		tmp = z * (c * -b);
	} else {
		tmp = i * (t * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -3.1e+108:
		tmp = z * (x * y)
	elif y <= -4.5e-101:
		tmp = b * (t * i)
	elif y <= -1e-261:
		tmp = j * (a * c)
	elif y <= 4e-242:
		tmp = (x * t) * -a
	elif y <= 1.95e+136:
		tmp = z * (c * -b)
	else:
		tmp = i * (t * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -3.1e+108)
		tmp = Float64(z * Float64(x * y));
	elseif (y <= -4.5e-101)
		tmp = Float64(b * Float64(t * i));
	elseif (y <= -1e-261)
		tmp = Float64(j * Float64(a * c));
	elseif (y <= 4e-242)
		tmp = Float64(Float64(x * t) * Float64(-a));
	elseif (y <= 1.95e+136)
		tmp = Float64(z * Float64(c * Float64(-b)));
	else
		tmp = Float64(i * Float64(t * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -3.1e+108)
		tmp = z * (x * y);
	elseif (y <= -4.5e-101)
		tmp = b * (t * i);
	elseif (y <= -1e-261)
		tmp = j * (a * c);
	elseif (y <= 4e-242)
		tmp = (x * t) * -a;
	elseif (y <= 1.95e+136)
		tmp = z * (c * -b);
	else
		tmp = i * (t * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -3.1e+108], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.5e-101], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1e-261], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e-242], N[(N[(x * t), $MachinePrecision] * (-a)), $MachinePrecision], If[LessEqual[y, 1.95e+136], N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -3.1000000000000001e108

   1. Initial program 60.6%

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

   3. Taylor expanded in z around inf 38.4%

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

      1. *-commutative 38.4%

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

      2. *-commutative 38.4%

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

   5. Simplified 38.4%

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

   6. Taylor expanded in y around inf 40.8%

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

      1. *-commutative 40.8%

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

      2. *-commutative 40.8%

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

      3. associate-*l* 42.8%

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

      4. *-commutative 42.8%

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

   8. Simplified 42.8%

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

   if -3.1000000000000001e108 < y < -4.4999999999999998e-101

   1. Initial program 76.8%

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

   3. Taylor expanded in b around inf 52.4%

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

   4. Taylor expanded in i around inf 36.6%

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

   if -4.4999999999999998e-101 < y < -9.99999999999999984e-262

   1. Initial program 81.5%

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

   3. Taylor expanded in i around -inf 79.5%

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

   4. Taylor expanded in x around 0 69.9%

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

      1. neg-mul-1 69.9%

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

      2. +-commutative 69.9%

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

      3. unsub-neg 69.9%

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

      4. *-commutative 69.9%

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

   6. Simplified 69.9%

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

   7. Taylor expanded in a around inf 35.2%

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

      1. *-commutative 35.2%

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

      2. *-commutative 35.2%

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

      3. associate-*l* 37.2%

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

   9. Simplified 37.2%

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

   if -9.99999999999999984e-262 < y < 4e-242

   1. Initial program 72.8%

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

   3. Taylor expanded in t around inf 68.9%

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

      1. distribute-lft-out-- 68.9%

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

      2. *-commutative 68.9%

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

   5. Simplified 68.9%

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

   6. Taylor expanded in a around inf 59.9%

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

      1. mul-1-neg 59.9%

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

      2. distribute-rgt-neg-in 59.9%

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

      3. distribute-rgt-neg-in 59.9%

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

   8. Simplified 59.9%

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

   if 4e-242 < y < 1.9500000000000001e136

   1. Initial program 76.1%

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

   3. Taylor expanded in z around inf 50.1%

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

      1. *-commutative 50.1%

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

      2. *-commutative 50.1%

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

   5. Simplified 50.1%

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

   6. Taylor expanded in y around 0 40.3%

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

      1. neg-mul-1 40.3%

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

      2. distribute-rgt-neg-in 40.3%

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

   8. Simplified 40.3%

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

   if 1.9500000000000001e136 < y

   1. Initial program 66.3%

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

   3. Taylor expanded in j around 0 58.7%

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

   4. Taylor expanded in i around inf 28.0%

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

      1. associate-*r* 28.1%

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

      2. *-commutative 28.1%

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

      3. associate-*l* 32.7%

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

   6. Simplified 32.7%

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

4. Final simplification 40.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+108}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-101}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-261}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-242}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+136}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 30.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{if}\;z \leq -1.45 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.1 \cdot 10^{-33}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-198}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-227}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{+109}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* z c) (- b))))
   (if (<= z -1.45e+49)
     t_1
     (if (<= z -6.1e-33)
       (* i (* t b))
       (if (<= z -5.2e-198)
         (* i (* y (- j)))
         (if (<= z -7.6e-227)
           (* a (* c j))
           (if (<= z 1.42e+109) (* b (* t i)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (z * c) * -b;
	double tmp;
	if (z <= -1.45e+49) {
		tmp = t_1;
	} else if (z <= -6.1e-33) {
		tmp = i * (t * b);
	} else if (z <= -5.2e-198) {
		tmp = i * (y * -j);
	} else if (z <= -7.6e-227) {
		tmp = a * (c * j);
	} else if (z <= 1.42e+109) {
		tmp = b * (t * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * c) * -b
    if (z <= (-1.45d+49)) then
        tmp = t_1
    else if (z <= (-6.1d-33)) then
        tmp = i * (t * b)
    else if (z <= (-5.2d-198)) then
        tmp = i * (y * -j)
    else if (z <= (-7.6d-227)) then
        tmp = a * (c * j)
    else if (z <= 1.42d+109) then
        tmp = b * (t * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (z * c) * -b;
	double tmp;
	if (z <= -1.45e+49) {
		tmp = t_1;
	} else if (z <= -6.1e-33) {
		tmp = i * (t * b);
	} else if (z <= -5.2e-198) {
		tmp = i * (y * -j);
	} else if (z <= -7.6e-227) {
		tmp = a * (c * j);
	} else if (z <= 1.42e+109) {
		tmp = b * (t * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (z * c) * -b
	tmp = 0
	if z <= -1.45e+49:
		tmp = t_1
	elif z <= -6.1e-33:
		tmp = i * (t * b)
	elif z <= -5.2e-198:
		tmp = i * (y * -j)
	elif z <= -7.6e-227:
		tmp = a * (c * j)
	elif z <= 1.42e+109:
		tmp = b * (t * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(z * c) * Float64(-b))
	tmp = 0.0
	if (z <= -1.45e+49)
		tmp = t_1;
	elseif (z <= -6.1e-33)
		tmp = Float64(i * Float64(t * b));
	elseif (z <= -5.2e-198)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (z <= -7.6e-227)
		tmp = Float64(a * Float64(c * j));
	elseif (z <= 1.42e+109)
		tmp = Float64(b * Float64(t * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (z * c) * -b;
	tmp = 0.0;
	if (z <= -1.45e+49)
		tmp = t_1;
	elseif (z <= -6.1e-33)
		tmp = i * (t * b);
	elseif (z <= -5.2e-198)
		tmp = i * (y * -j);
	elseif (z <= -7.6e-227)
		tmp = a * (c * j);
	elseif (z <= 1.42e+109)
		tmp = b * (t * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(z * c), $MachinePrecision] * (-b)), $MachinePrecision]}, If[LessEqual[z, -1.45e+49], t$95$1, If[LessEqual[z, -6.1e-33], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.2e-198], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.6e-227], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.42e+109], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.45e49 or 1.4200000000000001e109 < z

   1. Initial program 56.0%

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

   3. Taylor expanded in b around inf 45.9%

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

   4. Taylor expanded in i around 0 46.3%

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

      1. associate-*r* 46.3%

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

      2. neg-mul-1 46.3%

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

   6. Simplified 46.3%

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

   if -1.45e49 < z < -6.1000000000000001e-33

   1. Initial program 82.0%

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

   3. Taylor expanded in j around 0 74.1%

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

   4. Taylor expanded in i around inf 42.5%

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

      1. associate-*r* 42.5%

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

      2. *-commutative 42.5%

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

      3. associate-*l* 46.7%

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

   6. Simplified 46.7%

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

   if -6.1000000000000001e-33 < z < -5.20000000000000014e-198

   1. Initial program 88.1%

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

   3. Taylor expanded in i around inf 49.0%

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

      1. distribute-lft-out-- 49.0%

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

      2. *-commutative 49.0%

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

   5. Simplified 49.0%

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

   6. Taylor expanded in j around inf 38.2%

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

      1. associate-*r* 38.2%

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

      2. neg-mul-1 38.2%

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

      3. *-commutative 38.2%

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

   8. Simplified 38.2%

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

   if -5.20000000000000014e-198 < z < -7.60000000000000019e-227

   1. Initial program 83.1%

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

   3. Taylor expanded in a around inf 84.4%

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

   4. Taylor expanded in t around 0 84.0%

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

   if -7.60000000000000019e-227 < z < 1.4200000000000001e109

   1. Initial program 81.2%

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

   3. Taylor expanded in b around inf 42.6%

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

   4. Taylor expanded in i around inf 33.8%

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

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+49}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;z \leq -6.1 \cdot 10^{-33}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-198}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-227}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{+109}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 41.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot c\right) \cdot \left(-b\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -3.6 \cdot 10^{-55}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-249}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-192}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* z c) (- b))) (t_2 (* a (- (* c j) (* x t)))))
   (if (<= a -3.6e-55)
     t_2
     (if (<= a 3e-249)
       t_1
       (if (<= a 1.45e-192) (* i (* y (- j))) (if (<= a 2.1e-26) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (z * c) * -b;
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -3.6e-55) {
		tmp = t_2;
	} else if (a <= 3e-249) {
		tmp = t_1;
	} else if (a <= 1.45e-192) {
		tmp = i * (y * -j);
	} else if (a <= 2.1e-26) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z * c) * -b
    t_2 = a * ((c * j) - (x * t))
    if (a <= (-3.6d-55)) then
        tmp = t_2
    else if (a <= 3d-249) then
        tmp = t_1
    else if (a <= 1.45d-192) then
        tmp = i * (y * -j)
    else if (a <= 2.1d-26) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (z * c) * -b;
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -3.6e-55) {
		tmp = t_2;
	} else if (a <= 3e-249) {
		tmp = t_1;
	} else if (a <= 1.45e-192) {
		tmp = i * (y * -j);
	} else if (a <= 2.1e-26) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (z * c) * -b
	t_2 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -3.6e-55:
		tmp = t_2
	elif a <= 3e-249:
		tmp = t_1
	elif a <= 1.45e-192:
		tmp = i * (y * -j)
	elif a <= 2.1e-26:
		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(z * c) * Float64(-b))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -3.6e-55)
		tmp = t_2;
	elseif (a <= 3e-249)
		tmp = t_1;
	elseif (a <= 1.45e-192)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (a <= 2.1e-26)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (z * c) * -b;
	t_2 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -3.6e-55)
		tmp = t_2;
	elseif (a <= 3e-249)
		tmp = t_1;
	elseif (a <= 1.45e-192)
		tmp = i * (y * -j);
	elseif (a <= 2.1e-26)
		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[(z * c), $MachinePrecision] * (-b)), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.6e-55], t$95$2, If[LessEqual[a, 3e-249], t$95$1, If[LessEqual[a, 1.45e-192], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.1e-26], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.6000000000000001e-55 or 2.10000000000000008e-26 < a

   1. Initial program 66.7%

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

   3. Taylor expanded in a around inf 55.0%

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

      1. expm1-log1p-u 29.3%

         \[\leadsto a \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)\right)} \]

      2. expm1-udef 26.8%

         \[\leadsto a \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} - 1\right)} \]

      3. +-commutative 26.8%

         \[\leadsto a \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{c \cdot j + -1 \cdot \left(t \cdot x\right)}\right)} - 1\right) \]

      4. *-commutative 26.8%

         \[\leadsto a \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{j \cdot c} + -1 \cdot \left(t \cdot x\right)\right)} - 1\right) \]

      5. fma-def 26.8%

         \[\leadsto a \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\mathsf{fma}\left(j, c, -1 \cdot \left(t \cdot x\right)\right)}\right)} - 1\right) \]

      6. mul-1-neg 26.8%

         \[\leadsto a \cdot \left(e^{\mathsf{log1p}\left(\mathsf{fma}\left(j, c, \color{blue}{-t \cdot x}\right)\right)} - 1\right) \]

   5. Applied egg-rr 26.8%

      \[\leadsto a \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\mathsf{fma}\left(j, c, -t \cdot x\right)\right)} - 1\right)} \]
   6. Step-by-step derivation

      1. expm1-def 29.3%

         \[\leadsto a \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\mathsf{fma}\left(j, c, -t \cdot x\right)\right)\right)} \]

      2. expm1-log1p 55.0%

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

      3. fma-neg 55.0%

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

      4. *-commutative 55.0%

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

      5. *-commutative 55.0%

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

   7. Simplified 55.0%

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

   if -3.6000000000000001e-55 < a < 3.00000000000000004e-249 or 1.45000000000000008e-192 < a < 2.10000000000000008e-26

   1. Initial program 80.3%

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

   3. Taylor expanded in b around inf 62.7%

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

   4. Taylor expanded in i around 0 40.5%

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

      1. associate-*r* 40.5%

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

      2. neg-mul-1 40.5%

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

   6. Simplified 40.5%

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

   if 3.00000000000000004e-249 < a < 1.45000000000000008e-192

   1. Initial program 82.2%

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

   3. Taylor expanded in i around inf 47.5%

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

      1. distribute-lft-out-- 47.5%

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

      2. *-commutative 47.5%

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

   5. Simplified 47.5%

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

   6. Taylor expanded in j around inf 47.4%

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

      1. associate-*r* 47.4%

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

      2. neg-mul-1 47.4%

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

      3. *-commutative 47.4%

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

   8. Simplified 47.4%

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

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{-55}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-249}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-192}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-26}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 48.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -9 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-159}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+181}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+229}:\\ \;\;\;\;-t \cdot \left(x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -9e+38)
     t_1
     (if (<= a 1.25e-159)
       (* b (- (* t i) (* z c)))
       (if (<= a 4e+181)
         (* c (- (* a j) (* z b)))
         (if (<= a 1.65e+229) (- (* t (* x a))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -9e+38) {
		tmp = t_1;
	} else if (a <= 1.25e-159) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 4e+181) {
		tmp = c * ((a * j) - (z * b));
	} else if (a <= 1.65e+229) {
		tmp = -(t * (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (a <= (-9d+38)) then
        tmp = t_1
    else if (a <= 1.25d-159) then
        tmp = b * ((t * i) - (z * c))
    else if (a <= 4d+181) then
        tmp = c * ((a * j) - (z * b))
    else if (a <= 1.65d+229) then
        tmp = -(t * (x * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -9e+38) {
		tmp = t_1;
	} else if (a <= 1.25e-159) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 4e+181) {
		tmp = c * ((a * j) - (z * b));
	} else if (a <= 1.65e+229) {
		tmp = -(t * (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -9e+38:
		tmp = t_1
	elif a <= 1.25e-159:
		tmp = b * ((t * i) - (z * c))
	elif a <= 4e+181:
		tmp = c * ((a * j) - (z * b))
	elif a <= 1.65e+229:
		tmp = -(t * (x * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -9e+38)
		tmp = t_1;
	elseif (a <= 1.25e-159)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (a <= 4e+181)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (a <= 1.65e+229)
		tmp = Float64(-Float64(t * Float64(x * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -9e+38)
		tmp = t_1;
	elseif (a <= 1.25e-159)
		tmp = b * ((t * i) - (z * c));
	elseif (a <= 4e+181)
		tmp = c * ((a * j) - (z * b));
	elseif (a <= 1.65e+229)
		tmp = -(t * (x * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9e+38], t$95$1, If[LessEqual[a, 1.25e-159], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4e+181], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.65e+229], (-N[(t * N[(x * a), $MachinePrecision]), $MachinePrecision]), t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -8.99999999999999961e38 or 1.65e229 < a

   1. Initial program 61.0%

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

   3. Taylor expanded in a around inf 66.2%

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

      1. expm1-log1p-u 33.1%

         \[\leadsto a \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)\right)} \]

      2. expm1-udef 28.8%

         \[\leadsto a \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} - 1\right)} \]

      3. +-commutative 28.8%

         \[\leadsto a \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{c \cdot j + -1 \cdot \left(t \cdot x\right)}\right)} - 1\right) \]

      4. *-commutative 28.8%

         \[\leadsto a \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{j \cdot c} + -1 \cdot \left(t \cdot x\right)\right)} - 1\right) \]

      5. fma-def 28.8%

         \[\leadsto a \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\mathsf{fma}\left(j, c, -1 \cdot \left(t \cdot x\right)\right)}\right)} - 1\right) \]

      6. mul-1-neg 28.8%

         \[\leadsto a \cdot \left(e^{\mathsf{log1p}\left(\mathsf{fma}\left(j, c, \color{blue}{-t \cdot x}\right)\right)} - 1\right) \]

   5. Applied egg-rr 28.8%

      \[\leadsto a \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\mathsf{fma}\left(j, c, -t \cdot x\right)\right)} - 1\right)} \]
   6. Step-by-step derivation

      1. expm1-def 33.1%

         \[\leadsto a \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\mathsf{fma}\left(j, c, -t \cdot x\right)\right)\right)} \]

      2. expm1-log1p 66.2%

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

      3. fma-neg 66.2%

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

      4. *-commutative 66.2%

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

      5. *-commutative 66.2%

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

   7. Simplified 66.2%

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

   if -8.99999999999999961e38 < a < 1.25000000000000008e-159

   1. Initial program 82.5%

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

   3. Taylor expanded in b around inf 59.6%

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

   if 1.25000000000000008e-159 < a < 3.9999999999999997e181

   1. Initial program 75.6%

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

   3. Taylor expanded in c around inf 52.5%

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

   if 3.9999999999999997e181 < a < 1.65e229

   1. Initial program 44.3%

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

   3. Taylor expanded in j around 0 44.3%

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

   4. Taylor expanded in a around inf 46.6%

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

      1. associate-*r* 46.6%

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

      2. *-commutative 46.6%

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

      3. associate-*r* 57.2%

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

      4. associate-*r* 57.2%

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

      5. mul-1-neg 57.2%

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

      6. distribute-rgt-neg-in 57.2%

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

   6. Simplified 57.2%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{+38}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-159}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+181}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+229}:\\ \;\;\;\;-t \cdot \left(x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 49.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -3.9 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{-244}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-192}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 3900000000:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -3.9e+38)
     t_1
     (if (<= a 2.55e-244)
       (* b (- (* t i) (* z c)))
       (if (<= a 1.5e-192)
         (* j (- (* a c) (* y i)))
         (if (<= a 3900000000.0) (* c (- (* a 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 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -3.9e+38) {
		tmp = t_1;
	} else if (a <= 2.55e-244) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 1.5e-192) {
		tmp = j * ((a * c) - (y * i));
	} else if (a <= 3900000000.0) {
		tmp = c * ((a * 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 = a * ((c * j) - (x * t))
    if (a <= (-3.9d+38)) then
        tmp = t_1
    else if (a <= 2.55d-244) then
        tmp = b * ((t * i) - (z * c))
    else if (a <= 1.5d-192) then
        tmp = j * ((a * c) - (y * i))
    else if (a <= 3900000000.0d0) then
        tmp = c * ((a * 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 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -3.9e+38) {
		tmp = t_1;
	} else if (a <= 2.55e-244) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 1.5e-192) {
		tmp = j * ((a * c) - (y * i));
	} else if (a <= 3900000000.0) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -3.9e+38:
		tmp = t_1
	elif a <= 2.55e-244:
		tmp = b * ((t * i) - (z * c))
	elif a <= 1.5e-192:
		tmp = j * ((a * c) - (y * i))
	elif a <= 3900000000.0:
		tmp = c * ((a * j) - (z * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -3.9e+38)
		tmp = t_1;
	elseif (a <= 2.55e-244)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (a <= 1.5e-192)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (a <= 3900000000.0)
		tmp = Float64(c * Float64(Float64(a * 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 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -3.9e+38)
		tmp = t_1;
	elseif (a <= 2.55e-244)
		tmp = b * ((t * i) - (z * c));
	elseif (a <= 1.5e-192)
		tmp = j * ((a * c) - (y * i));
	elseif (a <= 3900000000.0)
		tmp = c * ((a * 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[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.9e+38], t$95$1, If[LessEqual[a, 2.55e-244], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.5e-192], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3900000000.0], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.90000000000000023e38 or 3.9e9 < a

   1. Initial program 63.9%

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

   3. Taylor expanded in a around inf 60.7%

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

      1. expm1-log1p-u 31.6%

         \[\leadsto a \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)\right)} \]

      2. expm1-udef 28.6%

         \[\leadsto a \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} - 1\right)} \]

      3. +-commutative 28.6%

         \[\leadsto a \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{c \cdot j + -1 \cdot \left(t \cdot x\right)}\right)} - 1\right) \]

      4. *-commutative 28.6%

         \[\leadsto a \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{j \cdot c} + -1 \cdot \left(t \cdot x\right)\right)} - 1\right) \]

      5. fma-def 28.6%

         \[\leadsto a \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\mathsf{fma}\left(j, c, -1 \cdot \left(t \cdot x\right)\right)}\right)} - 1\right) \]

      6. mul-1-neg 28.6%

         \[\leadsto a \cdot \left(e^{\mathsf{log1p}\left(\mathsf{fma}\left(j, c, \color{blue}{-t \cdot x}\right)\right)} - 1\right) \]

   5. Applied egg-rr 28.6%

      \[\leadsto a \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\mathsf{fma}\left(j, c, -t \cdot x\right)\right)} - 1\right)} \]
   6. Step-by-step derivation

      1. expm1-def 31.6%

         \[\leadsto a \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\mathsf{fma}\left(j, c, -t \cdot x\right)\right)\right)} \]

      2. expm1-log1p 60.7%

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

      3. fma-neg 60.7%

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

      4. *-commutative 60.7%

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

      5. *-commutative 60.7%

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

   7. Simplified 60.7%

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

   if -3.90000000000000023e38 < a < 2.5499999999999999e-244

   1. Initial program 81.7%

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

   3. Taylor expanded in b around inf 63.7%

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

   if 2.5499999999999999e-244 < a < 1.5e-192

   1. Initial program 82.2%

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

   3. Taylor expanded in b around 0 80.4%

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

   4. Taylor expanded in j around inf 64.6%

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

   if 1.5e-192 < a < 3.9e9

   1. Initial program 76.7%

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

   3. Taylor expanded in c around inf 50.4%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.9 \cdot 10^{+38}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{-244}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-192}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 3900000000:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 26.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+32}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -6.3 \cdot 10^{-257}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-242}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+137}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -1.85e+32)
   (* z (* x y))
   (if (<= y -6.3e-257)
     (* (* z c) (- b))
     (if (<= y 5.5e-242)
       (* (* x t) (- a))
       (if (<= y 9e+137) (* z (* c (- b))) (* i (* t 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 (y <= -1.85e+32) {
		tmp = z * (x * y);
	} else if (y <= -6.3e-257) {
		tmp = (z * c) * -b;
	} else if (y <= 5.5e-242) {
		tmp = (x * t) * -a;
	} else if (y <= 9e+137) {
		tmp = z * (c * -b);
	} else {
		tmp = i * (t * 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 (y <= (-1.85d+32)) then
        tmp = z * (x * y)
    else if (y <= (-6.3d-257)) then
        tmp = (z * c) * -b
    else if (y <= 5.5d-242) then
        tmp = (x * t) * -a
    else if (y <= 9d+137) then
        tmp = z * (c * -b)
    else
        tmp = i * (t * 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 (y <= -1.85e+32) {
		tmp = z * (x * y);
	} else if (y <= -6.3e-257) {
		tmp = (z * c) * -b;
	} else if (y <= 5.5e-242) {
		tmp = (x * t) * -a;
	} else if (y <= 9e+137) {
		tmp = z * (c * -b);
	} else {
		tmp = i * (t * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -1.85e+32:
		tmp = z * (x * y)
	elif y <= -6.3e-257:
		tmp = (z * c) * -b
	elif y <= 5.5e-242:
		tmp = (x * t) * -a
	elif y <= 9e+137:
		tmp = z * (c * -b)
	else:
		tmp = i * (t * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -1.85e+32)
		tmp = Float64(z * Float64(x * y));
	elseif (y <= -6.3e-257)
		tmp = Float64(Float64(z * c) * Float64(-b));
	elseif (y <= 5.5e-242)
		tmp = Float64(Float64(x * t) * Float64(-a));
	elseif (y <= 9e+137)
		tmp = Float64(z * Float64(c * Float64(-b)));
	else
		tmp = Float64(i * Float64(t * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -1.85e+32)
		tmp = z * (x * y);
	elseif (y <= -6.3e-257)
		tmp = (z * c) * -b;
	elseif (y <= 5.5e-242)
		tmp = (x * t) * -a;
	elseif (y <= 9e+137)
		tmp = z * (c * -b);
	else
		tmp = i * (t * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -1.85e+32], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.3e-257], N[(N[(z * c), $MachinePrecision] * (-b)), $MachinePrecision], If[LessEqual[y, 5.5e-242], N[(N[(x * t), $MachinePrecision] * (-a)), $MachinePrecision], If[LessEqual[y, 9e+137], N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.85e32

   1. Initial program 61.8%

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

   3. Taylor expanded in z around inf 41.1%

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

      1. *-commutative 41.1%

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

      2. *-commutative 41.1%

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

   5. Simplified 41.1%

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

   6. Taylor expanded in y around inf 38.0%

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

      1. *-commutative 38.0%

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

      2. *-commutative 38.0%

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

      3. associate-*l* 41.3%

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

      4. *-commutative 41.3%

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

   8. Simplified 41.3%

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

   if -1.85e32 < y < -6.29999999999999993e-257

   1. Initial program 81.8%

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

   3. Taylor expanded in b around inf 54.0%

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

   4. Taylor expanded in i around 0 33.9%

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

      1. associate-*r* 33.9%

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

      2. neg-mul-1 33.9%

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

   6. Simplified 33.9%

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

   if -6.29999999999999993e-257 < y < 5.4999999999999998e-242

   1. Initial program 72.0%

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

   3. Taylor expanded in t around inf 65.0%

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

      1. distribute-lft-out-- 65.0%

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

      2. *-commutative 65.0%

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

   5. Simplified 65.0%

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

   6. Taylor expanded in a around inf 52.9%

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

      1. mul-1-neg 52.9%

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

      2. distribute-rgt-neg-in 52.9%

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

      3. distribute-rgt-neg-in 52.9%

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

   8. Simplified 52.9%

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

   if 5.4999999999999998e-242 < y < 9.0000000000000003e137

   1. Initial program 76.1%

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

   3. Taylor expanded in z around inf 50.1%

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

      1. *-commutative 50.1%

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

      2. *-commutative 50.1%

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

   5. Simplified 50.1%

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

   6. Taylor expanded in y around 0 40.3%

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

      1. neg-mul-1 40.3%

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

      2. distribute-rgt-neg-in 40.3%

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

   8. Simplified 40.3%

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

   if 9.0000000000000003e137 < y

   1. Initial program 66.3%

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

   3. Taylor expanded in j around 0 58.7%

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

   4. Taylor expanded in i around inf 28.0%

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

      1. associate-*r* 28.1%

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

      2. *-commutative 28.1%

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

      3. associate-*l* 32.7%

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

   6. Simplified 32.7%

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

4. Final simplification 38.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+32}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -6.3 \cdot 10^{-257}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-242}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+137}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 50.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{+38} \lor \neg \left(a \leq 9.2 \cdot 10^{-27}\right):\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -1.4e+38) (not (<= a 9.2e-27)))
   (* a (- (* c j) (* x t)))
   (* b (- (* t i) (* z c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -1.4e+38) || !(a <= 9.2e-27)) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = b * ((t * i) - (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((a <= (-1.4d+38)) .or. (.not. (a <= 9.2d-27))) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = b * ((t * i) - (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -1.4e+38) || !(a <= 9.2e-27)) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = b * ((t * i) - (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (a <= -1.4e+38) or not (a <= 9.2e-27):
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = b * ((t * i) - (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -1.4e+38) || !(a <= 9.2e-27))
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((a <= -1.4e+38) || ~((a <= 9.2e-27)))
		tmp = a * ((c * j) - (x * t));
	else
		tmp = b * ((t * i) - (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -1.4e+38], N[Not[LessEqual[a, 9.2e-27]], $MachinePrecision]], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.4e38 or 9.1999999999999998e-27 < a

   1. Initial program 63.8%

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

   3. Taylor expanded in a around inf 59.3%

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

      1. expm1-log1p-u 30.5%

         \[\leadsto a \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)\right)} \]

      2. expm1-udef 27.6%

         \[\leadsto a \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} - 1\right)} \]

      3. +-commutative 27.6%

         \[\leadsto a \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{c \cdot j + -1 \cdot \left(t \cdot x\right)}\right)} - 1\right) \]

      4. *-commutative 27.6%

         \[\leadsto a \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{j \cdot c} + -1 \cdot \left(t \cdot x\right)\right)} - 1\right) \]

      5. fma-def 27.6%

         \[\leadsto a \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\mathsf{fma}\left(j, c, -1 \cdot \left(t \cdot x\right)\right)}\right)} - 1\right) \]

      6. mul-1-neg 27.6%

         \[\leadsto a \cdot \left(e^{\mathsf{log1p}\left(\mathsf{fma}\left(j, c, \color{blue}{-t \cdot x}\right)\right)} - 1\right) \]

   5. Applied egg-rr 27.6%

      \[\leadsto a \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\mathsf{fma}\left(j, c, -t \cdot x\right)\right)} - 1\right)} \]
   6. Step-by-step derivation

      1. expm1-def 30.5%

         \[\leadsto a \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\mathsf{fma}\left(j, c, -t \cdot x\right)\right)\right)} \]

      2. expm1-log1p 59.3%

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

      3. fma-neg 59.3%

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

      4. *-commutative 59.3%

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

      5. *-commutative 59.3%

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

   7. Simplified 59.3%

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

   if -1.4e38 < a < 9.1999999999999998e-27

   1. Initial program 81.2%

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

   3. Taylor expanded in b around inf 57.1%

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

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{+38} \lor \neg \left(a \leq 9.2 \cdot 10^{-27}\right):\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 28.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{+116} \lor \neg \left(b \leq 7.2 \cdot 10^{-119}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -9.5e+116) (not (<= b 7.2e-119))) (* b (* t i)) (* a (* c j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -9.5e+116) || !(b <= 7.2e-119)) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-9.5d+116)) .or. (.not. (b <= 7.2d-119))) then
        tmp = b * (t * i)
    else
        tmp = a * (c * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -9.5e+116) || !(b <= 7.2e-119)) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -9.5e+116) or not (b <= 7.2e-119):
		tmp = b * (t * i)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -9.5e+116) || !(b <= 7.2e-119))
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(a * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -9.5e+116) || ~((b <= 7.2e-119)))
		tmp = b * (t * i);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -9.5e+116], N[Not[LessEqual[b, 7.2e-119]], $MachinePrecision]], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -9.5000000000000004e116 or 7.2e-119 < b

   1. Initial program 74.5%

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

   3. Taylor expanded in b around inf 58.6%

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

   4. Taylor expanded in i around inf 37.3%

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

   if -9.5000000000000004e116 < b < 7.2e-119

   1. Initial program 70.1%

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

   3. Taylor expanded in a around inf 46.1%

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

   4. Taylor expanded in t around 0 27.5%

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

4. Final simplification 32.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{+116} \lor \neg \left(b \leq 7.2 \cdot 10^{-119}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 28.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{+117}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-119}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -8.2e+117)
   (* b (* t i))
   (if (<= b 3.8e-119) (* a (* c j)) (* i (* t b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -8.2e+117) {
		tmp = b * (t * i);
	} else if (b <= 3.8e-119) {
		tmp = a * (c * j);
	} else {
		tmp = i * (t * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-8.2d+117)) then
        tmp = b * (t * i)
    else if (b <= 3.8d-119) then
        tmp = a * (c * j)
    else
        tmp = i * (t * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -8.2e+117) {
		tmp = b * (t * i);
	} else if (b <= 3.8e-119) {
		tmp = a * (c * j);
	} else {
		tmp = i * (t * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -8.2e+117:
		tmp = b * (t * i)
	elif b <= 3.8e-119:
		tmp = a * (c * j)
	else:
		tmp = i * (t * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -8.2e+117)
		tmp = Float64(b * Float64(t * i));
	elseif (b <= 3.8e-119)
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(i * Float64(t * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -8.2e+117)
		tmp = b * (t * i);
	elseif (b <= 3.8e-119)
		tmp = a * (c * j);
	else
		tmp = i * (t * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -8.2e+117], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.8e-119], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.1999999999999999e117

   1. Initial program 69.8%

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

   3. Taylor expanded in b around inf 72.6%

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

   4. Taylor expanded in i around inf 52.6%

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

   if -8.1999999999999999e117 < b < 3.79999999999999975e-119

   1. Initial program 70.1%

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

   3. Taylor expanded in a around inf 46.1%

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

   4. Taylor expanded in t around 0 27.5%

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

   if 3.79999999999999975e-119 < b

   1. Initial program 76.6%

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

   3. Taylor expanded in j around 0 68.5%

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

   4. Taylor expanded in i around inf 30.3%

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

      1. associate-*r* 29.3%

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

      2. *-commutative 29.3%

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

      3. associate-*l* 32.3%

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

   6. Simplified 32.3%

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

4. Final simplification 33.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{+117}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-119}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 28.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{+116}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-118}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -9.5e+116)
   (* b (* t i))
   (if (<= b 1.4e-118) (* j (* a c)) (* i (* t b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -9.5e+116) {
		tmp = b * (t * i);
	} else if (b <= 1.4e-118) {
		tmp = j * (a * c);
	} else {
		tmp = i * (t * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-9.5d+116)) then
        tmp = b * (t * i)
    else if (b <= 1.4d-118) then
        tmp = j * (a * c)
    else
        tmp = i * (t * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -9.5e+116) {
		tmp = b * (t * i);
	} else if (b <= 1.4e-118) {
		tmp = j * (a * c);
	} else {
		tmp = i * (t * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -9.5e+116:
		tmp = b * (t * i)
	elif b <= 1.4e-118:
		tmp = j * (a * c)
	else:
		tmp = i * (t * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -9.5e+116)
		tmp = Float64(b * Float64(t * i));
	elseif (b <= 1.4e-118)
		tmp = Float64(j * Float64(a * c));
	else
		tmp = Float64(i * Float64(t * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -9.5e+116)
		tmp = b * (t * i);
	elseif (b <= 1.4e-118)
		tmp = j * (a * c);
	else
		tmp = i * (t * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -9.5e+116], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.4e-118], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.5000000000000004e116

   1. Initial program 69.8%

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

   3. Taylor expanded in b around inf 72.6%

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

   4. Taylor expanded in i around inf 52.6%

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

   if -9.5000000000000004e116 < b < 1.4e-118

   1. Initial program 70.1%

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

   3. Taylor expanded in i around -inf 69.4%

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

   4. Taylor expanded in x around 0 53.6%

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

      1. neg-mul-1 53.6%

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

      2. +-commutative 53.6%

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

      3. unsub-neg 53.6%

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

      4. *-commutative 53.6%

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

   6. Simplified 53.6%

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

   7. Taylor expanded in a around inf 27.5%

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

      1. *-commutative 27.5%

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

      2. *-commutative 27.5%

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

      3. associate-*l* 31.3%

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

   9. Simplified 31.3%

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

   if 1.4e-118 < b

   1. Initial program 76.6%

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

   3. Taylor expanded in j around 0 68.5%

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

   4. Taylor expanded in i around inf 30.3%

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

      1. associate-*r* 29.3%

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

      2. *-commutative 29.3%

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

      3. associate-*l* 32.3%

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

   6. Simplified 32.3%

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

4. Final simplification 35.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{+116}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-118}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 22.4% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(c \cdot j\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 72.5%

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

3. Taylor expanded in a around inf 39.2%

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

4. Taylor expanded in t around 0 20.0%

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

5. Final simplification 20.0%

   \[\leadsto a \cdot \left(c \cdot j\right) \]
6. Add Preprocessing

Developer target: 60.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right)\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + t_1\\ \mathbf{if}\;x < -1.469694296777705 \cdot 10^{-64}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x < 3.2113527362226803 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - t_1\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* c a) (* y i))))
        (t_2
         (+
          (-
           (* x (- (* y z) (* t a)))
           (/
            (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0)))
            (+ (* c z) (* t i))))
          t_1)))
   (if (< x -1.469694296777705e-64)
     t_2
     (if (< x 3.2113527362226803e-147)
       (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) t_1))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (pow((c * z), 2.0) - pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((c * a) - (y * i))
    t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ** 2.0d0) - ((t * i) ** 2.0d0))) / ((c * z) + (t * i)))) + t_1
    if (x < (-1.469694296777705d-64)) then
        tmp = t_2
    else if (x < 3.2113527362226803d-147) then
        tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (Math.pow((c * z), 2.0) - Math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((c * a) - (y * i))
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (math.pow((c * z), 2.0) - math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1
	tmp = 0
	if x < -1.469694296777705e-64:
		tmp = t_2
	elif x < 3.2113527362226803e-147:
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(c * a) - Float64(y * i)))
	t_2 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(Float64(b * Float64((Float64(c * z) ^ 2.0) - (Float64(t * i) ^ 2.0))) / Float64(Float64(c * z) + Float64(t * i)))) + t_1)
	tmp = 0.0
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = Float64(Float64(Float64(Float64(b * i) - Float64(x * a)) * t) - Float64(Float64(z * Float64(c * b)) - t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((c * a) - (y * i));
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ^ 2.0) - ((t * i) ^ 2.0))) / ((c * z) + (t * i)))) + t_1;
	tmp = 0.0;
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[Power[N[(c * z), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(t * i), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * z), $MachinePrecision] + N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[Less[x, -1.469694296777705e-64], t$95$2, If[Less[x, 3.2113527362226803e-147], N[(N[(N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] - N[(N[(z * N[(c * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024020 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (if (< x -1.469694296777705e-64) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 3.2113527362226803e-147) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i))))))

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