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

Percentage Accurate: 73.8% → 81.8%

Time: 30.3s

Alternatives: 23

Speedup: 0.5×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.8% 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: 81.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 89.7%

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

   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. Taylor expanded in z around inf 57.1%

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

4. Final simplification 83.2%

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

Alternative 2: 64.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -6.5 \cdot 10^{+145}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -4.5:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{-83}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq 195 \lor \neg \left(b \leq 3.1 \cdot 10^{+119}\right) \land b \leq 3.1 \cdot 10^{+158}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* j (- (* a c) (* y i))) (* x (- (* y z) (* t a)))))
        (t_2 (* b (- (* t i) (* z c)))))
   (if (<= b -6.5e+145)
     t_2
     (if (<= b -4.5)
       t_1
       (if (<= b -8.5e-83)
         (+ (* y (- (* x z) (* i j))) (* b (* t i)))
         (if (or (<= b 195.0) (and (not (<= b 3.1e+119)) (<= b 3.1e+158)))
           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 * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -6.5e+145) {
		tmp = t_2;
	} else if (b <= -4.5) {
		tmp = t_1;
	} else if (b <= -8.5e-83) {
		tmp = (y * ((x * z) - (i * j))) + (b * (t * i));
	} else if ((b <= 195.0) || (!(b <= 3.1e+119) && (b <= 3.1e+158))) {
		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 = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
    t_2 = b * ((t * i) - (z * c))
    if (b <= (-6.5d+145)) then
        tmp = t_2
    else if (b <= (-4.5d0)) then
        tmp = t_1
    else if (b <= (-8.5d-83)) then
        tmp = (y * ((x * z) - (i * j))) + (b * (t * i))
    else if ((b <= 195.0d0) .or. (.not. (b <= 3.1d+119)) .and. (b <= 3.1d+158)) 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 = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -6.5e+145) {
		tmp = t_2;
	} else if (b <= -4.5) {
		tmp = t_1;
	} else if (b <= -8.5e-83) {
		tmp = (y * ((x * z) - (i * j))) + (b * (t * i));
	} else if ((b <= 195.0) || (!(b <= 3.1e+119) && (b <= 3.1e+158))) {
		tmp = t_1;
	} 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))) + (x * ((y * z) - (t * a)))
	t_2 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -6.5e+145:
		tmp = t_2
	elif b <= -4.5:
		tmp = t_1
	elif b <= -8.5e-83:
		tmp = (y * ((x * z) - (i * j))) + (b * (t * i))
	elif (b <= 195.0) or (not (b <= 3.1e+119) and (b <= 3.1e+158)):
		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(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -6.5e+145)
		tmp = t_2;
	elseif (b <= -4.5)
		tmp = t_1;
	elseif (b <= -8.5e-83)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(b * Float64(t * i)));
	elseif ((b <= 195.0) || (!(b <= 3.1e+119) && (b <= 3.1e+158)))
		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 = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	t_2 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -6.5e+145)
		tmp = t_2;
	elseif (b <= -4.5)
		tmp = t_1;
	elseif (b <= -8.5e-83)
		tmp = (y * ((x * z) - (i * j))) + (b * (t * i));
	elseif ((b <= 195.0) || (~((b <= 3.1e+119)) && (b <= 3.1e+158)))
		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[(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]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.5e+145], t$95$2, If[LessEqual[b, -4.5], t$95$1, If[LessEqual[b, -8.5e-83], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, 195.0], And[N[Not[LessEqual[b, 3.1e+119]], $MachinePrecision], LessEqual[b, 3.1e+158]]], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.50000000000000034e145 or 195 < b < 3.09999999999999995e119 or 3.1000000000000002e158 < b

   1. Initial program 63.4%

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

   2. Taylor expanded in b around inf 75.0%

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

      1. *-commutative 75.0%

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

      2. *-commutative 75.0%

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

   4. Simplified 75.0%

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

   if -6.50000000000000034e145 < b < -4.5 or -8.49999999999999938e-83 < b < 195 or 3.09999999999999995e119 < b < 3.1000000000000002e158

   1. Initial program 76.3%

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

   2. Taylor expanded in b around 0 73.9%

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

   if -4.5 < b < -8.49999999999999938e-83

   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. Taylor expanded in a around 0 86.5%

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

      1. *-commutative 86.5%

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

      2. *-commutative 86.5%

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

      3. sub-neg 86.5%

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

      4. associate-*r* 86.3%

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

      5. associate-*r* 86.3%

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

      6. *-commutative 86.3%

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

      7. associate-*r* 86.3%

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

      8. distribute-rgt-in 86.3%

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

      9. +-commutative 86.3%

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

      10. mul-1-neg 86.3%

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

      11. unsub-neg 86.3%

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

      12. *-commutative 86.3%

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

      13. distribute-rgt-neg-in 86.3%

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

      14. neg-sub0 86.3%

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

      15. *-commutative 86.3%

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

      16. associate--r- 86.3%

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

   4. Simplified 86.3%

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

   5. Taylor expanded in t around inf 74.4%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.5 \cdot 10^{+145}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -4.5:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{-83}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq 195 \lor \neg \left(b \leq 3.1 \cdot 10^{+119}\right) \land b \leq 3.1 \cdot 10^{+158}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 3: 70.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;x \leq -280:\\ \;\;\;\;t_3 + t_2\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-102}:\\ \;\;\;\;t_3 + t_1\\ \mathbf{else}:\\ \;\;\;\;\left(t_2 + t_1\right) - y \cdot \left(i \cdot j\right)\\ \end{array} \end{array} \]

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))))
        (t_3 (* j (- (* a c) (* y i)))))
   (if (<= x -280.0)
     (+ t_3 t_2)
     (if (<= x 9e-102) (+ t_3 t_1) (- (+ t_2 t_1) (* y (* i j)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (x <= -280.0) {
		tmp = t_3 + t_2;
	} else if (x <= 9e-102) {
		tmp = t_3 + t_1;
	} else {
		tmp = (t_2 + t_1) - (y * (i * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = x * ((y * z) - (t * a))
    t_3 = j * ((a * c) - (y * i))
    if (x <= (-280.0d0)) then
        tmp = t_3 + t_2
    else if (x <= 9d-102) then
        tmp = t_3 + t_1
    else
        tmp = (t_2 + t_1) - (y * (i * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (x <= -280.0) {
		tmp = t_3 + t_2;
	} else if (x <= 9e-102) {
		tmp = t_3 + t_1;
	} else {
		tmp = (t_2 + t_1) - (y * (i * j));
	}
	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))
	t_3 = j * ((a * c) - (y * i))
	tmp = 0
	if x <= -280.0:
		tmp = t_3 + t_2
	elif x <= 9e-102:
		tmp = t_3 + t_1
	else:
		tmp = (t_2 + t_1) - (y * (i * j))
	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)))
	t_3 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (x <= -280.0)
		tmp = Float64(t_3 + t_2);
	elseif (x <= 9e-102)
		tmp = Float64(t_3 + t_1);
	else
		tmp = Float64(Float64(t_2 + t_1) - Float64(y * Float64(i * j)));
	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));
	t_3 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (x <= -280.0)
		tmp = t_3 + t_2;
	elseif (x <= 9e-102)
		tmp = t_3 + t_1;
	else
		tmp = (t_2 + t_1) - (y * (i * j));
	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]}, Block[{t$95$3 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -280.0], N[(t$95$3 + t$95$2), $MachinePrecision], If[LessEqual[x, 9e-102], N[(t$95$3 + t$95$1), $MachinePrecision], N[(N[(t$95$2 + t$95$1), $MachinePrecision] - N[(y * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -280

   1. Initial program 83.9%

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

   2. Taylor expanded in b around 0 80.4%

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

   if -280 < x < 8.99999999999999999e-102

   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. Taylor expanded in x around 0 75.2%

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

   if 8.99999999999999999e-102 < x

   1. Initial program 74.3%

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

   2. Taylor expanded in c around 0 71.9%

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

      1. associate-*r* 73.1%

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

      2. associate-*r* 73.1%

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

      3. *-commutative 73.1%

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

      4. mul-1-neg 73.1%

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

      5. *-commutative 73.1%

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

      6. distribute-rgt-neg-in 73.1%

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

   4. Simplified 73.1%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -280:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-102}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) - y \cdot \left(i \cdot j\right)\\ \end{array} \]

Alternative 4: 45.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_3 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;b \leq -4.6 \cdot 10^{+76}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -4.4 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -80000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-51}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{-101}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{-150}:\\ \;\;\;\;-j \cdot \left(y \cdot i\right)\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{-234}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-253}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-45}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z)))
        (t_2 (* b (- (* t i) (* z c))))
        (t_3 (* a (- (* c j) (* x t)))))
   (if (<= b -4.6e+76)
     t_2
     (if (<= b -4.4e+15)
       t_1
       (if (<= b -80000.0)
         t_3
         (if (<= b -2.4e-51)
           (* i (* j (- y)))
           (if (<= b -1.45e-101)
             t_2
             (if (<= b -4.2e-150)
               (- (* j (* y i)))
               (if (<= b -6.2e-234)
                 t_3
                 (if (<= b 7e-253) t_1 (if (<= b 1.05e-45) 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);
	double t_2 = b * ((t * i) - (z * c));
	double t_3 = a * ((c * j) - (x * t));
	double tmp;
	if (b <= -4.6e+76) {
		tmp = t_2;
	} else if (b <= -4.4e+15) {
		tmp = t_1;
	} else if (b <= -80000.0) {
		tmp = t_3;
	} else if (b <= -2.4e-51) {
		tmp = i * (j * -y);
	} else if (b <= -1.45e-101) {
		tmp = t_2;
	} else if (b <= -4.2e-150) {
		tmp = -(j * (y * i));
	} else if (b <= -6.2e-234) {
		tmp = t_3;
	} else if (b <= 7e-253) {
		tmp = t_1;
	} else if (b <= 1.05e-45) {
		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_2 = b * ((t * i) - (z * c))
    t_3 = a * ((c * j) - (x * t))
    if (b <= (-4.6d+76)) then
        tmp = t_2
    else if (b <= (-4.4d+15)) then
        tmp = t_1
    else if (b <= (-80000.0d0)) then
        tmp = t_3
    else if (b <= (-2.4d-51)) then
        tmp = i * (j * -y)
    else if (b <= (-1.45d-101)) then
        tmp = t_2
    else if (b <= (-4.2d-150)) then
        tmp = -(j * (y * i))
    else if (b <= (-6.2d-234)) then
        tmp = t_3
    else if (b <= 7d-253) then
        tmp = t_1
    else if (b <= 1.05d-45) 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);
	double t_2 = b * ((t * i) - (z * c));
	double t_3 = a * ((c * j) - (x * t));
	double tmp;
	if (b <= -4.6e+76) {
		tmp = t_2;
	} else if (b <= -4.4e+15) {
		tmp = t_1;
	} else if (b <= -80000.0) {
		tmp = t_3;
	} else if (b <= -2.4e-51) {
		tmp = i * (j * -y);
	} else if (b <= -1.45e-101) {
		tmp = t_2;
	} else if (b <= -4.2e-150) {
		tmp = -(j * (y * i));
	} else if (b <= -6.2e-234) {
		tmp = t_3;
	} else if (b <= 7e-253) {
		tmp = t_1;
	} else if (b <= 1.05e-45) {
		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_2 = b * ((t * i) - (z * c))
	t_3 = a * ((c * j) - (x * t))
	tmp = 0
	if b <= -4.6e+76:
		tmp = t_2
	elif b <= -4.4e+15:
		tmp = t_1
	elif b <= -80000.0:
		tmp = t_3
	elif b <= -2.4e-51:
		tmp = i * (j * -y)
	elif b <= -1.45e-101:
		tmp = t_2
	elif b <= -4.2e-150:
		tmp = -(j * (y * i))
	elif b <= -6.2e-234:
		tmp = t_3
	elif b <= 7e-253:
		tmp = t_1
	elif b <= 1.05e-45:
		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(y * z))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_3 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (b <= -4.6e+76)
		tmp = t_2;
	elseif (b <= -4.4e+15)
		tmp = t_1;
	elseif (b <= -80000.0)
		tmp = t_3;
	elseif (b <= -2.4e-51)
		tmp = Float64(i * Float64(j * Float64(-y)));
	elseif (b <= -1.45e-101)
		tmp = t_2;
	elseif (b <= -4.2e-150)
		tmp = Float64(-Float64(j * Float64(y * i)));
	elseif (b <= -6.2e-234)
		tmp = t_3;
	elseif (b <= 7e-253)
		tmp = t_1;
	elseif (b <= 1.05e-45)
		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_2 = b * ((t * i) - (z * c));
	t_3 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (b <= -4.6e+76)
		tmp = t_2;
	elseif (b <= -4.4e+15)
		tmp = t_1;
	elseif (b <= -80000.0)
		tmp = t_3;
	elseif (b <= -2.4e-51)
		tmp = i * (j * -y);
	elseif (b <= -1.45e-101)
		tmp = t_2;
	elseif (b <= -4.2e-150)
		tmp = -(j * (y * i));
	elseif (b <= -6.2e-234)
		tmp = t_3;
	elseif (b <= 7e-253)
		tmp = t_1;
	elseif (b <= 1.05e-45)
		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[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.6e+76], t$95$2, If[LessEqual[b, -4.4e+15], t$95$1, If[LessEqual[b, -80000.0], t$95$3, If[LessEqual[b, -2.4e-51], N[(i * N[(j * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.45e-101], t$95$2, If[LessEqual[b, -4.2e-150], (-N[(j * N[(y * i), $MachinePrecision]), $MachinePrecision]), If[LessEqual[b, -6.2e-234], t$95$3, If[LessEqual[b, 7e-253], t$95$1, If[LessEqual[b, 1.05e-45], t$95$3, t$95$2]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -4.60000000000000002e76 or -2.4e-51 < b < -1.45e-101 or 1.04999999999999998e-45 < b

   1. Initial program 69.7%

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

   2. Taylor expanded in b around inf 64.5%

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

      1. *-commutative 64.5%

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

      2. *-commutative 64.5%

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

   4. Simplified 64.5%

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

   if -4.60000000000000002e76 < b < -4.4e15 or -6.2000000000000003e-234 < b < 7.00000000000000045e-253

   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. Taylor expanded in a around 0 47.9%

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

      1. *-commutative 47.9%

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

      2. *-commutative 47.9%

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

      3. sub-neg 47.9%

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

      4. associate-*r* 48.0%

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

      5. associate-*r* 48.0%

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

      6. *-commutative 48.0%

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

      7. associate-*r* 47.8%

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

      8. distribute-rgt-in 53.7%

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

      9. +-commutative 53.7%

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

      10. mul-1-neg 53.7%

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

      11. unsub-neg 53.7%

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

      12. *-commutative 53.7%

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

      13. distribute-rgt-neg-in 53.7%

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

      14. neg-sub0 53.7%

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

      15. *-commutative 53.7%

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

      16. associate--r- 53.7%

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

   4. Simplified 53.7%

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

   5. Taylor expanded in x around inf 53.8%

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

   if -4.4e15 < b < -8e4 or -4.2000000000000002e-150 < b < -6.2000000000000003e-234 or 7.00000000000000045e-253 < b < 1.04999999999999998e-45

   1. Initial program 77.3%

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

   2. Taylor expanded in a around inf 54.6%

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

      1. +-commutative 54.6%

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

      2. mul-1-neg 54.6%

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

      3. unsub-neg 54.6%

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

      4. *-commutative 54.6%

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

      5. *-commutative 54.6%

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

   4. Simplified 54.6%

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

   if -8e4 < b < -2.4e-51

   1. Initial program 73.9%

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

   2. Taylor expanded in y around inf 70.8%

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

      1. +-commutative 70.8%

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

      2. mul-1-neg 70.8%

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

      3. unsub-neg 70.8%

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

      4. *-commutative 70.8%

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

   4. Simplified 70.8%

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

   5. Taylor expanded in x around 0 44.5%

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

      1. neg-mul-1 44.5%

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

      2. distribute-rgt-neg-in 44.5%

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

   7. Simplified 44.5%

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

   8. Taylor expanded in y around 0 53.0%

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

      1. associate-*r* 53.0%

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

      2. neg-mul-1 53.0%

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

   10. Simplified 53.0%

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

   if -1.45e-101 < b < -4.2000000000000002e-150

   1. Initial program 80.6%

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

      1. prod-diff 80.6%

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

      2. *-commutative 80.6%

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

      3. fma-neg 80.6%

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

      4. distribute-rgt-in 80.6%

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

      5. *-commutative 80.6%

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

      6. *-commutative 80.6%

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

      7. *-commutative 80.6%

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

   3. Applied egg-rr 80.6%

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

   4. Taylor expanded in j around inf 80.6%

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

   5. Taylor expanded in a around 0 70.9%

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

      1. associate-*r* 70.9%

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

      2. neg-mul-1 70.9%

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

      3. *-commutative 70.9%

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

   7. Simplified 70.9%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.6 \cdot 10^{+76}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -4.4 \cdot 10^{+15}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq -80000:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-51}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{-101}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{-150}:\\ \;\;\;\;-j \cdot \left(y \cdot i\right)\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{-234}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-253}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-45}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 5: 42.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_3 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;b \leq -2.75 \cdot 10^{+76}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.9 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -90000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{-50}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{-101}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{-150}:\\ \;\;\;\;-j \cdot \left(y \cdot i\right)\\ \mathbf{elif}\;b \leq -7 \cdot 10^{-234}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-235}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 180:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z)))
        (t_2 (* b (- (* t i) (* z c))))
        (t_3 (* a (- (* c j) (* x t)))))
   (if (<= b -2.75e+76)
     t_2
     (if (<= b -1.9e+17)
       t_1
       (if (<= b -90000.0)
         t_3
         (if (<= b -1.45e-50)
           (* i (* j (- y)))
           (if (<= b -1.2e-101)
             t_2
             (if (<= b -4.2e-150)
               (- (* j (* y i)))
               (if (<= b -7e-234)
                 t_3
                 (if (<= b 1.2e-235)
                   t_1
                   (if (<= b 180.0) (* c (- (* a j) (* z b))) t_2)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double t_2 = b * ((t * i) - (z * c));
	double t_3 = a * ((c * j) - (x * t));
	double tmp;
	if (b <= -2.75e+76) {
		tmp = t_2;
	} else if (b <= -1.9e+17) {
		tmp = t_1;
	} else if (b <= -90000.0) {
		tmp = t_3;
	} else if (b <= -1.45e-50) {
		tmp = i * (j * -y);
	} else if (b <= -1.2e-101) {
		tmp = t_2;
	} else if (b <= -4.2e-150) {
		tmp = -(j * (y * i));
	} else if (b <= -7e-234) {
		tmp = t_3;
	} else if (b <= 1.2e-235) {
		tmp = t_1;
	} else if (b <= 180.0) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * (y * z)
    t_2 = b * ((t * i) - (z * c))
    t_3 = a * ((c * j) - (x * t))
    if (b <= (-2.75d+76)) then
        tmp = t_2
    else if (b <= (-1.9d+17)) then
        tmp = t_1
    else if (b <= (-90000.0d0)) then
        tmp = t_3
    else if (b <= (-1.45d-50)) then
        tmp = i * (j * -y)
    else if (b <= (-1.2d-101)) then
        tmp = t_2
    else if (b <= (-4.2d-150)) then
        tmp = -(j * (y * i))
    else if (b <= (-7d-234)) then
        tmp = t_3
    else if (b <= 1.2d-235) then
        tmp = t_1
    else if (b <= 180.0d0) then
        tmp = c * ((a * j) - (z * b))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double t_2 = b * ((t * i) - (z * c));
	double t_3 = a * ((c * j) - (x * t));
	double tmp;
	if (b <= -2.75e+76) {
		tmp = t_2;
	} else if (b <= -1.9e+17) {
		tmp = t_1;
	} else if (b <= -90000.0) {
		tmp = t_3;
	} else if (b <= -1.45e-50) {
		tmp = i * (j * -y);
	} else if (b <= -1.2e-101) {
		tmp = t_2;
	} else if (b <= -4.2e-150) {
		tmp = -(j * (y * i));
	} else if (b <= -7e-234) {
		tmp = t_3;
	} else if (b <= 1.2e-235) {
		tmp = t_1;
	} else if (b <= 180.0) {
		tmp = c * ((a * j) - (z * b));
	} 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 = b * ((t * i) - (z * c))
	t_3 = a * ((c * j) - (x * t))
	tmp = 0
	if b <= -2.75e+76:
		tmp = t_2
	elif b <= -1.9e+17:
		tmp = t_1
	elif b <= -90000.0:
		tmp = t_3
	elif b <= -1.45e-50:
		tmp = i * (j * -y)
	elif b <= -1.2e-101:
		tmp = t_2
	elif b <= -4.2e-150:
		tmp = -(j * (y * i))
	elif b <= -7e-234:
		tmp = t_3
	elif b <= 1.2e-235:
		tmp = t_1
	elif b <= 180.0:
		tmp = c * ((a * j) - (z * b))
	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(b * Float64(Float64(t * i) - Float64(z * c)))
	t_3 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (b <= -2.75e+76)
		tmp = t_2;
	elseif (b <= -1.9e+17)
		tmp = t_1;
	elseif (b <= -90000.0)
		tmp = t_3;
	elseif (b <= -1.45e-50)
		tmp = Float64(i * Float64(j * Float64(-y)));
	elseif (b <= -1.2e-101)
		tmp = t_2;
	elseif (b <= -4.2e-150)
		tmp = Float64(-Float64(j * Float64(y * i)));
	elseif (b <= -7e-234)
		tmp = t_3;
	elseif (b <= 1.2e-235)
		tmp = t_1;
	elseif (b <= 180.0)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (y * z);
	t_2 = b * ((t * i) - (z * c));
	t_3 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (b <= -2.75e+76)
		tmp = t_2;
	elseif (b <= -1.9e+17)
		tmp = t_1;
	elseif (b <= -90000.0)
		tmp = t_3;
	elseif (b <= -1.45e-50)
		tmp = i * (j * -y);
	elseif (b <= -1.2e-101)
		tmp = t_2;
	elseif (b <= -4.2e-150)
		tmp = -(j * (y * i));
	elseif (b <= -7e-234)
		tmp = t_3;
	elseif (b <= 1.2e-235)
		tmp = t_1;
	elseif (b <= 180.0)
		tmp = c * ((a * j) - (z * b));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.75e+76], t$95$2, If[LessEqual[b, -1.9e+17], t$95$1, If[LessEqual[b, -90000.0], t$95$3, If[LessEqual[b, -1.45e-50], N[(i * N[(j * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.2e-101], t$95$2, If[LessEqual[b, -4.2e-150], (-N[(j * N[(y * i), $MachinePrecision]), $MachinePrecision]), If[LessEqual[b, -7e-234], t$95$3, If[LessEqual[b, 1.2e-235], t$95$1, If[LessEqual[b, 180.0], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -2.75e76 or -1.45000000000000004e-50 < b < -1.2e-101 or 180 < b

   1. Initial program 69.2%

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

   2. Taylor expanded in b around inf 67.3%

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

      1. *-commutative 67.3%

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

      2. *-commutative 67.3%

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

   4. Simplified 67.3%

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

   if -2.75e76 < b < -1.9e17 or -7.0000000000000003e-234 < b < 1.20000000000000005e-235

   1. Initial program 68.9%

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

   2. Taylor expanded in a around 0 45.8%

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

      1. *-commutative 45.8%

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

      2. *-commutative 45.8%

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

      3. sub-neg 45.8%

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

      4. associate-*r* 45.9%

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

      5. associate-*r* 45.9%

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

      6. *-commutative 45.9%

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

      7. associate-*r* 45.7%

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

      8. distribute-rgt-in 51.0%

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

      9. +-commutative 51.0%

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

      10. mul-1-neg 51.0%

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

      11. unsub-neg 51.0%

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

      12. *-commutative 51.0%

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

      13. distribute-rgt-neg-in 51.0%

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

      14. neg-sub0 51.0%

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

      15. *-commutative 51.0%

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

      16. associate--r- 51.0%

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

   4. Simplified 51.0%

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

   5. Taylor expanded in x around inf 50.9%

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

   if -1.9e17 < b < -9e4 or -4.2000000000000002e-150 < b < -7.0000000000000003e-234

   1. Initial program 78.7%

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

   2. Taylor expanded in a around inf 62.2%

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

      1. +-commutative 62.2%

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

      2. mul-1-neg 62.2%

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

      3. unsub-neg 62.2%

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

      4. *-commutative 62.2%

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

      5. *-commutative 62.2%

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

   4. Simplified 62.2%

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

   if -9e4 < b < -1.45000000000000004e-50

   1. Initial program 73.9%

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

   2. Taylor expanded in y around inf 70.8%

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

      1. +-commutative 70.8%

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

      2. mul-1-neg 70.8%

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

      3. unsub-neg 70.8%

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

      4. *-commutative 70.8%

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

   4. Simplified 70.8%

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

   5. Taylor expanded in x around 0 44.5%

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

      1. neg-mul-1 44.5%

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

      2. distribute-rgt-neg-in 44.5%

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

   7. Simplified 44.5%

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

   8. Taylor expanded in y around 0 53.0%

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

      1. associate-*r* 53.0%

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

      2. neg-mul-1 53.0%

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

   10. Simplified 53.0%

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

   if -1.2e-101 < b < -4.2000000000000002e-150

   1. Initial program 80.6%

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

      1. prod-diff 80.6%

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

      2. *-commutative 80.6%

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

      3. fma-neg 80.6%

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

      4. distribute-rgt-in 80.6%

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

      5. *-commutative 80.6%

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

      6. *-commutative 80.6%

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

      7. *-commutative 80.6%

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

   3. Applied egg-rr 80.6%

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

   4. Taylor expanded in j around inf 80.6%

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

   5. Taylor expanded in a around 0 70.9%

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

      1. associate-*r* 70.9%

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

      2. neg-mul-1 70.9%

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

      3. *-commutative 70.9%

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

   7. Simplified 70.9%

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

   if 1.20000000000000005e-235 < b < 180

   1. Initial program 75.9%

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

   2. Taylor expanded in c around inf 51.7%

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

      1. *-commutative 51.7%

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

   4. Simplified 51.7%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.75 \cdot 10^{+76}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.9 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq -90000:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{-50}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{-101}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{-150}:\\ \;\;\;\;-j \cdot \left(y \cdot i\right)\\ \mathbf{elif}\;b \leq -7 \cdot 10^{-234}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-235}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 180:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 6: 56.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -2 \cdot 10^{+146}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -8.2 \cdot 10^{-14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{-83}:\\ \;\;\;\;b \cdot \left(t \cdot i\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;b \leq 125 \lor \neg \left(b \leq 2.1 \cdot 10^{+119}\right) \land b \leq 1.15 \cdot 10^{+157}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* j (- (* a c) (* y i))) (* x (* y z))))
        (t_2 (* b (- (* t i) (* z c)))))
   (if (<= b -2e+146)
     t_2
     (if (<= b -8.2e-14)
       t_1
       (if (<= b -8.5e-83)
         (- (* b (* t i)) (* i (* y j)))
         (if (or (<= b 125.0) (and (not (<= b 2.1e+119)) (<= b 1.15e+157)))
           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 * ((a * c) - (y * i))) + (x * (y * z));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -2e+146) {
		tmp = t_2;
	} else if (b <= -8.2e-14) {
		tmp = t_1;
	} else if (b <= -8.5e-83) {
		tmp = (b * (t * i)) - (i * (y * j));
	} else if ((b <= 125.0) || (!(b <= 2.1e+119) && (b <= 1.15e+157))) {
		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 = (j * ((a * c) - (y * i))) + (x * (y * z))
    t_2 = b * ((t * i) - (z * c))
    if (b <= (-2d+146)) then
        tmp = t_2
    else if (b <= (-8.2d-14)) then
        tmp = t_1
    else if (b <= (-8.5d-83)) then
        tmp = (b * (t * i)) - (i * (y * j))
    else if ((b <= 125.0d0) .or. (.not. (b <= 2.1d+119)) .and. (b <= 1.15d+157)) 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 = (j * ((a * c) - (y * i))) + (x * (y * z));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -2e+146) {
		tmp = t_2;
	} else if (b <= -8.2e-14) {
		tmp = t_1;
	} else if (b <= -8.5e-83) {
		tmp = (b * (t * i)) - (i * (y * j));
	} else if ((b <= 125.0) || (!(b <= 2.1e+119) && (b <= 1.15e+157))) {
		tmp = t_1;
	} 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))) + (x * (y * z))
	t_2 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -2e+146:
		tmp = t_2
	elif b <= -8.2e-14:
		tmp = t_1
	elif b <= -8.5e-83:
		tmp = (b * (t * i)) - (i * (y * j))
	elif (b <= 125.0) or (not (b <= 2.1e+119) and (b <= 1.15e+157)):
		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(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(x * Float64(y * z)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -2e+146)
		tmp = t_2;
	elseif (b <= -8.2e-14)
		tmp = t_1;
	elseif (b <= -8.5e-83)
		tmp = Float64(Float64(b * Float64(t * i)) - Float64(i * Float64(y * j)));
	elseif ((b <= 125.0) || (!(b <= 2.1e+119) && (b <= 1.15e+157)))
		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 = (j * ((a * c) - (y * i))) + (x * (y * z));
	t_2 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -2e+146)
		tmp = t_2;
	elseif (b <= -8.2e-14)
		tmp = t_1;
	elseif (b <= -8.5e-83)
		tmp = (b * (t * i)) - (i * (y * j));
	elseif ((b <= 125.0) || (~((b <= 2.1e+119)) && (b <= 1.15e+157)))
		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[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2e+146], t$95$2, If[LessEqual[b, -8.2e-14], t$95$1, If[LessEqual[b, -8.5e-83], N[(N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, 125.0], And[N[Not[LessEqual[b, 2.1e+119]], $MachinePrecision], LessEqual[b, 1.15e+157]]], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.99999999999999987e146 or 125 < b < 2.09999999999999983e119 or 1.15000000000000002e157 < b

   1. Initial program 63.4%

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

   2. Taylor expanded in b around inf 75.0%

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

      1. *-commutative 75.0%

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

      2. *-commutative 75.0%

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

   4. Simplified 75.0%

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

   if -1.99999999999999987e146 < b < -8.2000000000000004e-14 or -8.49999999999999938e-83 < b < 125 or 2.09999999999999983e119 < b < 1.15000000000000002e157

   1. Initial program 76.3%

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

   2. Taylor expanded in b around 0 73.9%

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

   3. Taylor expanded in y around inf 64.8%

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

   if -8.2000000000000004e-14 < b < -8.49999999999999938e-83

   1. Initial program 83.8%

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

   2. Taylor expanded in x around 0 84.0%

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

   3. Taylor expanded in c around 0 68.6%

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

      1. distribute-lft-out-- 68.6%

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

   5. Simplified 68.6%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{+146}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -8.2 \cdot 10^{-14}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{-83}:\\ \;\;\;\;b \cdot \left(t \cdot i\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;b \leq 125 \lor \neg \left(b \leq 2.1 \cdot 10^{+119}\right) \land b \leq 1.15 \cdot 10^{+157}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 7: 57.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -4.4 \cdot 10^{+145}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{-99}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-179}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 165 \lor \neg \left(b \leq 3.15 \cdot 10^{+119}\right) \land b \leq 5.4 \cdot 10^{+157}:\\ \;\;\;\;t_1 + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))) (t_2 (* b (- (* t i) (* z c)))))
   (if (<= b -4.4e+145)
     t_2
     (if (<= b -2.9e-99)
       (+ (* y (- (* x z) (* i j))) (* b (* t i)))
       (if (<= b -2e-179)
         t_1
         (if (or (<= b 165.0) (and (not (<= b 3.15e+119)) (<= b 5.4e+157)))
           (+ t_1 (* x (* y z)))
           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 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -4.4e+145) {
		tmp = t_2;
	} else if (b <= -2.9e-99) {
		tmp = (y * ((x * z) - (i * j))) + (b * (t * i));
	} else if (b <= -2e-179) {
		tmp = t_1;
	} else if ((b <= 165.0) || (!(b <= 3.15e+119) && (b <= 5.4e+157))) {
		tmp = t_1 + (x * (y * z));
	} 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 = b * ((t * i) - (z * c))
    if (b <= (-4.4d+145)) then
        tmp = t_2
    else if (b <= (-2.9d-99)) then
        tmp = (y * ((x * z) - (i * j))) + (b * (t * i))
    else if (b <= (-2d-179)) then
        tmp = t_1
    else if ((b <= 165.0d0) .or. (.not. (b <= 3.15d+119)) .and. (b <= 5.4d+157)) then
        tmp = t_1 + (x * (y * z))
    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 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -4.4e+145) {
		tmp = t_2;
	} else if (b <= -2.9e-99) {
		tmp = (y * ((x * z) - (i * j))) + (b * (t * i));
	} else if (b <= -2e-179) {
		tmp = t_1;
	} else if ((b <= 165.0) || (!(b <= 3.15e+119) && (b <= 5.4e+157))) {
		tmp = t_1 + (x * (y * z));
	} 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 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -4.4e+145:
		tmp = t_2
	elif b <= -2.9e-99:
		tmp = (y * ((x * z) - (i * j))) + (b * (t * i))
	elif b <= -2e-179:
		tmp = t_1
	elif (b <= 165.0) or (not (b <= 3.15e+119) and (b <= 5.4e+157)):
		tmp = t_1 + (x * (y * z))
	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(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -4.4e+145)
		tmp = t_2;
	elseif (b <= -2.9e-99)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(b * Float64(t * i)));
	elseif (b <= -2e-179)
		tmp = t_1;
	elseif ((b <= 165.0) || (!(b <= 3.15e+119) && (b <= 5.4e+157)))
		tmp = Float64(t_1 + Float64(x * Float64(y * z)));
	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 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -4.4e+145)
		tmp = t_2;
	elseif (b <= -2.9e-99)
		tmp = (y * ((x * z) - (i * j))) + (b * (t * i));
	elseif (b <= -2e-179)
		tmp = t_1;
	elseif ((b <= 165.0) || (~((b <= 3.15e+119)) && (b <= 5.4e+157)))
		tmp = t_1 + (x * (y * z));
	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[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.4e+145], t$95$2, If[LessEqual[b, -2.9e-99], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2e-179], t$95$1, If[Or[LessEqual[b, 165.0], And[N[Not[LessEqual[b, 3.15e+119]], $MachinePrecision], LessEqual[b, 5.4e+157]]], N[(t$95$1 + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -4.40000000000000017e145 or 165 < b < 3.1499999999999999e119 or 5.4000000000000001e157 < b

   1. Initial program 63.4%

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

   2. Taylor expanded in b around inf 75.0%

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

      1. *-commutative 75.0%

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

      2. *-commutative 75.0%

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

   4. Simplified 75.0%

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

   if -4.40000000000000017e145 < b < -2.89999999999999985e-99

   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. Taylor expanded in a around 0 67.3%

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

      1. *-commutative 67.3%

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

      2. *-commutative 67.3%

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

      3. sub-neg 67.3%

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

      4. associate-*r* 67.2%

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

      5. associate-*r* 67.2%

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

      6. *-commutative 67.2%

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

      7. associate-*r* 65.3%

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

      8. distribute-rgt-in 67.3%

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

      9. +-commutative 67.3%

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

      10. mul-1-neg 67.3%

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

      11. unsub-neg 67.3%

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

      12. *-commutative 67.3%

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

      13. distribute-rgt-neg-in 67.3%

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

      14. neg-sub0 67.3%

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

      15. *-commutative 67.3%

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

      16. associate--r- 67.3%

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

   4. Simplified 67.3%

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

   5. Taylor expanded in t around inf 59.6%

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

   if -2.89999999999999985e-99 < b < -2e-179

   1. Initial program 78.3%

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

      1. prod-diff 78.0%

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

      2. *-commutative 78.0%

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

      3. fma-neg 78.0%

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

      4. distribute-rgt-in 78.0%

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

      5. *-commutative 78.0%

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

      6. *-commutative 78.0%

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

      7. *-commutative 78.0%

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

   3. Applied egg-rr 78.0%

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

   4. Taylor expanded in j around inf 73.0%

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

   if -2e-179 < b < 165 or 3.1499999999999999e119 < b < 5.4000000000000001e157

   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. Taylor expanded in b around 0 75.9%

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

   3. Taylor expanded in y around inf 66.5%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.4 \cdot 10^{+145}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{-99}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-179}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 165 \lor \neg \left(b \leq 3.15 \cdot 10^{+119}\right) \land b \leq 5.4 \cdot 10^{+157}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 8: 67.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -3.2 \cdot 10^{+145}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{+75} \lor \neg \left(b \leq -3.9 \cdot 10^{-85}\right) \land b \leq 140:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))))
   (if (<= b -3.2e+145)
     t_1
     (if (or (<= b -2.7e+75) (and (not (<= b -3.9e-85)) (<= b 140.0)))
       (+ (* j (- (* a c) (* y i))) (* x (- (* y z) (* t a))))
       (+ t_1 (* y (- (* x z) (* i j))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -3.2e+145) {
		tmp = t_1;
	} else if ((b <= -2.7e+75) || (!(b <= -3.9e-85) && (b <= 140.0))) {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else {
		tmp = t_1 + (y * ((x * z) - (i * j)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    if (b <= (-3.2d+145)) then
        tmp = t_1
    else if ((b <= (-2.7d+75)) .or. (.not. (b <= (-3.9d-85))) .and. (b <= 140.0d0)) then
        tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
    else
        tmp = t_1 + (y * ((x * z) - (i * j)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -3.2e+145) {
		tmp = t_1;
	} else if ((b <= -2.7e+75) || (!(b <= -3.9e-85) && (b <= 140.0))) {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else {
		tmp = t_1 + (y * ((x * z) - (i * j)));
	}
	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 <= -3.2e+145:
		tmp = t_1
	elif (b <= -2.7e+75) or (not (b <= -3.9e-85) and (b <= 140.0)):
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
	else:
		tmp = t_1 + (y * ((x * z) - (i * j)))
	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 <= -3.2e+145)
		tmp = t_1;
	elseif ((b <= -2.7e+75) || (!(b <= -3.9e-85) && (b <= 140.0)))
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	else
		tmp = Float64(t_1 + Float64(y * Float64(Float64(x * z) - Float64(i * j))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -3.2e+145)
		tmp = t_1;
	elseif ((b <= -2.7e+75) || (~((b <= -3.9e-85)) && (b <= 140.0)))
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	else
		tmp = t_1 + (y * ((x * z) - (i * j)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.2e+145], t$95$1, If[Or[LessEqual[b, -2.7e+75], And[N[Not[LessEqual[b, -3.9e-85]], $MachinePrecision], LessEqual[b, 140.0]]], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.20000000000000008e145

   1. Initial program 48.8%

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

   2. Taylor expanded in b around inf 72.1%

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

      1. *-commutative 72.1%

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

      2. *-commutative 72.1%

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

   4. Simplified 72.1%

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

   if -3.20000000000000008e145 < b < -2.69999999999999998e75 or -3.89999999999999988e-85 < b < 140

   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. Taylor expanded in b around 0 74.3%

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

   if -2.69999999999999998e75 < b < -3.89999999999999988e-85 or 140 < b

   1. Initial program 76.4%

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

   2. Taylor expanded in a around 0 71.2%

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

      1. *-commutative 71.2%

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

      2. *-commutative 71.2%

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

      3. sub-neg 71.2%

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

      4. associate-*r* 71.1%

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

      5. associate-*r* 71.1%

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

      6. *-commutative 71.1%

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

      7. associate-*r* 73.9%

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

      8. distribute-rgt-in 74.9%

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

      9. +-commutative 74.9%

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

      10. mul-1-neg 74.9%

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

      11. unsub-neg 74.9%

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

      12. *-commutative 74.9%

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

      13. distribute-rgt-neg-in 74.9%

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

      14. neg-sub0 74.9%

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

      15. *-commutative 74.9%

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

      16. associate--r- 74.9%

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

   4. Simplified 74.9%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.2 \cdot 10^{+145}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{+75} \lor \neg \left(b \leq -3.9 \cdot 10^{-85}\right) \land b \leq 140:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) + y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]

Alternative 9: 58.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ t_2 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -2.75 \cdot 10^{+91}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -5.2 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -4.4 \cdot 10^{-5}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;c \leq -7.4 \cdot 10^{-194}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.5 \cdot 10^{-27}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* x (- (* y z) (* t a))) (* i (* y j))))
        (t_2 (* c (- (* a j) (* z b)))))
   (if (<= c -2.75e+91)
     t_2
     (if (<= c -5.2e+47)
       t_1
       (if (<= c -4.4e-5)
         (- (* j (- (* a c) (* y i))) (* b (* z c)))
         (if (<= c -7.4e-194)
           t_1
           (if (<= c 1.5e-27)
             (+ (* y (- (* x z) (* i j))) (* b (* t i)))
             t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * ((y * z) - (t * a))) - (i * (y * j));
	double t_2 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -2.75e+91) {
		tmp = t_2;
	} else if (c <= -5.2e+47) {
		tmp = t_1;
	} else if (c <= -4.4e-5) {
		tmp = (j * ((a * c) - (y * i))) - (b * (z * c));
	} else if (c <= -7.4e-194) {
		tmp = t_1;
	} else if (c <= 1.5e-27) {
		tmp = (y * ((x * z) - (i * j))) + (b * (t * i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * ((y * z) - (t * a))) - (i * (y * j))
    t_2 = c * ((a * j) - (z * b))
    if (c <= (-2.75d+91)) then
        tmp = t_2
    else if (c <= (-5.2d+47)) then
        tmp = t_1
    else if (c <= (-4.4d-5)) then
        tmp = (j * ((a * c) - (y * i))) - (b * (z * c))
    else if (c <= (-7.4d-194)) then
        tmp = t_1
    else if (c <= 1.5d-27) then
        tmp = (y * ((x * z) - (i * j))) + (b * (t * i))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * ((y * z) - (t * a))) - (i * (y * j));
	double t_2 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -2.75e+91) {
		tmp = t_2;
	} else if (c <= -5.2e+47) {
		tmp = t_1;
	} else if (c <= -4.4e-5) {
		tmp = (j * ((a * c) - (y * i))) - (b * (z * c));
	} else if (c <= -7.4e-194) {
		tmp = t_1;
	} else if (c <= 1.5e-27) {
		tmp = (y * ((x * z) - (i * j))) + (b * (t * i));
	} 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))) - (i * (y * j))
	t_2 = c * ((a * j) - (z * b))
	tmp = 0
	if c <= -2.75e+91:
		tmp = t_2
	elif c <= -5.2e+47:
		tmp = t_1
	elif c <= -4.4e-5:
		tmp = (j * ((a * c) - (y * i))) - (b * (z * c))
	elif c <= -7.4e-194:
		tmp = t_1
	elif c <= 1.5e-27:
		tmp = (y * ((x * z) - (i * j))) + (b * (t * i))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(i * Float64(y * j)))
	t_2 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -2.75e+91)
		tmp = t_2;
	elseif (c <= -5.2e+47)
		tmp = t_1;
	elseif (c <= -4.4e-5)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) - Float64(b * Float64(z * c)));
	elseif (c <= -7.4e-194)
		tmp = t_1;
	elseif (c <= 1.5e-27)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(b * Float64(t * i)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (x * ((y * z) - (t * a))) - (i * (y * j));
	t_2 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -2.75e+91)
		tmp = t_2;
	elseif (c <= -5.2e+47)
		tmp = t_1;
	elseif (c <= -4.4e-5)
		tmp = (j * ((a * c) - (y * i))) - (b * (z * c));
	elseif (c <= -7.4e-194)
		tmp = t_1;
	elseif (c <= 1.5e-27)
		tmp = (y * ((x * z) - (i * j))) + (b * (t * i));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.75e+91], t$95$2, If[LessEqual[c, -5.2e+47], t$95$1, If[LessEqual[c, -4.4e-5], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -7.4e-194], t$95$1, If[LessEqual[c, 1.5e-27], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -2.7499999999999999e91 or 1.5000000000000001e-27 < c

   1. Initial program 58.3%

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

   2. Taylor expanded in c around inf 69.0%

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

      1. *-commutative 69.0%

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

   4. Simplified 69.0%

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

   if -2.7499999999999999e91 < c < -5.20000000000000007e47 or -4.3999999999999999e-5 < c < -7.40000000000000016e-194

   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. 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. Taylor expanded in c around 0 66.7%

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

      1. +-commutative 66.7%

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

      2. mul-1-neg 66.7%

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

      3. unsub-neg 66.7%

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

      4. *-commutative 66.7%

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

   5. Simplified 66.7%

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

   if -5.20000000000000007e47 < c < -4.3999999999999999e-5

   1. Initial program 77.8%

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

   2. Taylor expanded in x around 0 76.6%

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

   3. Taylor expanded in t around 0 68.9%

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

   if -7.40000000000000016e-194 < c < 1.5000000000000001e-27

   1. Initial program 83.2%

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

   2. Taylor expanded in a around 0 73.1%

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

      1. *-commutative 73.1%

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

      2. *-commutative 73.1%

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

      3. sub-neg 73.1%

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

      4. associate-*r* 73.0%

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

      5. associate-*r* 73.0%

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

      6. *-commutative 73.0%

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

      7. associate-*r* 73.0%

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

      8. distribute-rgt-in 75.6%

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

      9. +-commutative 75.6%

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

      10. mul-1-neg 75.6%

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

      11. unsub-neg 75.6%

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

      12. *-commutative 75.6%

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

      13. distribute-rgt-neg-in 75.6%

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

      14. neg-sub0 75.6%

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

      15. *-commutative 75.6%

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

      16. associate--r- 75.6%

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

   4. Simplified 75.6%

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

   5. Taylor expanded in t around inf 68.0%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.75 \cdot 10^{+91}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -5.2 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;c \leq -4.4 \cdot 10^{-5}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;c \leq -7.4 \cdot 10^{-194}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;c \leq 1.5 \cdot 10^{-27}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 10: 58.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -1.95 \cdot 10^{+115}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -3.9 \cdot 10^{+45}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;c \leq -1.7 \cdot 10^{-5}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;c \leq 9 \cdot 10^{-30}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* a j) (* z b)))))
   (if (<= c -1.95e+115)
     t_1
     (if (<= c -3.9e+45)
       (* a (- (* c j) (* x t)))
       (if (<= c -1.7e-5)
         (- (* j (- (* a c) (* y i))) (* b (* z c)))
         (if (<= c 9e-30) (+ (* y (- (* x z) (* i j))) (* 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 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -1.95e+115) {
		tmp = t_1;
	} else if (c <= -3.9e+45) {
		tmp = a * ((c * j) - (x * t));
	} else if (c <= -1.7e-5) {
		tmp = (j * ((a * c) - (y * i))) - (b * (z * c));
	} else if (c <= 9e-30) {
		tmp = (y * ((x * z) - (i * j))) + (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 = c * ((a * j) - (z * b))
    if (c <= (-1.95d+115)) then
        tmp = t_1
    else if (c <= (-3.9d+45)) then
        tmp = a * ((c * j) - (x * t))
    else if (c <= (-1.7d-5)) then
        tmp = (j * ((a * c) - (y * i))) - (b * (z * c))
    else if (c <= 9d-30) then
        tmp = (y * ((x * z) - (i * j))) + (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 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -1.95e+115) {
		tmp = t_1;
	} else if (c <= -3.9e+45) {
		tmp = a * ((c * j) - (x * t));
	} else if (c <= -1.7e-5) {
		tmp = (j * ((a * c) - (y * i))) - (b * (z * c));
	} else if (c <= 9e-30) {
		tmp = (y * ((x * z) - (i * j))) + (b * (t * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((a * j) - (z * b))
	tmp = 0
	if c <= -1.95e+115:
		tmp = t_1
	elif c <= -3.9e+45:
		tmp = a * ((c * j) - (x * t))
	elif c <= -1.7e-5:
		tmp = (j * ((a * c) - (y * i))) - (b * (z * c))
	elif c <= 9e-30:
		tmp = (y * ((x * z) - (i * j))) + (b * (t * i))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -1.95e+115)
		tmp = t_1;
	elseif (c <= -3.9e+45)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (c <= -1.7e-5)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) - Float64(b * Float64(z * c)));
	elseif (c <= 9e-30)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + 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 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -1.95e+115)
		tmp = t_1;
	elseif (c <= -3.9e+45)
		tmp = a * ((c * j) - (x * t));
	elseif (c <= -1.7e-5)
		tmp = (j * ((a * c) - (y * i))) - (b * (z * c));
	elseif (c <= 9e-30)
		tmp = (y * ((x * z) - (i * j))) + (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[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.95e+115], t$95$1, If[LessEqual[c, -3.9e+45], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.7e-5], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 9e-30], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.95000000000000003e115 or 8.99999999999999935e-30 < c

   1. Initial program 59.5%

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

   2. Taylor expanded in c around inf 68.7%

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

      1. *-commutative 68.7%

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

   4. Simplified 68.7%

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

   if -1.95000000000000003e115 < c < -3.8999999999999999e45

   1. Initial program 74.2%

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

   2. Taylor expanded in a around inf 73.9%

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

      1. +-commutative 73.9%

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

      2. mul-1-neg 73.9%

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

      3. unsub-neg 73.9%

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

      4. *-commutative 73.9%

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

      5. *-commutative 73.9%

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

   4. Simplified 73.9%

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

   if -3.8999999999999999e45 < c < -1.7e-5

   1. Initial program 77.8%

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

   2. Taylor expanded in x around 0 76.6%

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

   3. Taylor expanded in t around 0 68.9%

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

   if -1.7e-5 < c < 8.99999999999999935e-30

   1. Initial program 82.4%

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

   2. Taylor expanded in a around 0 67.6%

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

      1. *-commutative 67.6%

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

      2. *-commutative 67.6%

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

      3. sub-neg 67.6%

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

      4. associate-*r* 66.0%

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

      5. associate-*r* 66.0%

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

      6. *-commutative 66.0%

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

      7. associate-*r* 66.0%

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

      8. distribute-rgt-in 68.5%

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

      9. +-commutative 68.5%

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

      10. mul-1-neg 68.5%

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

      11. unsub-neg 68.5%

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

      12. *-commutative 68.5%

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

      13. distribute-rgt-neg-in 68.5%

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

      14. neg-sub0 68.5%

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

      15. *-commutative 68.5%

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

      16. associate--r- 68.5%

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

   4. Simplified 68.5%

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

   5. Taylor expanded in t around inf 62.8%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.95 \cdot 10^{+115}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -3.9 \cdot 10^{+45}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;c \leq -1.7 \cdot 10^{-5}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;c \leq 9 \cdot 10^{-30}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 11: 69.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;x \leq -3500 \lor \neg \left(x \leq 2800\right):\\ \;\;\;\;t_1 + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (or (<= x -3500.0) (not (<= x 2800.0)))
     (+ t_1 (* x (- (* y z) (* t a))))
     (+ t_1 (* 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 t_1 = j * ((a * c) - (y * i));
	double tmp;
	if ((x <= -3500.0) || !(x <= 2800.0)) {
		tmp = t_1 + (x * ((y * z) - (t * a)));
	} else {
		tmp = t_1 + (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) :: t_1
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    if ((x <= (-3500.0d0)) .or. (.not. (x <= 2800.0d0))) then
        tmp = t_1 + (x * ((y * z) - (t * a)))
    else
        tmp = t_1 + (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 t_1 = j * ((a * c) - (y * i));
	double tmp;
	if ((x <= -3500.0) || !(x <= 2800.0)) {
		tmp = t_1 + (x * ((y * z) - (t * a)));
	} else {
		tmp = t_1 + (b * ((t * i) - (z * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	tmp = 0
	if (x <= -3500.0) or not (x <= 2800.0):
		tmp = t_1 + (x * ((y * z) - (t * a)))
	else:
		tmp = t_1 + (b * ((t * i) - (z * c)))
	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)))
	tmp = 0.0
	if ((x <= -3500.0) || !(x <= 2800.0))
		tmp = Float64(t_1 + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	else
		tmp = Float64(t_1 + 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)
	t_1 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if ((x <= -3500.0) || ~((x <= 2800.0)))
		tmp = t_1 + (x * ((y * z) - (t * a)));
	else
		tmp = t_1 + (b * ((t * i) - (z * c)));
	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]}, If[Or[LessEqual[x, -3500.0], N[Not[LessEqual[x, 2800.0]], $MachinePrecision]], N[(t$95$1 + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -3500 or 2800 < x

   1. Initial program 79.1%

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

   2. Taylor expanded in b around 0 76.7%

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

   if -3500 < x < 2800

   1. Initial program 66.0%

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

   2. Taylor expanded in x around 0 73.6%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3500 \lor \neg \left(x \leq 2800\right):\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 12: 44.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -2.7 \cdot 10^{+76}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -2300000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{-150}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq -7 \cdot 10^{-234}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-236}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 190:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))) (t_2 (* b (- (* t i) (* z c)))))
   (if (<= b -2.7e+76)
     t_2
     (if (<= b -2300000000000.0)
       t_1
       (if (<= b -4.2e-150)
         (* i (- (* t b) (* y j)))
         (if (<= b -7e-234)
           (* a (- (* c j) (* x t)))
           (if (<= b 2.4e-236)
             t_1
             (if (<= b 190.0) (* c (- (* a j) (* z b))) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -2.7e+76) {
		tmp = t_2;
	} else if (b <= -2300000000000.0) {
		tmp = t_1;
	} else if (b <= -4.2e-150) {
		tmp = i * ((t * b) - (y * j));
	} else if (b <= -7e-234) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= 2.4e-236) {
		tmp = t_1;
	} else if (b <= 190.0) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (y * z)
    t_2 = b * ((t * i) - (z * c))
    if (b <= (-2.7d+76)) then
        tmp = t_2
    else if (b <= (-2300000000000.0d0)) then
        tmp = t_1
    else if (b <= (-4.2d-150)) then
        tmp = i * ((t * b) - (y * j))
    else if (b <= (-7d-234)) then
        tmp = a * ((c * j) - (x * t))
    else if (b <= 2.4d-236) then
        tmp = t_1
    else if (b <= 190.0d0) then
        tmp = c * ((a * j) - (z * b))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -2.7e+76) {
		tmp = t_2;
	} else if (b <= -2300000000000.0) {
		tmp = t_1;
	} else if (b <= -4.2e-150) {
		tmp = i * ((t * b) - (y * j));
	} else if (b <= -7e-234) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= 2.4e-236) {
		tmp = t_1;
	} else if (b <= 190.0) {
		tmp = c * ((a * j) - (z * b));
	} 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 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -2.7e+76:
		tmp = t_2
	elif b <= -2300000000000.0:
		tmp = t_1
	elif b <= -4.2e-150:
		tmp = i * ((t * b) - (y * j))
	elif b <= -7e-234:
		tmp = a * ((c * j) - (x * t))
	elif b <= 2.4e-236:
		tmp = t_1
	elif b <= 190.0:
		tmp = c * ((a * j) - (z * b))
	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(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -2.7e+76)
		tmp = t_2;
	elseif (b <= -2300000000000.0)
		tmp = t_1;
	elseif (b <= -4.2e-150)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (b <= -7e-234)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (b <= 2.4e-236)
		tmp = t_1;
	elseif (b <= 190.0)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (y * z);
	t_2 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -2.7e+76)
		tmp = t_2;
	elseif (b <= -2300000000000.0)
		tmp = t_1;
	elseif (b <= -4.2e-150)
		tmp = i * ((t * b) - (y * j));
	elseif (b <= -7e-234)
		tmp = a * ((c * j) - (x * t));
	elseif (b <= 2.4e-236)
		tmp = t_1;
	elseif (b <= 190.0)
		tmp = c * ((a * j) - (z * b));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.7e+76], t$95$2, If[LessEqual[b, -2300000000000.0], t$95$1, If[LessEqual[b, -4.2e-150], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -7e-234], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.4e-236], t$95$1, If[LessEqual[b, 190.0], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -2.6999999999999999e76 or 190 < b

   1. Initial program 67.1%

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

   2. Taylor expanded in b around inf 67.5%

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

      1. *-commutative 67.5%

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

      2. *-commutative 67.5%

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

   4. Simplified 67.5%

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

   if -2.6999999999999999e76 < b < -2.3e12 or -7.0000000000000003e-234 < b < 2.4000000000000002e-236

   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. Taylor expanded in a around 0 43.5%

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

      1. *-commutative 43.5%

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

      2. *-commutative 43.5%

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

      3. sub-neg 43.5%

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

      4. associate-*r* 43.6%

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

      5. associate-*r* 43.6%

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

      6. *-commutative 43.6%

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

      7. associate-*r* 43.5%

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

      8. distribute-rgt-in 48.4%

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

      9. +-commutative 48.4%

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

      10. mul-1-neg 48.4%

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

      11. unsub-neg 48.4%

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

      12. *-commutative 48.4%

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

      13. distribute-rgt-neg-in 48.4%

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

      14. neg-sub0 48.4%

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

      15. *-commutative 48.4%

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

      16. associate--r- 48.4%

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

   4. Simplified 48.4%

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

   5. Taylor expanded in x around inf 48.4%

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

   if -2.3e12 < b < -4.2000000000000002e-150

   1. Initial program 84.4%

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

      1. prod-diff 78.0%

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

      2. *-commutative 78.0%

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

      3. fma-neg 78.0%

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

      4. distribute-rgt-in 78.0%

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

      5. *-commutative 78.0%

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

      6. *-commutative 78.0%

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

      7. *-commutative 78.0%

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

   3. Applied egg-rr 78.0%

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

   4. Taylor expanded in i around inf 58.9%

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

   6. Simplified 58.9%

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

   if -4.2000000000000002e-150 < b < -7.0000000000000003e-234

   1. Initial program 79.3%

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

   2. Taylor expanded in a around inf 58.5%

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

      1. +-commutative 58.5%

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

      2. mul-1-neg 58.5%

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

      3. unsub-neg 58.5%

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

      4. *-commutative 58.5%

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

      5. *-commutative 58.5%

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

   4. Simplified 58.5%

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

   if 2.4000000000000002e-236 < b < 190

   1. Initial program 75.9%

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

   2. Taylor expanded in c around inf 51.7%

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

      1. *-commutative 51.7%

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

   4. Simplified 51.7%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.7 \cdot 10^{+76}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2300000000000:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{-150}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq -7 \cdot 10^{-234}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-236}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 190:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 13: 49.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_3 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -4 \cdot 10^{+102}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-66}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{-234}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-237}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-105}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-43}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i))))
        (t_2 (* y (- (* x z) (* i j))))
        (t_3 (* b (- (* t i) (* z c)))))
   (if (<= b -4e+102)
     t_3
     (if (<= b -2.3e-66)
       t_2
       (if (<= b -6.5e-234)
         t_1
         (if (<= b 3.2e-237)
           t_2
           (if (<= b 3.8e-105)
             (* c (- (* a j) (* z b)))
             (if (<= b 6.5e-43) t_1 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -4e+102) {
		tmp = t_3;
	} else if (b <= -2.3e-66) {
		tmp = t_2;
	} else if (b <= -6.5e-234) {
		tmp = t_1;
	} else if (b <= 3.2e-237) {
		tmp = t_2;
	} else if (b <= 3.8e-105) {
		tmp = c * ((a * j) - (z * b));
	} else if (b <= 6.5e-43) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = y * ((x * z) - (i * j))
    t_3 = b * ((t * i) - (z * c))
    if (b <= (-4d+102)) then
        tmp = t_3
    else if (b <= (-2.3d-66)) then
        tmp = t_2
    else if (b <= (-6.5d-234)) then
        tmp = t_1
    else if (b <= 3.2d-237) then
        tmp = t_2
    else if (b <= 3.8d-105) then
        tmp = c * ((a * j) - (z * b))
    else if (b <= 6.5d-43) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -4e+102) {
		tmp = t_3;
	} else if (b <= -2.3e-66) {
		tmp = t_2;
	} else if (b <= -6.5e-234) {
		tmp = t_1;
	} else if (b <= 3.2e-237) {
		tmp = t_2;
	} else if (b <= 3.8e-105) {
		tmp = c * ((a * j) - (z * b));
	} else if (b <= 6.5e-43) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = y * ((x * z) - (i * j))
	t_3 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -4e+102:
		tmp = t_3
	elif b <= -2.3e-66:
		tmp = t_2
	elif b <= -6.5e-234:
		tmp = t_1
	elif b <= 3.2e-237:
		tmp = t_2
	elif b <= 3.8e-105:
		tmp = c * ((a * j) - (z * b))
	elif b <= 6.5e-43:
		tmp = t_1
	else:
		tmp = t_3
	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(y * Float64(Float64(x * z) - Float64(i * j)))
	t_3 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -4e+102)
		tmp = t_3;
	elseif (b <= -2.3e-66)
		tmp = t_2;
	elseif (b <= -6.5e-234)
		tmp = t_1;
	elseif (b <= 3.2e-237)
		tmp = t_2;
	elseif (b <= 3.8e-105)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (b <= 6.5e-43)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = y * ((x * z) - (i * j));
	t_3 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -4e+102)
		tmp = t_3;
	elseif (b <= -2.3e-66)
		tmp = t_2;
	elseif (b <= -6.5e-234)
		tmp = t_1;
	elseif (b <= 3.2e-237)
		tmp = t_2;
	elseif (b <= 3.8e-105)
		tmp = c * ((a * j) - (z * b));
	elseif (b <= 6.5e-43)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4e+102], t$95$3, If[LessEqual[b, -2.3e-66], t$95$2, If[LessEqual[b, -6.5e-234], t$95$1, If[LessEqual[b, 3.2e-237], t$95$2, If[LessEqual[b, 3.8e-105], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.5e-43], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.99999999999999991e102 or 6.50000000000000001e-43 < b

   1. Initial program 67.1%

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

   2. Taylor expanded in b around inf 65.1%

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

      1. *-commutative 65.1%

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

      2. *-commutative 65.1%

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

   4. Simplified 65.1%

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

   if -3.99999999999999991e102 < b < -2.29999999999999992e-66 or -6.4999999999999994e-234 < b < 3.2e-237

   1. Initial program 73.2%

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

   2. Taylor expanded in y around inf 57.5%

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

      1. +-commutative 57.5%

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

      2. mul-1-neg 57.5%

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

      3. unsub-neg 57.5%

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

      4. *-commutative 57.5%

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

   4. Simplified 57.5%

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

   if -2.29999999999999992e-66 < b < -6.4999999999999994e-234 or 3.7999999999999998e-105 < b < 6.50000000000000001e-43

   1. Initial program 84.9%

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

      1. prod-diff 82.1%

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

      2. *-commutative 82.1%

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

      3. fma-neg 82.1%

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

      4. distribute-rgt-in 82.1%

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

      5. *-commutative 82.1%

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

      6. *-commutative 82.1%

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

      7. *-commutative 82.1%

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

   3. Applied egg-rr 82.1%

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

   4. Taylor expanded in j around inf 57.5%

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

   if 3.2e-237 < b < 3.7999999999999998e-105

   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. Taylor expanded in c around inf 61.4%

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

      1. *-commutative 61.4%

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

   4. Simplified 61.4%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{+102}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-66}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{-234}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-237}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-105}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-43}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 14: 43.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.55 \cdot 10^{-70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-298}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{-225}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 0.029:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -1.55e-70)
     t_1
     (if (<= a 4.4e-298)
       (* t (* b i))
       (if (<= a 1.08e-225)
         (* y (* i (- j)))
         (if (<= a 0.029) (* x (* y z)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.55e-70) {
		tmp = t_1;
	} else if (a <= 4.4e-298) {
		tmp = t * (b * i);
	} else if (a <= 1.08e-225) {
		tmp = y * (i * -j);
	} else if (a <= 0.029) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (a <= (-1.55d-70)) then
        tmp = t_1
    else if (a <= 4.4d-298) then
        tmp = t * (b * i)
    else if (a <= 1.08d-225) then
        tmp = y * (i * -j)
    else if (a <= 0.029d0) then
        tmp = x * (y * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.55e-70) {
		tmp = t_1;
	} else if (a <= 4.4e-298) {
		tmp = t * (b * i);
	} else if (a <= 1.08e-225) {
		tmp = y * (i * -j);
	} else if (a <= 0.029) {
		tmp = x * (y * z);
	} 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 <= -1.55e-70:
		tmp = t_1
	elif a <= 4.4e-298:
		tmp = t * (b * i)
	elif a <= 1.08e-225:
		tmp = y * (i * -j)
	elif a <= 0.029:
		tmp = x * (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -1.55e-70)
		tmp = t_1;
	elseif (a <= 4.4e-298)
		tmp = Float64(t * Float64(b * i));
	elseif (a <= 1.08e-225)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (a <= 0.029)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -1.55e-70)
		tmp = t_1;
	elseif (a <= 4.4e-298)
		tmp = t * (b * i);
	elseif (a <= 1.08e-225)
		tmp = y * (i * -j);
	elseif (a <= 0.029)
		tmp = x * (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.55e-70], t$95$1, If[LessEqual[a, 4.4e-298], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.08e-225], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 0.029], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.55e-70 or 0.0290000000000000015 < a

   1. Initial program 66.0%

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

   2. Taylor expanded in a around inf 50.1%

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

      1. +-commutative 50.1%

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

      2. mul-1-neg 50.1%

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

      3. unsub-neg 50.1%

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

      4. *-commutative 50.1%

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

      5. *-commutative 50.1%

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

   4. Simplified 50.1%

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

   if -1.55e-70 < a < 4.4e-298

   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. Taylor expanded in t around inf 40.3%

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

      1. distribute-lft-out-- 40.3%

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

      2. *-commutative 40.3%

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

      3. *-commutative 40.3%

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

   4. Simplified 40.3%

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

   5. Taylor expanded in x around 0 34.5%

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

      1. *-commutative 34.5%

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

      2. *-commutative 34.5%

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

      3. associate-*l* 38.3%

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

   7. Simplified 38.3%

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

   if 4.4e-298 < a < 1.08000000000000006e-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. Taylor expanded in y around inf 63.1%

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

      1. +-commutative 63.1%

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

      2. mul-1-neg 63.1%

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

      3. unsub-neg 63.1%

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

      4. *-commutative 63.1%

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

   4. Simplified 63.1%

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

   5. Taylor expanded in x around 0 56.5%

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

      1. neg-mul-1 56.5%

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

      2. distribute-rgt-neg-in 56.5%

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

   7. Simplified 56.5%

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

   if 1.08000000000000006e-225 < a < 0.0290000000000000015

   1. Initial program 82.9%

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

   2. Taylor expanded in a around 0 67.9%

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

      1. *-commutative 67.9%

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

      2. *-commutative 67.9%

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

      3. sub-neg 67.9%

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

      4. associate-*r* 67.9%

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

      5. associate-*r* 67.9%

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

      6. *-commutative 67.9%

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

      7. associate-*r* 60.6%

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

      8. distribute-rgt-in 60.6%

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

      9. +-commutative 60.6%

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

      10. mul-1-neg 60.6%

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

      11. unsub-neg 60.6%

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

      12. *-commutative 60.6%

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

      13. distribute-rgt-neg-in 60.6%

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

      14. neg-sub0 60.6%

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

      15. *-commutative 60.6%

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

      16. associate--r- 60.6%

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

   4. Simplified 60.6%

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

   5. Taylor expanded in x around inf 43.6%

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

4. Final simplification 46.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{-70}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-298}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{-225}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 0.029:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]

Alternative 15: 50.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -2.7 \cdot 10^{+76}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2600000000000:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-85}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-41}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))))
   (if (<= b -2.7e+76)
     t_1
     (if (<= b -2600000000000.0)
       (* x (* y z))
       (if (<= b -2e-85)
         (* i (- (* t b) (* y j)))
         (if (<= b 1.2e-41) (* j (- (* a c) (* y i))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -2.7e+76) {
		tmp = t_1;
	} else if (b <= -2600000000000.0) {
		tmp = x * (y * z);
	} else if (b <= -2e-85) {
		tmp = i * ((t * b) - (y * j));
	} else if (b <= 1.2e-41) {
		tmp = j * ((a * c) - (y * 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 = b * ((t * i) - (z * c))
    if (b <= (-2.7d+76)) then
        tmp = t_1
    else if (b <= (-2600000000000.0d0)) then
        tmp = x * (y * z)
    else if (b <= (-2d-85)) then
        tmp = i * ((t * b) - (y * j))
    else if (b <= 1.2d-41) then
        tmp = j * ((a * c) - (y * 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 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -2.7e+76) {
		tmp = t_1;
	} else if (b <= -2600000000000.0) {
		tmp = x * (y * z);
	} else if (b <= -2e-85) {
		tmp = i * ((t * b) - (y * j));
	} else if (b <= 1.2e-41) {
		tmp = j * ((a * c) - (y * i));
	} 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 <= -2.7e+76:
		tmp = t_1
	elif b <= -2600000000000.0:
		tmp = x * (y * z)
	elif b <= -2e-85:
		tmp = i * ((t * b) - (y * j))
	elif b <= 1.2e-41:
		tmp = j * ((a * c) - (y * i))
	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 <= -2.7e+76)
		tmp = t_1;
	elseif (b <= -2600000000000.0)
		tmp = Float64(x * Float64(y * z));
	elseif (b <= -2e-85)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (b <= 1.2e-41)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -2.7e+76)
		tmp = t_1;
	elseif (b <= -2600000000000.0)
		tmp = x * (y * z);
	elseif (b <= -2e-85)
		tmp = i * ((t * b) - (y * j));
	elseif (b <= 1.2e-41)
		tmp = j * ((a * c) - (y * i));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.7e+76], t$95$1, If[LessEqual[b, -2600000000000.0], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2e-85], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.2e-41], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.6999999999999999e76 or 1.20000000000000011e-41 < b

   1. Initial program 67.9%

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

   2. Taylor expanded in b around inf 64.5%

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

      1. *-commutative 64.5%

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

      2. *-commutative 64.5%

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

   4. Simplified 64.5%

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

   if -2.6999999999999999e76 < b < -2.6e12

   1. Initial program 69.5%

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

   2. Taylor expanded in a around 0 44.2%

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

      1. *-commutative 44.2%

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

      2. *-commutative 44.2%

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

      3. sub-neg 44.2%

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

      4. associate-*r* 44.2%

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

      5. associate-*r* 44.2%

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

      6. *-commutative 44.2%

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

      7. associate-*r* 49.8%

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

      8. distribute-rgt-in 56.0%

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

      9. +-commutative 56.0%

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

      10. mul-1-neg 56.0%

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

      11. unsub-neg 56.0%

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

      12. *-commutative 56.0%

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

      13. distribute-rgt-neg-in 56.0%

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

      14. neg-sub0 56.0%

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

      15. *-commutative 56.0%

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

      16. associate--r- 56.0%

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

   4. Simplified 56.0%

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

   5. Taylor expanded in x around inf 44.0%

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

   if -2.6e12 < b < -2e-85

   1. Initial program 85.6%

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

      1. prod-diff 75.6%

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

      2. *-commutative 75.6%

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

      3. fma-neg 75.6%

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

      4. distribute-rgt-in 75.6%

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

      5. *-commutative 75.6%

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

      6. *-commutative 75.6%

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

      7. *-commutative 75.6%

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

   3. Applied egg-rr 75.6%

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

   4. Taylor expanded in i around inf 60.5%

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

   6. Simplified 60.5%

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

   if -2e-85 < b < 1.20000000000000011e-41

   1. Initial program 75.2%

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

      1. prod-diff 74.9%

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

      2. *-commutative 74.9%

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

      3. fma-neg 74.9%

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

      4. distribute-rgt-in 74.9%

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

      5. *-commutative 74.9%

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

      6. *-commutative 74.9%

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

      7. *-commutative 74.9%

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

   3. Applied egg-rr 74.9%

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

   4. Taylor expanded in j around inf 56.1%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.7 \cdot 10^{+76}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2600000000000:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-85}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-41}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 16: 29.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{+168}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq -0.031:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-298}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-225}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -2.4e+168)
   (* t (* x (- a)))
   (if (<= a -0.031)
     (* a (* c j))
     (if (<= a 7e-298)
       (* i (* t b))
       (if (<= a 6.5e-225)
         (* y (* i (- j)))
         (if (<= a 3.6e+42) (* x (* y z)) (* j (* a 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 <= -2.4e+168) {
		tmp = t * (x * -a);
	} else if (a <= -0.031) {
		tmp = a * (c * j);
	} else if (a <= 7e-298) {
		tmp = i * (t * b);
	} else if (a <= 6.5e-225) {
		tmp = y * (i * -j);
	} else if (a <= 3.6e+42) {
		tmp = x * (y * z);
	} else {
		tmp = j * (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) :: tmp
    if (a <= (-2.4d+168)) then
        tmp = t * (x * -a)
    else if (a <= (-0.031d0)) then
        tmp = a * (c * j)
    else if (a <= 7d-298) then
        tmp = i * (t * b)
    else if (a <= 6.5d-225) then
        tmp = y * (i * -j)
    else if (a <= 3.6d+42) then
        tmp = x * (y * z)
    else
        tmp = j * (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 tmp;
	if (a <= -2.4e+168) {
		tmp = t * (x * -a);
	} else if (a <= -0.031) {
		tmp = a * (c * j);
	} else if (a <= 7e-298) {
		tmp = i * (t * b);
	} else if (a <= 6.5e-225) {
		tmp = y * (i * -j);
	} else if (a <= 3.6e+42) {
		tmp = x * (y * z);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -2.4e+168:
		tmp = t * (x * -a)
	elif a <= -0.031:
		tmp = a * (c * j)
	elif a <= 7e-298:
		tmp = i * (t * b)
	elif a <= 6.5e-225:
		tmp = y * (i * -j)
	elif a <= 3.6e+42:
		tmp = x * (y * z)
	else:
		tmp = j * (a * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -2.4e+168)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (a <= -0.031)
		tmp = Float64(a * Float64(c * j));
	elseif (a <= 7e-298)
		tmp = Float64(i * Float64(t * b));
	elseif (a <= 6.5e-225)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (a <= 3.6e+42)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(j * Float64(a * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -2.4e+168)
		tmp = t * (x * -a);
	elseif (a <= -0.031)
		tmp = a * (c * j);
	elseif (a <= 7e-298)
		tmp = i * (t * b);
	elseif (a <= 6.5e-225)
		tmp = y * (i * -j);
	elseif (a <= 3.6e+42)
		tmp = x * (y * z);
	else
		tmp = j * (a * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -2.4e+168], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -0.031], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7e-298], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.5e-225], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.6e+42], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -2.40000000000000009e168

   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. Taylor expanded in a around inf 58.4%

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

      1. +-commutative 58.4%

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

      2. mul-1-neg 58.4%

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

      3. unsub-neg 58.4%

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

      4. *-commutative 58.4%

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

      5. *-commutative 58.4%

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

   4. Simplified 58.4%

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

   5. Taylor expanded in j around 0 43.6%

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

      1. associate-*r* 43.6%

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

      2. *-commutative 43.6%

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

      3. associate-*r* 46.4%

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

      4. mul-1-neg 46.4%

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

   7. Simplified 46.4%

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

   if -2.40000000000000009e168 < a < -0.031

   1. Initial program 56.7%

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

   2. Taylor expanded in a around inf 43.3%

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

      1. +-commutative 43.3%

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

      2. mul-1-neg 43.3%

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

      3. unsub-neg 43.3%

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

      4. *-commutative 43.3%

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

      5. *-commutative 43.3%

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

   4. Simplified 43.3%

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

   5. Taylor expanded in j around inf 31.3%

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

      1. *-commutative 31.3%

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

   7. Simplified 31.3%

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

   if -0.031 < a < 6.9999999999999996e-298

   1. Initial program 78.3%

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

   2. Taylor expanded in i around inf 46.9%

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

      1. distribute-lft-out-- 46.9%

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

      2. *-commutative 46.9%

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

      3. *-commutative 46.9%

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

   4. Simplified 46.9%

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

   5. Taylor expanded in y around 0 34.1%

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

      1. *-commutative 34.1%

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

      2. associate-*r* 36.8%

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

   7. Simplified 36.8%

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

   if 6.9999999999999996e-298 < a < 6.5000000000000005e-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. Taylor expanded in y around inf 63.1%

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

      1. +-commutative 63.1%

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

      2. mul-1-neg 63.1%

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

      3. unsub-neg 63.1%

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

      4. *-commutative 63.1%

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

   4. Simplified 63.1%

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

   5. Taylor expanded in x around 0 56.5%

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

      1. neg-mul-1 56.5%

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

      2. distribute-rgt-neg-in 56.5%

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

   7. Simplified 56.5%

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

   if 6.5000000000000005e-225 < a < 3.6000000000000001e42

   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. Taylor expanded in a around 0 66.2%

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

      1. *-commutative 66.2%

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

      2. *-commutative 66.2%

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

      3. sub-neg 66.2%

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

      4. associate-*r* 66.2%

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

      5. associate-*r* 66.2%

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

      6. *-commutative 66.2%

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

      7. associate-*r* 59.6%

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

      8. distribute-rgt-in 59.6%

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

      9. +-commutative 59.6%

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

      10. mul-1-neg 59.6%

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

      11. unsub-neg 59.6%

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

      12. *-commutative 59.6%

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

      13. distribute-rgt-neg-in 59.6%

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

      14. neg-sub0 59.6%

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

      15. *-commutative 59.6%

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

      16. associate--r- 59.6%

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

   4. Simplified 59.6%

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

   5. Taylor expanded in x around inf 42.1%

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

   if 3.6000000000000001e42 < a

   1. Initial program 68.9%

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

      1. prod-diff 64.8%

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

      2. *-commutative 64.8%

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

      3. fma-neg 64.8%

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

      4. distribute-rgt-in 64.8%

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

      5. *-commutative 64.8%

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

      6. *-commutative 64.8%

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

      7. *-commutative 64.8%

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

   3. Applied egg-rr 64.8%

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

   4. Taylor expanded in j around inf 52.7%

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

   5. Taylor expanded in a around inf 46.4%

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

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{+168}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq -0.031:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-298}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-225}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \]

Alternative 17: 30.1% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c\right)\\ \mathbf{if}\;a \leq -1.5:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-297}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-225}:\\ \;\;\;\;-j \cdot \left(y \cdot i\right)\\ \mathbf{elif}\;a \leq 1.32 \cdot 10^{+39}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (* a c))))
   (if (<= a -1.5)
     t_1
     (if (<= a 1.65e-297)
       (* i (* t b))
       (if (<= a 5e-225)
         (- (* j (* y i)))
         (if (<= a 1.32e+39) (* x (* y z)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (a * c);
	double tmp;
	if (a <= -1.5) {
		tmp = t_1;
	} else if (a <= 1.65e-297) {
		tmp = i * (t * b);
	} else if (a <= 5e-225) {
		tmp = -(j * (y * i));
	} else if (a <= 1.32e+39) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (a * c)
    if (a <= (-1.5d0)) then
        tmp = t_1
    else if (a <= 1.65d-297) then
        tmp = i * (t * b)
    else if (a <= 5d-225) then
        tmp = -(j * (y * i))
    else if (a <= 1.32d+39) then
        tmp = x * (y * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (a * c);
	double tmp;
	if (a <= -1.5) {
		tmp = t_1;
	} else if (a <= 1.65e-297) {
		tmp = i * (t * b);
	} else if (a <= 5e-225) {
		tmp = -(j * (y * i));
	} else if (a <= 1.32e+39) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * (a * c)
	tmp = 0
	if a <= -1.5:
		tmp = t_1
	elif a <= 1.65e-297:
		tmp = i * (t * b)
	elif a <= 5e-225:
		tmp = -(j * (y * i))
	elif a <= 1.32e+39:
		tmp = x * (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(a * c))
	tmp = 0.0
	if (a <= -1.5)
		tmp = t_1;
	elseif (a <= 1.65e-297)
		tmp = Float64(i * Float64(t * b));
	elseif (a <= 5e-225)
		tmp = Float64(-Float64(j * Float64(y * i)));
	elseif (a <= 1.32e+39)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * (a * c);
	tmp = 0.0;
	if (a <= -1.5)
		tmp = t_1;
	elseif (a <= 1.65e-297)
		tmp = i * (t * b);
	elseif (a <= 5e-225)
		tmp = -(j * (y * i));
	elseif (a <= 1.32e+39)
		tmp = x * (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.5], t$95$1, If[LessEqual[a, 1.65e-297], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5e-225], (-N[(j * N[(y * i), $MachinePrecision]), $MachinePrecision]), If[LessEqual[a, 1.32e+39], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.5 or 1.32e39 < a

   1. Initial program 63.0%

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

      1. prod-diff 61.3%

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

      2. *-commutative 61.3%

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

      3. fma-neg 61.3%

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

      4. distribute-rgt-in 59.6%

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

      5. *-commutative 59.6%

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

      6. *-commutative 59.6%

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

      7. *-commutative 59.6%

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

   3. Applied egg-rr 59.6%

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

   4. Taylor expanded in j around inf 48.4%

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

   5. Taylor expanded in a around inf 37.7%

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

   if -1.5 < a < 1.6499999999999999e-297

   1. Initial program 78.3%

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

   2. Taylor expanded in i around inf 46.9%

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

      1. distribute-lft-out-- 46.9%

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

      2. *-commutative 46.9%

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

      3. *-commutative 46.9%

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

   4. Simplified 46.9%

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

   5. Taylor expanded in y around 0 34.1%

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

      1. *-commutative 34.1%

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

      2. associate-*r* 36.8%

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

   7. Simplified 36.8%

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

   if 1.6499999999999999e-297 < a < 5.0000000000000001e-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. Step-by-step derivation

      1. prod-diff 66.7%

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

      2. *-commutative 66.7%

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

      3. fma-neg 66.7%

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

      4. distribute-rgt-in 66.7%

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

      5. *-commutative 66.7%

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

      6. *-commutative 66.7%

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

      7. *-commutative 66.7%

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

   3. Applied egg-rr 66.7%

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

   4. Taylor expanded in j around inf 57.0%

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

   5. Taylor expanded in a around 0 50.5%

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

      1. associate-*r* 50.5%

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

      2. neg-mul-1 50.5%

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

      3. *-commutative 50.5%

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

   7. Simplified 50.5%

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

   if 5.0000000000000001e-225 < a < 1.32e39

   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. Taylor expanded in a around 0 66.2%

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

      1. *-commutative 66.2%

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

      2. *-commutative 66.2%

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

      3. sub-neg 66.2%

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

      4. associate-*r* 66.2%

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

      5. associate-*r* 66.2%

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

      6. *-commutative 66.2%

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

      7. associate-*r* 59.6%

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

      8. distribute-rgt-in 59.6%

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

      9. +-commutative 59.6%

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

      10. mul-1-neg 59.6%

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

      11. unsub-neg 59.6%

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

      12. *-commutative 59.6%

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

      13. distribute-rgt-neg-in 59.6%

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

      14. neg-sub0 59.6%

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

      15. *-commutative 59.6%

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

      16. associate--r- 59.6%

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

   4. Simplified 59.6%

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

   5. Taylor expanded in x around inf 42.1%

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

4. Final simplification 39.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.5:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-297}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-225}:\\ \;\;\;\;-j \cdot \left(y \cdot i\right)\\ \mathbf{elif}\;a \leq 1.32 \cdot 10^{+39}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \]

Alternative 18: 30.1% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c\right)\\ \mathbf{if}\;a \leq -1.6:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-297}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-226}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (* a c))))
   (if (<= a -1.6)
     t_1
     (if (<= a 4e-297)
       (* i (* t b))
       (if (<= a 3.4e-226)
         (* y (* i (- j)))
         (if (<= a 1.02e+41) (* x (* y z)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (a * c);
	double tmp;
	if (a <= -1.6) {
		tmp = t_1;
	} else if (a <= 4e-297) {
		tmp = i * (t * b);
	} else if (a <= 3.4e-226) {
		tmp = y * (i * -j);
	} else if (a <= 1.02e+41) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (a * c)
    if (a <= (-1.6d0)) then
        tmp = t_1
    else if (a <= 4d-297) then
        tmp = i * (t * b)
    else if (a <= 3.4d-226) then
        tmp = y * (i * -j)
    else if (a <= 1.02d+41) then
        tmp = x * (y * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (a * c);
	double tmp;
	if (a <= -1.6) {
		tmp = t_1;
	} else if (a <= 4e-297) {
		tmp = i * (t * b);
	} else if (a <= 3.4e-226) {
		tmp = y * (i * -j);
	} else if (a <= 1.02e+41) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * (a * c)
	tmp = 0
	if a <= -1.6:
		tmp = t_1
	elif a <= 4e-297:
		tmp = i * (t * b)
	elif a <= 3.4e-226:
		tmp = y * (i * -j)
	elif a <= 1.02e+41:
		tmp = x * (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(a * c))
	tmp = 0.0
	if (a <= -1.6)
		tmp = t_1;
	elseif (a <= 4e-297)
		tmp = Float64(i * Float64(t * b));
	elseif (a <= 3.4e-226)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (a <= 1.02e+41)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * (a * c);
	tmp = 0.0;
	if (a <= -1.6)
		tmp = t_1;
	elseif (a <= 4e-297)
		tmp = i * (t * b);
	elseif (a <= 3.4e-226)
		tmp = y * (i * -j);
	elseif (a <= 1.02e+41)
		tmp = x * (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.6], t$95$1, If[LessEqual[a, 4e-297], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.4e-226], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.02e+41], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.6000000000000001 or 1.01999999999999992e41 < a

   1. Initial program 63.0%

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

      1. prod-diff 61.3%

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

      2. *-commutative 61.3%

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

      3. fma-neg 61.3%

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

      4. distribute-rgt-in 59.6%

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

      5. *-commutative 59.6%

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

      6. *-commutative 59.6%

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

      7. *-commutative 59.6%

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

   3. Applied egg-rr 59.6%

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

   4. Taylor expanded in j around inf 48.4%

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

   5. Taylor expanded in a around inf 37.7%

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

   if -1.6000000000000001 < a < 4.00000000000000016e-297

   1. Initial program 78.3%

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

   2. Taylor expanded in i around inf 46.9%

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

      1. distribute-lft-out-- 46.9%

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

      2. *-commutative 46.9%

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

      3. *-commutative 46.9%

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

   4. Simplified 46.9%

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

   5. Taylor expanded in y around 0 34.1%

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

      1. *-commutative 34.1%

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

      2. associate-*r* 36.8%

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

   7. Simplified 36.8%

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

   if 4.00000000000000016e-297 < a < 3.40000000000000007e-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. Taylor expanded in y around inf 63.1%

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

      1. +-commutative 63.1%

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

      2. mul-1-neg 63.1%

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

      3. unsub-neg 63.1%

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

      4. *-commutative 63.1%

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

   4. Simplified 63.1%

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

   5. Taylor expanded in x around 0 56.5%

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

      1. neg-mul-1 56.5%

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

      2. distribute-rgt-neg-in 56.5%

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

   7. Simplified 56.5%

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

   if 3.40000000000000007e-226 < a < 1.01999999999999992e41

   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. Taylor expanded in a around 0 66.2%

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

      1. *-commutative 66.2%

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

      2. *-commutative 66.2%

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

      3. sub-neg 66.2%

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

      4. associate-*r* 66.2%

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

      5. associate-*r* 66.2%

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

      6. *-commutative 66.2%

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

      7. associate-*r* 59.6%

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

      8. distribute-rgt-in 59.6%

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

      9. +-commutative 59.6%

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

      10. mul-1-neg 59.6%

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

      11. unsub-neg 59.6%

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

      12. *-commutative 59.6%

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

      13. distribute-rgt-neg-in 59.6%

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

      14. neg-sub0 59.6%

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

      15. *-commutative 59.6%

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

      16. associate--r- 59.6%

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

   4. Simplified 59.6%

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

   5. Taylor expanded in x around inf 42.1%

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

4. Final simplification 39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-297}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-226}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \]

Alternative 19: 30.1% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c\right)\\ \mathbf{if}\;a \leq -7.2 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.85 \cdot 10^{-245}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{+44}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (* a c))))
   (if (<= a -7.2e-7)
     t_1
     (if (<= a 2.85e-245)
       (* t (* b i))
       (if (<= a 3.7e+44) (* x (* y z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (a * c);
	double tmp;
	if (a <= -7.2e-7) {
		tmp = t_1;
	} else if (a <= 2.85e-245) {
		tmp = t * (b * i);
	} else if (a <= 3.7e+44) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (a * c)
    if (a <= (-7.2d-7)) then
        tmp = t_1
    else if (a <= 2.85d-245) then
        tmp = t * (b * i)
    else if (a <= 3.7d+44) then
        tmp = x * (y * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (a * c);
	double tmp;
	if (a <= -7.2e-7) {
		tmp = t_1;
	} else if (a <= 2.85e-245) {
		tmp = t * (b * i);
	} else if (a <= 3.7e+44) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * (a * c)
	tmp = 0
	if a <= -7.2e-7:
		tmp = t_1
	elif a <= 2.85e-245:
		tmp = t * (b * i)
	elif a <= 3.7e+44:
		tmp = x * (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(a * c))
	tmp = 0.0
	if (a <= -7.2e-7)
		tmp = t_1;
	elseif (a <= 2.85e-245)
		tmp = Float64(t * Float64(b * i));
	elseif (a <= 3.7e+44)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * (a * c);
	tmp = 0.0;
	if (a <= -7.2e-7)
		tmp = t_1;
	elseif (a <= 2.85e-245)
		tmp = t * (b * i);
	elseif (a <= 3.7e+44)
		tmp = x * (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.2e-7], t$95$1, If[LessEqual[a, 2.85e-245], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.7e+44], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.19999999999999989e-7 or 3.7000000000000001e44 < a

   1. Initial program 63.0%

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

      1. prod-diff 61.3%

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

      2. *-commutative 61.3%

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

      3. fma-neg 61.3%

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

      4. distribute-rgt-in 59.6%

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

      5. *-commutative 59.6%

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

      6. *-commutative 59.6%

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

      7. *-commutative 59.6%

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

   3. Applied egg-rr 59.6%

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

   4. Taylor expanded in j around inf 48.4%

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

   5. Taylor expanded in a around inf 37.7%

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

   if -7.19999999999999989e-7 < a < 2.85e-245

   1. Initial program 77.0%

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

   2. Taylor expanded in t around inf 41.8%

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

      1. distribute-lft-out-- 41.8%

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

      2. *-commutative 41.8%

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

      3. *-commutative 41.8%

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

   4. Simplified 41.8%

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

   5. Taylor expanded in x around 0 31.6%

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

      1. *-commutative 31.6%

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

      2. *-commutative 31.6%

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

      3. associate-*l* 35.3%

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

   7. Simplified 35.3%

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

   if 2.85e-245 < a < 3.7000000000000001e44

   1. Initial program 81.4%

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

   2. Taylor expanded in a around 0 69.3%

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

      1. *-commutative 69.3%

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

      2. *-commutative 69.3%

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

      3. sub-neg 69.3%

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

      4. associate-*r* 69.3%

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

      5. associate-*r* 69.3%

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

      6. *-commutative 69.3%

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

      7. associate-*r* 63.4%

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

      8. distribute-rgt-in 63.4%

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

      9. +-commutative 63.4%

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

      10. mul-1-neg 63.4%

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

      11. unsub-neg 63.4%

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

      12. *-commutative 63.4%

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

      13. distribute-rgt-neg-in 63.4%

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

      14. neg-sub0 63.4%

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

      15. *-commutative 63.4%

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

      16. associate--r- 63.4%

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

   4. Simplified 63.4%

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

   5. Taylor expanded in x around inf 39.9%

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

4. Final simplification 37.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{-7}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;a \leq 2.85 \cdot 10^{-245}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{+44}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \]

Alternative 20: 30.5% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -0.00016 \lor \neg \left(c \leq 1.3 \cdot 10^{-31}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -0.00016) (not (<= c 1.3e-31))) (* a (* c j)) (* b (* t i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -0.00016) || !(c <= 1.3e-31)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((c <= (-0.00016d0)) .or. (.not. (c <= 1.3d-31))) then
        tmp = a * (c * j)
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -0.00016) || !(c <= 1.3e-31)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -0.00016) or not (c <= 1.3e-31):
		tmp = a * (c * j)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -0.00016) || !(c <= 1.3e-31))
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -0.00016) || ~((c <= 1.3e-31)))
		tmp = a * (c * j);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -0.00016], N[Not[LessEqual[c, 1.3e-31]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.60000000000000013e-4 or 1.29999999999999998e-31 < c

   1. Initial program 63.1%

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

   2. Taylor expanded in a around inf 40.0%

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

      1. +-commutative 40.0%

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

      2. mul-1-neg 40.0%

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

      3. unsub-neg 40.0%

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

      4. *-commutative 40.0%

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

      5. *-commutative 40.0%

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

   4. Simplified 40.0%

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

   5. Taylor expanded in j around inf 31.0%

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

      1. *-commutative 31.0%

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

   7. Simplified 31.0%

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

   if -1.60000000000000013e-4 < c < 1.29999999999999998e-31

   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. Taylor expanded in t around inf 40.1%

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

      1. distribute-lft-out-- 40.1%

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

      2. *-commutative 40.1%

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

      3. *-commutative 40.1%

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

   4. Simplified 40.1%

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

   5. Taylor expanded in x around 0 29.1%

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

4. Final simplification 30.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -0.00016 \lor \neg \left(c \leq 1.3 \cdot 10^{-31}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]

Alternative 21: 30.1% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -5.5 \cdot 10^{-10}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;i \leq 8:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -5.5e-10)
   (* b (* t i))
   (if (<= i 8.0) (* 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 (i <= -5.5e-10) {
		tmp = b * (t * i);
	} else if (i <= 8.0) {
		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 (i <= (-5.5d-10)) then
        tmp = b * (t * i)
    else if (i <= 8.0d0) 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 (i <= -5.5e-10) {
		tmp = b * (t * i);
	} else if (i <= 8.0) {
		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 i <= -5.5e-10:
		tmp = b * (t * i)
	elif i <= 8.0:
		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 (i <= -5.5e-10)
		tmp = Float64(b * Float64(t * i));
	elseif (i <= 8.0)
		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 (i <= -5.5e-10)
		tmp = b * (t * i);
	elseif (i <= 8.0)
		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[i, -5.5e-10], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 8.0], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if i < -5.4999999999999996e-10

   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. Taylor expanded in t around inf 43.7%

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

      1. distribute-lft-out-- 43.7%

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

      2. *-commutative 43.7%

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

      3. *-commutative 43.7%

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

   4. Simplified 43.7%

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

   5. Taylor expanded in x around 0 40.6%

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

   if -5.4999999999999996e-10 < i < 8

   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. Step-by-step derivation

      1. prod-diff 74.5%

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

      2. *-commutative 74.5%

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

      3. fma-neg 74.5%

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

      4. distribute-rgt-in 73.1%

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

      5. *-commutative 73.1%

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

      6. *-commutative 73.1%

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

      7. *-commutative 73.1%

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

   3. Applied egg-rr 73.1%

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

   4. Taylor expanded in j around inf 35.1%

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

   5. Taylor expanded in a around inf 29.9%

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

   if 8 < i

   1. Initial program 65.1%

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

   2. Taylor expanded in i around inf 50.2%

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

      1. distribute-lft-out-- 50.2%

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

      2. *-commutative 50.2%

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

      3. *-commutative 50.2%

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

   4. Simplified 50.2%

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

   5. Taylor expanded in y around 0 25.6%

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

      1. *-commutative 25.6%

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

      2. associate-*r* 27.3%

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

   7. Simplified 27.3%

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

4. Final simplification 31.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -5.5 \cdot 10^{-10}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;i \leq 8:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \]

Alternative 22: 30.3% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -4.4 \cdot 10^{-10}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;i \leq 1.75:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -4.4e-10)
   (* b (* t i))
   (if (<= i 1.75) (* j (* a c)) (* t (* b i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -4.4e-10) {
		tmp = b * (t * i);
	} else if (i <= 1.75) {
		tmp = j * (a * c);
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (i <= (-4.4d-10)) then
        tmp = b * (t * i)
    else if (i <= 1.75d0) then
        tmp = j * (a * c)
    else
        tmp = t * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -4.4e-10) {
		tmp = b * (t * i);
	} else if (i <= 1.75) {
		tmp = j * (a * c);
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -4.4e-10:
		tmp = b * (t * i)
	elif i <= 1.75:
		tmp = j * (a * c)
	else:
		tmp = t * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -4.4e-10)
		tmp = Float64(b * Float64(t * i));
	elseif (i <= 1.75)
		tmp = Float64(j * Float64(a * c));
	else
		tmp = Float64(t * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -4.4e-10)
		tmp = b * (t * i);
	elseif (i <= 1.75)
		tmp = j * (a * c);
	else
		tmp = t * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -4.4e-10], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.75], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if i < -4.3999999999999998e-10

   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. Taylor expanded in t around inf 43.7%

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

      1. distribute-lft-out-- 43.7%

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

      2. *-commutative 43.7%

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

      3. *-commutative 43.7%

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

   4. Simplified 43.7%

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

   5. Taylor expanded in x around 0 40.6%

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

   if -4.3999999999999998e-10 < i < 1.75

   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. Step-by-step derivation

      1. prod-diff 74.5%

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

      2. *-commutative 74.5%

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

      3. fma-neg 74.5%

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

      4. distribute-rgt-in 73.1%

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

      5. *-commutative 73.1%

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

      6. *-commutative 73.1%

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

      7. *-commutative 73.1%

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

   3. Applied egg-rr 73.1%

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

   4. Taylor expanded in j around inf 35.1%

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

   5. Taylor expanded in a around inf 29.9%

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

   if 1.75 < i

   1. Initial program 65.1%

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

   2. Taylor expanded in t around inf 36.7%

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

      1. distribute-lft-out-- 36.7%

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

      2. *-commutative 36.7%

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

      3. *-commutative 36.7%

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

   4. Simplified 36.7%

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

   5. Taylor expanded in x around 0 25.6%

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

      1. *-commutative 25.6%

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

      2. *-commutative 25.6%

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

      3. associate-*l* 29.1%

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

   7. Simplified 29.1%

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

4. Final simplification 32.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4.4 \cdot 10^{-10}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;i \leq 1.75:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 23: 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 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. Taylor expanded in a around inf 34.0%

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

   1. +-commutative 34.0%

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

   2. mul-1-neg 34.0%

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

   3. unsub-neg 34.0%

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

   4. *-commutative 34.0%

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

   5. *-commutative 34.0%

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

4. Simplified 34.0%

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

5. Taylor expanded in j around inf 21.2%

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

   1. *-commutative 21.2%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

7. Simplified 21.2%

   \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

8. Final simplification 21.2%

   \[\leadsto a \cdot \left(c \cdot j\right) \]

Developer target: 59.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right)\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + t_1\\ \mathbf{if}\;x < -1.469694296777705 \cdot 10^{-64}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x < 3.2113527362226803 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - t_1\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* c a) (* y i))))
        (t_2
         (+
          (-
           (* x (- (* y z) (* t a)))
           (/
            (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0)))
            (+ (* c z) (* t i))))
          t_1)))
   (if (< x -1.469694296777705e-64)
     t_2
     (if (< x 3.2113527362226803e-147)
       (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) t_1))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (pow((c * z), 2.0) - pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((c * a) - (y * i))
    t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ** 2.0d0) - ((t * i) ** 2.0d0))) / ((c * z) + (t * i)))) + t_1
    if (x < (-1.469694296777705d-64)) then
        tmp = t_2
    else if (x < 3.2113527362226803d-147) then
        tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (Math.pow((c * z), 2.0) - Math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((c * a) - (y * i))
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (math.pow((c * z), 2.0) - math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1
	tmp = 0
	if x < -1.469694296777705e-64:
		tmp = t_2
	elif x < 3.2113527362226803e-147:
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(c * a) - Float64(y * i)))
	t_2 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(Float64(b * Float64((Float64(c * z) ^ 2.0) - (Float64(t * i) ^ 2.0))) / Float64(Float64(c * z) + Float64(t * i)))) + t_1)
	tmp = 0.0
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = Float64(Float64(Float64(Float64(b * i) - Float64(x * a)) * t) - Float64(Float64(z * Float64(c * b)) - t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((c * a) - (y * i));
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ^ 2.0) - ((t * i) ^ 2.0))) / ((c * z) + (t * i)))) + t_1;
	tmp = 0.0;
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[Power[N[(c * z), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(t * i), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * z), $MachinePrecision] + N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[Less[x, -1.469694296777705e-64], t$95$2, If[Less[x, 3.2113527362226803e-147], N[(N[(N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] - N[(N[(z * N[(c * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2023310 
(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)))))