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

Percentage Accurate: 72.6% → 81.8%

Time: 22.2s

Alternatives: 28

Speedup: 0.5×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 72.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 81.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(a * N[(t * N[(N[(b * N[(i / a), $MachinePrecision]), $MachinePrecision] - x), $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 90.8%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in a around -inf 33.3%

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

   5. Simplified 41.6%

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

   6. Taylor expanded in t around inf 55.0%

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

      1. associate-*r* 55.0%

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

      2. neg-mul-1 55.0%

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

      3. associate-/l* 55.1%

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

   8. Simplified 55.1%

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

4. Final simplification 84.1%

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

Alternative 2: 29.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y \cdot j\right) \cdot \left(-i\right)\\ t_2 := t \cdot \left(b \cdot i\right)\\ \mathbf{if}\;i \leq -2.9 \cdot 10^{+171}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -1.55 \cdot 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 8 \cdot 10^{-187}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;i \leq 3.4 \cdot 10^{-63}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 1.02 \cdot 10^{+120}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;i \leq 1.06 \cdot 10^{+178}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* y j) (- i))) (t_2 (* t (* b i))))
   (if (<= i -2.9e+171)
     t_2
     (if (<= i -1.55e-31)
       t_1
       (if (<= i 8e-187)
         (* a (* x (- t)))
         (if (<= i 3.4e-63)
           (* a (* c j))
           (if (<= i 1.02e+120)
             (* b (* z (- c)))
             (if (<= i 1.06e+178) 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 = (y * j) * -i;
	double t_2 = t * (b * i);
	double tmp;
	if (i <= -2.9e+171) {
		tmp = t_2;
	} else if (i <= -1.55e-31) {
		tmp = t_1;
	} else if (i <= 8e-187) {
		tmp = a * (x * -t);
	} else if (i <= 3.4e-63) {
		tmp = a * (c * j);
	} else if (i <= 1.02e+120) {
		tmp = b * (z * -c);
	} else if (i <= 1.06e+178) {
		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 = (y * j) * -i
    t_2 = t * (b * i)
    if (i <= (-2.9d+171)) then
        tmp = t_2
    else if (i <= (-1.55d-31)) then
        tmp = t_1
    else if (i <= 8d-187) then
        tmp = a * (x * -t)
    else if (i <= 3.4d-63) then
        tmp = a * (c * j)
    else if (i <= 1.02d+120) then
        tmp = b * (z * -c)
    else if (i <= 1.06d+178) 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 = (y * j) * -i;
	double t_2 = t * (b * i);
	double tmp;
	if (i <= -2.9e+171) {
		tmp = t_2;
	} else if (i <= -1.55e-31) {
		tmp = t_1;
	} else if (i <= 8e-187) {
		tmp = a * (x * -t);
	} else if (i <= 3.4e-63) {
		tmp = a * (c * j);
	} else if (i <= 1.02e+120) {
		tmp = b * (z * -c);
	} else if (i <= 1.06e+178) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (y * j) * -i
	t_2 = t * (b * i)
	tmp = 0
	if i <= -2.9e+171:
		tmp = t_2
	elif i <= -1.55e-31:
		tmp = t_1
	elif i <= 8e-187:
		tmp = a * (x * -t)
	elif i <= 3.4e-63:
		tmp = a * (c * j)
	elif i <= 1.02e+120:
		tmp = b * (z * -c)
	elif i <= 1.06e+178:
		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(y * j) * Float64(-i))
	t_2 = Float64(t * Float64(b * i))
	tmp = 0.0
	if (i <= -2.9e+171)
		tmp = t_2;
	elseif (i <= -1.55e-31)
		tmp = t_1;
	elseif (i <= 8e-187)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (i <= 3.4e-63)
		tmp = Float64(a * Float64(c * j));
	elseif (i <= 1.02e+120)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (i <= 1.06e+178)
		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 = (y * j) * -i;
	t_2 = t * (b * i);
	tmp = 0.0;
	if (i <= -2.9e+171)
		tmp = t_2;
	elseif (i <= -1.55e-31)
		tmp = t_1;
	elseif (i <= 8e-187)
		tmp = a * (x * -t);
	elseif (i <= 3.4e-63)
		tmp = a * (c * j);
	elseif (i <= 1.02e+120)
		tmp = b * (z * -c);
	elseif (i <= 1.06e+178)
		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[(y * j), $MachinePrecision] * (-i)), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.9e+171], t$95$2, If[LessEqual[i, -1.55e-31], t$95$1, If[LessEqual[i, 8e-187], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.4e-63], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.02e+120], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.06e+178], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -2.89999999999999985e171 or 1.05999999999999994e178 < i

   1. Initial program 60.6%

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

   3. Taylor expanded in j around 0 59.1%

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

      1. *-commutative 59.1%

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

      2. *-commutative 59.1%

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

   5. Simplified 59.1%

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

   6. Taylor expanded in i around inf 46.3%

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

      1. associate-*r* 52.0%

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

   8. Simplified 52.0%

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

   if -2.89999999999999985e171 < i < -1.55e-31 or 1.01999999999999997e120 < i < 1.05999999999999994e178

   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. Add Preprocessing

   3. Taylor expanded in a around -inf 72.8%

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

   5. Simplified 73.1%

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

   6. Taylor expanded in j around inf 58.3%

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

      1. associate-*r* 57.5%

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

      2. mul-1-neg 57.5%

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

      3. unsub-neg 57.5%

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

      4. associate-/l* 57.6%

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

   8. Simplified 57.6%

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

   9. Taylor expanded in a around 0 55.5%

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

       1. mul-1-neg 55.5%

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

       2. *-commutative 55.5%

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

       3. distribute-rgt-neg-in 55.5%

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

       4. *-commutative 55.5%

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

   11. Simplified 55.5%

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

   if -1.55e-31 < i < 8.0000000000000001e-187

   1. Initial program 82.3%

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

   3. Taylor expanded in a around inf 45.6%

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

      1. +-commutative 45.6%

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

      2. mul-1-neg 45.6%

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

      3. unsub-neg 45.6%

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

   5. Simplified 45.6%

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

   6. Taylor expanded in c around 0 37.2%

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

      1. associate-*r* 37.2%

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

      2. neg-mul-1 37.2%

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

   8. Simplified 37.2%

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

   if 8.0000000000000001e-187 < i < 3.39999999999999998e-63

   1. Initial program 77.6%

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

   3. Taylor expanded in a around inf 60.7%

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

      1. +-commutative 60.7%

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

      2. mul-1-neg 60.7%

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

      3. unsub-neg 60.7%

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

   5. Simplified 60.7%

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

   6. Taylor expanded in c around inf 46.8%

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

   if 3.39999999999999998e-63 < i < 1.01999999999999997e120

   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. Add Preprocessing

   3. Taylor expanded in z around inf 54.6%

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

      1. *-commutative 54.6%

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

   5. Simplified 54.6%

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

   6. Taylor expanded in y around 0 39.4%

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

      1. associate-*r* 39.4%

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

      2. neg-mul-1 39.4%

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

   8. Simplified 39.4%

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

4. Final simplification 45.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.9 \cdot 10^{+171}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -1.55 \cdot 10^{-31}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \mathbf{elif}\;i \leq 8 \cdot 10^{-187}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;i \leq 3.4 \cdot 10^{-63}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 1.02 \cdot 10^{+120}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;i \leq 1.06 \cdot 10^{+178}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 55.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{if}\;t \leq -6.1 \cdot 10^{+136}:\\ \;\;\;\;a \cdot \left(t \cdot \left(b \cdot \frac{i}{a} - x\right)\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-304}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-190}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* y (- (* x z) (* i j))) (* b (* t i)))))
   (if (<= t -6.1e+136)
     (* a (* t (- (* b (/ i a)) x)))
     (if (<= t 1.1e-304)
       t_1
       (if (<= t 5.5e-190)
         (* z (- (* x y) (* b c)))
         (if (<= t 3.8e+70) t_1 (* t (- (* b i) (* x a)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * ((x * z) - (i * j))) + (b * (t * i));
	double tmp;
	if (t <= -6.1e+136) {
		tmp = a * (t * ((b * (i / a)) - x));
	} else if (t <= 1.1e-304) {
		tmp = t_1;
	} else if (t <= 5.5e-190) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 3.8e+70) {
		tmp = t_1;
	} else {
		tmp = t * ((b * i) - (x * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * ((x * z) - (i * j))) + (b * (t * i))
    if (t <= (-6.1d+136)) then
        tmp = a * (t * ((b * (i / a)) - x))
    else if (t <= 1.1d-304) then
        tmp = t_1
    else if (t <= 5.5d-190) then
        tmp = z * ((x * y) - (b * c))
    else if (t <= 3.8d+70) then
        tmp = t_1
    else
        tmp = t * ((b * i) - (x * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * ((x * z) - (i * j))) + (b * (t * i));
	double tmp;
	if (t <= -6.1e+136) {
		tmp = a * (t * ((b * (i / a)) - x));
	} else if (t <= 1.1e-304) {
		tmp = t_1;
	} else if (t <= 5.5e-190) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 3.8e+70) {
		tmp = t_1;
	} else {
		tmp = t * ((b * i) - (x * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (y * ((x * z) - (i * j))) + (b * (t * i))
	tmp = 0
	if t <= -6.1e+136:
		tmp = a * (t * ((b * (i / a)) - x))
	elif t <= 1.1e-304:
		tmp = t_1
	elif t <= 5.5e-190:
		tmp = z * ((x * y) - (b * c))
	elif t <= 3.8e+70:
		tmp = t_1
	else:
		tmp = t * ((b * i) - (x * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(b * Float64(t * i)))
	tmp = 0.0
	if (t <= -6.1e+136)
		tmp = Float64(a * Float64(t * Float64(Float64(b * Float64(i / a)) - x)));
	elseif (t <= 1.1e-304)
		tmp = t_1;
	elseif (t <= 5.5e-190)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (t <= 3.8e+70)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (y * ((x * z) - (i * j))) + (b * (t * i));
	tmp = 0.0;
	if (t <= -6.1e+136)
		tmp = a * (t * ((b * (i / a)) - x));
	elseif (t <= 1.1e-304)
		tmp = t_1;
	elseif (t <= 5.5e-190)
		tmp = z * ((x * y) - (b * c));
	elseif (t <= 3.8e+70)
		tmp = t_1;
	else
		tmp = t * ((b * i) - (x * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.1e+136], N[(a * N[(t * N[(N[(b * N[(i / a), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.1e-304], t$95$1, If[LessEqual[t, 5.5e-190], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.8e+70], t$95$1, N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.0999999999999996e136

   1. Initial program 41.6%

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

   3. Taylor expanded in a around -inf 51.8%

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

   5. Simplified 59.9%

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

   6. Taylor expanded in t around inf 65.4%

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

      1. associate-*r* 65.4%

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

      2. neg-mul-1 65.4%

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

      3. associate-/l* 73.4%

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

   8. Simplified 73.4%

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

   if -6.0999999999999996e136 < t < 1.1e-304 or 5.50000000000000048e-190 < t < 3.7999999999999998e70

   1. Initial program 82.2%

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

   3. Taylor expanded in a around 0 71.2%

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

   5. Simplified 72.4%

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

   6. Taylor expanded in i around inf 61.3%

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

   if 1.1e-304 < t < 5.50000000000000048e-190

   1. Initial program 79.2%

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

   3. Taylor expanded in z around inf 72.9%

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

      1. *-commutative 72.9%

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

   5. Simplified 72.9%

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

   if 3.7999999999999998e70 < t

   1. Initial program 70.4%

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

   3. Taylor expanded in t around inf 79.7%

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

      1. distribute-lft-out-- 79.7%

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

   5. Simplified 79.7%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x - b \cdot i\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.1 \cdot 10^{+136}:\\ \;\;\;\;a \cdot \left(t \cdot \left(b \cdot \frac{i}{a} - x\right)\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-304}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-190}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+70}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 29.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i\right)\\ \mathbf{if}\;i \leq -7.8 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 4.3 \cdot 10^{-302}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 9.2 \cdot 10^{-187}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;i \leq 4.6 \cdot 10^{-63}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 0.55:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (* b i))))
   (if (<= i -7.8e+63)
     t_1
     (if (<= i 4.3e-302)
       (* z (* x y))
       (if (<= i 9.2e-187)
         (* x (* t (- a)))
         (if (<= i 4.6e-63)
           (* a (* c j))
           (if (<= i 0.55) (* z (* b (- c))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (b * i);
	double tmp;
	if (i <= -7.8e+63) {
		tmp = t_1;
	} else if (i <= 4.3e-302) {
		tmp = z * (x * y);
	} else if (i <= 9.2e-187) {
		tmp = x * (t * -a);
	} else if (i <= 4.6e-63) {
		tmp = a * (c * j);
	} else if (i <= 0.55) {
		tmp = z * (b * -c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b * i)
    if (i <= (-7.8d+63)) then
        tmp = t_1
    else if (i <= 4.3d-302) then
        tmp = z * (x * y)
    else if (i <= 9.2d-187) then
        tmp = x * (t * -a)
    else if (i <= 4.6d-63) then
        tmp = a * (c * j)
    else if (i <= 0.55d0) then
        tmp = z * (b * -c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (b * i);
	double tmp;
	if (i <= -7.8e+63) {
		tmp = t_1;
	} else if (i <= 4.3e-302) {
		tmp = z * (x * y);
	} else if (i <= 9.2e-187) {
		tmp = x * (t * -a);
	} else if (i <= 4.6e-63) {
		tmp = a * (c * j);
	} else if (i <= 0.55) {
		tmp = z * (b * -c);
	} 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 <= -7.8e+63:
		tmp = t_1
	elif i <= 4.3e-302:
		tmp = z * (x * y)
	elif i <= 9.2e-187:
		tmp = x * (t * -a)
	elif i <= 4.6e-63:
		tmp = a * (c * j)
	elif i <= 0.55:
		tmp = z * (b * -c)
	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 <= -7.8e+63)
		tmp = t_1;
	elseif (i <= 4.3e-302)
		tmp = Float64(z * Float64(x * y));
	elseif (i <= 9.2e-187)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (i <= 4.6e-63)
		tmp = Float64(a * Float64(c * j));
	elseif (i <= 0.55)
		tmp = Float64(z * Float64(b * Float64(-c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * (b * i);
	tmp = 0.0;
	if (i <= -7.8e+63)
		tmp = t_1;
	elseif (i <= 4.3e-302)
		tmp = z * (x * y);
	elseif (i <= 9.2e-187)
		tmp = x * (t * -a);
	elseif (i <= 4.6e-63)
		tmp = a * (c * j);
	elseif (i <= 0.55)
		tmp = z * (b * -c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -7.8e+63], t$95$1, If[LessEqual[i, 4.3e-302], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 9.2e-187], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4.6e-63], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 0.55], N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -7.8e63 or 0.55000000000000004 < i

   1. Initial program 68.8%

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

   3. Taylor expanded in j around 0 55.1%

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

      1. *-commutative 55.1%

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

      2. *-commutative 55.1%

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

   5. Simplified 55.1%

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

   6. Taylor expanded in i around inf 35.3%

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

      1. associate-*r* 40.1%

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

   8. Simplified 40.1%

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

   if -7.8e63 < i < 4.3000000000000002e-302

   1. Initial program 78.1%

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

   3. Taylor expanded in z around inf 51.1%

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

      1. *-commutative 51.1%

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

   5. Simplified 51.1%

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

   6. Taylor expanded in y around inf 33.4%

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

   if 4.3000000000000002e-302 < i < 9.19999999999999991e-187

   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. Add Preprocessing

   3. Taylor expanded in a around inf 62.9%

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

      1. +-commutative 62.9%

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

      2. mul-1-neg 62.9%

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

      3. unsub-neg 62.9%

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

   5. Simplified 62.9%

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

   6. Taylor expanded in x around inf 56.4%

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

      1. +-commutative 56.4%

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

      2. mul-1-neg 56.4%

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

      3. unsub-neg 56.4%

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

      4. associate-*r* 62.3%

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

      5. *-commutative 62.3%

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

      6. *-commutative 62.3%

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

   8. Simplified 62.3%

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

   9. Taylor expanded in c around 0 58.4%

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

       1. mul-1-neg 58.4%

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

       2. *-commutative 58.4%

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

       3. distribute-rgt-neg-in 58.4%

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

   11. Simplified 58.4%

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

   if 9.19999999999999991e-187 < i < 4.6e-63

   1. Initial program 77.6%

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

   3. Taylor expanded in a around inf 60.7%

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

      1. +-commutative 60.7%

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

      2. mul-1-neg 60.7%

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

      3. unsub-neg 60.7%

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

   5. Simplified 60.7%

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

   6. Taylor expanded in c around inf 46.8%

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

   if 4.6e-63 < i < 0.55000000000000004

   1. Initial program 69.0%

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

   3. Taylor expanded in z around inf 64.3%

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

      1. *-commutative 64.3%

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

   5. Simplified 64.3%

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

   6. Taylor expanded in y around 0 52.2%

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

      1. neg-mul-1 52.2%

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

      2. distribute-rgt-neg-in 52.2%

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

   8. Simplified 52.2%

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

4. Final simplification 40.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -7.8 \cdot 10^{+63}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 4.3 \cdot 10^{-302}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 9.2 \cdot 10^{-187}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;i \leq 4.6 \cdot 10^{-63}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 0.55:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 52.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -2.9 \cdot 10^{-32}:\\ \;\;\;\;i \cdot \left(y \cdot \left(\frac{t \cdot b}{y} - j\right)\right)\\ \mathbf{elif}\;i \leq 7.2 \cdot 10^{-302}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 2.8 \cdot 10^{-118}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 1.8 \cdot 10^{+51}:\\ \;\;\;\;a \cdot \left(x \cdot \left(\frac{y \cdot z}{a} - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -2.9e-32)
   (* i (* y (- (/ (* t b) y) j)))
   (if (<= i 7.2e-302)
     (* z (- (* x y) (* b c)))
     (if (<= i 2.8e-118)
       (* a (- (* c j) (* x t)))
       (if (<= i 1.8e+51)
         (* a (* x (- (/ (* y z) a) t)))
         (* i (- (* t b) (* y j))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -2.9e-32) {
		tmp = i * (y * (((t * b) / y) - j));
	} else if (i <= 7.2e-302) {
		tmp = z * ((x * y) - (b * c));
	} else if (i <= 2.8e-118) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= 1.8e+51) {
		tmp = a * (x * (((y * z) / a) - t));
	} else {
		tmp = i * ((t * b) - (y * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (i <= (-2.9d-32)) then
        tmp = i * (y * (((t * b) / y) - j))
    else if (i <= 7.2d-302) then
        tmp = z * ((x * y) - (b * c))
    else if (i <= 2.8d-118) then
        tmp = a * ((c * j) - (x * t))
    else if (i <= 1.8d+51) then
        tmp = a * (x * (((y * z) / a) - t))
    else
        tmp = i * ((t * b) - (y * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -2.9e-32) {
		tmp = i * (y * (((t * b) / y) - j));
	} else if (i <= 7.2e-302) {
		tmp = z * ((x * y) - (b * c));
	} else if (i <= 2.8e-118) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= 1.8e+51) {
		tmp = a * (x * (((y * z) / a) - t));
	} else {
		tmp = i * ((t * b) - (y * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -2.9e-32:
		tmp = i * (y * (((t * b) / y) - j))
	elif i <= 7.2e-302:
		tmp = z * ((x * y) - (b * c))
	elif i <= 2.8e-118:
		tmp = a * ((c * j) - (x * t))
	elif i <= 1.8e+51:
		tmp = a * (x * (((y * z) / a) - t))
	else:
		tmp = i * ((t * b) - (y * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -2.9e-32)
		tmp = Float64(i * Float64(y * Float64(Float64(Float64(t * b) / y) - j)));
	elseif (i <= 7.2e-302)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (i <= 2.8e-118)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (i <= 1.8e+51)
		tmp = Float64(a * Float64(x * Float64(Float64(Float64(y * z) / a) - t)));
	else
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -2.9e-32)
		tmp = i * (y * (((t * b) / y) - j));
	elseif (i <= 7.2e-302)
		tmp = z * ((x * y) - (b * c));
	elseif (i <= 2.8e-118)
		tmp = a * ((c * j) - (x * t));
	elseif (i <= 1.8e+51)
		tmp = a * (x * (((y * z) / a) - t));
	else
		tmp = i * ((t * b) - (y * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -2.9e-32], N[(i * N[(y * N[(N[(N[(t * b), $MachinePrecision] / y), $MachinePrecision] - j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 7.2e-302], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.8e-118], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.8e+51], N[(a * N[(x * N[(N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -2.89999999999999996e-32

   1. Initial program 62.7%

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

   3. Taylor expanded in a around 0 68.6%

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

   5. Simplified 67.2%

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

   6. Taylor expanded in i around inf 69.2%

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

      1. +-commutative 69.2%

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

      2. mul-1-neg 69.2%

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

      3. unsub-neg 69.2%

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

   8. Simplified 69.2%

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

   9. Taylor expanded in y around inf 70.5%

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

   if -2.89999999999999996e-32 < i < 7.2000000000000001e-302

   1. Initial program 82.4%

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

   3. Taylor expanded in z around inf 58.5%

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

      1. *-commutative 58.5%

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

   5. Simplified 58.5%

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

   if 7.2000000000000001e-302 < i < 2.8e-118

   1. Initial program 77.7%

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

   3. Taylor expanded in a around inf 69.7%

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

      1. +-commutative 69.7%

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

      2. mul-1-neg 69.7%

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

      3. unsub-neg 69.7%

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

   5. Simplified 69.7%

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

   if 2.8e-118 < i < 1.80000000000000005e51

   1. Initial program 80.6%

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

   3. Taylor expanded in a around -inf 73.0%

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

   5. Simplified 78.3%

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

   6. Taylor expanded in x around inf 57.6%

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

      1. associate-*r* 57.6%

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

      2. neg-mul-1 57.6%

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

      3. *-commutative 57.6%

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

   8. Simplified 57.6%

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

   if 1.80000000000000005e51 < i

   1. Initial program 71.1%

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

   3. Taylor expanded in a around 0 73.2%

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

   5. Simplified 73.2%

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

   6. Taylor expanded in i around inf 67.2%

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

      1. +-commutative 67.2%

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

      2. mul-1-neg 67.2%

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

      3. unsub-neg 67.2%

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

   8. Simplified 67.2%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.9 \cdot 10^{-32}:\\ \;\;\;\;i \cdot \left(y \cdot \left(\frac{t \cdot b}{y} - j\right)\right)\\ \mathbf{elif}\;i \leq 7.2 \cdot 10^{-302}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 2.8 \cdot 10^{-118}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 1.8 \cdot 10^{+51}:\\ \;\;\;\;a \cdot \left(x \cdot \left(\frac{y \cdot z}{a} - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 29.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i\right)\\ \mathbf{if}\;i \leq -2.6 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{-302}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 6.8 \cdot 10^{-186}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;i \leq 8.5 \cdot 10^{-63}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 1.1 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (* b i))))
   (if (<= i -2.6e+60)
     t_1
     (if (<= i 4.8e-302)
       (* z (* x y))
       (if (<= i 6.8e-186)
         (* x (* t (- a)))
         (if (<= i 8.5e-63)
           (* a (* c j))
           (if (<= i 1.1e+42) (* x (* y z)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (b * i);
	double tmp;
	if (i <= -2.6e+60) {
		tmp = t_1;
	} else if (i <= 4.8e-302) {
		tmp = z * (x * y);
	} else if (i <= 6.8e-186) {
		tmp = x * (t * -a);
	} else if (i <= 8.5e-63) {
		tmp = a * (c * j);
	} else if (i <= 1.1e+42) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b * i)
    if (i <= (-2.6d+60)) then
        tmp = t_1
    else if (i <= 4.8d-302) then
        tmp = z * (x * y)
    else if (i <= 6.8d-186) then
        tmp = x * (t * -a)
    else if (i <= 8.5d-63) then
        tmp = a * (c * j)
    else if (i <= 1.1d+42) then
        tmp = x * (y * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (b * i);
	double tmp;
	if (i <= -2.6e+60) {
		tmp = t_1;
	} else if (i <= 4.8e-302) {
		tmp = z * (x * y);
	} else if (i <= 6.8e-186) {
		tmp = x * (t * -a);
	} else if (i <= 8.5e-63) {
		tmp = a * (c * j);
	} else if (i <= 1.1e+42) {
		tmp = x * (y * z);
	} 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 <= -2.6e+60:
		tmp = t_1
	elif i <= 4.8e-302:
		tmp = z * (x * y)
	elif i <= 6.8e-186:
		tmp = x * (t * -a)
	elif i <= 8.5e-63:
		tmp = a * (c * j)
	elif i <= 1.1e+42:
		tmp = x * (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(b * i))
	tmp = 0.0
	if (i <= -2.6e+60)
		tmp = t_1;
	elseif (i <= 4.8e-302)
		tmp = Float64(z * Float64(x * y));
	elseif (i <= 6.8e-186)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (i <= 8.5e-63)
		tmp = Float64(a * Float64(c * j));
	elseif (i <= 1.1e+42)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * (b * i);
	tmp = 0.0;
	if (i <= -2.6e+60)
		tmp = t_1;
	elseif (i <= 4.8e-302)
		tmp = z * (x * y);
	elseif (i <= 6.8e-186)
		tmp = x * (t * -a);
	elseif (i <= 8.5e-63)
		tmp = a * (c * j);
	elseif (i <= 1.1e+42)
		tmp = x * (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.6e+60], t$95$1, If[LessEqual[i, 4.8e-302], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 6.8e-186], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 8.5e-63], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.1e+42], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -2.60000000000000008e60 or 1.1000000000000001e42 < i

   1. Initial program 66.8%

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

   3. Taylor expanded in j around 0 53.1%

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

      1. *-commutative 53.1%

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

      2. *-commutative 53.1%

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

   5. Simplified 53.1%

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

   6. Taylor expanded in i around inf 36.6%

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

      1. associate-*r* 41.6%

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

   8. Simplified 41.6%

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

   if -2.60000000000000008e60 < i < 4.80000000000000044e-302

   1. Initial program 78.1%

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

   3. Taylor expanded in z around inf 51.1%

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

      1. *-commutative 51.1%

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

   5. Simplified 51.1%

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

   6. Taylor expanded in y around inf 33.4%

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

   if 4.80000000000000044e-302 < i < 6.7999999999999999e-186

   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. Add Preprocessing

   3. Taylor expanded in a around inf 62.9%

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

      1. +-commutative 62.9%

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

      2. mul-1-neg 62.9%

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

      3. unsub-neg 62.9%

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

   5. Simplified 62.9%

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

   6. Taylor expanded in x around inf 56.4%

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

      1. +-commutative 56.4%

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

      2. mul-1-neg 56.4%

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

      3. unsub-neg 56.4%

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

      4. associate-*r* 62.3%

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

      5. *-commutative 62.3%

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

      6. *-commutative 62.3%

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

   8. Simplified 62.3%

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

   9. Taylor expanded in c around 0 58.4%

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

       1. mul-1-neg 58.4%

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

       2. *-commutative 58.4%

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

       3. distribute-rgt-neg-in 58.4%

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

   11. Simplified 58.4%

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

   if 6.7999999999999999e-186 < i < 8.49999999999999969e-63

   1. Initial program 77.6%

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

   3. Taylor expanded in a around inf 60.7%

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

      1. +-commutative 60.7%

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

      2. mul-1-neg 60.7%

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

      3. unsub-neg 60.7%

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

   5. Simplified 60.7%

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

   6. Taylor expanded in c around inf 46.8%

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

   if 8.49999999999999969e-63 < i < 1.1000000000000001e42

   1. Initial program 78.5%

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

   3. Taylor expanded in z around inf 63.1%

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

      1. *-commutative 63.1%

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

   5. Simplified 63.1%

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

   6. Taylor expanded in y around inf 36.7%

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

      1. *-commutative 36.7%

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

   8. Simplified 36.7%

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

4. Final simplification 40.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.6 \cdot 10^{+60}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{-302}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 6.8 \cdot 10^{-186}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;i \leq 8.5 \cdot 10^{-63}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 1.1 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 29.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;i \leq -5.4 \cdot 10^{+110}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;i \leq -2.1 \cdot 10^{-33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 1.02 \cdot 10^{-212}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 1.05 \cdot 10^{-62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 5.6 \cdot 10^{+37}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))))
   (if (<= i -5.4e+110)
     (* i (* t b))
     (if (<= i -2.1e-33)
       t_1
       (if (<= i 1.02e-212)
         (* z (* x y))
         (if (<= i 1.05e-62)
           t_1
           (if (<= i 5.6e+37) (* x (* y z)) (* 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 t_1 = a * (c * j);
	double tmp;
	if (i <= -5.4e+110) {
		tmp = i * (t * b);
	} else if (i <= -2.1e-33) {
		tmp = t_1;
	} else if (i <= 1.02e-212) {
		tmp = z * (x * y);
	} else if (i <= 1.05e-62) {
		tmp = t_1;
	} else if (i <= 5.6e+37) {
		tmp = x * (y * z);
	} 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) :: t_1
    real(8) :: tmp
    t_1 = a * (c * j)
    if (i <= (-5.4d+110)) then
        tmp = i * (t * b)
    else if (i <= (-2.1d-33)) then
        tmp = t_1
    else if (i <= 1.02d-212) then
        tmp = z * (x * y)
    else if (i <= 1.05d-62) then
        tmp = t_1
    else if (i <= 5.6d+37) then
        tmp = x * (y * z)
    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 t_1 = a * (c * j);
	double tmp;
	if (i <= -5.4e+110) {
		tmp = i * (t * b);
	} else if (i <= -2.1e-33) {
		tmp = t_1;
	} else if (i <= 1.02e-212) {
		tmp = z * (x * y);
	} else if (i <= 1.05e-62) {
		tmp = t_1;
	} else if (i <= 5.6e+37) {
		tmp = x * (y * z);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	tmp = 0
	if i <= -5.4e+110:
		tmp = i * (t * b)
	elif i <= -2.1e-33:
		tmp = t_1
	elif i <= 1.02e-212:
		tmp = z * (x * y)
	elif i <= 1.05e-62:
		tmp = t_1
	elif i <= 5.6e+37:
		tmp = x * (y * z)
	else:
		tmp = b * (t * i)
	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 (i <= -5.4e+110)
		tmp = Float64(i * Float64(t * b));
	elseif (i <= -2.1e-33)
		tmp = t_1;
	elseif (i <= 1.02e-212)
		tmp = Float64(z * Float64(x * y));
	elseif (i <= 1.05e-62)
		tmp = t_1;
	elseif (i <= 5.6e+37)
		tmp = Float64(x * Float64(y * z));
	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)
	t_1 = a * (c * j);
	tmp = 0.0;
	if (i <= -5.4e+110)
		tmp = i * (t * b);
	elseif (i <= -2.1e-33)
		tmp = t_1;
	elseif (i <= 1.02e-212)
		tmp = z * (x * y);
	elseif (i <= 1.05e-62)
		tmp = t_1;
	elseif (i <= 5.6e+37)
		tmp = x * (y * z);
	else
		tmp = b * (t * i);
	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[i, -5.4e+110], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -2.1e-33], t$95$1, If[LessEqual[i, 1.02e-212], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.05e-62], t$95$1, If[LessEqual[i, 5.6e+37], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -5.40000000000000019e110

   1. Initial program 58.6%

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

   3. Taylor expanded in a around 0 67.4%

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

   5. Simplified 65.3%

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

   6. Taylor expanded in i around inf 73.9%

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

      1. +-commutative 73.9%

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

      2. mul-1-neg 73.9%

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

      3. unsub-neg 73.9%

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

   8. Simplified 73.9%

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

   9. Taylor expanded in b around inf 43.9%

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

   if -5.40000000000000019e110 < i < -2.1e-33 or 1.0199999999999999e-212 < i < 1.05e-62

   1. Initial program 77.2%

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

   3. Taylor expanded in a around inf 49.2%

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

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

   5. Simplified 49.2%

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

   6. Taylor expanded in c around inf 35.6%

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

   if -2.1e-33 < i < 1.0199999999999999e-212

   1. Initial program 82.1%

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

   3. Taylor expanded in z around inf 54.8%

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

      1. *-commutative 54.8%

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

   5. Simplified 54.8%

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

   6. Taylor expanded in y around inf 36.1%

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

   if 1.05e-62 < i < 5.5999999999999996e37

   1. Initial program 78.5%

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

   3. Taylor expanded in z around inf 63.1%

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

      1. *-commutative 63.1%

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

   5. Simplified 63.1%

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

   6. Taylor expanded in y around inf 36.7%

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

      1. *-commutative 36.7%

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

   8. Simplified 36.7%

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

   if 5.5999999999999996e37 < i

   1. Initial program 70.2%

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

   3. Taylor expanded in j around 0 52.9%

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

      1. *-commutative 52.9%

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

      2. *-commutative 52.9%

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

   5. Simplified 52.9%

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

   6. Taylor expanded in i around inf 36.1%

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

4. Final simplification 37.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -5.4 \cdot 10^{+110}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;i \leq -2.1 \cdot 10^{-33}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 1.02 \cdot 10^{-212}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 1.05 \cdot 10^{-62}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 5.6 \cdot 10^{+37}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;i \leq -2.45 \cdot 10^{-32}:\\ \;\;\;\;i \cdot \left(y \cdot \left(\frac{t \cdot b}{y} - j\right)\right)\\ \mathbf{elif}\;i \leq 5.5 \cdot 10^{-302}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 7.8 \cdot 10^{-59}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 3.8 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c)))))
   (if (<= i -2.45e-32)
     (* i (* y (- (/ (* t b) y) j)))
     (if (<= i 5.5e-302)
       t_1
       (if (<= i 7.8e-59)
         (* a (- (* c j) (* x t)))
         (if (<= i 3.8e+32) t_1 (* i (- (* t b) (* y j)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double tmp;
	if (i <= -2.45e-32) {
		tmp = i * (y * (((t * b) / y) - j));
	} else if (i <= 5.5e-302) {
		tmp = t_1;
	} else if (i <= 7.8e-59) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= 3.8e+32) {
		tmp = t_1;
	} else {
		tmp = i * ((t * b) - (y * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * ((x * y) - (b * c))
    if (i <= (-2.45d-32)) then
        tmp = i * (y * (((t * b) / y) - j))
    else if (i <= 5.5d-302) then
        tmp = t_1
    else if (i <= 7.8d-59) then
        tmp = a * ((c * j) - (x * t))
    else if (i <= 3.8d+32) then
        tmp = t_1
    else
        tmp = i * ((t * b) - (y * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double tmp;
	if (i <= -2.45e-32) {
		tmp = i * (y * (((t * b) / y) - j));
	} else if (i <= 5.5e-302) {
		tmp = t_1;
	} else if (i <= 7.8e-59) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= 3.8e+32) {
		tmp = t_1;
	} else {
		tmp = i * ((t * b) - (y * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * ((x * y) - (b * c))
	tmp = 0
	if i <= -2.45e-32:
		tmp = i * (y * (((t * b) / y) - j))
	elif i <= 5.5e-302:
		tmp = t_1
	elif i <= 7.8e-59:
		tmp = a * ((c * j) - (x * t))
	elif i <= 3.8e+32:
		tmp = t_1
	else:
		tmp = i * ((t * b) - (y * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (i <= -2.45e-32)
		tmp = Float64(i * Float64(y * Float64(Float64(Float64(t * b) / y) - j)));
	elseif (i <= 5.5e-302)
		tmp = t_1;
	elseif (i <= 7.8e-59)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (i <= 3.8e+32)
		tmp = t_1;
	else
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (i <= -2.45e-32)
		tmp = i * (y * (((t * b) / y) - j));
	elseif (i <= 5.5e-302)
		tmp = t_1;
	elseif (i <= 7.8e-59)
		tmp = a * ((c * j) - (x * t));
	elseif (i <= 3.8e+32)
		tmp = t_1;
	else
		tmp = i * ((t * b) - (y * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.45e-32], N[(i * N[(y * N[(N[(N[(t * b), $MachinePrecision] / y), $MachinePrecision] - j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5.5e-302], t$95$1, If[LessEqual[i, 7.8e-59], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.8e+32], t$95$1, N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -2.4499999999999999e-32

   1. Initial program 62.7%

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

   3. Taylor expanded in a around 0 68.6%

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

   5. Simplified 67.2%

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

   6. Taylor expanded in i around inf 69.2%

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

      1. +-commutative 69.2%

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

      2. mul-1-neg 69.2%

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

      3. unsub-neg 69.2%

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

   8. Simplified 69.2%

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

   9. Taylor expanded in y around inf 70.5%

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

   if -2.4499999999999999e-32 < i < 5.5000000000000001e-302 or 7.80000000000000038e-59 < i < 3.8000000000000003e32

   1. Initial program 80.6%

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

   3. Taylor expanded in z around inf 61.2%

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

      1. *-commutative 61.2%

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

   5. Simplified 61.2%

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

   if 5.5000000000000001e-302 < i < 7.80000000000000038e-59

   1. Initial program 82.4%

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

   3. Taylor expanded in a around inf 59.7%

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

      1. +-commutative 59.7%

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

      2. mul-1-neg 59.7%

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

      3. unsub-neg 59.7%

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

   5. Simplified 59.7%

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

   if 3.8000000000000003e32 < i

   1. Initial program 70.8%

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

   3. Taylor expanded in a around 0 71.0%

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

   5. Simplified 70.9%

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

   6. Taylor expanded in i around inf 65.4%

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

      1. +-commutative 65.4%

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

      2. mul-1-neg 65.4%

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

      3. unsub-neg 65.4%

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

   8. Simplified 65.4%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.45 \cdot 10^{-32}:\\ \;\;\;\;i \cdot \left(y \cdot \left(\frac{t \cdot b}{y} - j\right)\right)\\ \mathbf{elif}\;i \leq 5.5 \cdot 10^{-302}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 7.8 \cdot 10^{-59}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 3.8 \cdot 10^{+32}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 52.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -1.5 \cdot 10^{-32}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq 5.2 \cdot 10^{-302}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 3.1 \cdot 10^{-59}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 2 \cdot 10^{+36}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c)))) (t_2 (* i (- (* t b) (* y j)))))
   (if (<= i -1.5e-32)
     t_2
     (if (<= i 5.2e-302)
       t_1
       (if (<= i 3.1e-59)
         (* a (- (* c j) (* x t)))
         (if (<= i 2e+36) 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) - (b * c));
	double t_2 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -1.5e-32) {
		tmp = t_2;
	} else if (i <= 5.2e-302) {
		tmp = t_1;
	} else if (i <= 3.1e-59) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= 2e+36) {
		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) - (b * c))
    t_2 = i * ((t * b) - (y * j))
    if (i <= (-1.5d-32)) then
        tmp = t_2
    else if (i <= 5.2d-302) then
        tmp = t_1
    else if (i <= 3.1d-59) then
        tmp = a * ((c * j) - (x * t))
    else if (i <= 2d+36) 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) - (b * c));
	double t_2 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -1.5e-32) {
		tmp = t_2;
	} else if (i <= 5.2e-302) {
		tmp = t_1;
	} else if (i <= 3.1e-59) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= 2e+36) {
		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) - (b * c))
	t_2 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -1.5e-32:
		tmp = t_2
	elif i <= 5.2e-302:
		tmp = t_1
	elif i <= 3.1e-59:
		tmp = a * ((c * j) - (x * t))
	elif i <= 2e+36:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	t_2 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -1.5e-32)
		tmp = t_2;
	elseif (i <= 5.2e-302)
		tmp = t_1;
	elseif (i <= 3.1e-59)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (i <= 2e+36)
		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) - (b * c));
	t_2 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -1.5e-32)
		tmp = t_2;
	elseif (i <= 5.2e-302)
		tmp = t_1;
	elseif (i <= 3.1e-59)
		tmp = a * ((c * j) - (x * t));
	elseif (i <= 2e+36)
		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[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.5e-32], t$95$2, If[LessEqual[i, 5.2e-302], t$95$1, If[LessEqual[i, 3.1e-59], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2e+36], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -1.5e-32 or 2.00000000000000008e36 < i

   1. Initial program 66.0%

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

   3. Taylor expanded in a around 0 69.6%

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

   5. Simplified 68.7%

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

   6. Taylor expanded in i around inf 67.6%

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

      1. +-commutative 67.6%

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

      2. mul-1-neg 67.6%

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

      3. unsub-neg 67.6%

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

   8. Simplified 67.6%

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

   if -1.5e-32 < i < 5.20000000000000022e-302 or 3.09999999999999999e-59 < i < 2.00000000000000008e36

   1. Initial program 80.6%

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

   3. Taylor expanded in z around inf 61.2%

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

      1. *-commutative 61.2%

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

   5. Simplified 61.2%

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

   if 5.20000000000000022e-302 < i < 3.09999999999999999e-59

   1. Initial program 82.4%

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

   3. Taylor expanded in a around inf 59.7%

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

      1. +-commutative 59.7%

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

      2. mul-1-neg 59.7%

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

      3. unsub-neg 59.7%

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

   5. Simplified 59.7%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.5 \cdot 10^{-32}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq 5.2 \cdot 10^{-302}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 3.1 \cdot 10^{-59}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 2 \cdot 10^{+36}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -15.5:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-143}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-106}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+93}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j)))))
   (if (<= y -15.5)
     t_1
     (if (<= y -1.95e-143)
       (* c (- (* a j) (* z b)))
       (if (<= y 2.9e-106)
         (* a (- (* c j) (* x t)))
         (if (<= y 1.35e+93) (* b (- (* t i) (* z c))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -15.5) {
		tmp = t_1;
	} else if (y <= -1.95e-143) {
		tmp = c * ((a * j) - (z * b));
	} else if (y <= 2.9e-106) {
		tmp = a * ((c * j) - (x * t));
	} else if (y <= 1.35e+93) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((x * z) - (i * j))
    if (y <= (-15.5d0)) then
        tmp = t_1
    else if (y <= (-1.95d-143)) then
        tmp = c * ((a * j) - (z * b))
    else if (y <= 2.9d-106) then
        tmp = a * ((c * j) - (x * t))
    else if (y <= 1.35d+93) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -15.5) {
		tmp = t_1;
	} else if (y <= -1.95e-143) {
		tmp = c * ((a * j) - (z * b));
	} else if (y <= 2.9e-106) {
		tmp = a * ((c * j) - (x * t));
	} else if (y <= 1.35e+93) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -15.5:
		tmp = t_1
	elif y <= -1.95e-143:
		tmp = c * ((a * j) - (z * b))
	elif y <= 2.9e-106:
		tmp = a * ((c * j) - (x * t))
	elif y <= 1.35e+93:
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -15.5)
		tmp = t_1;
	elseif (y <= -1.95e-143)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (y <= 2.9e-106)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (y <= 1.35e+93)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -15.5)
		tmp = t_1;
	elseif (y <= -1.95e-143)
		tmp = c * ((a * j) - (z * b));
	elseif (y <= 2.9e-106)
		tmp = a * ((c * j) - (x * t));
	elseif (y <= 1.35e+93)
		tmp = b * ((t * i) - (z * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -15.5], t$95$1, If[LessEqual[y, -1.95e-143], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.9e-106], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.35e+93], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -15.5 or 1.35e93 < y

   1. Initial program 68.0%

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

   3. Taylor expanded in y around inf 70.4%

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

      1. +-commutative 70.4%

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

      2. mul-1-neg 70.4%

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

      3. unsub-neg 70.4%

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

      4. *-commutative 70.4%

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

   5. Simplified 70.4%

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

   if -15.5 < y < -1.95000000000000002e-143

   1. Initial program 81.5%

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

   3. Taylor expanded in c around inf 64.0%

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

      1. *-commutative 64.0%

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

   5. Simplified 64.0%

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

   if -1.95000000000000002e-143 < y < 2.9e-106

   1. Initial program 77.0%

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

   3. Taylor expanded in a around inf 53.9%

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

      1. +-commutative 53.9%

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

      2. mul-1-neg 53.9%

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

      3. unsub-neg 53.9%

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

   5. Simplified 53.9%

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

   if 2.9e-106 < y < 1.35e93

   1. Initial program 79.7%

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

   3. Taylor expanded in b around inf 55.3%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -15.5:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-143}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-106}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+93}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 67.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;j \leq -3.5 \cdot 10^{-56}:\\ \;\;\;\;t\_1 + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{+118}:\\ \;\;\;\;t\_1 + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= j -3.5e-56)
     (+ t_1 (* j (- (* a c) (* y i))))
     (if (<= j 2.3e+118)
       (+ t_1 (* b (- (* t i) (* z c))))
       (- (* b (* t i)) (* j (- (* y i) (* a c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (j <= -3.5e-56) {
		tmp = t_1 + (j * ((a * c) - (y * i)));
	} else if (j <= 2.3e+118) {
		tmp = t_1 + (b * ((t * i) - (z * c)));
	} else {
		tmp = (b * (t * i)) - (j * ((y * i) - (a * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (j <= (-3.5d-56)) then
        tmp = t_1 + (j * ((a * c) - (y * i)))
    else if (j <= 2.3d+118) then
        tmp = t_1 + (b * ((t * i) - (z * c)))
    else
        tmp = (b * (t * i)) - (j * ((y * i) - (a * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (j <= -3.5e-56) {
		tmp = t_1 + (j * ((a * c) - (y * i)));
	} else if (j <= 2.3e+118) {
		tmp = t_1 + (b * ((t * i) - (z * c)));
	} else {
		tmp = (b * (t * i)) - (j * ((y * i) - (a * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if j <= -3.5e-56:
		tmp = t_1 + (j * ((a * c) - (y * i)))
	elif j <= 2.3e+118:
		tmp = t_1 + (b * ((t * i) - (z * c)))
	else:
		tmp = (b * (t * i)) - (j * ((y * i) - (a * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (j <= -3.5e-56)
		tmp = Float64(t_1 + Float64(j * Float64(Float64(a * c) - Float64(y * i))));
	elseif (j <= 2.3e+118)
		tmp = Float64(t_1 + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	else
		tmp = Float64(Float64(b * Float64(t * i)) - Float64(j * Float64(Float64(y * i) - Float64(a * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (j <= -3.5e-56)
		tmp = t_1 + (j * ((a * c) - (y * i)));
	elseif (j <= 2.3e+118)
		tmp = t_1 + (b * ((t * i) - (z * c)));
	else
		tmp = (b * (t * i)) - (j * ((y * i) - (a * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.5e-56], N[(t$95$1 + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.3e+118], N[(t$95$1 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(y * i), $MachinePrecision] - N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if j < -3.4999999999999998e-56

   1. Initial program 79.2%

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

   3. Taylor expanded in b around 0 78.9%

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

   if -3.4999999999999998e-56 < j < 2.30000000000000016e118

   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. Add Preprocessing

   3. Taylor expanded in j around 0 73.7%

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

      1. *-commutative 73.7%

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

      2. *-commutative 73.7%

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

   5. Simplified 73.7%

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

   if 2.30000000000000016e118 < j

   1. Initial program 73.1%

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

   3. Taylor expanded in x around 0 76.4%

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

      1. *-commutative 76.4%

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

   5. Simplified 76.4%

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

   6. Taylor expanded in c around 0 76.7%

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

      1. mul-1-neg 76.7%

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

      2. *-commutative 76.7%

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

      3. distribute-rgt-neg-in 76.7%

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

   8. Simplified 76.7%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.5 \cdot 10^{-56}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{+118}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 64.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;j \leq -2.35 \cdot 10^{-113}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 1.15 \cdot 10^{+60}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_1 - j \cdot \left(y \cdot i - a \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))))
   (if (<= j -2.35e-113)
     (+ (* x (- (* y z) (* t a))) (* j (- (* a c) (* y i))))
     (if (<= j 1.15e+60)
       (+ (* y (- (* x z) (* i j))) t_1)
       (- t_1 (* j (- (* y i) (* a c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (j <= -2.35e-113) {
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	} else if (j <= 1.15e+60) {
		tmp = (y * ((x * z) - (i * j))) + t_1;
	} else {
		tmp = t_1 - (j * ((y * i) - (a * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    if (j <= (-2.35d-113)) then
        tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)))
    else if (j <= 1.15d+60) then
        tmp = (y * ((x * z) - (i * j))) + t_1
    else
        tmp = t_1 - (j * ((y * i) - (a * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (j <= -2.35e-113) {
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	} else if (j <= 1.15e+60) {
		tmp = (y * ((x * z) - (i * j))) + t_1;
	} else {
		tmp = t_1 - (j * ((y * i) - (a * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	tmp = 0
	if j <= -2.35e-113:
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)))
	elif j <= 1.15e+60:
		tmp = (y * ((x * z) - (i * j))) + t_1
	else:
		tmp = t_1 - (j * ((y * i) - (a * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (j <= -2.35e-113)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))));
	elseif (j <= 1.15e+60)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + t_1);
	else
		tmp = Float64(t_1 - Float64(j * Float64(Float64(y * i) - Float64(a * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (j <= -2.35e-113)
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	elseif (j <= 1.15e+60)
		tmp = (y * ((x * z) - (i * j))) + t_1;
	else
		tmp = t_1 - (j * ((y * i) - (a * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.35e-113], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.15e+60], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(t$95$1 - N[(j * N[(N[(y * i), $MachinePrecision] - N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if j < -2.3500000000000001e-113

   1. Initial program 78.3%

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

   3. Taylor expanded in b around 0 76.9%

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

   if -2.3500000000000001e-113 < j < 1.15000000000000008e60

   1. Initial program 71.1%

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

   3. Taylor expanded in a around 0 70.9%

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

   5. Simplified 73.5%

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

   if 1.15000000000000008e60 < j

   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. Add Preprocessing

   3. Taylor expanded in x around 0 70.5%

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

      1. *-commutative 70.5%

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

   5. Simplified 70.5%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.35 \cdot 10^{-113}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 1.15 \cdot 10^{+60}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 64.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+128}:\\ \;\;\;\;a \cdot \left(t \cdot \left(b \cdot \frac{i}{a} - x\right)\right)\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{+70}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -3.4e+128)
   (* a (* t (- (* b (/ i a)) x)))
   (if (<= t 2.15e+70)
     (+ (* y (- (* x z) (* i j))) (* b (- (* t i) (* z c))))
     (* t (- (* b i) (* x a))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -3.4e+128) {
		tmp = a * (t * ((b * (i / a)) - x));
	} else if (t <= 2.15e+70) {
		tmp = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)));
	} else {
		tmp = t * ((b * i) - (x * a));
	}
	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 (t <= (-3.4d+128)) then
        tmp = a * (t * ((b * (i / a)) - x))
    else if (t <= 2.15d+70) then
        tmp = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)))
    else
        tmp = t * ((b * i) - (x * a))
    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 (t <= -3.4e+128) {
		tmp = a * (t * ((b * (i / a)) - x));
	} else if (t <= 2.15e+70) {
		tmp = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)));
	} else {
		tmp = t * ((b * i) - (x * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -3.4e+128:
		tmp = a * (t * ((b * (i / a)) - x))
	elif t <= 2.15e+70:
		tmp = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)))
	else:
		tmp = t * ((b * i) - (x * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -3.4e+128)
		tmp = Float64(a * Float64(t * Float64(Float64(b * Float64(i / a)) - x)));
	elseif (t <= 2.15e+70)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	else
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -3.4e+128)
		tmp = a * (t * ((b * (i / a)) - x));
	elseif (t <= 2.15e+70)
		tmp = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)));
	else
		tmp = t * ((b * i) - (x * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -3.4e+128], N[(a * N[(t * N[(N[(b * N[(i / a), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.15e+70], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.3999999999999999e128

   1. Initial program 43.2%

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

   3. Taylor expanded in a around -inf 53.1%

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

   5. Simplified 58.3%

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

   6. Taylor expanded in t around inf 63.7%

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

      1. associate-*r* 63.7%

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

      2. neg-mul-1 63.7%

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

      3. associate-/l* 71.4%

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

   8. Simplified 71.4%

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

   if -3.3999999999999999e128 < t < 2.15e70

   1. Initial program 81.7%

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

   3. Taylor expanded in a around 0 71.2%

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

   5. Simplified 72.7%

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

   if 2.15e70 < t

   1. Initial program 70.4%

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

   3. Taylor expanded in t around inf 79.7%

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

      1. distribute-lft-out-- 79.7%

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

   5. Simplified 79.7%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+128}:\\ \;\;\;\;a \cdot \left(t \cdot \left(b \cdot \frac{i}{a} - x\right)\right)\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{+70}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 29.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i\right)\\ \mathbf{if}\;i \leq -2.05 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 2.7 \cdot 10^{-216}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 3.6 \cdot 10^{-63}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;i \leq 4.2 \cdot 10^{+44}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (* b i))))
   (if (<= i -2.05e+61)
     t_1
     (if (<= i 2.7e-216)
       (* z (* x y))
       (if (<= i 3.6e-63)
         (* j (* a c))
         (if (<= i 4.2e+44) (* x (* y z)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (b * i);
	double tmp;
	if (i <= -2.05e+61) {
		tmp = t_1;
	} else if (i <= 2.7e-216) {
		tmp = z * (x * y);
	} else if (i <= 3.6e-63) {
		tmp = j * (a * c);
	} else if (i <= 4.2e+44) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b * i)
    if (i <= (-2.05d+61)) then
        tmp = t_1
    else if (i <= 2.7d-216) then
        tmp = z * (x * y)
    else if (i <= 3.6d-63) then
        tmp = j * (a * c)
    else if (i <= 4.2d+44) then
        tmp = x * (y * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (b * i);
	double tmp;
	if (i <= -2.05e+61) {
		tmp = t_1;
	} else if (i <= 2.7e-216) {
		tmp = z * (x * y);
	} else if (i <= 3.6e-63) {
		tmp = j * (a * c);
	} else if (i <= 4.2e+44) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * (b * i)
	tmp = 0
	if i <= -2.05e+61:
		tmp = t_1
	elif i <= 2.7e-216:
		tmp = z * (x * y)
	elif i <= 3.6e-63:
		tmp = j * (a * c)
	elif i <= 4.2e+44:
		tmp = x * (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(b * i))
	tmp = 0.0
	if (i <= -2.05e+61)
		tmp = t_1;
	elseif (i <= 2.7e-216)
		tmp = Float64(z * Float64(x * y));
	elseif (i <= 3.6e-63)
		tmp = Float64(j * Float64(a * c));
	elseif (i <= 4.2e+44)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * (b * i);
	tmp = 0.0;
	if (i <= -2.05e+61)
		tmp = t_1;
	elseif (i <= 2.7e-216)
		tmp = z * (x * y);
	elseif (i <= 3.6e-63)
		tmp = j * (a * c);
	elseif (i <= 4.2e+44)
		tmp = x * (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.05e+61], t$95$1, If[LessEqual[i, 2.7e-216], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.6e-63], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4.2e+44], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -2.04999999999999986e61 or 4.19999999999999974e44 < i

   1. Initial program 66.8%

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

   3. Taylor expanded in j around 0 53.1%

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

      1. *-commutative 53.1%

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

      2. *-commutative 53.1%

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

   5. Simplified 53.1%

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

   6. Taylor expanded in i around inf 36.6%

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

      1. associate-*r* 41.6%

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

   8. Simplified 41.6%

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

   if -2.04999999999999986e61 < i < 2.6999999999999999e-216

   1. Initial program 78.5%

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

   3. Taylor expanded in z around inf 48.2%

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

      1. *-commutative 48.2%

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

   5. Simplified 48.2%

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

   6. Taylor expanded in y around inf 32.6%

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

   if 2.6999999999999999e-216 < i < 3.60000000000000008e-63

   1. Initial program 81.0%

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

   3. Taylor expanded in a around inf 61.0%

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

      1. +-commutative 61.0%

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

      2. mul-1-neg 61.0%

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

      3. unsub-neg 61.0%

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

   5. Simplified 61.0%

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

   6. Taylor expanded in c around inf 40.2%

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

      1. associate-*r* 40.4%

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

      2. *-commutative 40.4%

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

   8. Simplified 40.4%

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

   if 3.60000000000000008e-63 < i < 4.19999999999999974e44

   1. Initial program 78.5%

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

   3. Taylor expanded in z around inf 63.1%

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

      1. *-commutative 63.1%

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

   5. Simplified 63.1%

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

   6. Taylor expanded in y around inf 36.7%

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

      1. *-commutative 36.7%

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

   8. Simplified 36.7%

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

4. Final simplification 37.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.05 \cdot 10^{+61}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 2.7 \cdot 10^{-216}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 3.6 \cdot 10^{-63}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;i \leq 4.2 \cdot 10^{+44}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 29.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i\right)\\ \mathbf{if}\;i \leq -7.5 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 7 \cdot 10^{-218}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 4.2 \cdot 10^{-63}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 8.2 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (* b i))))
   (if (<= i -7.5e+62)
     t_1
     (if (<= i 7e-218)
       (* z (* x y))
       (if (<= i 4.2e-63)
         (* a (* c j))
         (if (<= i 8.2e+38) (* x (* y z)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (b * i);
	double tmp;
	if (i <= -7.5e+62) {
		tmp = t_1;
	} else if (i <= 7e-218) {
		tmp = z * (x * y);
	} else if (i <= 4.2e-63) {
		tmp = a * (c * j);
	} else if (i <= 8.2e+38) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b * i)
    if (i <= (-7.5d+62)) then
        tmp = t_1
    else if (i <= 7d-218) then
        tmp = z * (x * y)
    else if (i <= 4.2d-63) then
        tmp = a * (c * j)
    else if (i <= 8.2d+38) then
        tmp = x * (y * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (b * i);
	double tmp;
	if (i <= -7.5e+62) {
		tmp = t_1;
	} else if (i <= 7e-218) {
		tmp = z * (x * y);
	} else if (i <= 4.2e-63) {
		tmp = a * (c * j);
	} else if (i <= 8.2e+38) {
		tmp = x * (y * z);
	} 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 <= -7.5e+62:
		tmp = t_1
	elif i <= 7e-218:
		tmp = z * (x * y)
	elif i <= 4.2e-63:
		tmp = a * (c * j)
	elif i <= 8.2e+38:
		tmp = x * (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(b * i))
	tmp = 0.0
	if (i <= -7.5e+62)
		tmp = t_1;
	elseif (i <= 7e-218)
		tmp = Float64(z * Float64(x * y));
	elseif (i <= 4.2e-63)
		tmp = Float64(a * Float64(c * j));
	elseif (i <= 8.2e+38)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * (b * i);
	tmp = 0.0;
	if (i <= -7.5e+62)
		tmp = t_1;
	elseif (i <= 7e-218)
		tmp = z * (x * y);
	elseif (i <= 4.2e-63)
		tmp = a * (c * j);
	elseif (i <= 8.2e+38)
		tmp = x * (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -7.5e+62], t$95$1, If[LessEqual[i, 7e-218], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4.2e-63], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 8.2e+38], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -7.49999999999999998e62 or 8.2000000000000007e38 < i

   1. Initial program 66.8%

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

   3. Taylor expanded in j around 0 53.1%

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

      1. *-commutative 53.1%

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

      2. *-commutative 53.1%

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

   5. Simplified 53.1%

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

   6. Taylor expanded in i around inf 36.6%

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

      1. associate-*r* 41.6%

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

   8. Simplified 41.6%

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

   if -7.49999999999999998e62 < i < 7e-218

   1. Initial program 78.5%

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

   3. Taylor expanded in z around inf 48.2%

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

      1. *-commutative 48.2%

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

   5. Simplified 48.2%

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

   6. Taylor expanded in y around inf 32.6%

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

   if 7e-218 < i < 4.2e-63

   1. Initial program 81.0%

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

   3. Taylor expanded in a around inf 61.0%

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

      1. +-commutative 61.0%

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

      2. mul-1-neg 61.0%

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

      3. unsub-neg 61.0%

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

   5. Simplified 61.0%

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

   6. Taylor expanded in c around inf 40.2%

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

   if 4.2e-63 < i < 8.2000000000000007e38

   1. Initial program 78.5%

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

   3. Taylor expanded in z around inf 63.1%

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

      1. *-commutative 63.1%

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

   5. Simplified 63.1%

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

   6. Taylor expanded in y around inf 36.7%

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

      1. *-commutative 36.7%

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

   8. Simplified 36.7%

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

4. Final simplification 37.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -7.5 \cdot 10^{+62}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 7 \cdot 10^{-218}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 4.2 \cdot 10^{-63}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 8.2 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 59.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1 \cdot 10^{-31} \lor \neg \left(j \leq 10^{+119}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -1e-31) (not (<= j 1e+119)))
   (- (* b (* t i)) (* j (- (* y i) (* a c))))
   (- (* x (- (* y z) (* t a))) (* z (* b c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -1e-31) || !(j <= 1e+119)) {
		tmp = (b * (t * i)) - (j * ((y * i) - (a * c)));
	} else {
		tmp = (x * ((y * z) - (t * a))) - (z * (b * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((j <= (-1d-31)) .or. (.not. (j <= 1d+119))) then
        tmp = (b * (t * i)) - (j * ((y * i) - (a * c)))
    else
        tmp = (x * ((y * z) - (t * a))) - (z * (b * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -1e-31) || !(j <= 1e+119)) {
		tmp = (b * (t * i)) - (j * ((y * i) - (a * c)));
	} else {
		tmp = (x * ((y * z) - (t * a))) - (z * (b * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -1e-31) or not (j <= 1e+119):
		tmp = (b * (t * i)) - (j * ((y * i) - (a * c)))
	else:
		tmp = (x * ((y * z) - (t * a))) - (z * (b * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -1e-31) || !(j <= 1e+119))
		tmp = Float64(Float64(b * Float64(t * i)) - Float64(j * Float64(Float64(y * i) - Float64(a * c))));
	else
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(z * Float64(b * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -1e-31) || ~((j <= 1e+119)))
		tmp = (b * (t * i)) - (j * ((y * i) - (a * c)));
	else
		tmp = (x * ((y * z) - (t * a))) - (z * (b * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -1e-31], N[Not[LessEqual[j, 1e+119]], $MachinePrecision]], N[(N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(y * i), $MachinePrecision] - N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -1e-31 or 9.99999999999999944e118 < j

   1. Initial program 77.4%

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

   3. Taylor expanded in x around 0 72.9%

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

      1. *-commutative 72.9%

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

   5. Simplified 72.9%

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

   6. Taylor expanded in c around 0 73.0%

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

      1. mul-1-neg 73.0%

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

      2. *-commutative 73.0%

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

      3. distribute-rgt-neg-in 73.0%

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

   8. Simplified 73.0%

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

   if -1e-31 < j < 9.99999999999999944e118

   1. Initial program 70.8%

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

   3. Taylor expanded in j around 0 73.1%

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

      1. *-commutative 73.1%

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

      2. *-commutative 73.1%

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

   5. Simplified 73.1%

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

   6. Taylor expanded in c around inf 63.4%

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

      1. associate-*r* 66.2%

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

   8. Simplified 66.2%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1 \cdot 10^{-31} \lor \neg \left(j \leq 10^{+119}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 61.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;j \leq -1.2 \cdot 10^{-47}:\\ \;\;\;\;t\_1 + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{+118}:\\ \;\;\;\;t\_1 - z \cdot \left(b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= j -1.2e-47)
     (+ t_1 (* j (- (* a c) (* y i))))
     (if (<= j 2.5e+118)
       (- t_1 (* z (* b c)))
       (- (* b (* t i)) (* j (- (* y i) (* a c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (j <= -1.2e-47) {
		tmp = t_1 + (j * ((a * c) - (y * i)));
	} else if (j <= 2.5e+118) {
		tmp = t_1 - (z * (b * c));
	} else {
		tmp = (b * (t * i)) - (j * ((y * i) - (a * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (j <= (-1.2d-47)) then
        tmp = t_1 + (j * ((a * c) - (y * i)))
    else if (j <= 2.5d+118) then
        tmp = t_1 - (z * (b * c))
    else
        tmp = (b * (t * i)) - (j * ((y * i) - (a * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (j <= -1.2e-47) {
		tmp = t_1 + (j * ((a * c) - (y * i)));
	} else if (j <= 2.5e+118) {
		tmp = t_1 - (z * (b * c));
	} else {
		tmp = (b * (t * i)) - (j * ((y * i) - (a * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if j <= -1.2e-47:
		tmp = t_1 + (j * ((a * c) - (y * i)))
	elif j <= 2.5e+118:
		tmp = t_1 - (z * (b * c))
	else:
		tmp = (b * (t * i)) - (j * ((y * i) - (a * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (j <= -1.2e-47)
		tmp = Float64(t_1 + Float64(j * Float64(Float64(a * c) - Float64(y * i))));
	elseif (j <= 2.5e+118)
		tmp = Float64(t_1 - Float64(z * Float64(b * c)));
	else
		tmp = Float64(Float64(b * Float64(t * i)) - Float64(j * Float64(Float64(y * i) - Float64(a * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (j <= -1.2e-47)
		tmp = t_1 + (j * ((a * c) - (y * i)));
	elseif (j <= 2.5e+118)
		tmp = t_1 - (z * (b * c));
	else
		tmp = (b * (t * i)) - (j * ((y * i) - (a * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.2e-47], N[(t$95$1 + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.5e+118], N[(t$95$1 - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(y * i), $MachinePrecision] - N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.2e-47

   1. Initial program 80.0%

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

   3. Taylor expanded in b around 0 79.5%

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

   if -1.2e-47 < j < 2.49999999999999986e118

   1. Initial program 70.3%

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

   3. Taylor expanded in j around 0 73.4%

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

      1. *-commutative 73.4%

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

      2. *-commutative 73.4%

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

   5. Simplified 73.4%

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

   6. Taylor expanded in c around inf 63.2%

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

      1. associate-*r* 66.1%

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

   8. Simplified 66.1%

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

   if 2.49999999999999986e118 < j

   1. Initial program 73.1%

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

   3. Taylor expanded in x around 0 76.4%

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

      1. *-commutative 76.4%

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

   5. Simplified 76.4%

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

   6. Taylor expanded in c around 0 76.7%

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

      1. mul-1-neg 76.7%

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

      2. *-commutative 76.7%

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

      3. distribute-rgt-neg-in 76.7%

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

   8. Simplified 76.7%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.2 \cdot 10^{-47}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{+118}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right) - j \cdot \left(y \cdot i - a \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 59.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.9 \cdot 10^{-31}:\\ \;\;\;\;i \cdot \left(y \cdot \left(\frac{t \cdot b}{y} - j\right)\right)\\ \mathbf{elif}\;i \leq 5.9 \cdot 10^{+128}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -1.9e-31)
   (* i (* y (- (/ (* t b) y) j)))
   (if (<= i 5.9e+128)
     (- (* x (- (* y z) (* t a))) (* z (* b c)))
     (* i (- (* t b) (* y j))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -1.9e-31) {
		tmp = i * (y * (((t * b) / y) - j));
	} else if (i <= 5.9e+128) {
		tmp = (x * ((y * z) - (t * a))) - (z * (b * c));
	} else {
		tmp = i * ((t * b) - (y * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (i <= (-1.9d-31)) then
        tmp = i * (y * (((t * b) / y) - j))
    else if (i <= 5.9d+128) then
        tmp = (x * ((y * z) - (t * a))) - (z * (b * c))
    else
        tmp = i * ((t * b) - (y * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -1.9e-31) {
		tmp = i * (y * (((t * b) / y) - j));
	} else if (i <= 5.9e+128) {
		tmp = (x * ((y * z) - (t * a))) - (z * (b * c));
	} else {
		tmp = i * ((t * b) - (y * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -1.9e-31:
		tmp = i * (y * (((t * b) / y) - j))
	elif i <= 5.9e+128:
		tmp = (x * ((y * z) - (t * a))) - (z * (b * c))
	else:
		tmp = i * ((t * b) - (y * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -1.9e-31)
		tmp = Float64(i * Float64(y * Float64(Float64(Float64(t * b) / y) - j)));
	elseif (i <= 5.9e+128)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(z * Float64(b * c)));
	else
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -1.9e-31)
		tmp = i * (y * (((t * b) / y) - j));
	elseif (i <= 5.9e+128)
		tmp = (x * ((y * z) - (t * a))) - (z * (b * c));
	else
		tmp = i * ((t * b) - (y * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -1.9e-31], N[(i * N[(y * N[(N[(N[(t * b), $MachinePrecision] / y), $MachinePrecision] - j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5.9e+128], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if i < -1.9e-31

   1. Initial program 63.5%

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

   3. Taylor expanded in a around 0 69.5%

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

   5. Simplified 68.1%

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

   6. Taylor expanded in i around inf 70.1%

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

      1. +-commutative 70.1%

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

      2. mul-1-neg 70.1%

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

      3. unsub-neg 70.1%

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

   8. Simplified 70.1%

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

   9. Taylor expanded in y around inf 71.4%

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

   if -1.9e-31 < i < 5.89999999999999987e128

   1. Initial program 79.2%

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

   3. Taylor expanded in j around 0 66.4%

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

      1. *-commutative 66.4%

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

      2. *-commutative 66.4%

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

   5. Simplified 66.4%

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

   6. Taylor expanded in c around inf 63.0%

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

      1. associate-*r* 65.4%

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

   8. Simplified 65.4%

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

   if 5.89999999999999987e128 < i

   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. Add Preprocessing

   3. Taylor expanded in a around 0 75.4%

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

   5. Simplified 75.3%

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

   6. Taylor expanded in i around inf 72.7%

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

      1. +-commutative 72.7%

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

      2. mul-1-neg 72.7%

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

      3. unsub-neg 72.7%

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

   8. Simplified 72.7%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.9 \cdot 10^{-31}:\\ \;\;\;\;i \cdot \left(y \cdot \left(\frac{t \cdot b}{y} - j\right)\right)\\ \mathbf{elif}\;i \leq 5.9 \cdot 10^{+128}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 51.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.65 \cdot 10^{+25}:\\ \;\;\;\;a \cdot \left(t \cdot \left(b \cdot \frac{i}{a} - x\right)\right)\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-192}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 53000000000000:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -3.65e+25)
   (* a (* t (- (* b (/ i a)) x)))
   (if (<= t 7.5e-192)
     (* z (- (* x y) (* b c)))
     (if (<= t 53000000000000.0)
       (* y (- (* x z) (* i j)))
       (* t (- (* b i) (* x a)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -3.65e+25) {
		tmp = a * (t * ((b * (i / a)) - x));
	} else if (t <= 7.5e-192) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 53000000000000.0) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t * ((b * i) - (x * a));
	}
	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 (t <= (-3.65d+25)) then
        tmp = a * (t * ((b * (i / a)) - x))
    else if (t <= 7.5d-192) then
        tmp = z * ((x * y) - (b * c))
    else if (t <= 53000000000000.0d0) then
        tmp = y * ((x * z) - (i * j))
    else
        tmp = t * ((b * i) - (x * a))
    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 (t <= -3.65e+25) {
		tmp = a * (t * ((b * (i / a)) - x));
	} else if (t <= 7.5e-192) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 53000000000000.0) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t * ((b * i) - (x * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -3.65e+25:
		tmp = a * (t * ((b * (i / a)) - x))
	elif t <= 7.5e-192:
		tmp = z * ((x * y) - (b * c))
	elif t <= 53000000000000.0:
		tmp = y * ((x * z) - (i * j))
	else:
		tmp = t * ((b * i) - (x * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -3.65e+25)
		tmp = Float64(a * Float64(t * Float64(Float64(b * Float64(i / a)) - x)));
	elseif (t <= 7.5e-192)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (t <= 53000000000000.0)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	else
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -3.65e+25)
		tmp = a * (t * ((b * (i / a)) - x));
	elseif (t <= 7.5e-192)
		tmp = z * ((x * y) - (b * c));
	elseif (t <= 53000000000000.0)
		tmp = y * ((x * z) - (i * j));
	else
		tmp = t * ((b * i) - (x * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -3.65e+25], N[(a * N[(t * N[(N[(b * N[(i / a), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.5e-192], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 53000000000000.0], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.6499999999999998e25

   1. Initial program 56.8%

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

   3. Taylor expanded in a around -inf 64.4%

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

   5. Simplified 67.6%

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

   6. Taylor expanded in t around inf 58.6%

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

      1. associate-*r* 58.6%

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

      2. neg-mul-1 58.6%

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

      3. associate-/l* 63.2%

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

   8. Simplified 63.2%

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

   if -3.6499999999999998e25 < t < 7.5000000000000001e-192

   1. Initial program 80.3%

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

   3. Taylor expanded in z around inf 56.4%

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

      1. *-commutative 56.4%

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

   5. Simplified 56.4%

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

   if 7.5000000000000001e-192 < t < 5.3e13

   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. Add Preprocessing

   3. Taylor expanded in y around inf 68.3%

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

      1. +-commutative 68.3%

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

      2. mul-1-neg 68.3%

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

      3. unsub-neg 68.3%

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

      4. *-commutative 68.3%

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

   5. Simplified 68.3%

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

   if 5.3e13 < t

   1. Initial program 73.5%

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

   3. Taylor expanded in t around inf 72.1%

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

      1. distribute-lft-out-- 72.1%

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

   5. Simplified 72.1%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x - b \cdot i\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.65 \cdot 10^{+25}:\\ \;\;\;\;a \cdot \left(t \cdot \left(b \cdot \frac{i}{a} - x\right)\right)\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-192}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 53000000000000:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 51.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -1 \cdot 10^{-13}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 3.3 \cdot 10^{-80}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 0.105:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j)))))
   (if (<= i -1e-13)
     t_1
     (if (<= i 3.3e-80)
       (* a (- (* c j) (* x t)))
       (if (<= i 0.105) (* c (- (* a j) (* z b))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -1e-13) {
		tmp = t_1;
	} else if (i <= 3.3e-80) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= 0.105) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * ((t * b) - (y * j))
    if (i <= (-1d-13)) then
        tmp = t_1
    else if (i <= 3.3d-80) then
        tmp = a * ((c * j) - (x * t))
    else if (i <= 0.105d0) then
        tmp = c * ((a * j) - (z * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -1e-13) {
		tmp = t_1;
	} else if (i <= 3.3e-80) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= 0.105) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -1e-13:
		tmp = t_1
	elif i <= 3.3e-80:
		tmp = a * ((c * j) - (x * t))
	elif i <= 0.105:
		tmp = c * ((a * j) - (z * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -1e-13)
		tmp = t_1;
	elseif (i <= 3.3e-80)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (i <= 0.105)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -1e-13)
		tmp = t_1;
	elseif (i <= 3.3e-80)
		tmp = a * ((c * j) - (x * t));
	elseif (i <= 0.105)
		tmp = c * ((a * j) - (z * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1e-13], t$95$1, If[LessEqual[i, 3.3e-80], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 0.105], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if i < -1e-13 or 0.104999999999999996 < i

   1. Initial program 68.6%

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

   3. Taylor expanded in a around 0 70.6%

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

   5. Simplified 69.8%

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

   6. Taylor expanded in i around inf 66.4%

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

      1. +-commutative 66.4%

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

      2. mul-1-neg 66.4%

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

      3. unsub-neg 66.4%

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

   8. Simplified 66.4%

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

   if -1e-13 < i < 3.3e-80

   1. Initial program 80.5%

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

   3. Taylor expanded in a around inf 50.2%

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

      1. +-commutative 50.2%

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

      2. mul-1-neg 50.2%

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

      3. unsub-neg 50.2%

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

   5. Simplified 50.2%

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

   if 3.3e-80 < i < 0.104999999999999996

   1. Initial program 71.6%

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

   3. Taylor expanded in c around inf 63.1%

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

      1. *-commutative 63.1%

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

   5. Simplified 63.1%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1 \cdot 10^{-13}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq 3.3 \cdot 10^{-80}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 0.105:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 46.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -2.5 \cdot 10^{+116}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-300}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-22}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -2.5e+116)
     t_1
     (if (<= a -9e-300)
       (* b (- (* t i) (* z c)))
       (if (<= a 1.65e-22) (* (* 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 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -2.5e+116) {
		tmp = t_1;
	} else if (a <= -9e-300) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 1.65e-22) {
		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 = a * ((c * j) - (x * t))
    if (a <= (-2.5d+116)) then
        tmp = t_1
    else if (a <= (-9d-300)) then
        tmp = b * ((t * i) - (z * c))
    else if (a <= 1.65d-22) 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 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -2.5e+116) {
		tmp = t_1;
	} else if (a <= -9e-300) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 1.65e-22) {
		tmp = (y * j) * -i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -2.5e+116:
		tmp = t_1
	elif a <= -9e-300:
		tmp = b * ((t * i) - (z * c))
	elif a <= 1.65e-22:
		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(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -2.5e+116)
		tmp = t_1;
	elseif (a <= -9e-300)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (a <= 1.65e-22)
		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 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -2.5e+116)
		tmp = t_1;
	elseif (a <= -9e-300)
		tmp = b * ((t * i) - (z * c));
	elseif (a <= 1.65e-22)
		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[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.5e+116], t$95$1, If[LessEqual[a, -9e-300], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.65e-22], N[(N[(y * j), $MachinePrecision] * (-i)), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.50000000000000013e116 or 1.65e-22 < a

   1. Initial program 66.9%

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

   3. Taylor expanded in a around inf 62.8%

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

      1. +-commutative 62.8%

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

      2. mul-1-neg 62.8%

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

      3. unsub-neg 62.8%

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

   5. Simplified 62.8%

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

   if -2.50000000000000013e116 < a < -9.0000000000000001e-300

   1. Initial program 76.4%

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

   3. Taylor expanded in b around inf 50.4%

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

   if -9.0000000000000001e-300 < a < 1.65e-22

   1. Initial program 83.6%

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

   3. Taylor expanded in a around -inf 62.1%

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

   5. Simplified 59.8%

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

   6. Taylor expanded in j around inf 41.7%

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

      1. associate-*r* 41.3%

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

      2. mul-1-neg 41.3%

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

      3. unsub-neg 41.3%

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

      4. associate-/l* 45.1%

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

   8. Simplified 45.1%

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

   9. Taylor expanded in a around 0 41.4%

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

       1. mul-1-neg 41.4%

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

       2. *-commutative 41.4%

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

       3. distribute-rgt-neg-in 41.4%

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

       4. *-commutative 41.4%

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

   11. Simplified 41.4%

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

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{+116}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-300}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-22}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 39.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -3.15 \cdot 10^{+115}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{-291}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-23}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -3.15e+115)
     t_1
     (if (<= a -1.45e-291)
       (* t (* b i))
       (if (<= a 5e-23) (* (* 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 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -3.15e+115) {
		tmp = t_1;
	} else if (a <= -1.45e-291) {
		tmp = t * (b * i);
	} else if (a <= 5e-23) {
		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 = a * ((c * j) - (x * t))
    if (a <= (-3.15d+115)) then
        tmp = t_1
    else if (a <= (-1.45d-291)) then
        tmp = t * (b * i)
    else if (a <= 5d-23) 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 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -3.15e+115) {
		tmp = t_1;
	} else if (a <= -1.45e-291) {
		tmp = t * (b * i);
	} else if (a <= 5e-23) {
		tmp = (y * j) * -i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -3.15e+115:
		tmp = t_1
	elif a <= -1.45e-291:
		tmp = t * (b * i)
	elif a <= 5e-23:
		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(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -3.15e+115)
		tmp = t_1;
	elseif (a <= -1.45e-291)
		tmp = Float64(t * Float64(b * i));
	elseif (a <= 5e-23)
		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 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -3.15e+115)
		tmp = t_1;
	elseif (a <= -1.45e-291)
		tmp = t * (b * i);
	elseif (a <= 5e-23)
		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[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.15e+115], t$95$1, If[LessEqual[a, -1.45e-291], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5e-23], N[(N[(y * j), $MachinePrecision] * (-i)), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.1499999999999998e115 or 5.0000000000000002e-23 < a

   1. Initial program 67.2%

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

   3. Taylor expanded in a around inf 62.3%

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

      1. +-commutative 62.3%

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

      2. mul-1-neg 62.3%

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

      3. unsub-neg 62.3%

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

   5. Simplified 62.3%

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

   if -3.1499999999999998e115 < a < -1.45000000000000001e-291

   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. Add Preprocessing

   3. Taylor expanded in j around 0 66.5%

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

      1. *-commutative 66.5%

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

      2. *-commutative 66.5%

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

   5. Simplified 66.5%

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

   6. Taylor expanded in i around inf 30.7%

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

      1. associate-*r* 34.4%

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

   8. Simplified 34.4%

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

   if -1.45000000000000001e-291 < a < 5.0000000000000002e-23

   1. Initial program 83.6%

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

   3. Taylor expanded in a around -inf 62.1%

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

   5. Simplified 59.8%

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

   6. Taylor expanded in j around inf 41.7%

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

      1. associate-*r* 41.3%

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

      2. mul-1-neg 41.3%

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

      3. unsub-neg 41.3%

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

      4. associate-/l* 45.1%

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

   8. Simplified 45.1%

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

   9. Taylor expanded in a around 0 41.4%

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

       1. mul-1-neg 41.4%

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

       2. *-commutative 41.4%

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

       3. distribute-rgt-neg-in 41.4%

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

       4. *-commutative 41.4%

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

   11. Simplified 41.4%

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

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.15 \cdot 10^{+115}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{-291}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-23}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 30.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+15}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;t \leq 3.25 \cdot 10^{-199}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{+56}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -5e+15)
   (* a (* x (- t)))
   (if (<= t 3.25e-199)
     (* z (* b (- c)))
     (if (<= t 6.6e+56) (* z (* x y)) (* x (* t (- a)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -5e+15) {
		tmp = a * (x * -t);
	} else if (t <= 3.25e-199) {
		tmp = z * (b * -c);
	} else if (t <= 6.6e+56) {
		tmp = z * (x * y);
	} else {
		tmp = x * (t * -a);
	}
	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 (t <= (-5d+15)) then
        tmp = a * (x * -t)
    else if (t <= 3.25d-199) then
        tmp = z * (b * -c)
    else if (t <= 6.6d+56) then
        tmp = z * (x * y)
    else
        tmp = x * (t * -a)
    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 (t <= -5e+15) {
		tmp = a * (x * -t);
	} else if (t <= 3.25e-199) {
		tmp = z * (b * -c);
	} else if (t <= 6.6e+56) {
		tmp = z * (x * y);
	} else {
		tmp = x * (t * -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -5e+15:
		tmp = a * (x * -t)
	elif t <= 3.25e-199:
		tmp = z * (b * -c)
	elif t <= 6.6e+56:
		tmp = z * (x * y)
	else:
		tmp = x * (t * -a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -5e+15)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (t <= 3.25e-199)
		tmp = Float64(z * Float64(b * Float64(-c)));
	elseif (t <= 6.6e+56)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = Float64(x * Float64(t * Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -5e+15)
		tmp = a * (x * -t);
	elseif (t <= 3.25e-199)
		tmp = z * (b * -c);
	elseif (t <= 6.6e+56)
		tmp = z * (x * y);
	else
		tmp = x * (t * -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -5e+15], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.25e-199], N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.6e+56], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5e15

   1. Initial program 57.9%

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

   3. Taylor expanded in a around inf 52.5%

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

      1. +-commutative 52.5%

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

      2. mul-1-neg 52.5%

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

      3. unsub-neg 52.5%

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

   5. Simplified 52.5%

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

   6. Taylor expanded in c around 0 42.3%

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

      1. associate-*r* 42.3%

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

      2. neg-mul-1 42.3%

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

   8. Simplified 42.3%

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

   if -5e15 < t < 3.25000000000000009e-199

   1. Initial program 80.8%

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

   3. Taylor expanded in z around inf 55.8%

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

      1. *-commutative 55.8%

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

   5. Simplified 55.8%

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

   6. Taylor expanded in y around 0 35.1%

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

      1. neg-mul-1 35.1%

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

      2. distribute-rgt-neg-in 35.1%

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

   8. Simplified 35.1%

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

   if 3.25000000000000009e-199 < t < 6.60000000000000004e56

   1. Initial program 86.0%

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

   3. Taylor expanded in z around inf 40.2%

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

      1. *-commutative 40.2%

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

   5. Simplified 40.2%

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

   6. Taylor expanded in y around inf 32.4%

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

   if 6.60000000000000004e56 < t

   1. Initial program 72.0%

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

   3. Taylor expanded in a around inf 47.5%

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

      1. +-commutative 47.5%

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

      2. mul-1-neg 47.5%

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

      3. unsub-neg 47.5%

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

   5. Simplified 47.5%

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

   6. Taylor expanded in x around inf 51.2%

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

      1. +-commutative 51.2%

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

      2. mul-1-neg 51.2%

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

      3. unsub-neg 51.2%

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

      4. associate-*r* 49.2%

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

      5. *-commutative 49.2%

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

      6. *-commutative 49.2%

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

   8. Simplified 49.2%

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

   9. Taylor expanded in c around 0 44.7%

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

       1. mul-1-neg 44.7%

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

       2. *-commutative 44.7%

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

       3. distribute-rgt-neg-in 44.7%

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

   11. Simplified 44.7%

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

4. Final simplification 38.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+15}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;t \leq 3.25 \cdot 10^{-199}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{+56}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 29.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.5 \cdot 10^{+76}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq 1.05 \cdot 10^{-200}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{-14}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -1.5e+76)
   (* a (* c j))
   (if (<= c 1.05e-200)
     (* z (* x y))
     (if (<= c 9.5e-14) (* i (* t b)) (* c (* a 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 (c <= -1.5e+76) {
		tmp = a * (c * j);
	} else if (c <= 1.05e-200) {
		tmp = z * (x * y);
	} else if (c <= 9.5e-14) {
		tmp = i * (t * b);
	} else {
		tmp = c * (a * 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 (c <= (-1.5d+76)) then
        tmp = a * (c * j)
    else if (c <= 1.05d-200) then
        tmp = z * (x * y)
    else if (c <= 9.5d-14) then
        tmp = i * (t * b)
    else
        tmp = c * (a * 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 (c <= -1.5e+76) {
		tmp = a * (c * j);
	} else if (c <= 1.05e-200) {
		tmp = z * (x * y);
	} else if (c <= 9.5e-14) {
		tmp = i * (t * b);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -1.5e+76:
		tmp = a * (c * j)
	elif c <= 1.05e-200:
		tmp = z * (x * y)
	elif c <= 9.5e-14:
		tmp = i * (t * b)
	else:
		tmp = c * (a * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -1.5e+76)
		tmp = Float64(a * Float64(c * j));
	elseif (c <= 1.05e-200)
		tmp = Float64(z * Float64(x * y));
	elseif (c <= 9.5e-14)
		tmp = Float64(i * Float64(t * b));
	else
		tmp = Float64(c * Float64(a * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -1.5e+76)
		tmp = a * (c * j);
	elseif (c <= 1.05e-200)
		tmp = z * (x * y);
	elseif (c <= 9.5e-14)
		tmp = i * (t * b);
	else
		tmp = c * (a * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -1.5e+76], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.05e-200], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 9.5e-14], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.4999999999999999e76

   1. Initial program 66.6%

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

   3. Taylor expanded in a around inf 48.2%

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

      1. +-commutative 48.2%

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

      2. mul-1-neg 48.2%

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

      3. unsub-neg 48.2%

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

   5. Simplified 48.2%

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

   6. Taylor expanded in c around inf 37.6%

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

   if -1.4999999999999999e76 < c < 1.05e-200

   1. Initial program 81.3%

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

   3. Taylor expanded in z around inf 39.6%

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

      1. *-commutative 39.6%

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

   5. Simplified 39.6%

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

   6. Taylor expanded in y around inf 34.5%

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

   if 1.05e-200 < c < 9.4999999999999999e-14

   1. Initial program 75.2%

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

   3. Taylor expanded in a around 0 62.1%

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

   5. Simplified 68.5%

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

   6. Taylor expanded in i around inf 55.6%

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

      1. +-commutative 55.6%

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

      2. mul-1-neg 55.6%

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

      3. unsub-neg 55.6%

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

   8. Simplified 55.6%

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

   9. Taylor expanded in b around inf 29.2%

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

   if 9.4999999999999999e-14 < c

   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. Add Preprocessing

   3. Taylor expanded in a around -inf 63.5%

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

   5. Simplified 61.7%

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

   6. Taylor expanded in j around inf 49.4%

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

      1. associate-*r* 54.1%

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

      2. mul-1-neg 54.1%

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

      3. unsub-neg 54.1%

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

      4. associate-/l* 54.1%

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

   8. Simplified 54.1%

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

   9. Taylor expanded in c around inf 36.1%

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

4. Final simplification 34.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.5 \cdot 10^{+76}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq 1.05 \cdot 10^{-200}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{-14}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 29.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;y \leq -3.5 \cdot 10^{-13}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-210}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+122}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))))
   (if (<= y -3.5e-13)
     t_1
     (if (<= y 4.4e-210) (* a (* c j)) (if (<= y 8e+122) (* i (* t b)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double tmp;
	if (y <= -3.5e-13) {
		tmp = t_1;
	} else if (y <= 4.4e-210) {
		tmp = a * (c * j);
	} else if (y <= 8e+122) {
		tmp = i * (t * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y * z)
    if (y <= (-3.5d-13)) then
        tmp = t_1
    else if (y <= 4.4d-210) then
        tmp = a * (c * j)
    else if (y <= 8d+122) then
        tmp = i * (t * b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double tmp;
	if (y <= -3.5e-13) {
		tmp = t_1;
	} else if (y <= 4.4e-210) {
		tmp = a * (c * j);
	} else if (y <= 8e+122) {
		tmp = i * (t * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	tmp = 0
	if y <= -3.5e-13:
		tmp = t_1
	elif y <= 4.4e-210:
		tmp = a * (c * j)
	elif y <= 8e+122:
		tmp = i * (t * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (y <= -3.5e-13)
		tmp = t_1;
	elseif (y <= 4.4e-210)
		tmp = Float64(a * Float64(c * j));
	elseif (y <= 8e+122)
		tmp = Float64(i * Float64(t * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (y * z);
	tmp = 0.0;
	if (y <= -3.5e-13)
		tmp = t_1;
	elseif (y <= 4.4e-210)
		tmp = a * (c * j);
	elseif (y <= 8e+122)
		tmp = i * (t * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.5e-13], t$95$1, If[LessEqual[y, 4.4e-210], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8e+122], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.5000000000000002e-13 or 8.00000000000000012e122 < y

   1. Initial program 66.9%

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

   3. Taylor expanded in z around inf 48.8%

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

      1. *-commutative 48.8%

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

   5. Simplified 48.8%

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

   6. Taylor expanded in y around inf 35.6%

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

      1. *-commutative 35.6%

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

   8. Simplified 35.6%

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

   if -3.5000000000000002e-13 < y < 4.39999999999999979e-210

   1. Initial program 76.4%

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

   3. Taylor expanded in a around inf 51.5%

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

      1. +-commutative 51.5%

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

      2. mul-1-neg 51.5%

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

      3. unsub-neg 51.5%

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

   5. Simplified 51.5%

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

   6. Taylor expanded in c around inf 32.3%

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

   if 4.39999999999999979e-210 < y < 8.00000000000000012e122

   1. Initial program 81.1%

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

   3. Taylor expanded in a around 0 65.9%

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

   5. Simplified 64.7%

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

   6. Taylor expanded in i around inf 41.9%

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

      1. +-commutative 41.9%

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

      2. mul-1-neg 41.9%

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

      3. unsub-neg 41.9%

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

   8. Simplified 41.9%

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

   9. Taylor expanded in b around inf 30.9%

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

4. Final simplification 33.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-210}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+122}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 28.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{+117} \lor \neg \left(a \leq 8 \cdot 10^{+107}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -2.3e+117) (not (<= a 8e+107))) (* a (* c j)) (* i (* t b))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -2.3e+117) || !(a <= 8e+107)) {
		tmp = a * (c * j);
	} else {
		tmp = i * (t * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((a <= (-2.3d+117)) .or. (.not. (a <= 8d+107))) then
        tmp = a * (c * j)
    else
        tmp = i * (t * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -2.3e+117) || !(a <= 8e+107)) {
		tmp = a * (c * j);
	} else {
		tmp = i * (t * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (a <= -2.3e+117) or not (a <= 8e+107):
		tmp = a * (c * j)
	else:
		tmp = i * (t * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -2.3e+117) || !(a <= 8e+107))
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(i * Float64(t * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((a <= -2.3e+117) || ~((a <= 8e+107)))
		tmp = a * (c * j);
	else
		tmp = i * (t * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -2.3e+117], N[Not[LessEqual[a, 8e+107]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.29999999999999988e117 or 7.9999999999999998e107 < a

   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. Add Preprocessing

   3. Taylor expanded in a around inf 66.1%

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

      1. +-commutative 66.1%

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

      2. mul-1-neg 66.1%

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

      3. unsub-neg 66.1%

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

   5. Simplified 66.1%

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

   6. Taylor expanded in c around inf 37.6%

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

   if -2.29999999999999988e117 < a < 7.9999999999999998e107

   1. Initial program 79.4%

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

   3. Taylor expanded in a around 0 70.8%

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

   5. Simplified 71.5%

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

   6. Taylor expanded in i around inf 49.6%

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

      1. +-commutative 49.6%

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

      2. mul-1-neg 49.6%

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

      3. unsub-neg 49.6%

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

   8. Simplified 49.6%

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

   9. Taylor expanded in b around inf 27.8%

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

4. Final simplification 31.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{+117} \lor \neg \left(a \leq 8 \cdot 10^{+107}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 28.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.4 \cdot 10^{+118} \lor \neg \left(a \leq 6 \cdot 10^{+108}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -5.4e+118) (not (<= a 6e+108))) (* 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 ((a <= -5.4e+118) || !(a <= 6e+108)) {
		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 ((a <= (-5.4d+118)) .or. (.not. (a <= 6d+108))) 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 ((a <= -5.4e+118) || !(a <= 6e+108)) {
		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 (a <= -5.4e+118) or not (a <= 6e+108):
		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 ((a <= -5.4e+118) || !(a <= 6e+108))
		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 ((a <= -5.4e+118) || ~((a <= 6e+108)))
		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[a, -5.4e+118], N[Not[LessEqual[a, 6e+108]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.4e118 or 5.99999999999999968e108 < a

   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. Add Preprocessing

   3. Taylor expanded in a around inf 66.1%

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

      1. +-commutative 66.1%

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

      2. mul-1-neg 66.1%

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

      3. unsub-neg 66.1%

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

   5. Simplified 66.1%

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

   6. Taylor expanded in c around inf 37.6%

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

   if -5.4e118 < a < 5.99999999999999968e108

   1. Initial program 79.4%

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

   3. Taylor expanded in j around 0 65.4%

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

      1. *-commutative 65.4%

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

      2. *-commutative 65.4%

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

   5. Simplified 65.4%

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

   6. Taylor expanded in i around inf 26.1%

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

4. Final simplification 30.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.4 \cdot 10^{+118} \lor \neg \left(a \leq 6 \cdot 10^{+108}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 21.3% 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 73.8%

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

3. Taylor expanded in a around inf 37.2%

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

   1. +-commutative 37.2%

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

   2. mul-1-neg 37.2%

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

   3. unsub-neg 37.2%

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

5. Simplified 37.2%

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

6. Taylor expanded in c around inf 19.2%

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

Developer Target 1: 58.9% 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 2024131 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< x -293938859355541/2000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2) (pow (* t i) 2))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 32113527362226803/10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2) (pow (* t i) 2))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i)))))