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

Percentage Accurate: 73.9% → 82.3%

Time: 30.8s

Alternatives: 22

Speedup: 0.5×

• 57.6% 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: 73.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 82.3% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) - Float64(Float64(x * Float64(Float64(t * a) - Float64(y * z))) - Float64(b * Float64(Float64(t * i) - Float64(z * c)))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(z * Float64(x * y)) - Float64(a * Float64(Float64(x * t) - Float64(c * j))));
	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 * ((t * a) - (y * z))) - (b * ((t * i) - (z * c))));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = (z * (x * y)) - (a * ((x * t) - (c * j)));
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 90.6%

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

   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 y around -inf 17.7%

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

   4. Simplified 27.4%

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

   5. Taylor expanded in i around 0 35.7%

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

      1. +-commutative 35.7%

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

      2. associate-+l+ 35.7%

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

      3. +-commutative 35.7%

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

      4. mul-1-neg 35.7%

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

      5. associate-*r* 39.1%

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

      6. *-commutative 39.1%

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

      7. distribute-lft-neg-in 39.1%

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

      8. *-commutative 39.1%

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

      9. mul-1-neg 39.1%

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

      10. associate-*r* 42.4%

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

      11. distribute-rgt-in 48.8%

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

      12. +-commutative 48.8%

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

      13. mul-1-neg 48.8%

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

      14. sub-neg 48.8%

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

   7. Simplified 48.8%

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

   8. Taylor expanded in x around inf 53.6%

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

      1. associate-*r* 55.1%

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

      2. *-commutative 55.1%

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

   10. Simplified 55.1%

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

4. Final simplification 82.0%

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

Alternative 2: 57.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right) - a \cdot \left(x \cdot t - c \cdot j\right)\\ t_2 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -2.9 \cdot 10^{+51}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 3.7 \cdot 10^{-184}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 1.65 \cdot 10^{-138}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 1.15 \cdot 10^{-6} \lor \neg \left(i \leq 7800000\right) \land i \leq 6.6 \cdot 10^{+202}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* z (* x y)) (* a (- (* x t) (* c j)))))
        (t_2 (* i (- (* t b) (* y j)))))
   (if (<= i -2.9e+51)
     t_2
     (if (<= i 3.7e-184)
       t_1
       (if (<= i 1.65e-138)
         (* c (- (* a j) (* z b)))
         (if (or (<= i 1.15e-6) (and (not (<= i 7800000.0)) (<= i 6.6e+202)))
           t_1
           t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (z * (x * y)) - (a * ((x * t) - (c * j)));
	double t_2 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -2.9e+51) {
		tmp = t_2;
	} else if (i <= 3.7e-184) {
		tmp = t_1;
	} else if (i <= 1.65e-138) {
		tmp = c * ((a * j) - (z * b));
	} else if ((i <= 1.15e-6) || (!(i <= 7800000.0) && (i <= 6.6e+202))) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z * (x * y)) - (a * ((x * t) - (c * j)))
    t_2 = i * ((t * b) - (y * j))
    if (i <= (-2.9d+51)) then
        tmp = t_2
    else if (i <= 3.7d-184) then
        tmp = t_1
    else if (i <= 1.65d-138) then
        tmp = c * ((a * j) - (z * b))
    else if ((i <= 1.15d-6) .or. (.not. (i <= 7800000.0d0)) .and. (i <= 6.6d+202)) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (z * (x * y)) - (a * ((x * t) - (c * j)));
	double t_2 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -2.9e+51) {
		tmp = t_2;
	} else if (i <= 3.7e-184) {
		tmp = t_1;
	} else if (i <= 1.65e-138) {
		tmp = c * ((a * j) - (z * b));
	} else if ((i <= 1.15e-6) || (!(i <= 7800000.0) && (i <= 6.6e+202))) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (z * (x * y)) - (a * ((x * t) - (c * j)))
	t_2 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -2.9e+51:
		tmp = t_2
	elif i <= 3.7e-184:
		tmp = t_1
	elif i <= 1.65e-138:
		tmp = c * ((a * j) - (z * b))
	elif (i <= 1.15e-6) or (not (i <= 7800000.0) and (i <= 6.6e+202)):
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(z * Float64(x * y)) - Float64(a * Float64(Float64(x * t) - Float64(c * j))))
	t_2 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -2.9e+51)
		tmp = t_2;
	elseif (i <= 3.7e-184)
		tmp = t_1;
	elseif (i <= 1.65e-138)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif ((i <= 1.15e-6) || (!(i <= 7800000.0) && (i <= 6.6e+202)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (z * (x * y)) - (a * ((x * t) - (c * j)));
	t_2 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -2.9e+51)
		tmp = t_2;
	elseif (i <= 3.7e-184)
		tmp = t_1;
	elseif (i <= 1.65e-138)
		tmp = c * ((a * j) - (z * b));
	elseif ((i <= 1.15e-6) || (~((i <= 7800000.0)) && (i <= 6.6e+202)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(N[(x * t), $MachinePrecision] - N[(c * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.9e+51], t$95$2, If[LessEqual[i, 3.7e-184], t$95$1, If[LessEqual[i, 1.65e-138], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[i, 1.15e-6], And[N[Not[LessEqual[i, 7800000.0]], $MachinePrecision], LessEqual[i, 6.6e+202]]], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -2.8999999999999998e51 or 1.15e-6 < i < 7.8e6 or 6.5999999999999998e202 < i

   1. Initial program 60.9%

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

   2. Taylor expanded in y around -inf 64.6%

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

   4. Simplified 64.6%

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

   5. Taylor expanded in i around inf 74.8%

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

   6. Taylor expanded in j around 0 69.7%

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

      1. +-commutative 69.7%

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

      2. mul-1-neg 69.7%

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

      3. *-commutative 69.7%

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

      4. *-commutative 69.7%

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

      5. fma-def 69.7%

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

      6. fma-neg 69.7%

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

      7. *-commutative 69.7%

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

      8. associate-*l* 72.3%

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

      9. distribute-rgt-out-- 74.8%

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

   8. Simplified 74.8%

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

   if -2.8999999999999998e51 < i < 3.6999999999999999e-184 or 1.64999999999999991e-138 < i < 1.15e-6 or 7.8e6 < i < 6.5999999999999998e202

   1. Initial program 73.7%

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

   2. Taylor expanded in y around -inf 70.6%

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

   4. Simplified 74.2%

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

   5. Taylor expanded in i around 0 69.3%

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

      1. +-commutative 69.3%

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

      2. associate-+l+ 69.3%

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

      3. +-commutative 69.3%

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

      4. mul-1-neg 69.3%

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

      5. associate-*r* 71.9%

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

      6. *-commutative 71.9%

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

      7. distribute-lft-neg-in 71.9%

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

      8. *-commutative 71.9%

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

      9. mul-1-neg 71.9%

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

      10. associate-*r* 73.2%

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

      11. distribute-rgt-in 74.5%

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

      12. +-commutative 74.5%

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

      13. mul-1-neg 74.5%

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

      14. sub-neg 74.5%

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

   7. Simplified 74.5%

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

   8. Taylor expanded in x around inf 67.4%

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

      1. associate-*r* 66.9%

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

      2. *-commutative 66.9%

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

   10. Simplified 66.9%

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

   if 3.6999999999999999e-184 < i < 1.64999999999999991e-138

   1. Initial program 50.9%

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

   2. Taylor expanded in c around inf 83.7%

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

      1. *-commutative 83.7%

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

   4. Simplified 83.7%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.9 \cdot 10^{+51}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq 3.7 \cdot 10^{-184}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) - a \cdot \left(x \cdot t - c \cdot j\right)\\ \mathbf{elif}\;i \leq 1.65 \cdot 10^{-138}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 1.15 \cdot 10^{-6} \lor \neg \left(i \leq 7800000\right) \land i \leq 6.6 \cdot 10^{+202}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) - a \cdot \left(x \cdot t - c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]

Alternative 3: 64.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -2.6 \cdot 10^{+51} \lor \neg \left(i \leq 9.5 \cdot 10^{-7}\right) \land \left(i \leq 3200000 \lor \neg \left(i \leq 1.85 \cdot 10^{+202}\right)\right):\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - a \cdot \left(x \cdot t - c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -2.6e+51)
         (and (not (<= i 9.5e-7))
              (or (<= i 3200000.0) (not (<= i 1.85e+202)))))
   (* i (- (* t b) (* y j)))
   (- (* z (- (* x y) (* b c))) (* a (- (* x t) (* c j))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -2.6e+51) || (!(i <= 9.5e-7) && ((i <= 3200000.0) || !(i <= 1.85e+202)))) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = (z * ((x * y) - (b * c))) - (a * ((x * t) - (c * j)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((i <= (-2.6d+51)) .or. (.not. (i <= 9.5d-7)) .and. (i <= 3200000.0d0) .or. (.not. (i <= 1.85d+202))) then
        tmp = i * ((t * b) - (y * j))
    else
        tmp = (z * ((x * y) - (b * c))) - (a * ((x * t) - (c * j)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -2.6e+51) || (!(i <= 9.5e-7) && ((i <= 3200000.0) || !(i <= 1.85e+202)))) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = (z * ((x * y) - (b * c))) - (a * ((x * t) - (c * j)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (i <= -2.6e+51) or (not (i <= 9.5e-7) and ((i <= 3200000.0) or not (i <= 1.85e+202))):
		tmp = i * ((t * b) - (y * j))
	else:
		tmp = (z * ((x * y) - (b * c))) - (a * ((x * t) - (c * j)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((i <= -2.6e+51) || (!(i <= 9.5e-7) && ((i <= 3200000.0) || !(i <= 1.85e+202))))
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	else
		tmp = Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) - Float64(a * Float64(Float64(x * t) - Float64(c * j))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((i <= -2.6e+51) || (~((i <= 9.5e-7)) && ((i <= 3200000.0) || ~((i <= 1.85e+202)))))
		tmp = i * ((t * b) - (y * j));
	else
		tmp = (z * ((x * y) - (b * c))) - (a * ((x * t) - (c * j)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[i, -2.6e+51], And[N[Not[LessEqual[i, 9.5e-7]], $MachinePrecision], Or[LessEqual[i, 3200000.0], N[Not[LessEqual[i, 1.85e+202]], $MachinePrecision]]]], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(N[(x * t), $MachinePrecision] - N[(c * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -2.6000000000000001e51 or 9.5000000000000001e-7 < i < 3.2e6 or 1.8499999999999999e202 < i

   1. Initial program 60.9%

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

   2. Taylor expanded in y around -inf 64.6%

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

   4. Simplified 64.6%

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

   5. Taylor expanded in i around inf 74.8%

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

   6. Taylor expanded in j around 0 69.7%

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

      1. +-commutative 69.7%

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

      2. mul-1-neg 69.7%

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

      3. *-commutative 69.7%

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

      4. *-commutative 69.7%

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

      5. fma-def 69.7%

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

      6. fma-neg 69.7%

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

      7. *-commutative 69.7%

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

      8. associate-*l* 72.3%

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

      9. distribute-rgt-out-- 74.8%

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

   8. Simplified 74.8%

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

   if -2.6000000000000001e51 < i < 9.5000000000000001e-7 or 3.2e6 < i < 1.8499999999999999e202

   1. Initial program 72.2%

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

   2. Taylor expanded in y around -inf 70.3%

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

   4. Simplified 73.7%

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

   5. Taylor expanded in i around 0 67.5%

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

      1. +-commutative 67.5%

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

      2. associate-+l+ 67.5%

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

      3. +-commutative 67.5%

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

      4. mul-1-neg 67.5%

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

      5. associate-*r* 70.5%

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

      6. *-commutative 70.5%

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

      7. distribute-lft-neg-in 70.5%

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

      8. *-commutative 70.5%

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

      9. mul-1-neg 70.5%

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

      10. associate-*r* 72.8%

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

      11. distribute-rgt-in 73.9%

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

      12. +-commutative 73.9%

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

      13. mul-1-neg 73.9%

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

      14. sub-neg 73.9%

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

   7. Simplified 73.9%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.6 \cdot 10^{+51} \lor \neg \left(i \leq 9.5 \cdot 10^{-7}\right) \land \left(i \leq 3200000 \lor \neg \left(i \leq 1.85 \cdot 10^{+202}\right)\right):\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - a \cdot \left(x \cdot t - c \cdot j\right)\\ \end{array} \]

Alternative 4: 51.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_3 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_4 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;t \leq -4.6 \cdot 10^{+53}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-32}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-293}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-84}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 6.3 \cdot 10^{-16}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+76}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+129}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* a j) (* z b))))
        (t_2 (* z (- (* x y) (* b c))))
        (t_3 (* t (- (* b i) (* x a))))
        (t_4 (* i (- (* t b) (* y j)))))
   (if (<= t -4.6e+53)
     t_3
     (if (<= t -6e-32)
       t_2
       (if (<= t 7.8e-293)
         t_1
         (if (<= t 2.1e-84)
           t_2
           (if (<= t 6.3e-16)
             t_4
             (if (<= t 6.8e+33)
               t_1
               (if (<= t 5.4e+76)
                 (* x (- (* y z) (* t a)))
                 (if (<= t 2.1e+129) t_4 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 = c * ((a * j) - (z * b));
	double t_2 = z * ((x * y) - (b * c));
	double t_3 = t * ((b * i) - (x * a));
	double t_4 = i * ((t * b) - (y * j));
	double tmp;
	if (t <= -4.6e+53) {
		tmp = t_3;
	} else if (t <= -6e-32) {
		tmp = t_2;
	} else if (t <= 7.8e-293) {
		tmp = t_1;
	} else if (t <= 2.1e-84) {
		tmp = t_2;
	} else if (t <= 6.3e-16) {
		tmp = t_4;
	} else if (t <= 6.8e+33) {
		tmp = t_1;
	} else if (t <= 5.4e+76) {
		tmp = x * ((y * z) - (t * a));
	} else if (t <= 2.1e+129) {
		tmp = t_4;
	} 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) :: t_4
    real(8) :: tmp
    t_1 = c * ((a * j) - (z * b))
    t_2 = z * ((x * y) - (b * c))
    t_3 = t * ((b * i) - (x * a))
    t_4 = i * ((t * b) - (y * j))
    if (t <= (-4.6d+53)) then
        tmp = t_3
    else if (t <= (-6d-32)) then
        tmp = t_2
    else if (t <= 7.8d-293) then
        tmp = t_1
    else if (t <= 2.1d-84) then
        tmp = t_2
    else if (t <= 6.3d-16) then
        tmp = t_4
    else if (t <= 6.8d+33) then
        tmp = t_1
    else if (t <= 5.4d+76) then
        tmp = x * ((y * z) - (t * a))
    else if (t <= 2.1d+129) then
        tmp = t_4
    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 = c * ((a * j) - (z * b));
	double t_2 = z * ((x * y) - (b * c));
	double t_3 = t * ((b * i) - (x * a));
	double t_4 = i * ((t * b) - (y * j));
	double tmp;
	if (t <= -4.6e+53) {
		tmp = t_3;
	} else if (t <= -6e-32) {
		tmp = t_2;
	} else if (t <= 7.8e-293) {
		tmp = t_1;
	} else if (t <= 2.1e-84) {
		tmp = t_2;
	} else if (t <= 6.3e-16) {
		tmp = t_4;
	} else if (t <= 6.8e+33) {
		tmp = t_1;
	} else if (t <= 5.4e+76) {
		tmp = x * ((y * z) - (t * a));
	} else if (t <= 2.1e+129) {
		tmp = t_4;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((a * j) - (z * b))
	t_2 = z * ((x * y) - (b * c))
	t_3 = t * ((b * i) - (x * a))
	t_4 = i * ((t * b) - (y * j))
	tmp = 0
	if t <= -4.6e+53:
		tmp = t_3
	elif t <= -6e-32:
		tmp = t_2
	elif t <= 7.8e-293:
		tmp = t_1
	elif t <= 2.1e-84:
		tmp = t_2
	elif t <= 6.3e-16:
		tmp = t_4
	elif t <= 6.8e+33:
		tmp = t_1
	elif t <= 5.4e+76:
		tmp = x * ((y * z) - (t * a))
	elif t <= 2.1e+129:
		tmp = t_4
	else:
		tmp = t_3
	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)))
	t_2 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	t_3 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	t_4 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (t <= -4.6e+53)
		tmp = t_3;
	elseif (t <= -6e-32)
		tmp = t_2;
	elseif (t <= 7.8e-293)
		tmp = t_1;
	elseif (t <= 2.1e-84)
		tmp = t_2;
	elseif (t <= 6.3e-16)
		tmp = t_4;
	elseif (t <= 6.8e+33)
		tmp = t_1;
	elseif (t <= 5.4e+76)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (t <= 2.1e+129)
		tmp = t_4;
	else
		tmp = t_3;
	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));
	t_2 = z * ((x * y) - (b * c));
	t_3 = t * ((b * i) - (x * a));
	t_4 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (t <= -4.6e+53)
		tmp = t_3;
	elseif (t <= -6e-32)
		tmp = t_2;
	elseif (t <= 7.8e-293)
		tmp = t_1;
	elseif (t <= 2.1e-84)
		tmp = t_2;
	elseif (t <= 6.3e-16)
		tmp = t_4;
	elseif (t <= 6.8e+33)
		tmp = t_1;
	elseif (t <= 5.4e+76)
		tmp = x * ((y * z) - (t * a));
	elseif (t <= 2.1e+129)
		tmp = t_4;
	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[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.6e+53], t$95$3, If[LessEqual[t, -6e-32], t$95$2, If[LessEqual[t, 7.8e-293], t$95$1, If[LessEqual[t, 2.1e-84], t$95$2, If[LessEqual[t, 6.3e-16], t$95$4, If[LessEqual[t, 6.8e+33], t$95$1, If[LessEqual[t, 5.4e+76], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.1e+129], t$95$4, t$95$3]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -4.60000000000000039e53 or 2.09999999999999997e129 < t

   1. Initial program 62.5%

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

   2. Taylor expanded in y around -inf 56.2%

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

   4. Simplified 60.5%

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

   5. Taylor expanded in t around inf 71.3%

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

      1. +-commutative 71.3%

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

      2. mul-1-neg 71.3%

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

      3. unsub-neg 71.3%

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

   7. Simplified 71.3%

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

   if -4.60000000000000039e53 < t < -6.0000000000000001e-32 or 7.8e-293 < t < 2.09999999999999998e-84

   1. Initial program 76.9%

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

   2. Taylor expanded in z around inf 72.0%

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

      1. *-commutative 72.0%

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

      2. *-commutative 72.0%

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

   4. Simplified 72.0%

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

   if -6.0000000000000001e-32 < t < 7.8e-293 or 6.2999999999999998e-16 < t < 6.7999999999999999e33

   1. Initial program 69.9%

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

   2. Taylor expanded in c around inf 55.2%

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

      1. *-commutative 55.2%

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

   4. Simplified 55.2%

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

   if 2.09999999999999998e-84 < t < 6.2999999999999998e-16 or 5.3999999999999998e76 < t < 2.09999999999999997e129

   1. Initial program 65.4%

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

   2. Taylor expanded in y around -inf 76.9%

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

   4. Simplified 80.7%

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

   5. Taylor expanded in i around inf 77.1%

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

   6. Taylor expanded in j around 0 69.4%

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

      1. +-commutative 69.4%

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

      2. mul-1-neg 69.4%

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

      3. *-commutative 69.4%

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

      4. *-commutative 69.4%

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

      5. fma-def 73.2%

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

      6. fma-neg 69.4%

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

      7. *-commutative 69.4%

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

      8. associate-*l* 69.4%

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

      9. distribute-rgt-out-- 77.1%

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

   8. Simplified 77.1%

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

   if 6.7999999999999999e33 < t < 5.3999999999999998e76

   1. Initial program 79.8%

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

   2. Taylor expanded in x around inf 71.1%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+53}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-32}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-293}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-84}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 6.3 \cdot 10^{-16}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+33}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+76}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+129}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]

Alternative 5: 57.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right) - z \cdot \left(b \cdot c\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{+85}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-191}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) - a \cdot \left(x \cdot t - c \cdot j\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-16}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* a (- (* c j) (* x t))) (* z (* b c))))
        (t_2 (* y (- (* x z) (* i j)))))
   (if (<= y -2.4e+85)
     t_2
     (if (<= y -3e-191)
       (- (* z (* x y)) (* a (- (* x t) (* c j))))
       (if (<= y 4.5e-65)
         t_1
         (if (<= y 7.2e-16)
           (* z (- (* x y) (* b c)))
           (if (<= y 4.3e+15) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (a * ((c * j) - (x * t))) - (z * (b * c));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -2.4e+85) {
		tmp = t_2;
	} else if (y <= -3e-191) {
		tmp = (z * (x * y)) - (a * ((x * t) - (c * j)));
	} else if (y <= 4.5e-65) {
		tmp = t_1;
	} else if (y <= 7.2e-16) {
		tmp = z * ((x * y) - (b * c));
	} else if (y <= 4.3e+15) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a * ((c * j) - (x * t))) - (z * (b * c))
    t_2 = y * ((x * z) - (i * j))
    if (y <= (-2.4d+85)) then
        tmp = t_2
    else if (y <= (-3d-191)) then
        tmp = (z * (x * y)) - (a * ((x * t) - (c * j)))
    else if (y <= 4.5d-65) then
        tmp = t_1
    else if (y <= 7.2d-16) then
        tmp = z * ((x * y) - (b * c))
    else if (y <= 4.3d+15) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (a * ((c * j) - (x * t))) - (z * (b * c));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -2.4e+85) {
		tmp = t_2;
	} else if (y <= -3e-191) {
		tmp = (z * (x * y)) - (a * ((x * t) - (c * j)));
	} else if (y <= 4.5e-65) {
		tmp = t_1;
	} else if (y <= 7.2e-16) {
		tmp = z * ((x * y) - (b * c));
	} else if (y <= 4.3e+15) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (a * ((c * j) - (x * t))) - (z * (b * c))
	t_2 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -2.4e+85:
		tmp = t_2
	elif y <= -3e-191:
		tmp = (z * (x * y)) - (a * ((x * t) - (c * j)))
	elif y <= 4.5e-65:
		tmp = t_1
	elif y <= 7.2e-16:
		tmp = z * ((x * y) - (b * c))
	elif y <= 4.3e+15:
		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(a * Float64(Float64(c * j) - Float64(x * t))) - Float64(z * Float64(b * c)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -2.4e+85)
		tmp = t_2;
	elseif (y <= -3e-191)
		tmp = Float64(Float64(z * Float64(x * y)) - Float64(a * Float64(Float64(x * t) - Float64(c * j))));
	elseif (y <= 4.5e-65)
		tmp = t_1;
	elseif (y <= 7.2e-16)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (y <= 4.3e+15)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (a * ((c * j) - (x * t))) - (z * (b * c));
	t_2 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -2.4e+85)
		tmp = t_2;
	elseif (y <= -3e-191)
		tmp = (z * (x * y)) - (a * ((x * t) - (c * j)));
	elseif (y <= 4.5e-65)
		tmp = t_1;
	elseif (y <= 7.2e-16)
		tmp = z * ((x * y) - (b * c));
	elseif (y <= 4.3e+15)
		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[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.4e+85], t$95$2, If[LessEqual[y, -3e-191], N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(N[(x * t), $MachinePrecision] - N[(c * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.5e-65], t$95$1, If[LessEqual[y, 7.2e-16], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.3e+15], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.39999999999999997e85 or 4.3e15 < y

   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 y around inf 67.1%

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

      1. +-commutative 67.1%

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

      2. mul-1-neg 67.1%

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

      3. unsub-neg 67.1%

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

      4. *-commutative 67.1%

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

      5. *-commutative 67.1%

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

   4. Simplified 67.1%

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

   if -2.39999999999999997e85 < y < -3.0000000000000001e-191

   1. Initial program 72.1%

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

   2. Taylor expanded in y around -inf 65.7%

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

   4. Simplified 69.0%

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

   5. Taylor expanded in i around 0 65.0%

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

      1. +-commutative 65.0%

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

      2. associate-+l+ 65.0%

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

      3. +-commutative 65.0%

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

      4. mul-1-neg 65.0%

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

      5. associate-*r* 60.1%

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

      6. *-commutative 60.1%

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

      7. distribute-lft-neg-in 60.1%

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

      8. *-commutative 60.1%

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

      9. mul-1-neg 60.1%

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

      10. associate-*r* 63.2%

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

      11. distribute-rgt-in 63.2%

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

      12. +-commutative 63.2%

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

      13. mul-1-neg 63.2%

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

      14. sub-neg 63.2%

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

   7. Simplified 63.2%

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

   8. Taylor expanded in x around inf 63.8%

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

      1. associate-*r* 63.8%

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

      2. *-commutative 63.8%

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

   10. Simplified 63.8%

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

   if -3.0000000000000001e-191 < y < 4.4999999999999998e-65 or 7.19999999999999965e-16 < y < 4.3e15

   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. Taylor expanded in y around -inf 68.0%

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

   4. Simplified 70.6%

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

   5. Taylor expanded in i around 0 68.7%

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

      1. +-commutative 68.7%

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

      2. associate-+l+ 68.7%

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

      3. +-commutative 68.7%

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

      4. mul-1-neg 68.7%

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

      5. associate-*r* 74.1%

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

      6. *-commutative 74.1%

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

      7. distribute-lft-neg-in 74.1%

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

      8. *-commutative 74.1%

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

      9. mul-1-neg 74.1%

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

      10. associate-*r* 74.6%

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

      11. distribute-rgt-in 74.6%

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

      12. +-commutative 74.6%

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

      13. mul-1-neg 74.6%

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

      14. sub-neg 74.6%

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

   7. Simplified 74.6%

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

   8. Taylor expanded in y around 0 68.8%

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

      1. +-commutative 68.8%

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

      2. sub-neg 68.8%

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

      3. *-commutative 68.8%

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

      4. sub-neg 68.8%

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

      5. mul-1-neg 68.8%

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

      6. unsub-neg 68.8%

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

      7. associate-*r* 74.2%

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

      8. *-commutative 74.2%

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

   10. Simplified 74.2%

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

   if 4.4999999999999998e-65 < y < 7.19999999999999965e-16

   1. Initial program 61.3%

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

   2. Taylor expanded in z around inf 70.3%

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

      1. *-commutative 70.3%

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

      2. *-commutative 70.3%

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

   4. Simplified 70.3%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+85}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-191}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) - a \cdot \left(x \cdot t - c \cdot j\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-65}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-16}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+15}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]

Alternative 6: 58.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right) - z \cdot \left(b \cdot c\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{+89}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-192}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) - a \cdot \left(x \cdot t - c \cdot j\right)\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-16}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* a (- (* c j) (* x t))) (* z (* b c))))
        (t_2 (* y (- (* x z) (* i j)))))
   (if (<= y -4.8e+89)
     t_2
     (if (<= y -1.4e-192)
       (- (* z (* x y)) (* a (- (* x t) (* c j))))
       (if (<= y 1.5e-68)
         t_1
         (if (<= y 2.4e-16)
           (+ (* x (* y z)) (* b (- (* t i) (* z c))))
           (if (<= y 4.6e+15) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (a * ((c * j) - (x * t))) - (z * (b * c));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -4.8e+89) {
		tmp = t_2;
	} else if (y <= -1.4e-192) {
		tmp = (z * (x * y)) - (a * ((x * t) - (c * j)));
	} else if (y <= 1.5e-68) {
		tmp = t_1;
	} else if (y <= 2.4e-16) {
		tmp = (x * (y * z)) + (b * ((t * i) - (z * c)));
	} else if (y <= 4.6e+15) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a * ((c * j) - (x * t))) - (z * (b * c))
    t_2 = y * ((x * z) - (i * j))
    if (y <= (-4.8d+89)) then
        tmp = t_2
    else if (y <= (-1.4d-192)) then
        tmp = (z * (x * y)) - (a * ((x * t) - (c * j)))
    else if (y <= 1.5d-68) then
        tmp = t_1
    else if (y <= 2.4d-16) then
        tmp = (x * (y * z)) + (b * ((t * i) - (z * c)))
    else if (y <= 4.6d+15) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (a * ((c * j) - (x * t))) - (z * (b * c));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -4.8e+89) {
		tmp = t_2;
	} else if (y <= -1.4e-192) {
		tmp = (z * (x * y)) - (a * ((x * t) - (c * j)));
	} else if (y <= 1.5e-68) {
		tmp = t_1;
	} else if (y <= 2.4e-16) {
		tmp = (x * (y * z)) + (b * ((t * i) - (z * c)));
	} else if (y <= 4.6e+15) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (a * ((c * j) - (x * t))) - (z * (b * c))
	t_2 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -4.8e+89:
		tmp = t_2
	elif y <= -1.4e-192:
		tmp = (z * (x * y)) - (a * ((x * t) - (c * j)))
	elif y <= 1.5e-68:
		tmp = t_1
	elif y <= 2.4e-16:
		tmp = (x * (y * z)) + (b * ((t * i) - (z * c)))
	elif y <= 4.6e+15:
		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(a * Float64(Float64(c * j) - Float64(x * t))) - Float64(z * Float64(b * c)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -4.8e+89)
		tmp = t_2;
	elseif (y <= -1.4e-192)
		tmp = Float64(Float64(z * Float64(x * y)) - Float64(a * Float64(Float64(x * t) - Float64(c * j))));
	elseif (y <= 1.5e-68)
		tmp = t_1;
	elseif (y <= 2.4e-16)
		tmp = Float64(Float64(x * Float64(y * z)) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	elseif (y <= 4.6e+15)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (a * ((c * j) - (x * t))) - (z * (b * c));
	t_2 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -4.8e+89)
		tmp = t_2;
	elseif (y <= -1.4e-192)
		tmp = (z * (x * y)) - (a * ((x * t) - (c * j)));
	elseif (y <= 1.5e-68)
		tmp = t_1;
	elseif (y <= 2.4e-16)
		tmp = (x * (y * z)) + (b * ((t * i) - (z * c)));
	elseif (y <= 4.6e+15)
		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[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.8e+89], t$95$2, If[LessEqual[y, -1.4e-192], N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(N[(x * t), $MachinePrecision] - N[(c * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.5e-68], t$95$1, If[LessEqual[y, 2.4e-16], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.6e+15], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.80000000000000009e89 or 4.6e15 < y

   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 y around inf 67.1%

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

      1. +-commutative 67.1%

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

      2. mul-1-neg 67.1%

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

      3. unsub-neg 67.1%

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

      4. *-commutative 67.1%

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

      5. *-commutative 67.1%

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

   4. Simplified 67.1%

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

   if -4.80000000000000009e89 < y < -1.40000000000000002e-192

   1. Initial program 72.1%

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

   2. Taylor expanded in y around -inf 65.7%

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

   4. Simplified 69.0%

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

   5. Taylor expanded in i around 0 65.0%

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

      1. +-commutative 65.0%

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

      2. associate-+l+ 65.0%

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

      3. +-commutative 65.0%

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

      4. mul-1-neg 65.0%

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

      5. associate-*r* 60.1%

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

      6. *-commutative 60.1%

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

      7. distribute-lft-neg-in 60.1%

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

      8. *-commutative 60.1%

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

      9. mul-1-neg 60.1%

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

      10. associate-*r* 63.2%

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

      11. distribute-rgt-in 63.2%

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

      12. +-commutative 63.2%

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

      13. mul-1-neg 63.2%

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

      14. sub-neg 63.2%

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

   7. Simplified 63.2%

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

   8. Taylor expanded in x around inf 63.8%

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

      1. associate-*r* 63.8%

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

      2. *-commutative 63.8%

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

   10. Simplified 63.8%

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

   if -1.40000000000000002e-192 < y < 1.5e-68 or 2.40000000000000005e-16 < y < 4.6e15

   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. Taylor expanded in y around -inf 68.0%

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

   4. Simplified 70.6%

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

   5. Taylor expanded in i around 0 68.7%

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

      1. +-commutative 68.7%

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

      2. associate-+l+ 68.7%

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

      3. +-commutative 68.7%

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

      4. mul-1-neg 68.7%

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

      5. associate-*r* 74.1%

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

      6. *-commutative 74.1%

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

      7. distribute-lft-neg-in 74.1%

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

      8. *-commutative 74.1%

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

      9. mul-1-neg 74.1%

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

      10. associate-*r* 74.6%

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

      11. distribute-rgt-in 74.6%

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

      12. +-commutative 74.6%

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

      13. mul-1-neg 74.6%

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

      14. sub-neg 74.6%

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

   7. Simplified 74.6%

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

   8. Taylor expanded in y around 0 68.8%

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

      1. +-commutative 68.8%

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

      2. sub-neg 68.8%

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

      3. *-commutative 68.8%

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

      4. sub-neg 68.8%

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

      5. mul-1-neg 68.8%

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

      6. unsub-neg 68.8%

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

      7. associate-*r* 74.2%

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

      8. *-commutative 74.2%

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

   10. Simplified 74.2%

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

   if 1.5e-68 < y < 2.40000000000000005e-16

   1. Initial program 61.3%

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

   2. Taylor expanded in j around 0 84.4%

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

   3. Taylor expanded in a around 0 77.3%

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

      1. *-commutative 77.3%

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

      2. *-commutative 77.3%

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

   5. Simplified 77.3%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+89}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-192}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) - a \cdot \left(x \cdot t - c \cdot j\right)\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-68}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-16}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+15}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]

Alternative 7: 65.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.4 \cdot 10^{+30} \lor \neg \left(b \leq 1.35 \cdot 10^{-107}\right):\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - a \cdot \left(x \cdot t - c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -4.4e+30) (not (<= b 1.35e-107)))
   (+ (* x (- (* y z) (* t a))) (* b (- (* t i) (* z c))))
   (- (* z (- (* x y) (* b c))) (* a (- (* x t) (* c j))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -4.4e+30) || !(b <= 1.35e-107)) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	} else {
		tmp = (z * ((x * y) - (b * c))) - (a * ((x * t) - (c * j)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-4.4d+30)) .or. (.not. (b <= 1.35d-107))) then
        tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))
    else
        tmp = (z * ((x * y) - (b * c))) - (a * ((x * t) - (c * j)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -4.4e+30) || !(b <= 1.35e-107)) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	} else {
		tmp = (z * ((x * y) - (b * c))) - (a * ((x * t) - (c * j)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -4.4e+30) or not (b <= 1.35e-107):
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))
	else:
		tmp = (z * ((x * y) - (b * c))) - (a * ((x * t) - (c * j)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -4.4e+30) || !(b <= 1.35e-107))
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	else
		tmp = Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) - Float64(a * Float64(Float64(x * t) - Float64(c * j))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -4.4e+30) || ~((b <= 1.35e-107)))
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	else
		tmp = (z * ((x * y) - (b * c))) - (a * ((x * t) - (c * j)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -4.4e+30], N[Not[LessEqual[b, 1.35e-107]], $MachinePrecision]], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(N[(x * t), $MachinePrecision] - N[(c * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.4e30 or 1.35e-107 < b

   1. Initial program 73.6%

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

   2. Taylor expanded in j around 0 67.9%

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

   if -4.4e30 < b < 1.35e-107

   1. Initial program 63.3%

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

   2. Taylor expanded in y around -inf 69.5%

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

   4. Simplified 72.9%

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

   5. Taylor expanded in i around 0 62.4%

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

      1. +-commutative 62.4%

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

      2. associate-+l+ 62.4%

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

      3. +-commutative 62.4%

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

      4. mul-1-neg 62.4%

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

      5. associate-*r* 69.6%

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

      6. *-commutative 69.6%

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

      7. distribute-lft-neg-in 69.6%

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

      8. *-commutative 69.6%

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

      9. mul-1-neg 69.6%

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

      10. associate-*r* 70.6%

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

      11. distribute-rgt-in 73.1%

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

      12. +-commutative 73.1%

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

      13. mul-1-neg 73.1%

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

      14. sub-neg 73.1%

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

   7. Simplified 73.1%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.4 \cdot 10^{+30} \lor \neg \left(b \leq 1.35 \cdot 10^{-107}\right):\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - a \cdot \left(x \cdot t - c \cdot j\right)\\ \end{array} \]

Alternative 8: 28.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(z \cdot \left(-b\right)\right)\\ t_2 := a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{if}\;b \leq -2.05 \cdot 10^{+163}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{+79}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-152}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{-256}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-249}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-153}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{-6}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* z (- b)))) (t_2 (* a (* t (- x)))))
   (if (<= b -2.05e+163)
     t_1
     (if (<= b -2.9e+79)
       (* x (* y z))
       (if (<= b -2e-58)
         t_1
         (if (<= b -2.3e-152)
           t_2
           (if (<= b -1.75e-256)
             (* z (* x y))
             (if (<= b 1.9e-249)
               (* a (* c j))
               (if (<= b 7e-153)
                 t_2
                 (if (<= b 6.8e-6) (* c (* a j)) (* 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 t_1 = c * (z * -b);
	double t_2 = a * (t * -x);
	double tmp;
	if (b <= -2.05e+163) {
		tmp = t_1;
	} else if (b <= -2.9e+79) {
		tmp = x * (y * z);
	} else if (b <= -2e-58) {
		tmp = t_1;
	} else if (b <= -2.3e-152) {
		tmp = t_2;
	} else if (b <= -1.75e-256) {
		tmp = z * (x * y);
	} else if (b <= 1.9e-249) {
		tmp = a * (c * j);
	} else if (b <= 7e-153) {
		tmp = t_2;
	} else if (b <= 6.8e-6) {
		tmp = c * (a * j);
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * (z * -b)
    t_2 = a * (t * -x)
    if (b <= (-2.05d+163)) then
        tmp = t_1
    else if (b <= (-2.9d+79)) then
        tmp = x * (y * z)
    else if (b <= (-2d-58)) then
        tmp = t_1
    else if (b <= (-2.3d-152)) then
        tmp = t_2
    else if (b <= (-1.75d-256)) then
        tmp = z * (x * y)
    else if (b <= 1.9d-249) then
        tmp = a * (c * j)
    else if (b <= 7d-153) then
        tmp = t_2
    else if (b <= 6.8d-6) then
        tmp = c * (a * j)
    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 t_1 = c * (z * -b);
	double t_2 = a * (t * -x);
	double tmp;
	if (b <= -2.05e+163) {
		tmp = t_1;
	} else if (b <= -2.9e+79) {
		tmp = x * (y * z);
	} else if (b <= -2e-58) {
		tmp = t_1;
	} else if (b <= -2.3e-152) {
		tmp = t_2;
	} else if (b <= -1.75e-256) {
		tmp = z * (x * y);
	} else if (b <= 1.9e-249) {
		tmp = a * (c * j);
	} else if (b <= 7e-153) {
		tmp = t_2;
	} else if (b <= 6.8e-6) {
		tmp = c * (a * j);
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (z * -b)
	t_2 = a * (t * -x)
	tmp = 0
	if b <= -2.05e+163:
		tmp = t_1
	elif b <= -2.9e+79:
		tmp = x * (y * z)
	elif b <= -2e-58:
		tmp = t_1
	elif b <= -2.3e-152:
		tmp = t_2
	elif b <= -1.75e-256:
		tmp = z * (x * y)
	elif b <= 1.9e-249:
		tmp = a * (c * j)
	elif b <= 7e-153:
		tmp = t_2
	elif b <= 6.8e-6:
		tmp = c * (a * j)
	else:
		tmp = t * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(z * Float64(-b)))
	t_2 = Float64(a * Float64(t * Float64(-x)))
	tmp = 0.0
	if (b <= -2.05e+163)
		tmp = t_1;
	elseif (b <= -2.9e+79)
		tmp = Float64(x * Float64(y * z));
	elseif (b <= -2e-58)
		tmp = t_1;
	elseif (b <= -2.3e-152)
		tmp = t_2;
	elseif (b <= -1.75e-256)
		tmp = Float64(z * Float64(x * y));
	elseif (b <= 1.9e-249)
		tmp = Float64(a * Float64(c * j));
	elseif (b <= 7e-153)
		tmp = t_2;
	elseif (b <= 6.8e-6)
		tmp = Float64(c * Float64(a * j));
	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)
	t_1 = c * (z * -b);
	t_2 = a * (t * -x);
	tmp = 0.0;
	if (b <= -2.05e+163)
		tmp = t_1;
	elseif (b <= -2.9e+79)
		tmp = x * (y * z);
	elseif (b <= -2e-58)
		tmp = t_1;
	elseif (b <= -2.3e-152)
		tmp = t_2;
	elseif (b <= -1.75e-256)
		tmp = z * (x * y);
	elseif (b <= 1.9e-249)
		tmp = a * (c * j);
	elseif (b <= 7e-153)
		tmp = t_2;
	elseif (b <= 6.8e-6)
		tmp = c * (a * j);
	else
		tmp = t * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.05e+163], t$95$1, If[LessEqual[b, -2.9e+79], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2e-58], t$95$1, If[LessEqual[b, -2.3e-152], t$95$2, If[LessEqual[b, -1.75e-256], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.9e-249], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7e-153], t$95$2, If[LessEqual[b, 6.8e-6], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -2.05e163 or -2.89999999999999992e79 < b < -2.0000000000000001e-58

   1. Initial program 64.1%

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

   2. Taylor expanded in c around inf 60.8%

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

      1. *-commutative 60.8%

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

   4. Simplified 60.8%

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

   5. Taylor expanded in j around 0 46.0%

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

      1. mul-1-neg 46.0%

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

      2. distribute-lft-neg-out 46.0%

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

      3. *-commutative 46.0%

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

   7. Simplified 46.0%

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

   if -2.05e163 < b < -2.89999999999999992e79

   1. Initial program 64.9%

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

   2. Taylor expanded in z around inf 51.5%

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

      1. *-commutative 51.5%

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

      2. *-commutative 51.5%

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

   4. Simplified 51.5%

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

   5. Taylor expanded in y around inf 36.7%

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

   6. Taylor expanded in z around 0 46.1%

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

   if -2.0000000000000001e-58 < b < -2.3000000000000001e-152 or 1.9e-249 < b < 6.99999999999999961e-153

   1. Initial program 58.7%

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

   2. Taylor expanded in a around inf 64.8%

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

      1. +-commutative 64.8%

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

      2. mul-1-neg 64.8%

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

      3. unsub-neg 64.8%

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

      4. *-commutative 64.8%

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

   4. Simplified 64.8%

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

   5. Taylor expanded in j around 0 51.3%

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

      1. mul-1-neg 51.3%

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

      2. distribute-lft-neg-out 51.3%

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

      3. *-commutative 51.3%

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

   7. Simplified 51.3%

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

   if -2.3000000000000001e-152 < b < -1.75000000000000007e-256

   1. Initial program 68.1%

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

   2. Taylor expanded in z around inf 45.6%

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

      1. *-commutative 45.6%

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

      2. *-commutative 45.6%

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

   4. Simplified 45.6%

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

   5. Taylor expanded in y around inf 37.7%

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

   if -1.75000000000000007e-256 < b < 1.9e-249

   1. Initial program 72.4%

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

   2. Taylor expanded in a around inf 72.9%

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

      1. +-commutative 72.9%

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

      2. mul-1-neg 72.9%

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

      3. unsub-neg 72.9%

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

      4. *-commutative 72.9%

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

   4. Simplified 72.9%

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

   5. Taylor expanded in j around inf 56.9%

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

   if 6.99999999999999961e-153 < b < 6.80000000000000012e-6

   1. Initial program 80.1%

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

   2. Taylor expanded in c around inf 43.1%

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

      1. *-commutative 43.1%

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

   4. Simplified 43.1%

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

   5. Taylor expanded in j around inf 33.0%

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

   if 6.80000000000000012e-6 < b

   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 y around -inf 70.1%

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

   4. Simplified 70.1%

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

   5. Taylor expanded in i around inf 60.7%

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

   6. Taylor expanded in j around 0 46.5%

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

      1. associate-*r* 50.0%

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

      2. *-commutative 50.0%

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

   8. Simplified 50.0%

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

4. Final simplification 46.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.05 \cdot 10^{+163}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{+79}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-58}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-152}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{-256}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-249}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-153}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{-6}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 9: 51.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -2.7 \cdot 10^{+181}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -7 \cdot 10^{+101}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-12}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.85 \cdot 10^{-300}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+30}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+131}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= x -2.7e+181)
     t_1
     (if (<= x -7e+101)
       (* a (- (* c j) (* x t)))
       (if (<= x -1.9e-12)
         t_1
         (if (<= x -2.85e-300)
           (* i (- (* t b) (* y j)))
           (if (<= x 7.2e+30)
             (* c (- (* a j) (* z b)))
             (if (<= x 6.5e+131) (* t (- (* b i) (* x a))) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -2.7e+181) {
		tmp = t_1;
	} else if (x <= -7e+101) {
		tmp = a * ((c * j) - (x * t));
	} else if (x <= -1.9e-12) {
		tmp = t_1;
	} else if (x <= -2.85e-300) {
		tmp = i * ((t * b) - (y * j));
	} else if (x <= 7.2e+30) {
		tmp = c * ((a * j) - (z * b));
	} else if (x <= 6.5e+131) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (x <= (-2.7d+181)) then
        tmp = t_1
    else if (x <= (-7d+101)) then
        tmp = a * ((c * j) - (x * t))
    else if (x <= (-1.9d-12)) then
        tmp = t_1
    else if (x <= (-2.85d-300)) then
        tmp = i * ((t * b) - (y * j))
    else if (x <= 7.2d+30) then
        tmp = c * ((a * j) - (z * b))
    else if (x <= 6.5d+131) then
        tmp = t * ((b * i) - (x * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -2.7e+181) {
		tmp = t_1;
	} else if (x <= -7e+101) {
		tmp = a * ((c * j) - (x * t));
	} else if (x <= -1.9e-12) {
		tmp = t_1;
	} else if (x <= -2.85e-300) {
		tmp = i * ((t * b) - (y * j));
	} else if (x <= 7.2e+30) {
		tmp = c * ((a * j) - (z * b));
	} else if (x <= 6.5e+131) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -2.7e+181:
		tmp = t_1
	elif x <= -7e+101:
		tmp = a * ((c * j) - (x * t))
	elif x <= -1.9e-12:
		tmp = t_1
	elif x <= -2.85e-300:
		tmp = i * ((t * b) - (y * j))
	elif x <= 7.2e+30:
		tmp = c * ((a * j) - (z * b))
	elif x <= 6.5e+131:
		tmp = t * ((b * i) - (x * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -2.7e+181)
		tmp = t_1;
	elseif (x <= -7e+101)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (x <= -1.9e-12)
		tmp = t_1;
	elseif (x <= -2.85e-300)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (x <= 7.2e+30)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (x <= 6.5e+131)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -2.7e+181)
		tmp = t_1;
	elseif (x <= -7e+101)
		tmp = a * ((c * j) - (x * t));
	elseif (x <= -1.9e-12)
		tmp = t_1;
	elseif (x <= -2.85e-300)
		tmp = i * ((t * b) - (y * j));
	elseif (x <= 7.2e+30)
		tmp = c * ((a * j) - (z * b));
	elseif (x <= 6.5e+131)
		tmp = t * ((b * i) - (x * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.7e+181], t$95$1, If[LessEqual[x, -7e+101], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.9e-12], t$95$1, If[LessEqual[x, -2.85e-300], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.2e+30], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.5e+131], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -2.70000000000000007e181 or -7.00000000000000046e101 < x < -1.89999999999999998e-12 or 6.5e131 < x

   1. Initial program 68.1%

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

   2. Taylor expanded in x around inf 69.2%

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

   if -2.70000000000000007e181 < x < -7.00000000000000046e101

   1. Initial program 53.7%

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

   2. Taylor expanded in a around inf 86.8%

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

      1. +-commutative 86.8%

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

      2. mul-1-neg 86.8%

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

      3. unsub-neg 86.8%

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

      4. *-commutative 86.8%

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

   4. Simplified 86.8%

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

   if -1.89999999999999998e-12 < x < -2.8499999999999999e-300

   1. Initial program 70.7%

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

   2. Taylor expanded in y around -inf 84.0%

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

   4. Simplified 85.9%

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

   5. Taylor expanded in i around inf 52.3%

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

   6. Taylor expanded in j around 0 52.1%

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

      1. +-commutative 52.1%

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

      2. mul-1-neg 52.1%

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

      3. *-commutative 52.1%

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

      4. *-commutative 52.1%

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

      5. fma-def 52.1%

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

      6. fma-neg 52.1%

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

      7. *-commutative 52.1%

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

      8. associate-*l* 52.3%

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

      9. distribute-rgt-out-- 52.3%

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

   8. Simplified 52.3%

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

   if -2.8499999999999999e-300 < x < 7.2000000000000004e30

   1. Initial program 69.8%

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

   2. Taylor expanded in c around inf 59.5%

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

      1. *-commutative 59.5%

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

   4. Simplified 59.5%

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

   if 7.2000000000000004e30 < x < 6.5e131

   1. Initial program 73.6%

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

   2. Taylor expanded in y around -inf 68.4%

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

   4. Simplified 68.4%

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

   5. Taylor expanded in t around inf 63.7%

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

      1. +-commutative 63.7%

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

      2. mul-1-neg 63.7%

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

      3. unsub-neg 63.7%

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

   7. Simplified 63.7%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+181}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -7 \cdot 10^{+101}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-12}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -2.85 \cdot 10^{-300}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+30}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+131}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]

Alternative 10: 29.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{if}\;b \leq -2.4 \cdot 10^{-57}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;b \leq -4.8 \cdot 10^{-152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -7.5 \cdot 10^{-243}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq -1.65 \cdot 10^{-256}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-239}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{-153}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;b \leq 19500000:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* t (- a)))))
   (if (<= b -2.4e-57)
     (* z (* c (- b)))
     (if (<= b -4.8e-152)
       t_1
       (if (<= b -7.5e-243)
         (* z (* x y))
         (if (<= b -1.65e-256)
           t_1
           (if (<= b 1.2e-239)
             (* a (* c j))
             (if (<= b 6.6e-153)
               (* a (* t (- x)))
               (if (<= b 19500000.0) (* c (* a j)) (* 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 t_1 = x * (t * -a);
	double tmp;
	if (b <= -2.4e-57) {
		tmp = z * (c * -b);
	} else if (b <= -4.8e-152) {
		tmp = t_1;
	} else if (b <= -7.5e-243) {
		tmp = z * (x * y);
	} else if (b <= -1.65e-256) {
		tmp = t_1;
	} else if (b <= 1.2e-239) {
		tmp = a * (c * j);
	} else if (b <= 6.6e-153) {
		tmp = a * (t * -x);
	} else if (b <= 19500000.0) {
		tmp = c * (a * j);
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * (t * -a)
    if (b <= (-2.4d-57)) then
        tmp = z * (c * -b)
    else if (b <= (-4.8d-152)) then
        tmp = t_1
    else if (b <= (-7.5d-243)) then
        tmp = z * (x * y)
    else if (b <= (-1.65d-256)) then
        tmp = t_1
    else if (b <= 1.2d-239) then
        tmp = a * (c * j)
    else if (b <= 6.6d-153) then
        tmp = a * (t * -x)
    else if (b <= 19500000.0d0) then
        tmp = c * (a * j)
    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 t_1 = x * (t * -a);
	double tmp;
	if (b <= -2.4e-57) {
		tmp = z * (c * -b);
	} else if (b <= -4.8e-152) {
		tmp = t_1;
	} else if (b <= -7.5e-243) {
		tmp = z * (x * y);
	} else if (b <= -1.65e-256) {
		tmp = t_1;
	} else if (b <= 1.2e-239) {
		tmp = a * (c * j);
	} else if (b <= 6.6e-153) {
		tmp = a * (t * -x);
	} else if (b <= 19500000.0) {
		tmp = c * (a * j);
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (t * -a)
	tmp = 0
	if b <= -2.4e-57:
		tmp = z * (c * -b)
	elif b <= -4.8e-152:
		tmp = t_1
	elif b <= -7.5e-243:
		tmp = z * (x * y)
	elif b <= -1.65e-256:
		tmp = t_1
	elif b <= 1.2e-239:
		tmp = a * (c * j)
	elif b <= 6.6e-153:
		tmp = a * (t * -x)
	elif b <= 19500000.0:
		tmp = c * (a * j)
	else:
		tmp = t * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(t * Float64(-a)))
	tmp = 0.0
	if (b <= -2.4e-57)
		tmp = Float64(z * Float64(c * Float64(-b)));
	elseif (b <= -4.8e-152)
		tmp = t_1;
	elseif (b <= -7.5e-243)
		tmp = Float64(z * Float64(x * y));
	elseif (b <= -1.65e-256)
		tmp = t_1;
	elseif (b <= 1.2e-239)
		tmp = Float64(a * Float64(c * j));
	elseif (b <= 6.6e-153)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (b <= 19500000.0)
		tmp = Float64(c * Float64(a * j));
	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)
	t_1 = x * (t * -a);
	tmp = 0.0;
	if (b <= -2.4e-57)
		tmp = z * (c * -b);
	elseif (b <= -4.8e-152)
		tmp = t_1;
	elseif (b <= -7.5e-243)
		tmp = z * (x * y);
	elseif (b <= -1.65e-256)
		tmp = t_1;
	elseif (b <= 1.2e-239)
		tmp = a * (c * j);
	elseif (b <= 6.6e-153)
		tmp = a * (t * -x);
	elseif (b <= 19500000.0)
		tmp = c * (a * j);
	else
		tmp = t * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.4e-57], N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.8e-152], t$95$1, If[LessEqual[b, -7.5e-243], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.65e-256], t$95$1, If[LessEqual[b, 1.2e-239], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.6e-153], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 19500000.0], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -2.40000000000000006e-57

   1. Initial program 63.8%

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

   2. Taylor expanded in z around inf 54.3%

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

      1. *-commutative 54.3%

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

      2. *-commutative 54.3%

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

   4. Simplified 54.3%

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

   5. Taylor expanded in y around 0 41.6%

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

      1. mul-1-neg 41.6%

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

      2. *-commutative 41.6%

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

      3. distribute-rgt-neg-in 41.6%

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

   7. Simplified 41.6%

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

   if -2.40000000000000006e-57 < b < -4.8e-152 or -7.5e-243 < b < -1.65e-256

   1. Initial program 55.3%

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

   2. Taylor expanded in a around inf 64.3%

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

      1. +-commutative 64.3%

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

      2. mul-1-neg 64.3%

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

      3. unsub-neg 64.3%

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

      4. *-commutative 64.3%

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

   4. Simplified 64.3%

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

   5. Taylor expanded in j around 0 42.6%

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

      1. mul-1-neg 42.6%

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

      2. *-commutative 42.6%

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

      3. associate-*r* 42.6%

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

      4. *-commutative 42.6%

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

      5. associate-*r* 46.9%

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

      6. distribute-rgt-neg-out 46.9%

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

      7. distribute-rgt-neg-in 46.9%

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

   7. Simplified 46.9%

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

   if -4.8e-152 < b < -7.5e-243

   1. Initial program 71.7%

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

   2. Taylor expanded in z around inf 46.9%

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

      1. *-commutative 46.9%

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

      2. *-commutative 46.9%

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

   4. Simplified 46.9%

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

   5. Taylor expanded in y around inf 41.5%

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

   if -1.65e-256 < b < 1.19999999999999996e-239

   1. Initial program 72.4%

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

   2. Taylor expanded in a around inf 72.9%

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

      1. +-commutative 72.9%

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

      2. mul-1-neg 72.9%

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

      3. unsub-neg 72.9%

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

      4. *-commutative 72.9%

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

   4. Simplified 72.9%

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

   5. Taylor expanded in j around inf 56.9%

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

   if 1.19999999999999996e-239 < b < 6.59999999999999975e-153

   1. Initial program 60.4%

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

   2. Taylor expanded in a around inf 59.2%

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

      1. +-commutative 59.2%

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

      2. mul-1-neg 59.2%

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

      3. unsub-neg 59.2%

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

      4. *-commutative 59.2%

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

   4. Simplified 59.2%

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

   5. Taylor expanded in j around 0 55.0%

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

      1. mul-1-neg 55.0%

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

      2. distribute-lft-neg-out 55.0%

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

      3. *-commutative 55.0%

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

   7. Simplified 55.0%

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

   if 6.59999999999999975e-153 < b < 1.95e7

   1. Initial program 80.1%

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

   2. Taylor expanded in c around inf 43.1%

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

      1. *-commutative 43.1%

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

   4. Simplified 43.1%

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

   5. Taylor expanded in j around inf 33.0%

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

   if 1.95e7 < b

   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 y around -inf 70.1%

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

   4. Simplified 70.1%

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

   5. Taylor expanded in i around inf 60.7%

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

   6. Taylor expanded in j around 0 46.5%

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

      1. associate-*r* 50.0%

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

      2. *-commutative 50.0%

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

   8. Simplified 50.0%

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

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.4 \cdot 10^{-57}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;b \leq -4.8 \cdot 10^{-152}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;b \leq -7.5 \cdot 10^{-243}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq -1.65 \cdot 10^{-256}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-239}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{-153}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;b \leq 19500000:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 11: 51.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -3.6 \cdot 10^{+30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-157}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -3.4 \cdot 10^{-214}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+139}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))) (t_2 (* b (- (* t i) (* z c)))))
   (if (<= b -3.6e+30)
     t_2
     (if (<= b -3e-157)
       t_1
       (if (<= b -3.4e-214)
         (* y (* x z))
         (if (<= b 1.9e-74)
           t_1
           (if (<= b 4e+139) (* i (- (* t b) (* y j))) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -3.6e+30) {
		tmp = t_2;
	} else if (b <= -3e-157) {
		tmp = t_1;
	} else if (b <= -3.4e-214) {
		tmp = y * (x * z);
	} else if (b <= 1.9e-74) {
		tmp = t_1;
	} else if (b <= 4e+139) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    t_2 = b * ((t * i) - (z * c))
    if (b <= (-3.6d+30)) then
        tmp = t_2
    else if (b <= (-3d-157)) then
        tmp = t_1
    else if (b <= (-3.4d-214)) then
        tmp = y * (x * z)
    else if (b <= 1.9d-74) then
        tmp = t_1
    else if (b <= 4d+139) then
        tmp = i * ((t * b) - (y * j))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -3.6e+30) {
		tmp = t_2;
	} else if (b <= -3e-157) {
		tmp = t_1;
	} else if (b <= -3.4e-214) {
		tmp = y * (x * z);
	} else if (b <= 1.9e-74) {
		tmp = t_1;
	} else if (b <= 4e+139) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -3.6e+30:
		tmp = t_2
	elif b <= -3e-157:
		tmp = t_1
	elif b <= -3.4e-214:
		tmp = y * (x * z)
	elif b <= 1.9e-74:
		tmp = t_1
	elif b <= 4e+139:
		tmp = i * ((t * b) - (y * j))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -3.6e+30)
		tmp = t_2;
	elseif (b <= -3e-157)
		tmp = t_1;
	elseif (b <= -3.4e-214)
		tmp = Float64(y * Float64(x * z));
	elseif (b <= 1.9e-74)
		tmp = t_1;
	elseif (b <= 4e+139)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	t_2 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -3.6e+30)
		tmp = t_2;
	elseif (b <= -3e-157)
		tmp = t_1;
	elseif (b <= -3.4e-214)
		tmp = y * (x * z);
	elseif (b <= 1.9e-74)
		tmp = t_1;
	elseif (b <= 4e+139)
		tmp = i * ((t * b) - (y * j));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.6e+30], t$95$2, If[LessEqual[b, -3e-157], t$95$1, If[LessEqual[b, -3.4e-214], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.9e-74], t$95$1, If[LessEqual[b, 4e+139], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.6000000000000002e30 or 4.00000000000000013e139 < b

   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 b around inf 67.2%

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

   if -3.6000000000000002e30 < b < -3e-157 or -3.3999999999999999e-214 < b < 1.8999999999999998e-74

   1. Initial program 63.6%

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

   2. Taylor expanded in a around inf 57.9%

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

      1. +-commutative 57.9%

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

      2. mul-1-neg 57.9%

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

      3. unsub-neg 57.9%

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

      4. *-commutative 57.9%

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

   4. Simplified 57.9%

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

   if -3e-157 < b < -3.3999999999999999e-214

   1. Initial program 75.4%

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

   2. Taylor expanded in z around inf 59.5%

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

      1. *-commutative 59.5%

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

      2. *-commutative 59.5%

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

   4. Simplified 59.5%

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

   5. Taylor expanded in y around inf 51.8%

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

   6. Taylor expanded in z around 0 44.2%

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

      1. associate-*r* 51.8%

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

      2. *-commutative 51.8%

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

      3. associate-*r* 52.0%

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

      4. *-commutative 52.0%

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

   8. Simplified 52.0%

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

   if 1.8999999999999998e-74 < b < 4.00000000000000013e139

   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 y around -inf 76.8%

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

   4. Simplified 76.8%

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

   5. Taylor expanded in i around inf 59.0%

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

   6. Taylor expanded in j around 0 56.5%

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

      1. +-commutative 56.5%

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

      2. mul-1-neg 56.5%

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

      3. *-commutative 56.5%

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

      4. *-commutative 56.5%

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

      5. fma-def 56.5%

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

      6. fma-neg 56.5%

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

      7. *-commutative 56.5%

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

      8. associate-*l* 56.4%

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

      9. distribute-rgt-out-- 59.0%

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

   8. Simplified 59.0%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.6 \cdot 10^{+30}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-157}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq -3.4 \cdot 10^{-214}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-74}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+139}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 12: 52.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -3.7 \cdot 10^{+30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -5 \cdot 10^{-156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2.25 \cdot 10^{-231}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+139}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))) (t_2 (* b (- (* t i) (* z c)))))
   (if (<= b -3.7e+30)
     t_2
     (if (<= b -5e-156)
       t_1
       (if (<= b -2.25e-231)
         (* j (- (* a c) (* y i)))
         (if (<= b 2.1e-74)
           t_1
           (if (<= b 3.7e+139) (* i (- (* t b) (* y j))) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -3.7e+30) {
		tmp = t_2;
	} else if (b <= -5e-156) {
		tmp = t_1;
	} else if (b <= -2.25e-231) {
		tmp = j * ((a * c) - (y * i));
	} else if (b <= 2.1e-74) {
		tmp = t_1;
	} else if (b <= 3.7e+139) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    t_2 = b * ((t * i) - (z * c))
    if (b <= (-3.7d+30)) then
        tmp = t_2
    else if (b <= (-5d-156)) then
        tmp = t_1
    else if (b <= (-2.25d-231)) then
        tmp = j * ((a * c) - (y * i))
    else if (b <= 2.1d-74) then
        tmp = t_1
    else if (b <= 3.7d+139) then
        tmp = i * ((t * b) - (y * j))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -3.7e+30) {
		tmp = t_2;
	} else if (b <= -5e-156) {
		tmp = t_1;
	} else if (b <= -2.25e-231) {
		tmp = j * ((a * c) - (y * i));
	} else if (b <= 2.1e-74) {
		tmp = t_1;
	} else if (b <= 3.7e+139) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -3.7e+30:
		tmp = t_2
	elif b <= -5e-156:
		tmp = t_1
	elif b <= -2.25e-231:
		tmp = j * ((a * c) - (y * i))
	elif b <= 2.1e-74:
		tmp = t_1
	elif b <= 3.7e+139:
		tmp = i * ((t * b) - (y * j))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -3.7e+30)
		tmp = t_2;
	elseif (b <= -5e-156)
		tmp = t_1;
	elseif (b <= -2.25e-231)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (b <= 2.1e-74)
		tmp = t_1;
	elseif (b <= 3.7e+139)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	t_2 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -3.7e+30)
		tmp = t_2;
	elseif (b <= -5e-156)
		tmp = t_1;
	elseif (b <= -2.25e-231)
		tmp = j * ((a * c) - (y * i));
	elseif (b <= 2.1e-74)
		tmp = t_1;
	elseif (b <= 3.7e+139)
		tmp = i * ((t * b) - (y * j));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.7e+30], t$95$2, If[LessEqual[b, -5e-156], t$95$1, If[LessEqual[b, -2.25e-231], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.1e-74], t$95$1, If[LessEqual[b, 3.7e+139], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.70000000000000016e30 or 3.69999999999999992e139 < b

   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 b around inf 67.2%

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

   if -3.70000000000000016e30 < b < -5.00000000000000007e-156 or -2.2499999999999999e-231 < b < 2.1e-74

   1. Initial program 62.4%

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

   2. Taylor expanded in a around inf 58.8%

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

      1. +-commutative 58.8%

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

      2. mul-1-neg 58.8%

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

      3. unsub-neg 58.8%

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

      4. *-commutative 58.8%

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

   4. Simplified 58.8%

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

   if -5.00000000000000007e-156 < b < -2.2499999999999999e-231

   1. Initial program 76.5%

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

   2. Taylor expanded in j around inf 53.6%

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

   if 2.1e-74 < b < 3.69999999999999992e139

   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 y around -inf 76.8%

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

   4. Simplified 76.8%

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

   5. Taylor expanded in i around inf 59.0%

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

   6. Taylor expanded in j around 0 56.5%

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

      1. +-commutative 56.5%

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

      2. mul-1-neg 56.5%

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

      3. *-commutative 56.5%

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

      4. *-commutative 56.5%

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

      5. fma-def 56.5%

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

      6. fma-neg 56.5%

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

      7. *-commutative 56.5%

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

      8. associate-*l* 56.4%

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

      9. distribute-rgt-out-- 59.0%

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

   8. Simplified 59.0%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.7 \cdot 10^{+30}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -5 \cdot 10^{-156}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq -2.25 \cdot 10^{-231}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-74}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+139}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 13: 39.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;b \leq -1.8 \cdot 10^{+31}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-157}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -3.4 \cdot 10^{-214}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq 4.7 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= b -1.8e+31)
     (* z (* c (- b)))
     (if (<= b -2.4e-157)
       t_1
       (if (<= b -3.4e-214)
         (* y (* x z))
         (if (<= b 4.7e+32) t_1 (* 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 t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (b <= -1.8e+31) {
		tmp = z * (c * -b);
	} else if (b <= -2.4e-157) {
		tmp = t_1;
	} else if (b <= -3.4e-214) {
		tmp = y * (x * z);
	} else if (b <= 4.7e+32) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (b <= (-1.8d+31)) then
        tmp = z * (c * -b)
    else if (b <= (-2.4d-157)) then
        tmp = t_1
    else if (b <= (-3.4d-214)) then
        tmp = y * (x * z)
    else if (b <= 4.7d+32) then
        tmp = t_1
    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 t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (b <= -1.8e+31) {
		tmp = z * (c * -b);
	} else if (b <= -2.4e-157) {
		tmp = t_1;
	} else if (b <= -3.4e-214) {
		tmp = y * (x * z);
	} else if (b <= 4.7e+32) {
		tmp = t_1;
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if b <= -1.8e+31:
		tmp = z * (c * -b)
	elif b <= -2.4e-157:
		tmp = t_1
	elif b <= -3.4e-214:
		tmp = y * (x * z)
	elif b <= 4.7e+32:
		tmp = t_1
	else:
		tmp = t * (b * i)
	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 (b <= -1.8e+31)
		tmp = Float64(z * Float64(c * Float64(-b)));
	elseif (b <= -2.4e-157)
		tmp = t_1;
	elseif (b <= -3.4e-214)
		tmp = Float64(y * Float64(x * z));
	elseif (b <= 4.7e+32)
		tmp = t_1;
	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)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (b <= -1.8e+31)
		tmp = z * (c * -b);
	elseif (b <= -2.4e-157)
		tmp = t_1;
	elseif (b <= -3.4e-214)
		tmp = y * (x * z);
	elseif (b <= 4.7e+32)
		tmp = t_1;
	else
		tmp = t * (b * i);
	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[b, -1.8e+31], N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.4e-157], t$95$1, If[LessEqual[b, -3.4e-214], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.7e+32], t$95$1, N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.79999999999999998e31

   1. Initial program 70.0%

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

   2. Taylor expanded in z around inf 56.1%

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

      1. *-commutative 56.1%

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

      2. *-commutative 56.1%

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

   4. Simplified 56.1%

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

   5. Taylor expanded in y around 0 46.5%

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

      1. mul-1-neg 46.5%

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

      2. *-commutative 46.5%

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

      3. distribute-rgt-neg-in 46.5%

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

   7. Simplified 46.5%

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

   if -1.79999999999999998e31 < b < -2.4e-157 or -3.3999999999999999e-214 < b < 4.70000000000000023e32

   1. Initial program 64.1%

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

   2. Taylor expanded in a around inf 53.4%

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

      1. +-commutative 53.4%

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

      2. mul-1-neg 53.4%

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

      3. unsub-neg 53.4%

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

      4. *-commutative 53.4%

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

   4. Simplified 53.4%

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

   if -2.4e-157 < b < -3.3999999999999999e-214

   1. Initial program 75.4%

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

   2. Taylor expanded in z around inf 59.5%

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

      1. *-commutative 59.5%

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

      2. *-commutative 59.5%

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

   4. Simplified 59.5%

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

   5. Taylor expanded in y around inf 51.8%

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

   6. Taylor expanded in z around 0 44.2%

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

      1. associate-*r* 51.8%

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

      2. *-commutative 51.8%

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

      3. associate-*r* 52.0%

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

      4. *-commutative 52.0%

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

   8. Simplified 52.0%

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

   if 4.70000000000000023e32 < b

   1. Initial program 77.1%

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

   2. Taylor expanded in y around -inf 74.8%

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

   4. Simplified 74.8%

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

   5. Taylor expanded in i around inf 60.8%

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

   6. Taylor expanded in j around 0 47.6%

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

      1. associate-*r* 51.4%

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

      2. *-commutative 51.4%

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

   8. Simplified 51.4%

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

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.8 \cdot 10^{+31}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-157}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq -3.4 \cdot 10^{-214}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq 4.7 \cdot 10^{+32}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 14: 51.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -7.8 \cdot 10^{+30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-157}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -3.4 \cdot 10^{-214}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-90}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))) (t_2 (* b (- (* t i) (* z c)))))
   (if (<= b -7.8e+30)
     t_2
     (if (<= b -2.4e-157)
       t_1
       (if (<= b -3.4e-214) (* y (* x z)) (if (<= b 1.15e-90) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -7.8e+30) {
		tmp = t_2;
	} else if (b <= -2.4e-157) {
		tmp = t_1;
	} else if (b <= -3.4e-214) {
		tmp = y * (x * z);
	} else if (b <= 1.15e-90) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    t_2 = b * ((t * i) - (z * c))
    if (b <= (-7.8d+30)) then
        tmp = t_2
    else if (b <= (-2.4d-157)) then
        tmp = t_1
    else if (b <= (-3.4d-214)) then
        tmp = y * (x * z)
    else if (b <= 1.15d-90) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -7.8e+30) {
		tmp = t_2;
	} else if (b <= -2.4e-157) {
		tmp = t_1;
	} else if (b <= -3.4e-214) {
		tmp = y * (x * z);
	} else if (b <= 1.15e-90) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -7.8e+30:
		tmp = t_2
	elif b <= -2.4e-157:
		tmp = t_1
	elif b <= -3.4e-214:
		tmp = y * (x * z)
	elif b <= 1.15e-90:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -7.8e+30)
		tmp = t_2;
	elseif (b <= -2.4e-157)
		tmp = t_1;
	elseif (b <= -3.4e-214)
		tmp = Float64(y * Float64(x * z));
	elseif (b <= 1.15e-90)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	t_2 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -7.8e+30)
		tmp = t_2;
	elseif (b <= -2.4e-157)
		tmp = t_1;
	elseif (b <= -3.4e-214)
		tmp = y * (x * z);
	elseif (b <= 1.15e-90)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.8e+30], t$95$2, If[LessEqual[b, -2.4e-157], t$95$1, If[LessEqual[b, -3.4e-214], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.15e-90], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.80000000000000021e30 or 1.1499999999999999e-90 < b

   1. Initial program 73.4%

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

   2. Taylor expanded in b around inf 58.4%

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

   if -7.80000000000000021e30 < b < -2.4e-157 or -3.3999999999999999e-214 < b < 1.1499999999999999e-90

   1. Initial program 62.3%

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

   2. Taylor expanded in a around inf 58.9%

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

      1. +-commutative 58.9%

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

      2. mul-1-neg 58.9%

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

      3. unsub-neg 58.9%

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

      4. *-commutative 58.9%

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

   4. Simplified 58.9%

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

   if -2.4e-157 < b < -3.3999999999999999e-214

   1. Initial program 75.4%

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

   2. Taylor expanded in z around inf 59.5%

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

      1. *-commutative 59.5%

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

      2. *-commutative 59.5%

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

   4. Simplified 59.5%

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

   5. Taylor expanded in y around inf 51.8%

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

   6. Taylor expanded in z around 0 44.2%

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

      1. associate-*r* 51.8%

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

      2. *-commutative 51.8%

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

      3. associate-*r* 52.0%

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

      4. *-commutative 52.0%

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

   8. Simplified 52.0%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.8 \cdot 10^{+30}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-157}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq -3.4 \cdot 10^{-214}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-90}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 15: 28.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;z \leq -1.86 \cdot 10^{-76}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-196}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-177}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-151}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-48}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))))
   (if (<= z -1.86e-76)
     (* y (* x z))
     (if (<= z 1.05e-196)
       t_1
       (if (<= z 1.5e-177)
         (* b (* t i))
         (if (<= z 5.4e-151)
           t_1
           (if (<= z 7.5e-48) (* a (* t (- x))) (* x (* y z)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double tmp;
	if (z <= -1.86e-76) {
		tmp = y * (x * z);
	} else if (z <= 1.05e-196) {
		tmp = t_1;
	} else if (z <= 1.5e-177) {
		tmp = b * (t * i);
	} else if (z <= 5.4e-151) {
		tmp = t_1;
	} else if (z <= 7.5e-48) {
		tmp = a * (t * -x);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (c * j)
    if (z <= (-1.86d-76)) then
        tmp = y * (x * z)
    else if (z <= 1.05d-196) then
        tmp = t_1
    else if (z <= 1.5d-177) then
        tmp = b * (t * i)
    else if (z <= 5.4d-151) then
        tmp = t_1
    else if (z <= 7.5d-48) then
        tmp = a * (t * -x)
    else
        tmp = x * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double tmp;
	if (z <= -1.86e-76) {
		tmp = y * (x * z);
	} else if (z <= 1.05e-196) {
		tmp = t_1;
	} else if (z <= 1.5e-177) {
		tmp = b * (t * i);
	} else if (z <= 5.4e-151) {
		tmp = t_1;
	} else if (z <= 7.5e-48) {
		tmp = a * (t * -x);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	tmp = 0
	if z <= -1.86e-76:
		tmp = y * (x * z)
	elif z <= 1.05e-196:
		tmp = t_1
	elif z <= 1.5e-177:
		tmp = b * (t * i)
	elif z <= 5.4e-151:
		tmp = t_1
	elif z <= 7.5e-48:
		tmp = a * (t * -x)
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	tmp = 0.0
	if (z <= -1.86e-76)
		tmp = Float64(y * Float64(x * z));
	elseif (z <= 1.05e-196)
		tmp = t_1;
	elseif (z <= 1.5e-177)
		tmp = Float64(b * Float64(t * i));
	elseif (z <= 5.4e-151)
		tmp = t_1;
	elseif (z <= 7.5e-48)
		tmp = Float64(a * Float64(t * Float64(-x)));
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (c * j);
	tmp = 0.0;
	if (z <= -1.86e-76)
		tmp = y * (x * z);
	elseif (z <= 1.05e-196)
		tmp = t_1;
	elseif (z <= 1.5e-177)
		tmp = b * (t * i);
	elseif (z <= 5.4e-151)
		tmp = t_1;
	elseif (z <= 7.5e-48)
		tmp = a * (t * -x);
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.86e-76], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05e-196], t$95$1, If[LessEqual[z, 1.5e-177], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.4e-151], t$95$1, If[LessEqual[z, 7.5e-48], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.86000000000000012e-76

   1. Initial program 57.4%

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

   2. Taylor expanded in z around inf 56.9%

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

      1. *-commutative 56.9%

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

      2. *-commutative 56.9%

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

   4. Simplified 56.9%

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

   5. Taylor expanded in y around inf 34.6%

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

   6. Taylor expanded in z around 0 33.6%

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

      1. associate-*r* 34.6%

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

      2. *-commutative 34.6%

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

      3. associate-*r* 38.3%

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

      4. *-commutative 38.3%

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

   8. Simplified 38.3%

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

   if -1.86000000000000012e-76 < z < 1.04999999999999994e-196 or 1.50000000000000004e-177 < z < 5.40000000000000014e-151

   1. Initial program 72.6%

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

   2. Taylor expanded in a around inf 52.2%

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

      1. +-commutative 52.2%

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

      2. mul-1-neg 52.2%

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

      3. unsub-neg 52.2%

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

      4. *-commutative 52.2%

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

   4. Simplified 52.2%

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

   5. Taylor expanded in j around inf 36.0%

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

   if 1.04999999999999994e-196 < z < 1.50000000000000004e-177

   1. Initial program 87.5%

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

   2. Taylor expanded in y around -inf 87.3%

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

   4. Simplified 87.3%

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

   5. Taylor expanded in i around inf 75.8%

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

   6. Taylor expanded in j around 0 72.4%

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

   if 5.40000000000000014e-151 < z < 7.50000000000000042e-48

   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 inf 63.7%

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

      1. +-commutative 63.7%

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

      2. mul-1-neg 63.7%

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

      3. unsub-neg 63.7%

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

      4. *-commutative 63.7%

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

   4. Simplified 63.7%

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

   5. Taylor expanded in j around 0 51.6%

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

      1. mul-1-neg 51.6%

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

      2. distribute-lft-neg-out 51.6%

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

      3. *-commutative 51.6%

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

   7. Simplified 51.6%

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

   if 7.50000000000000042e-48 < z

   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 z around inf 62.2%

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

      1. *-commutative 62.2%

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

      2. *-commutative 62.2%

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

   4. Simplified 62.2%

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

   5. Taylor expanded in y around inf 36.3%

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

   6. Taylor expanded in z around 0 37.6%

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

4. Final simplification 39.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.86 \cdot 10^{-76}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-196}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-177}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-151}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-48}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 16: 29.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j\right)\\ \mathbf{if}\;j \leq -6.5 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1 \cdot 10^{-181}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;j \leq 95000:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq 7.2 \cdot 10^{+92}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* a j))))
   (if (<= j -6.5e+23)
     t_1
     (if (<= j -1e-181)
       (* x (* t (- a)))
       (if (<= j 95000.0)
         (* z (* x y))
         (if (<= j 7.2e+92) (* (* y j) (- 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);
	double tmp;
	if (j <= -6.5e+23) {
		tmp = t_1;
	} else if (j <= -1e-181) {
		tmp = x * (t * -a);
	} else if (j <= 95000.0) {
		tmp = z * (x * y);
	} else if (j <= 7.2e+92) {
		tmp = (y * j) * -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)
    if (j <= (-6.5d+23)) then
        tmp = t_1
    else if (j <= (-1d-181)) then
        tmp = x * (t * -a)
    else if (j <= 95000.0d0) then
        tmp = z * (x * y)
    else if (j <= 7.2d+92) then
        tmp = (y * j) * -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);
	double tmp;
	if (j <= -6.5e+23) {
		tmp = t_1;
	} else if (j <= -1e-181) {
		tmp = x * (t * -a);
	} else if (j <= 95000.0) {
		tmp = z * (x * y);
	} else if (j <= 7.2e+92) {
		tmp = (y * j) * -i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (a * j)
	tmp = 0
	if j <= -6.5e+23:
		tmp = t_1
	elif j <= -1e-181:
		tmp = x * (t * -a)
	elif j <= 95000.0:
		tmp = z * (x * y)
	elif j <= 7.2e+92:
		tmp = (y * j) * -i
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(a * j))
	tmp = 0.0
	if (j <= -6.5e+23)
		tmp = t_1;
	elseif (j <= -1e-181)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (j <= 95000.0)
		tmp = Float64(z * Float64(x * y));
	elseif (j <= 7.2e+92)
		tmp = Float64(Float64(y * j) * Float64(-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);
	tmp = 0.0;
	if (j <= -6.5e+23)
		tmp = t_1;
	elseif (j <= -1e-181)
		tmp = x * (t * -a);
	elseif (j <= 95000.0)
		tmp = z * (x * y);
	elseif (j <= 7.2e+92)
		tmp = (y * j) * -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[(a * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -6.5e+23], t$95$1, If[LessEqual[j, -1e-181], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 95000.0], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7.2e+92], N[(N[(y * j), $MachinePrecision] * (-i)), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -6.4999999999999996e23 or 7.2e92 < j

   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 c around inf 56.5%

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

      1. *-commutative 56.5%

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

   4. Simplified 56.5%

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

   5. Taylor expanded in j around inf 43.5%

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

   if -6.4999999999999996e23 < j < -1.00000000000000005e-181

   1. Initial program 75.1%

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

   2. Taylor expanded in a around inf 45.2%

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

      1. +-commutative 45.2%

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

      2. mul-1-neg 45.2%

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

      3. unsub-neg 45.2%

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

      4. *-commutative 45.2%

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

   4. Simplified 45.2%

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

   5. Taylor expanded in j around 0 31.2%

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

      1. mul-1-neg 31.2%

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

      2. *-commutative 31.2%

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

      3. associate-*r* 33.2%

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

      4. *-commutative 33.2%

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

      5. associate-*r* 35.1%

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

      6. distribute-rgt-neg-out 35.1%

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

      7. distribute-rgt-neg-in 35.1%

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

   7. Simplified 35.1%

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

   if -1.00000000000000005e-181 < j < 95000

   1. Initial program 70.6%

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

   2. Taylor expanded in z around inf 57.5%

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

      1. *-commutative 57.5%

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

      2. *-commutative 57.5%

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

   4. Simplified 57.5%

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

   5. Taylor expanded in y around inf 37.6%

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

   if 95000 < j < 7.2e92

   1. Initial program 69.6%

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

   2. Taylor expanded in y around -inf 78.4%

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

   4. Simplified 82.7%

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

   5. Taylor expanded in i around inf 75.1%

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

   6. Taylor expanded in j around inf 57.7%

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

      1. associate-*r* 57.7%

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

      2. mul-1-neg 57.7%

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

   8. Simplified 57.7%

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

4. Final simplification 41.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -6.5 \cdot 10^{+23}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;j \leq -1 \cdot 10^{-181}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;j \leq 95000:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq 7.2 \cdot 10^{+92}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]

Alternative 17: 28.3% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j\right)\\ \mathbf{if}\;j \leq -2.6 \cdot 10^{-120}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{-12}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq 1.25 \cdot 10^{+47} \lor \neg \left(j \leq 2.9 \cdot 10^{+91}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* a j))))
   (if (<= j -2.6e-120)
     t_1
     (if (<= j 4.5e-12)
       (* z (* x y))
       (if (or (<= j 1.25e+47) (not (<= j 2.9e+91))) t_1 (* x (* y z)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (a * j);
	double tmp;
	if (j <= -2.6e-120) {
		tmp = t_1;
	} else if (j <= 4.5e-12) {
		tmp = z * (x * y);
	} else if ((j <= 1.25e+47) || !(j <= 2.9e+91)) {
		tmp = t_1;
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (a * j)
    if (j <= (-2.6d-120)) then
        tmp = t_1
    else if (j <= 4.5d-12) then
        tmp = z * (x * y)
    else if ((j <= 1.25d+47) .or. (.not. (j <= 2.9d+91))) then
        tmp = t_1
    else
        tmp = x * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (a * j);
	double tmp;
	if (j <= -2.6e-120) {
		tmp = t_1;
	} else if (j <= 4.5e-12) {
		tmp = z * (x * y);
	} else if ((j <= 1.25e+47) || !(j <= 2.9e+91)) {
		tmp = t_1;
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (a * j)
	tmp = 0
	if j <= -2.6e-120:
		tmp = t_1
	elif j <= 4.5e-12:
		tmp = z * (x * y)
	elif (j <= 1.25e+47) or not (j <= 2.9e+91):
		tmp = t_1
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(a * j))
	tmp = 0.0
	if (j <= -2.6e-120)
		tmp = t_1;
	elseif (j <= 4.5e-12)
		tmp = Float64(z * Float64(x * y));
	elseif ((j <= 1.25e+47) || !(j <= 2.9e+91))
		tmp = t_1;
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (a * j);
	tmp = 0.0;
	if (j <= -2.6e-120)
		tmp = t_1;
	elseif (j <= 4.5e-12)
		tmp = z * (x * y);
	elseif ((j <= 1.25e+47) || ~((j <= 2.9e+91)))
		tmp = t_1;
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.6e-120], t$95$1, If[LessEqual[j, 4.5e-12], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[j, 1.25e+47], N[Not[LessEqual[j, 2.9e+91]], $MachinePrecision]], t$95$1, N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -2.6000000000000001e-120 or 4.49999999999999981e-12 < j < 1.25000000000000005e47 or 2.90000000000000014e91 < j

   1. Initial program 65.8%

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

   2. Taylor expanded in c around inf 50.5%

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

      1. *-commutative 50.5%

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

   4. Simplified 50.5%

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

   5. Taylor expanded in j around inf 38.5%

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

   if -2.6000000000000001e-120 < j < 4.49999999999999981e-12

   1. Initial program 71.4%

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

   2. Taylor expanded in z around inf 55.9%

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

      1. *-commutative 55.9%

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

      2. *-commutative 55.9%

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

   4. Simplified 55.9%

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

   5. Taylor expanded in y around inf 36.1%

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

   if 1.25000000000000005e47 < j < 2.90000000000000014e91

   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 z around inf 60.3%

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

      1. *-commutative 60.3%

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

      2. *-commutative 60.3%

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

   4. Simplified 60.3%

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

   5. Taylor expanded in y around inf 50.6%

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

   6. Taylor expanded in z around 0 50.7%

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

4. Final simplification 38.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.6 \cdot 10^{-120}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{-12}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq 1.25 \cdot 10^{+47} \lor \neg \left(j \leq 2.9 \cdot 10^{+91}\right):\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 18: 30.0% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i\right)\\ \mathbf{if}\;i \leq -4.5 \cdot 10^{+29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 3 \cdot 10^{-184}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 1.96 \cdot 10^{+87}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (* b i))))
   (if (<= i -4.5e+29)
     t_1
     (if (<= i 3e-184) (* x (* y z)) (if (<= i 1.96e+87) (* a (* c j)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (b * i);
	double tmp;
	if (i <= -4.5e+29) {
		tmp = t_1;
	} else if (i <= 3e-184) {
		tmp = x * (y * z);
	} else if (i <= 1.96e+87) {
		tmp = a * (c * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b * i)
    if (i <= (-4.5d+29)) then
        tmp = t_1
    else if (i <= 3d-184) then
        tmp = x * (y * z)
    else if (i <= 1.96d+87) then
        tmp = a * (c * j)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (b * i);
	double tmp;
	if (i <= -4.5e+29) {
		tmp = t_1;
	} else if (i <= 3e-184) {
		tmp = x * (y * z);
	} else if (i <= 1.96e+87) {
		tmp = a * (c * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * (b * i)
	tmp = 0
	if i <= -4.5e+29:
		tmp = t_1
	elif i <= 3e-184:
		tmp = x * (y * z)
	elif i <= 1.96e+87:
		tmp = a * (c * j)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(b * i))
	tmp = 0.0
	if (i <= -4.5e+29)
		tmp = t_1;
	elseif (i <= 3e-184)
		tmp = Float64(x * Float64(y * z));
	elseif (i <= 1.96e+87)
		tmp = Float64(a * Float64(c * j));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * (b * i);
	tmp = 0.0;
	if (i <= -4.5e+29)
		tmp = t_1;
	elseif (i <= 3e-184)
		tmp = x * (y * z);
	elseif (i <= 1.96e+87)
		tmp = a * (c * j);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -4.5e+29], t$95$1, If[LessEqual[i, 3e-184], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.96e+87], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if i < -4.5000000000000002e29 or 1.96e87 < i

   1. Initial program 62.9%

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

   2. Taylor expanded in y around -inf 65.5%

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

   4. Simplified 65.5%

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

   5. Taylor expanded in i around inf 62.4%

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

   6. Taylor expanded in j around 0 34.6%

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

      1. associate-*r* 38.2%

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

      2. *-commutative 38.2%

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

   8. Simplified 38.2%

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

   if -4.5000000000000002e29 < i < 2.99999999999999991e-184

   1. Initial program 76.2%

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

   2. Taylor expanded in z around inf 55.6%

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

      1. *-commutative 55.6%

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

      2. *-commutative 55.6%

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

   4. Simplified 55.6%

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

   5. Taylor expanded in y around inf 33.8%

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

   6. Taylor expanded in z around 0 32.9%

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

   if 2.99999999999999991e-184 < i < 1.96e87

   1. Initial program 66.7%

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

   2. Taylor expanded in a around inf 49.2%

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

      1. +-commutative 49.2%

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

      2. mul-1-neg 49.2%

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

      3. unsub-neg 49.2%

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

      4. *-commutative 49.2%

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

   4. Simplified 49.2%

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

   5. Taylor expanded in j around inf 31.9%

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

4. Final simplification 34.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4.5 \cdot 10^{+29}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 3 \cdot 10^{-184}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 1.96 \cdot 10^{+87}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 19: 29.1% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{-79}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-204}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 3.55 \cdot 10^{-72}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -1.08e-79)
   (* y (* x z))
   (if (<= z 9.2e-204)
     (* a (* c j))
     (if (<= z 3.55e-72) (* i (* t b)) (* x (* y z))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -1.08e-79) {
		tmp = y * (x * z);
	} else if (z <= 9.2e-204) {
		tmp = a * (c * j);
	} else if (z <= 3.55e-72) {
		tmp = i * (t * b);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-1.08d-79)) then
        tmp = y * (x * z)
    else if (z <= 9.2d-204) then
        tmp = a * (c * j)
    else if (z <= 3.55d-72) then
        tmp = i * (t * b)
    else
        tmp = x * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -1.08e-79) {
		tmp = y * (x * z);
	} else if (z <= 9.2e-204) {
		tmp = a * (c * j);
	} else if (z <= 3.55e-72) {
		tmp = i * (t * b);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -1.08e-79:
		tmp = y * (x * z)
	elif z <= 9.2e-204:
		tmp = a * (c * j)
	elif z <= 3.55e-72:
		tmp = i * (t * b)
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -1.08e-79)
		tmp = Float64(y * Float64(x * z));
	elseif (z <= 9.2e-204)
		tmp = Float64(a * Float64(c * j));
	elseif (z <= 3.55e-72)
		tmp = Float64(i * Float64(t * b));
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -1.08e-79)
		tmp = y * (x * z);
	elseif (z <= 9.2e-204)
		tmp = a * (c * j);
	elseif (z <= 3.55e-72)
		tmp = i * (t * b);
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -1.08e-79], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.2e-204], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.55e-72], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.0800000000000001e-79

   1. Initial program 57.4%

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

   2. Taylor expanded in z around inf 56.9%

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

      1. *-commutative 56.9%

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

      2. *-commutative 56.9%

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

   4. Simplified 56.9%

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

   5. Taylor expanded in y around inf 34.6%

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

   6. Taylor expanded in z around 0 33.6%

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

      1. associate-*r* 34.6%

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

      2. *-commutative 34.6%

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

      3. associate-*r* 38.3%

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

      4. *-commutative 38.3%

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

   8. Simplified 38.3%

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

   if -1.0800000000000001e-79 < z < 9.1999999999999997e-204

   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 a around inf 50.9%

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

      1. +-commutative 50.9%

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

      2. mul-1-neg 50.9%

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

      3. unsub-neg 50.9%

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

      4. *-commutative 50.9%

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

   4. Simplified 50.9%

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

   5. Taylor expanded in j around inf 34.2%

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

   if 9.1999999999999997e-204 < z < 3.5499999999999998e-72

   1. Initial program 78.5%

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

   2. Taylor expanded in y around -inf 75.0%

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

   4. Simplified 75.0%

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

   5. Taylor expanded in i around inf 54.7%

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

   6. Taylor expanded in j around 0 46.6%

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

      1. *-commutative 46.6%

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

      2. associate-*l* 46.8%

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

      3. *-commutative 46.8%

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

   8. Simplified 46.8%

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

   if 3.5499999999999998e-72 < z

   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 z around inf 60.0%

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

      1. *-commutative 60.0%

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

      2. *-commutative 60.0%

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

   4. Simplified 60.0%

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

   5. Taylor expanded in y around inf 34.9%

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

   6. Taylor expanded in z around 0 36.1%

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

4. Final simplification 37.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{-79}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-204}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 3.55 \cdot 10^{-72}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 20: 29.3% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3.2 \cdot 10^{-39} \lor \neg \left(c \leq 2.05 \cdot 10^{+121}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -3.2e-39) (not (<= c 2.05e+121))) (* 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 <= -3.2e-39) || !(c <= 2.05e+121)) {
		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 <= (-3.2d-39)) .or. (.not. (c <= 2.05d+121))) 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 <= -3.2e-39) || !(c <= 2.05e+121)) {
		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 <= -3.2e-39) or not (c <= 2.05e+121):
		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 <= -3.2e-39) || !(c <= 2.05e+121))
		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 <= -3.2e-39) || ~((c <= 2.05e+121)))
		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, -3.2e-39], N[Not[LessEqual[c, 2.05e+121]], $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 < -3.1999999999999998e-39 or 2.05e121 < c

   1. Initial program 61.9%

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

   2. Taylor expanded in a around inf 54.4%

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

      1. +-commutative 54.4%

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

      2. mul-1-neg 54.4%

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

      3. unsub-neg 54.4%

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

      4. *-commutative 54.4%

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

   4. Simplified 54.4%

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

   5. Taylor expanded in j around inf 40.7%

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

   if -3.1999999999999998e-39 < c < 2.05e121

   1. Initial program 74.7%

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

   2. Taylor expanded in y around -inf 75.3%

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

   4. Simplified 76.8%

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

   5. Taylor expanded in i around inf 44.8%

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

   6. Taylor expanded in j around 0 27.2%

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

4. Final simplification 33.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.2 \cdot 10^{-39} \lor \neg \left(c \leq 2.05 \cdot 10^{+121}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]

Alternative 21: 29.4% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3.8 \cdot 10^{-39} \lor \neg \left(c \leq 2.5 \cdot 10^{+80}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -3.8e-39) (not (<= c 2.5e+80))) (* a (* c j)) (* 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 ((c <= -3.8e-39) || !(c <= 2.5e+80)) {
		tmp = a * (c * j);
	} 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 ((c <= (-3.8d-39)) .or. (.not. (c <= 2.5d+80))) then
        tmp = a * (c * j)
    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 ((c <= -3.8e-39) || !(c <= 2.5e+80)) {
		tmp = a * (c * j);
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -3.8e-39) or not (c <= 2.5e+80):
		tmp = a * (c * j)
	else:
		tmp = t * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -3.8e-39) || !(c <= 2.5e+80))
		tmp = Float64(a * Float64(c * j));
	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 ((c <= -3.8e-39) || ~((c <= 2.5e+80)))
		tmp = a * (c * j);
	else
		tmp = t * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -3.8e-39], N[Not[LessEqual[c, 2.5e+80]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -3.8000000000000002e-39 or 2.4999999999999998e80 < c

   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 54.2%

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

      1. +-commutative 54.2%

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

      2. mul-1-neg 54.2%

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

      3. unsub-neg 54.2%

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

      4. *-commutative 54.2%

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

   4. Simplified 54.2%

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

   5. Taylor expanded in j around inf 39.9%

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

   if -3.8000000000000002e-39 < c < 2.4999999999999998e80

   1. Initial program 76.6%

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

   2. Taylor expanded in y around -inf 75.7%

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

   4. Simplified 77.3%

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

   5. Taylor expanded in i around inf 46.6%

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

   6. Taylor expanded in j around 0 26.9%

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

      1. associate-*r* 27.7%

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

      2. *-commutative 27.7%

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

   8. Simplified 27.7%

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

4. Final simplification 33.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.8 \cdot 10^{-39} \lor \neg \left(c \leq 2.5 \cdot 10^{+80}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 22: 21.7% 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 68.7%

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

2. Taylor expanded in a around inf 41.6%

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

   1. +-commutative 41.6%

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

   2. mul-1-neg 41.6%

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

   3. unsub-neg 41.6%

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

   4. *-commutative 41.6%

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

4. Simplified 41.6%

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

5. Taylor expanded in j around inf 23.3%

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

6. Final simplification 23.3%

   \[\leadsto a \cdot \left(c \cdot j\right) \]

Developer target: 59.9% 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 2023318 
(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)))))