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

Percentage Accurate: 74.3% → 84.6%

Time: 25.8s

Alternatives: 32

Speedup: 0.5×

• 57.5% 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: 74.3% 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: 84.6% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 90.4%

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

   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 26.8%

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

   5. Simplified 39.3%

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

   6. Taylor expanded in y around inf 60.8%

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

4. Final simplification 83.9%

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

Alternative 2: 52.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(b \cdot \left(i \cdot \frac{t}{z} - c\right)\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{-5}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-259}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 10^{-203}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+36}:\\ \;\;\;\;a \cdot \left(t \cdot \left(c \cdot \frac{j}{t} - x\right)\right)\\ \mathbf{elif}\;y \leq 10^{+73}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+137}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* b (- (* i (/ t z)) c)))) (t_2 (* y (- (* x z) (* i j)))))
   (if (<= y -2.5e-5)
     t_2
     (if (<= y -1.35e-63)
       t_1
       (if (<= y -2.2e-259)
         (* a (- (* c j) (* x t)))
         (if (<= y 1e-203)
           t_1
           (if (<= y 1.35e+36)
             (* a (* t (- (* c (/ j t)) x)))
             (if (<= y 1e+73)
               (* b (- (* t i) (* z c)))
               (if (<= y 3.9e+137) (* j (- (* a c) (* y i))) t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (b * ((i * (t / z)) - c));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -2.5e-5) {
		tmp = t_2;
	} else if (y <= -1.35e-63) {
		tmp = t_1;
	} else if (y <= -2.2e-259) {
		tmp = a * ((c * j) - (x * t));
	} else if (y <= 1e-203) {
		tmp = t_1;
	} else if (y <= 1.35e+36) {
		tmp = a * (t * ((c * (j / t)) - x));
	} else if (y <= 1e+73) {
		tmp = b * ((t * i) - (z * c));
	} else if (y <= 3.9e+137) {
		tmp = j * ((a * c) - (y * i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (b * ((i * (t / z)) - c))
    t_2 = y * ((x * z) - (i * j))
    if (y <= (-2.5d-5)) then
        tmp = t_2
    else if (y <= (-1.35d-63)) then
        tmp = t_1
    else if (y <= (-2.2d-259)) then
        tmp = a * ((c * j) - (x * t))
    else if (y <= 1d-203) then
        tmp = t_1
    else if (y <= 1.35d+36) then
        tmp = a * (t * ((c * (j / t)) - x))
    else if (y <= 1d+73) then
        tmp = b * ((t * i) - (z * c))
    else if (y <= 3.9d+137) then
        tmp = j * ((a * c) - (y * i))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (b * ((i * (t / z)) - c));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -2.5e-5) {
		tmp = t_2;
	} else if (y <= -1.35e-63) {
		tmp = t_1;
	} else if (y <= -2.2e-259) {
		tmp = a * ((c * j) - (x * t));
	} else if (y <= 1e-203) {
		tmp = t_1;
	} else if (y <= 1.35e+36) {
		tmp = a * (t * ((c * (j / t)) - x));
	} else if (y <= 1e+73) {
		tmp = b * ((t * i) - (z * c));
	} else if (y <= 3.9e+137) {
		tmp = j * ((a * c) - (y * i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (b * ((i * (t / z)) - c))
	t_2 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -2.5e-5:
		tmp = t_2
	elif y <= -1.35e-63:
		tmp = t_1
	elif y <= -2.2e-259:
		tmp = a * ((c * j) - (x * t))
	elif y <= 1e-203:
		tmp = t_1
	elif y <= 1.35e+36:
		tmp = a * (t * ((c * (j / t)) - x))
	elif y <= 1e+73:
		tmp = b * ((t * i) - (z * c))
	elif y <= 3.9e+137:
		tmp = j * ((a * c) - (y * i))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(b * Float64(Float64(i * Float64(t / z)) - c)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -2.5e-5)
		tmp = t_2;
	elseif (y <= -1.35e-63)
		tmp = t_1;
	elseif (y <= -2.2e-259)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (y <= 1e-203)
		tmp = t_1;
	elseif (y <= 1.35e+36)
		tmp = Float64(a * Float64(t * Float64(Float64(c * Float64(j / t)) - x)));
	elseif (y <= 1e+73)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (y <= 3.9e+137)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * (b * ((i * (t / z)) - c));
	t_2 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -2.5e-5)
		tmp = t_2;
	elseif (y <= -1.35e-63)
		tmp = t_1;
	elseif (y <= -2.2e-259)
		tmp = a * ((c * j) - (x * t));
	elseif (y <= 1e-203)
		tmp = t_1;
	elseif (y <= 1.35e+36)
		tmp = a * (t * ((c * (j / t)) - x));
	elseif (y <= 1e+73)
		tmp = b * ((t * i) - (z * c));
	elseif (y <= 3.9e+137)
		tmp = j * ((a * c) - (y * i));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(b * N[(N[(i * N[(t / z), $MachinePrecision]), $MachinePrecision] - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.5e-5], t$95$2, If[LessEqual[y, -1.35e-63], t$95$1, If[LessEqual[y, -2.2e-259], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e-203], t$95$1, If[LessEqual[y, 1.35e+36], N[(a * N[(t * N[(N[(c * N[(j / t), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e+73], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.9e+137], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -2.50000000000000012e-5 or 3.90000000000000029e137 < y

   1. Initial program 58.4%

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

   3. Taylor expanded in y around inf 72.8%

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

      1. +-commutative 72.8%

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

      2. mul-1-neg 72.8%

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

      3. unsub-neg 72.8%

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

      4. *-commutative 72.8%

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

      5. *-commutative 72.8%

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

   5. Simplified 72.8%

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

   if -2.50000000000000012e-5 < y < -1.3500000000000001e-63 or -2.2000000000000001e-259 < y < 1e-203

   1. Initial program 77.5%

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

   3. Taylor expanded in a around -inf 62.4%

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

   5. Simplified 53.8%

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

   6. Taylor expanded in b around inf 43.6%

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

      1. mul-1-neg 43.6%

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

      2. distribute-rgt-neg-in 43.6%

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

      3. distribute-lft-neg-in 43.6%

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

      4. div-sub 45.5%

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

      5. *-commutative 45.5%

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

   8. Simplified 45.5%

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

   9. Taylor expanded in z around inf 55.4%

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

       1. +-commutative 55.4%

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

       2. associate-/l* 57.1%

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

       3. mul-1-neg 57.1%

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

       4. distribute-rgt-neg-in 57.1%

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

       5. distribute-lft-out 58.8%

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

       6. unsub-neg 58.8%

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

       7. associate-/l* 60.6%

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

   11. Simplified 60.6%

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

   if -1.3500000000000001e-63 < y < -2.2000000000000001e-259

   1. Initial program 80.1%

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

   3. Taylor expanded in a around inf 70.7%

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

      1. +-commutative 70.7%

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

      2. mul-1-neg 70.7%

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

      3. unsub-neg 70.7%

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

      4. *-commutative 70.7%

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

   5. Simplified 70.7%

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

   if 1e-203 < y < 1.35e36

   1. Initial program 81.9%

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

   3. Taylor expanded in a around inf 55.3%

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

      1. +-commutative 55.3%

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

      2. mul-1-neg 55.3%

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

      3. unsub-neg 55.3%

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

      4. *-commutative 55.3%

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

   5. Simplified 55.3%

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

   6. Taylor expanded in t around inf 53.8%

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

      1. associate-/l* 58.2%

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

   8. Simplified 58.2%

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

   if 1.35e36 < y < 9.99999999999999983e72

   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. Step-by-step derivation

      1. sub-neg 70.2%

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

      2. distribute-rgt-in 70.2%

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

      3. distribute-rgt-neg-in 70.2%

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

   4. Applied egg-rr 70.2%

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

   5. Taylor expanded in j around 0 80.4%

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

      1. mul-1-neg 80.4%

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

      2. associate-*r* 70.2%

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

      3. distribute-lft-neg-in 70.2%

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

      4. mul-1-neg 70.2%

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

      5. *-commutative 70.2%

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

      6. distribute-rgt-in 70.2%

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

      7. +-commutative 70.2%

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

      8. mul-1-neg 70.2%

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

      9. unsub-neg 70.2%

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

      10. *-commutative 70.2%

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

      11. *-commutative 70.2%

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

      12. *-commutative 70.2%

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

      13. *-commutative 70.2%

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

   7. Simplified 70.2%

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

   8. Taylor expanded in x around 0 70.8%

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

      1. associate-*r* 70.8%

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

      2. *-commutative 70.8%

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

      3. associate-*r* 70.8%

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

      4. mul-1-neg 70.8%

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

      5. neg-sub0 70.8%

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

      6. associate--r- 70.8%

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

      7. neg-sub0 70.8%

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

      8. +-commutative 70.8%

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

      9. sub-neg 70.8%

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

      10. *-commutative 70.8%

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

      11. *-commutative 70.8%

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

   10. Simplified 70.8%

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

   if 9.99999999999999983e72 < y < 3.90000000000000029e137

   1. Initial program 51.6%

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

   3. Taylor expanded in j around inf 70.9%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-5}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-63}:\\ \;\;\;\;z \cdot \left(b \cdot \left(i \cdot \frac{t}{z} - c\right)\right)\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-259}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 10^{-203}:\\ \;\;\;\;z \cdot \left(b \cdot \left(i \cdot \frac{t}{z} - c\right)\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+36}:\\ \;\;\;\;a \cdot \left(t \cdot \left(c \cdot \frac{j}{t} - x\right)\right)\\ \mathbf{elif}\;y \leq 10^{+73}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+137}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 52.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{-5}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-252}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-204}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+36}:\\ \;\;\;\;a \cdot \left(t \cdot \left(c \cdot \frac{j}{t} - x\right)\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+137}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* y (- (* x z) (* i j)))))
   (if (<= y -2.7e-5)
     t_2
     (if (<= y -2.6e-65)
       t_1
       (if (<= y -1.8e-252)
         (* a (- (* c j) (* x t)))
         (if (<= y 7.4e-204)
           t_1
           (if (<= y 1.45e+36)
             (* a (* t (- (* c (/ j t)) x)))
             (if (<= y 6.5e+71)
               t_1
               (if (<= y 4.2e+137) (* j (- (* a c) (* y i))) t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -2.7e-5) {
		tmp = t_2;
	} else if (y <= -2.6e-65) {
		tmp = t_1;
	} else if (y <= -1.8e-252) {
		tmp = a * ((c * j) - (x * t));
	} else if (y <= 7.4e-204) {
		tmp = t_1;
	} else if (y <= 1.45e+36) {
		tmp = a * (t * ((c * (j / t)) - x));
	} else if (y <= 6.5e+71) {
		tmp = t_1;
	} else if (y <= 4.2e+137) {
		tmp = j * ((a * c) - (y * i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = y * ((x * z) - (i * j))
    if (y <= (-2.7d-5)) then
        tmp = t_2
    else if (y <= (-2.6d-65)) then
        tmp = t_1
    else if (y <= (-1.8d-252)) then
        tmp = a * ((c * j) - (x * t))
    else if (y <= 7.4d-204) then
        tmp = t_1
    else if (y <= 1.45d+36) then
        tmp = a * (t * ((c * (j / t)) - x))
    else if (y <= 6.5d+71) then
        tmp = t_1
    else if (y <= 4.2d+137) then
        tmp = j * ((a * c) - (y * i))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -2.7e-5) {
		tmp = t_2;
	} else if (y <= -2.6e-65) {
		tmp = t_1;
	} else if (y <= -1.8e-252) {
		tmp = a * ((c * j) - (x * t));
	} else if (y <= 7.4e-204) {
		tmp = t_1;
	} else if (y <= 1.45e+36) {
		tmp = a * (t * ((c * (j / t)) - x));
	} else if (y <= 6.5e+71) {
		tmp = t_1;
	} else if (y <= 4.2e+137) {
		tmp = j * ((a * c) - (y * i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -2.7e-5:
		tmp = t_2
	elif y <= -2.6e-65:
		tmp = t_1
	elif y <= -1.8e-252:
		tmp = a * ((c * j) - (x * t))
	elif y <= 7.4e-204:
		tmp = t_1
	elif y <= 1.45e+36:
		tmp = a * (t * ((c * (j / t)) - x))
	elif y <= 6.5e+71:
		tmp = t_1
	elif y <= 4.2e+137:
		tmp = j * ((a * c) - (y * i))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -2.7e-5)
		tmp = t_2;
	elseif (y <= -2.6e-65)
		tmp = t_1;
	elseif (y <= -1.8e-252)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (y <= 7.4e-204)
		tmp = t_1;
	elseif (y <= 1.45e+36)
		tmp = Float64(a * Float64(t * Float64(Float64(c * Float64(j / t)) - x)));
	elseif (y <= 6.5e+71)
		tmp = t_1;
	elseif (y <= 4.2e+137)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -2.7e-5)
		tmp = t_2;
	elseif (y <= -2.6e-65)
		tmp = t_1;
	elseif (y <= -1.8e-252)
		tmp = a * ((c * j) - (x * t));
	elseif (y <= 7.4e-204)
		tmp = t_1;
	elseif (y <= 1.45e+36)
		tmp = a * (t * ((c * (j / t)) - x));
	elseif (y <= 6.5e+71)
		tmp = t_1;
	elseif (y <= 4.2e+137)
		tmp = j * ((a * c) - (y * i));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.7e-5], t$95$2, If[LessEqual[y, -2.6e-65], t$95$1, If[LessEqual[y, -1.8e-252], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.4e-204], t$95$1, If[LessEqual[y, 1.45e+36], N[(a * N[(t * N[(N[(c * N[(j / t), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e+71], t$95$1, If[LessEqual[y, 4.2e+137], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.6999999999999999e-5 or 4.1999999999999998e137 < y

   1. Initial program 58.4%

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

   3. Taylor expanded in y around inf 72.8%

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

      1. +-commutative 72.8%

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

      2. mul-1-neg 72.8%

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

      3. unsub-neg 72.8%

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

      4. *-commutative 72.8%

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

      5. *-commutative 72.8%

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

   5. Simplified 72.8%

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

   if -2.6999999999999999e-5 < y < -2.6000000000000001e-65 or -1.80000000000000011e-252 < y < 7.3999999999999995e-204 or 1.45e36 < y < 6.49999999999999954e71

   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. Step-by-step derivation

      1. sub-neg 76.4%

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

      2. distribute-rgt-in 76.4%

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

      3. distribute-rgt-neg-in 76.4%

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

   4. Applied egg-rr 76.4%

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

   5. Taylor expanded in j around 0 75.2%

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

      1. mul-1-neg 75.2%

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

      2. associate-*r* 75.2%

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

      3. distribute-lft-neg-in 75.2%

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

      4. mul-1-neg 75.2%

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

      5. *-commutative 75.2%

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

      6. distribute-rgt-in 75.2%

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

      7. +-commutative 75.2%

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

      8. mul-1-neg 75.2%

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

      9. unsub-neg 75.2%

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

      10. *-commutative 75.2%

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

      11. *-commutative 75.2%

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

      12. *-commutative 75.2%

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

      13. *-commutative 75.2%

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

   7. Simplified 75.2%

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

   8. Taylor expanded in x around 0 60.7%

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

      1. associate-*r* 60.7%

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

      2. *-commutative 60.7%

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

      3. associate-*r* 60.7%

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

      4. mul-1-neg 60.7%

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

      5. neg-sub0 60.7%

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

      6. associate--r- 60.7%

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

      7. neg-sub0 60.7%

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

      8. +-commutative 60.7%

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

      9. sub-neg 60.7%

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

      10. *-commutative 60.7%

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

      11. *-commutative 60.7%

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

   10. Simplified 60.7%

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

   if -2.6000000000000001e-65 < y < -1.80000000000000011e-252

   1. Initial program 80.1%

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

   3. Taylor expanded in a around inf 70.7%

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

      1. +-commutative 70.7%

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

      2. mul-1-neg 70.7%

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

      3. unsub-neg 70.7%

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

      4. *-commutative 70.7%

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

   5. Simplified 70.7%

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

   if 7.3999999999999995e-204 < y < 1.45e36

   1. Initial program 81.9%

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

   3. Taylor expanded in a around inf 55.3%

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

      1. +-commutative 55.3%

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

      2. mul-1-neg 55.3%

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

      3. unsub-neg 55.3%

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

      4. *-commutative 55.3%

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

   5. Simplified 55.3%

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

   6. Taylor expanded in t around inf 53.8%

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

      1. associate-/l* 58.2%

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

   8. Simplified 58.2%

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

   if 6.49999999999999954e71 < y < 4.1999999999999998e137

   1. Initial program 51.6%

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

   3. Taylor expanded in j around inf 70.9%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-5}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-65}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-252}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-204}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+36}:\\ \;\;\;\;a \cdot \left(t \cdot \left(c \cdot \frac{j}{t} - x\right)\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+71}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+137}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 28.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c\right)\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{+206}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-55}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-288}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-203}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-47}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 6.7 \cdot 10^{-18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+177}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (* a c))))
   (if (<= y -3.2e+206)
     (* i (* y (- j)))
     (if (<= y -4.8e-55)
       (* y (* x z))
       (if (<= y -6.5e-288)
         t_1
         (if (<= y 1.3e-203)
           (* i (* t b))
           (if (<= y 3.7e-47)
             (* x (* t (- a)))
             (if (<= y 6.7e-18)
               t_1
               (if (<= y 9.5e+177) (* t (* b i)) (* x (* y z)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (a * c);
	double tmp;
	if (y <= -3.2e+206) {
		tmp = i * (y * -j);
	} else if (y <= -4.8e-55) {
		tmp = y * (x * z);
	} else if (y <= -6.5e-288) {
		tmp = t_1;
	} else if (y <= 1.3e-203) {
		tmp = i * (t * b);
	} else if (y <= 3.7e-47) {
		tmp = x * (t * -a);
	} else if (y <= 6.7e-18) {
		tmp = t_1;
	} else if (y <= 9.5e+177) {
		tmp = t * (b * i);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (a * c)
    if (y <= (-3.2d+206)) then
        tmp = i * (y * -j)
    else if (y <= (-4.8d-55)) then
        tmp = y * (x * z)
    else if (y <= (-6.5d-288)) then
        tmp = t_1
    else if (y <= 1.3d-203) then
        tmp = i * (t * b)
    else if (y <= 3.7d-47) then
        tmp = x * (t * -a)
    else if (y <= 6.7d-18) then
        tmp = t_1
    else if (y <= 9.5d+177) then
        tmp = t * (b * i)
    else
        tmp = x * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (a * c);
	double tmp;
	if (y <= -3.2e+206) {
		tmp = i * (y * -j);
	} else if (y <= -4.8e-55) {
		tmp = y * (x * z);
	} else if (y <= -6.5e-288) {
		tmp = t_1;
	} else if (y <= 1.3e-203) {
		tmp = i * (t * b);
	} else if (y <= 3.7e-47) {
		tmp = x * (t * -a);
	} else if (y <= 6.7e-18) {
		tmp = t_1;
	} else if (y <= 9.5e+177) {
		tmp = t * (b * i);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * (a * c)
	tmp = 0
	if y <= -3.2e+206:
		tmp = i * (y * -j)
	elif y <= -4.8e-55:
		tmp = y * (x * z)
	elif y <= -6.5e-288:
		tmp = t_1
	elif y <= 1.3e-203:
		tmp = i * (t * b)
	elif y <= 3.7e-47:
		tmp = x * (t * -a)
	elif y <= 6.7e-18:
		tmp = t_1
	elif y <= 9.5e+177:
		tmp = t * (b * i)
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(a * c))
	tmp = 0.0
	if (y <= -3.2e+206)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (y <= -4.8e-55)
		tmp = Float64(y * Float64(x * z));
	elseif (y <= -6.5e-288)
		tmp = t_1;
	elseif (y <= 1.3e-203)
		tmp = Float64(i * Float64(t * b));
	elseif (y <= 3.7e-47)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (y <= 6.7e-18)
		tmp = t_1;
	elseif (y <= 9.5e+177)
		tmp = Float64(t * Float64(b * i));
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * (a * c);
	tmp = 0.0;
	if (y <= -3.2e+206)
		tmp = i * (y * -j);
	elseif (y <= -4.8e-55)
		tmp = y * (x * z);
	elseif (y <= -6.5e-288)
		tmp = t_1;
	elseif (y <= 1.3e-203)
		tmp = i * (t * b);
	elseif (y <= 3.7e-47)
		tmp = x * (t * -a);
	elseif (y <= 6.7e-18)
		tmp = t_1;
	elseif (y <= 9.5e+177)
		tmp = t * (b * i);
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.2e+206], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.8e-55], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.5e-288], t$95$1, If[LessEqual[y, 1.3e-203], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.7e-47], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.7e-18], t$95$1, If[LessEqual[y, 9.5e+177], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -3.20000000000000005e206

   1. Initial program 46.0%

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

      1. sub-neg 46.0%

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

      2. distribute-rgt-in 41.4%

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

      3. distribute-rgt-neg-in 41.4%

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

   4. Applied egg-rr 41.4%

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

   5. Taylor expanded in i around inf 59.8%

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

      1. associate-*r* 59.8%

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

      2. neg-mul-1 59.8%

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

      3. cancel-sign-sub 59.8%

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

      4. +-commutative 59.8%

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

      5. mul-1-neg 59.8%

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

      6. unsub-neg 59.8%

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

      7. *-commutative 59.8%

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

   7. Simplified 59.8%

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

   8. Taylor expanded in t around 0 64.0%

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

      1. mul-1-neg 64.0%

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

      2. *-commutative 64.0%

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

      3. distribute-rgt-neg-in 64.0%

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

      4. distribute-lft-neg-in 64.0%

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

   10. Simplified 64.0%

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

   if -3.20000000000000005e206 < y < -4.79999999999999983e-55

   1. Initial program 71.7%

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

   3. Taylor expanded in z around inf 55.7%

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

      1. *-commutative 55.7%

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

      2. *-commutative 55.7%

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

   5. Simplified 55.7%

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

   6. Taylor expanded in y around inf 35.3%

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

      1. *-commutative 35.3%

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

      2. associate-*r* 38.6%

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

   8. Simplified 38.6%

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

   if -4.79999999999999983e-55 < y < -6.4999999999999999e-288 or 3.7e-47 < y < 6.6999999999999998e-18

   1. Initial program 79.6%

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

   3. Taylor expanded in a around inf 60.2%

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

      1. +-commutative 60.2%

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

      2. mul-1-neg 60.2%

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

      3. unsub-neg 60.2%

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

      4. *-commutative 60.2%

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

   5. Simplified 60.2%

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

   6. Taylor expanded in j around inf 39.6%

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

      1. associate-*r* 44.5%

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

   8. Simplified 44.5%

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

   if -6.4999999999999999e-288 < y < 1.29999999999999988e-203

   1. Initial program 73.3%

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

      1. sub-neg 73.3%

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

      2. distribute-rgt-in 73.3%

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

      3. distribute-rgt-neg-in 73.3%

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

   4. Applied egg-rr 73.3%

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

   5. Taylor expanded in i around inf 40.9%

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

      1. associate-*r* 40.9%

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

      2. neg-mul-1 40.9%

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

      3. cancel-sign-sub 40.9%

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

      4. +-commutative 40.9%

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

      5. mul-1-neg 40.9%

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

      6. unsub-neg 40.9%

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

      7. *-commutative 40.9%

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

   7. Simplified 40.9%

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

   8. Taylor expanded in t around inf 37.8%

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

      1. *-commutative 37.8%

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

   10. Simplified 37.8%

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

   if 1.29999999999999988e-203 < y < 3.7e-47

   1. Initial program 84.8%

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

   3. Taylor expanded in x around inf 50.4%

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

   4. Taylor expanded in y around 0 44.2%

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

      1. associate-*r* 44.2%

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

      2. neg-mul-1 44.2%

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

      3. *-commutative 44.2%

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

   6. Simplified 44.2%

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

   if 6.6999999999999998e-18 < y < 9.49999999999999996e177

   1. Initial program 69.5%

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

      1. sub-neg 69.5%

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

      2. distribute-rgt-in 69.5%

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

      3. distribute-rgt-neg-in 69.5%

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

   4. Applied egg-rr 69.5%

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

   5. Taylor expanded in j around 0 54.4%

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

      1. mul-1-neg 54.4%

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

      2. associate-*r* 52.1%

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

      3. distribute-lft-neg-in 52.1%

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

      4. mul-1-neg 52.1%

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

      5. *-commutative 52.1%

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

      6. distribute-rgt-in 52.1%

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

      7. +-commutative 52.1%

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

      8. mul-1-neg 52.1%

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

      9. unsub-neg 52.1%

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

      10. *-commutative 52.1%

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

      11. *-commutative 52.1%

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

      12. *-commutative 52.1%

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

      13. *-commutative 52.1%

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

   7. Simplified 52.1%

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

   8. Taylor expanded in i around inf 37.2%

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

      1. *-commutative 37.2%

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

      2. associate-*r* 37.1%

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

      3. *-commutative 37.1%

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

      4. associate-*r* 37.3%

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

   10. Simplified 37.3%

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

   if 9.49999999999999996e177 < y

   1. Initial program 50.1%

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

   3. Taylor expanded in x around inf 68.6%

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

   4. Taylor expanded in y around inf 73.3%

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

      1. *-commutative 73.3%

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

   6. Simplified 73.3%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 45.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+206}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-55}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-288}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-203}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-47}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 6.7 \cdot 10^{-18}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+177}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 52.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_3 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -3 \cdot 10^{-5}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-66}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-257}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-203}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 4.15 \cdot 10^{-19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+74}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t))))
        (t_2 (* b (- (* t i) (* z c))))
        (t_3 (* y (- (* x z) (* i j)))))
   (if (<= y -3e-5)
     t_3
     (if (<= y -1.02e-66)
       t_2
       (if (<= y -6.6e-257)
         t_1
         (if (<= y 1.35e-203)
           t_2
           (if (<= y 4.15e-19) t_1 (if (<= y 4.1e+74) t_2 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -3e-5) {
		tmp = t_3;
	} else if (y <= -1.02e-66) {
		tmp = t_2;
	} else if (y <= -6.6e-257) {
		tmp = t_1;
	} else if (y <= 1.35e-203) {
		tmp = t_2;
	} else if (y <= 4.15e-19) {
		tmp = t_1;
	} else if (y <= 4.1e+74) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    t_2 = b * ((t * i) - (z * c))
    t_3 = y * ((x * z) - (i * j))
    if (y <= (-3d-5)) then
        tmp = t_3
    else if (y <= (-1.02d-66)) then
        tmp = t_2
    else if (y <= (-6.6d-257)) then
        tmp = t_1
    else if (y <= 1.35d-203) then
        tmp = t_2
    else if (y <= 4.15d-19) then
        tmp = t_1
    else if (y <= 4.1d+74) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -3e-5) {
		tmp = t_3;
	} else if (y <= -1.02e-66) {
		tmp = t_2;
	} else if (y <= -6.6e-257) {
		tmp = t_1;
	} else if (y <= 1.35e-203) {
		tmp = t_2;
	} else if (y <= 4.15e-19) {
		tmp = t_1;
	} else if (y <= 4.1e+74) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = b * ((t * i) - (z * c))
	t_3 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -3e-5:
		tmp = t_3
	elif y <= -1.02e-66:
		tmp = t_2
	elif y <= -6.6e-257:
		tmp = t_1
	elif y <= 1.35e-203:
		tmp = t_2
	elif y <= 4.15e-19:
		tmp = t_1
	elif y <= 4.1e+74:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_3 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -3e-5)
		tmp = t_3;
	elseif (y <= -1.02e-66)
		tmp = t_2;
	elseif (y <= -6.6e-257)
		tmp = t_1;
	elseif (y <= 1.35e-203)
		tmp = t_2;
	elseif (y <= 4.15e-19)
		tmp = t_1;
	elseif (y <= 4.1e+74)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	t_2 = b * ((t * i) - (z * c));
	t_3 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -3e-5)
		tmp = t_3;
	elseif (y <= -1.02e-66)
		tmp = t_2;
	elseif (y <= -6.6e-257)
		tmp = t_1;
	elseif (y <= 1.35e-203)
		tmp = t_2;
	elseif (y <= 4.15e-19)
		tmp = t_1;
	elseif (y <= 4.1e+74)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3e-5], t$95$3, If[LessEqual[y, -1.02e-66], t$95$2, If[LessEqual[y, -6.6e-257], t$95$1, If[LessEqual[y, 1.35e-203], t$95$2, If[LessEqual[y, 4.15e-19], t$95$1, If[LessEqual[y, 4.1e+74], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.00000000000000008e-5 or 4.1e74 < y

   1. Initial program 57.8%

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

   3. Taylor expanded in y around inf 69.9%

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

      1. +-commutative 69.9%

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

      2. mul-1-neg 69.9%

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

      3. unsub-neg 69.9%

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

      4. *-commutative 69.9%

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

      5. *-commutative 69.9%

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

   5. Simplified 69.9%

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

   if -3.00000000000000008e-5 < y < -1.01999999999999996e-66 or -6.6e-257 < y < 1.34999999999999999e-203 or 4.1500000000000001e-19 < y < 4.1e74

   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. Step-by-step derivation

      1. sub-neg 77.6%

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

      2. distribute-rgt-in 77.6%

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

      3. distribute-rgt-neg-in 77.6%

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

   4. Applied egg-rr 77.6%

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

   5. Taylor expanded in j around 0 69.7%

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

      1. mul-1-neg 69.7%

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

      2. associate-*r* 70.9%

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

      3. distribute-lft-neg-in 70.9%

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

      4. mul-1-neg 70.9%

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

      5. *-commutative 70.9%

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

      6. distribute-rgt-in 70.9%

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

      7. +-commutative 70.9%

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

      8. mul-1-neg 70.9%

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

      9. unsub-neg 70.9%

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

      10. *-commutative 70.9%

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

      11. *-commutative 70.9%

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

      12. *-commutative 70.9%

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

      13. *-commutative 70.9%

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

   7. Simplified 70.9%

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

   8. Taylor expanded in x around 0 58.2%

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

      1. associate-*r* 58.2%

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

      2. *-commutative 58.2%

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

      3. associate-*r* 58.2%

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

      4. mul-1-neg 58.2%

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

      5. neg-sub0 58.2%

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

      6. associate--r- 58.2%

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

      7. neg-sub0 58.2%

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

      8. +-commutative 58.2%

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

      9. sub-neg 58.2%

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

      10. *-commutative 58.2%

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

      11. *-commutative 58.2%

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

   10. Simplified 58.2%

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

   if -1.01999999999999996e-66 < y < -6.6e-257 or 1.34999999999999999e-203 < y < 4.1500000000000001e-19

   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 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%

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

      4. *-commutative 62.9%

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

   5. Simplified 62.9%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-5}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-66}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-257}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-203}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 4.15 \cdot 10^{-19}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+74}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -28:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -7 \cdot 10^{-159}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 1.06 \cdot 10^{-80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{-26}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{-21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{+35}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (* b (- (* t i) (* z c)))))
   (if (<= b -28.0)
     t_2
     (if (<= b -7e-159)
       (* j (- (* a c) (* y i)))
       (if (<= b 1.06e-80)
         t_1
         (if (<= b 9.2e-26)
           (* c (- (* a j) (* z b)))
           (if (<= b 4.4e-21)
             t_1
             (if (<= b 2.05e+35) (* a (- (* c j) (* x t))) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -28.0) {
		tmp = t_2;
	} else if (b <= -7e-159) {
		tmp = j * ((a * c) - (y * i));
	} else if (b <= 1.06e-80) {
		tmp = t_1;
	} else if (b <= 9.2e-26) {
		tmp = c * ((a * j) - (z * b));
	} else if (b <= 4.4e-21) {
		tmp = t_1;
	} else if (b <= 2.05e+35) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = b * ((t * i) - (z * c))
    if (b <= (-28.0d0)) then
        tmp = t_2
    else if (b <= (-7d-159)) then
        tmp = j * ((a * c) - (y * i))
    else if (b <= 1.06d-80) then
        tmp = t_1
    else if (b <= 9.2d-26) then
        tmp = c * ((a * j) - (z * b))
    else if (b <= 4.4d-21) then
        tmp = t_1
    else if (b <= 2.05d+35) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -28.0) {
		tmp = t_2;
	} else if (b <= -7e-159) {
		tmp = j * ((a * c) - (y * i));
	} else if (b <= 1.06e-80) {
		tmp = t_1;
	} else if (b <= 9.2e-26) {
		tmp = c * ((a * j) - (z * b));
	} else if (b <= 4.4e-21) {
		tmp = t_1;
	} else if (b <= 2.05e+35) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -28.0:
		tmp = t_2
	elif b <= -7e-159:
		tmp = j * ((a * c) - (y * i))
	elif b <= 1.06e-80:
		tmp = t_1
	elif b <= 9.2e-26:
		tmp = c * ((a * j) - (z * b))
	elif b <= 4.4e-21:
		tmp = t_1
	elif b <= 2.05e+35:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -28.0)
		tmp = t_2;
	elseif (b <= -7e-159)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (b <= 1.06e-80)
		tmp = t_1;
	elseif (b <= 9.2e-26)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (b <= 4.4e-21)
		tmp = t_1;
	elseif (b <= 2.05e+35)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -28.0)
		tmp = t_2;
	elseif (b <= -7e-159)
		tmp = j * ((a * c) - (y * i));
	elseif (b <= 1.06e-80)
		tmp = t_1;
	elseif (b <= 9.2e-26)
		tmp = c * ((a * j) - (z * b));
	elseif (b <= 4.4e-21)
		tmp = t_1;
	elseif (b <= 2.05e+35)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -28.0], t$95$2, If[LessEqual[b, -7e-159], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.06e-80], t$95$1, If[LessEqual[b, 9.2e-26], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.4e-21], t$95$1, If[LessEqual[b, 2.05e+35], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -28

   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 b around inf 58.2%

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

   if -28 < b < -7.00000000000000005e-159

   1. Initial program 68.3%

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

   3. Taylor expanded in j around inf 58.6%

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

   if -7.00000000000000005e-159 < b < 1.0600000000000001e-80 or 9.20000000000000035e-26 < b < 4.4000000000000001e-21

   1. Initial program 75.5%

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

   3. Taylor expanded in x around inf 62.0%

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

   if 1.0600000000000001e-80 < b < 9.20000000000000035e-26

   1. Initial program 51.6%

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

   3. Taylor expanded in c around inf 79.8%

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

      1. *-commutative 79.8%

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

   5. Simplified 79.8%

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

   if 4.4000000000000001e-21 < b < 2.0499999999999999e35

   1. Initial program 80.0%

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

   3. Taylor expanded in a around inf 80.0%

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

      1. +-commutative 80.0%

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

      2. mul-1-neg 80.0%

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

      3. unsub-neg 80.0%

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

      4. *-commutative 80.0%

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

   5. Simplified 80.0%

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

   if 2.0499999999999999e35 < b

   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. Step-by-step derivation

      1. sub-neg 66.8%

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

      2. distribute-rgt-in 66.8%

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

      3. distribute-rgt-neg-in 66.8%

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

   4. Applied egg-rr 66.8%

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

   5. Taylor expanded in j around 0 65.7%

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

      1. mul-1-neg 65.7%

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

      2. associate-*r* 65.8%

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

      3. distribute-lft-neg-in 65.8%

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

      4. mul-1-neg 65.8%

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

      5. *-commutative 65.8%

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

      6. distribute-rgt-in 65.8%

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

      7. +-commutative 65.8%

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

      8. mul-1-neg 65.8%

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

      9. unsub-neg 65.8%

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

      10. *-commutative 65.8%

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

      11. *-commutative 65.8%

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

      12. *-commutative 65.8%

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

      13. *-commutative 65.8%

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

   7. Simplified 65.8%

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

   8. Taylor expanded in x around 0 70.2%

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

      1. associate-*r* 70.2%

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

      2. *-commutative 70.2%

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

      3. associate-*r* 70.2%

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

      4. mul-1-neg 70.2%

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

      5. neg-sub0 70.2%

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

      6. associate--r- 70.2%

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

      7. neg-sub0 70.2%

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

      8. +-commutative 70.2%

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

      9. sub-neg 70.2%

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

      10. *-commutative 70.2%

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

      11. *-commutative 70.2%

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

   10. Simplified 70.2%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -28:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -7 \cdot 10^{-159}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 1.06 \cdot 10^{-80}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{-26}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{-21}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{+35}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 28.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+206}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-54}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{-265}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-203}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-17}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+170}:\\ \;\;\;\;a \cdot \left(i \cdot \left(b \cdot \frac{t}{a}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -9e+206)
   (* i (* y (- j)))
   (if (<= y -3e-54)
     (* y (* x z))
     (if (<= y -7.6e-265)
       (* j (* a c))
       (if (<= y 1.2e-203)
         (* z (* b (- c)))
         (if (<= y 4.5e-17)
           (* t (* x (- a)))
           (if (<= y 4.6e+170) (* a (* i (* b (/ t a)))) (* x (* y z)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -9e+206) {
		tmp = i * (y * -j);
	} else if (y <= -3e-54) {
		tmp = y * (x * z);
	} else if (y <= -7.6e-265) {
		tmp = j * (a * c);
	} else if (y <= 1.2e-203) {
		tmp = z * (b * -c);
	} else if (y <= 4.5e-17) {
		tmp = t * (x * -a);
	} else if (y <= 4.6e+170) {
		tmp = a * (i * (b * (t / a)));
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-9d+206)) then
        tmp = i * (y * -j)
    else if (y <= (-3d-54)) then
        tmp = y * (x * z)
    else if (y <= (-7.6d-265)) then
        tmp = j * (a * c)
    else if (y <= 1.2d-203) then
        tmp = z * (b * -c)
    else if (y <= 4.5d-17) then
        tmp = t * (x * -a)
    else if (y <= 4.6d+170) then
        tmp = a * (i * (b * (t / a)))
    else
        tmp = x * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -9e+206) {
		tmp = i * (y * -j);
	} else if (y <= -3e-54) {
		tmp = y * (x * z);
	} else if (y <= -7.6e-265) {
		tmp = j * (a * c);
	} else if (y <= 1.2e-203) {
		tmp = z * (b * -c);
	} else if (y <= 4.5e-17) {
		tmp = t * (x * -a);
	} else if (y <= 4.6e+170) {
		tmp = a * (i * (b * (t / a)));
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -9e+206:
		tmp = i * (y * -j)
	elif y <= -3e-54:
		tmp = y * (x * z)
	elif y <= -7.6e-265:
		tmp = j * (a * c)
	elif y <= 1.2e-203:
		tmp = z * (b * -c)
	elif y <= 4.5e-17:
		tmp = t * (x * -a)
	elif y <= 4.6e+170:
		tmp = a * (i * (b * (t / a)))
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -9e+206)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (y <= -3e-54)
		tmp = Float64(y * Float64(x * z));
	elseif (y <= -7.6e-265)
		tmp = Float64(j * Float64(a * c));
	elseif (y <= 1.2e-203)
		tmp = Float64(z * Float64(b * Float64(-c)));
	elseif (y <= 4.5e-17)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (y <= 4.6e+170)
		tmp = Float64(a * Float64(i * Float64(b * Float64(t / a))));
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -9e+206)
		tmp = i * (y * -j);
	elseif (y <= -3e-54)
		tmp = y * (x * z);
	elseif (y <= -7.6e-265)
		tmp = j * (a * c);
	elseif (y <= 1.2e-203)
		tmp = z * (b * -c);
	elseif (y <= 4.5e-17)
		tmp = t * (x * -a);
	elseif (y <= 4.6e+170)
		tmp = a * (i * (b * (t / a)));
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -9e+206], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3e-54], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.6e-265], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e-203], N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.5e-17], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.6e+170], N[(a * N[(i * N[(b * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -9.00000000000000035e206

   1. Initial program 46.0%

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

      1. sub-neg 46.0%

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

      2. distribute-rgt-in 41.4%

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

      3. distribute-rgt-neg-in 41.4%

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

   4. Applied egg-rr 41.4%

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

   5. Taylor expanded in i around inf 59.8%

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

      1. associate-*r* 59.8%

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

      2. neg-mul-1 59.8%

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

      3. cancel-sign-sub 59.8%

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

      4. +-commutative 59.8%

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

      5. mul-1-neg 59.8%

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

      6. unsub-neg 59.8%

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

      7. *-commutative 59.8%

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

   7. Simplified 59.8%

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

   8. Taylor expanded in t around 0 64.0%

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

      1. mul-1-neg 64.0%

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

      2. *-commutative 64.0%

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

      3. distribute-rgt-neg-in 64.0%

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

      4. distribute-lft-neg-in 64.0%

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

   10. Simplified 64.0%

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

   if -9.00000000000000035e206 < y < -3.00000000000000009e-54

   1. Initial program 71.7%

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

   3. Taylor expanded in z around inf 55.7%

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

      1. *-commutative 55.7%

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

      2. *-commutative 55.7%

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

   5. Simplified 55.7%

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

   6. Taylor expanded in y around inf 35.3%

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

      1. *-commutative 35.3%

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

      2. associate-*r* 38.6%

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

   8. Simplified 38.6%

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

   if -3.00000000000000009e-54 < y < -7.59999999999999961e-265

   1. Initial program 82.7%

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

   3. Taylor expanded in a around inf 61.8%

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

      1. +-commutative 61.8%

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

      2. mul-1-neg 61.8%

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

      3. unsub-neg 61.8%

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

      4. *-commutative 61.8%

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

   5. Simplified 61.8%

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

   6. Taylor expanded in j around inf 40.4%

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

      1. associate-*r* 48.7%

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

   8. Simplified 48.7%

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

   if -7.59999999999999961e-265 < y < 1.1999999999999999e-203

   1. Initial program 74.8%

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

   3. Taylor expanded in z around inf 45.5%

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

      1. *-commutative 45.5%

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

      2. *-commutative 45.5%

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

   5. Simplified 45.5%

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

   6. Taylor expanded in y around 0 45.0%

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

      1. mul-1-neg 45.0%

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

      2. *-commutative 45.0%

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

      3. distribute-rgt-neg-in 45.0%

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

   8. Simplified 45.0%

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

   if 1.1999999999999999e-203 < y < 4.49999999999999978e-17

   1. Initial program 81.8%

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

   3. Taylor expanded in t around inf 52.6%

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

      1. distribute-lft-out-- 52.6%

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

      2. *-commutative 52.6%

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

   5. Simplified 52.6%

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

   6. Taylor expanded in a around inf 41.6%

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

   if 4.49999999999999978e-17 < y < 4.6000000000000001e170

   1. Initial program 71.0%

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

   3. Taylor expanded in a around -inf 66.9%

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

   5. Simplified 71.3%

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

   6. Taylor expanded in b around inf 44.9%

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

      1. mul-1-neg 44.9%

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

      2. distribute-rgt-neg-in 44.9%

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

      3. distribute-lft-neg-in 44.9%

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

      4. div-sub 44.9%

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

      5. *-commutative 44.9%

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

   8. Simplified 44.9%

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

   9. Taylor expanded in c around 0 38.2%

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

       1. associate-/l* 38.1%

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

       2. associate-/l* 38.1%

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

       3. associate-*r* 40.2%

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

       4. *-commutative 40.2%

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

       5. associate-*r* 40.2%

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

   11. Simplified 40.2%

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

   if 4.6000000000000001e170 < y

   1. Initial program 47.9%

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

   3. Taylor expanded in x around inf 65.6%

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

   4. Taylor expanded in y around inf 70.1%

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

      1. *-commutative 70.1%

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

   6. Simplified 70.1%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 46.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+206}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-54}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{-265}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-203}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-17}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+170}:\\ \;\;\;\;a \cdot \left(i \cdot \left(b \cdot \frac{t}{a}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_3 := \left(t\_2 + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{if}\;j \leq -6600:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq 6 \cdot 10^{-106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 1.4 \cdot 10^{+26}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq 1.46 \cdot 10^{+180}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* b (- (* t i) (* z c))) (* x (- (* t a) (* y z)))))
        (t_2 (* j (- (* a c) (* y i))))
        (t_3 (- (+ t_2 (* x (* y z))) (* b (* z c)))))
   (if (<= j -6600.0)
     t_3
     (if (<= j 6e-106)
       t_1
       (if (<= j 1.4e+26) t_3 (if (<= j 1.46e+180) 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 = (b * ((t * i) - (z * c))) - (x * ((t * a) - (y * z)));
	double t_2 = j * ((a * c) - (y * i));
	double t_3 = (t_2 + (x * (y * z))) - (b * (z * c));
	double tmp;
	if (j <= -6600.0) {
		tmp = t_3;
	} else if (j <= 6e-106) {
		tmp = t_1;
	} else if (j <= 1.4e+26) {
		tmp = t_3;
	} else if (j <= 1.46e+180) {
		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) :: t_3
    real(8) :: tmp
    t_1 = (b * ((t * i) - (z * c))) - (x * ((t * a) - (y * z)))
    t_2 = j * ((a * c) - (y * i))
    t_3 = (t_2 + (x * (y * z))) - (b * (z * c))
    if (j <= (-6600.0d0)) then
        tmp = t_3
    else if (j <= 6d-106) then
        tmp = t_1
    else if (j <= 1.4d+26) then
        tmp = t_3
    else if (j <= 1.46d+180) 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 = (b * ((t * i) - (z * c))) - (x * ((t * a) - (y * z)));
	double t_2 = j * ((a * c) - (y * i));
	double t_3 = (t_2 + (x * (y * z))) - (b * (z * c));
	double tmp;
	if (j <= -6600.0) {
		tmp = t_3;
	} else if (j <= 6e-106) {
		tmp = t_1;
	} else if (j <= 1.4e+26) {
		tmp = t_3;
	} else if (j <= 1.46e+180) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (b * ((t * i) - (z * c))) - (x * ((t * a) - (y * z)))
	t_2 = j * ((a * c) - (y * i))
	t_3 = (t_2 + (x * (y * z))) - (b * (z * c))
	tmp = 0
	if j <= -6600.0:
		tmp = t_3
	elif j <= 6e-106:
		tmp = t_1
	elif j <= 1.4e+26:
		tmp = t_3
	elif j <= 1.46e+180:
		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(b * Float64(Float64(t * i) - Float64(z * c))) - Float64(x * Float64(Float64(t * a) - Float64(y * z))))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_3 = Float64(Float64(t_2 + Float64(x * Float64(y * z))) - Float64(b * Float64(z * c)))
	tmp = 0.0
	if (j <= -6600.0)
		tmp = t_3;
	elseif (j <= 6e-106)
		tmp = t_1;
	elseif (j <= 1.4e+26)
		tmp = t_3;
	elseif (j <= 1.46e+180)
		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 = (b * ((t * i) - (z * c))) - (x * ((t * a) - (y * z)));
	t_2 = j * ((a * c) - (y * i));
	t_3 = (t_2 + (x * (y * z))) - (b * (z * c));
	tmp = 0.0;
	if (j <= -6600.0)
		tmp = t_3;
	elseif (j <= 6e-106)
		tmp = t_1;
	elseif (j <= 1.4e+26)
		tmp = t_3;
	elseif (j <= 1.46e+180)
		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[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t$95$2 + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -6600.0], t$95$3, If[LessEqual[j, 6e-106], t$95$1, If[LessEqual[j, 1.4e+26], t$95$3, If[LessEqual[j, 1.46e+180], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -6600 or 6.00000000000000037e-106 < j < 1.4e26

   1. Initial program 66.2%

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

      1. sub-neg 66.2%

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

      2. distribute-rgt-in 66.2%

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

      3. distribute-rgt-neg-in 66.2%

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

   4. Applied egg-rr 66.2%

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

   5. Taylor expanded in t around 0 69.8%

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

   if -6600 < j < 6.00000000000000037e-106 or 1.4e26 < j < 1.45999999999999994e180

   1. Initial program 73.2%

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

      1. sub-neg 73.2%

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

      2. distribute-rgt-in 72.5%

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

      3. distribute-rgt-neg-in 72.5%

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

   4. Applied egg-rr 72.5%

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

   5. Taylor expanded in j around 0 74.0%

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

      1. mul-1-neg 74.0%

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

      2. associate-*r* 76.1%

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

      3. distribute-lft-neg-in 76.1%

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

      4. mul-1-neg 76.1%

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

      5. *-commutative 76.1%

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

      6. distribute-rgt-in 78.2%

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

      7. +-commutative 78.2%

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

      8. mul-1-neg 78.2%

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

      9. unsub-neg 78.2%

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

      10. *-commutative 78.2%

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

      11. *-commutative 78.2%

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

      12. *-commutative 78.2%

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

      13. *-commutative 78.2%

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

   7. Simplified 78.2%

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

   if 1.45999999999999994e180 < 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 j around inf 78.4%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -6600:\\ \;\;\;\;\left(j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;j \leq 6 \cdot 10^{-106}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;j \leq 1.4 \cdot 10^{+26}:\\ \;\;\;\;\left(j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.46 \cdot 10^{+180}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t \cdot a - y \cdot z\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right) - t\_1\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -9 \cdot 10^{+52}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq 5600:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 1.02 \cdot 10^{+23}:\\ \;\;\;\;t\_3 - t\_1\\ \mathbf{elif}\;j \leq 1.3 \cdot 10^{+180}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* t a) (* y z))))
        (t_2 (- (* b (- (* t i) (* z c))) t_1))
        (t_3 (* j (- (* a c) (* y i)))))
   (if (<= j -9e+52)
     t_3
     (if (<= j 5600.0)
       t_2
       (if (<= j 1.02e+23) (- t_3 t_1) (if (<= j 1.3e+180) t_2 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((t * a) - (y * z));
	double t_2 = (b * ((t * i) - (z * c))) - t_1;
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -9e+52) {
		tmp = t_3;
	} else if (j <= 5600.0) {
		tmp = t_2;
	} else if (j <= 1.02e+23) {
		tmp = t_3 - t_1;
	} else if (j <= 1.3e+180) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * ((t * a) - (y * z))
    t_2 = (b * ((t * i) - (z * c))) - t_1
    t_3 = j * ((a * c) - (y * i))
    if (j <= (-9d+52)) then
        tmp = t_3
    else if (j <= 5600.0d0) then
        tmp = t_2
    else if (j <= 1.02d+23) then
        tmp = t_3 - t_1
    else if (j <= 1.3d+180) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((t * a) - (y * z));
	double t_2 = (b * ((t * i) - (z * c))) - t_1;
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -9e+52) {
		tmp = t_3;
	} else if (j <= 5600.0) {
		tmp = t_2;
	} else if (j <= 1.02e+23) {
		tmp = t_3 - t_1;
	} else if (j <= 1.3e+180) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((t * a) - (y * z))
	t_2 = (b * ((t * i) - (z * c))) - t_1
	t_3 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -9e+52:
		tmp = t_3
	elif j <= 5600.0:
		tmp = t_2
	elif j <= 1.02e+23:
		tmp = t_3 - t_1
	elif j <= 1.3e+180:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(t * a) - Float64(y * z)))
	t_2 = Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) - t_1)
	t_3 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -9e+52)
		tmp = t_3;
	elseif (j <= 5600.0)
		tmp = t_2;
	elseif (j <= 1.02e+23)
		tmp = Float64(t_3 - t_1);
	elseif (j <= 1.3e+180)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((t * a) - (y * z));
	t_2 = (b * ((t * i) - (z * c))) - t_1;
	t_3 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -9e+52)
		tmp = t_3;
	elseif (j <= 5600.0)
		tmp = t_2;
	elseif (j <= 1.02e+23)
		tmp = t_3 - t_1;
	elseif (j <= 1.3e+180)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -9e+52], t$95$3, If[LessEqual[j, 5600.0], t$95$2, If[LessEqual[j, 1.02e+23], N[(t$95$3 - t$95$1), $MachinePrecision], If[LessEqual[j, 1.3e+180], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -8.9999999999999999e52 or 1.3000000000000001e180 < j

   1. Initial program 61.6%

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

   3. Taylor expanded in j around inf 72.1%

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

   if -8.9999999999999999e52 < j < 5600 or 1.02e23 < j < 1.3000000000000001e180

   1. Initial program 73.4%

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

      1. sub-neg 73.4%

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

      2. distribute-rgt-in 72.9%

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

      3. distribute-rgt-neg-in 72.9%

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

   4. Applied egg-rr 72.9%

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

   5. Taylor expanded in j around 0 72.4%

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

      1. mul-1-neg 72.4%

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

      2. associate-*r* 73.5%

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

      3. distribute-lft-neg-in 73.5%

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

      4. mul-1-neg 73.5%

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

      5. *-commutative 73.5%

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

      6. distribute-rgt-in 75.2%

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

      7. +-commutative 75.2%

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

      8. mul-1-neg 75.2%

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

      9. unsub-neg 75.2%

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

      10. *-commutative 75.2%

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

      11. *-commutative 75.2%

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

      12. *-commutative 75.2%

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

      13. *-commutative 75.2%

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

   7. Simplified 75.2%

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

   if 5600 < j < 1.02e23

   1. Initial program 88.7%

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

   3. Taylor expanded in b around 0 88.7%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -9 \cdot 10^{+52}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 5600:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;j \leq 1.02 \cdot 10^{+23}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;j \leq 1.3 \cdot 10^{+180}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t \cdot a - y \cdot z\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right) - t\_1\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -3.8 \cdot 10^{+53}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq 7000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{+25}:\\ \;\;\;\;t\_3 - t\_1\\ \mathbf{elif}\;j \leq 1.3 \cdot 10^{+180}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* t a) (* y z))))
        (t_2 (- (* b (- (* t i) (* z c))) t_1))
        (t_3 (* j (- (* a c) (* y i)))))
   (if (<= j -3.8e+53)
     t_3
     (if (<= j 7000.0)
       t_2
       (if (<= j 1.5e+25) (- t_3 t_1) (if (<= j 1.3e+180) t_2 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((t * a) - (y * z));
	double t_2 = (b * ((t * i) - (z * c))) - t_1;
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -3.8e+53) {
		tmp = t_3;
	} else if (j <= 7000.0) {
		tmp = t_2;
	} else if (j <= 1.5e+25) {
		tmp = t_3 - t_1;
	} else if (j <= 1.3e+180) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * ((t * a) - (y * z))
    t_2 = (b * ((t * i) - (z * c))) - t_1
    t_3 = j * ((a * c) - (y * i))
    if (j <= (-3.8d+53)) then
        tmp = t_3
    else if (j <= 7000.0d0) then
        tmp = t_2
    else if (j <= 1.5d+25) then
        tmp = t_3 - t_1
    else if (j <= 1.3d+180) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((t * a) - (y * z));
	double t_2 = (b * ((t * i) - (z * c))) - t_1;
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -3.8e+53) {
		tmp = t_3;
	} else if (j <= 7000.0) {
		tmp = t_2;
	} else if (j <= 1.5e+25) {
		tmp = t_3 - t_1;
	} else if (j <= 1.3e+180) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((t * a) - (y * z))
	t_2 = (b * ((t * i) - (z * c))) - t_1
	t_3 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -3.8e+53:
		tmp = t_3
	elif j <= 7000.0:
		tmp = t_2
	elif j <= 1.5e+25:
		tmp = t_3 - t_1
	elif j <= 1.3e+180:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(t * a) - Float64(y * z)))
	t_2 = Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) - t_1)
	t_3 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -3.8e+53)
		tmp = t_3;
	elseif (j <= 7000.0)
		tmp = t_2;
	elseif (j <= 1.5e+25)
		tmp = Float64(t_3 - t_1);
	elseif (j <= 1.3e+180)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((t * a) - (y * z));
	t_2 = (b * ((t * i) - (z * c))) - t_1;
	t_3 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -3.8e+53)
		tmp = t_3;
	elseif (j <= 7000.0)
		tmp = t_2;
	elseif (j <= 1.5e+25)
		tmp = t_3 - t_1;
	elseif (j <= 1.3e+180)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.8e+53], t$95$3, If[LessEqual[j, 7000.0], t$95$2, If[LessEqual[j, 1.5e+25], N[(t$95$3 - t$95$1), $MachinePrecision], If[LessEqual[j, 1.3e+180], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -3.79999999999999997e53 or 1.3000000000000001e180 < j

   1. Initial program 61.6%

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

   3. Taylor expanded in j around inf 72.1%

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

   if -3.79999999999999997e53 < j < 7e3 or 1.50000000000000003e25 < j < 1.3000000000000001e180

   1. Initial program 73.4%

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

   3. Taylor expanded in j around 0 75.2%

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

   if 7e3 < j < 1.50000000000000003e25

   1. Initial program 88.7%

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

   3. Taylor expanded in b around 0 88.7%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.8 \cdot 10^{+53}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 7000:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{+25}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;j \leq 1.3 \cdot 10^{+180}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 28.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+205}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq -1.36 \cdot 10^{-55}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq -9.8 \cdot 10^{-265}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-203}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-17}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+171}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -3.2e+205)
   (* i (* y (- j)))
   (if (<= y -1.36e-55)
     (* y (* x z))
     (if (<= y -9.8e-265)
       (* j (* a c))
       (if (<= y 1.35e-203)
         (* z (* b (- c)))
         (if (<= y 2.7e-17)
           (* t (* x (- a)))
           (if (<= y 5.2e+171) (* t (* b i)) (* x (* y z)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -3.2e+205) {
		tmp = i * (y * -j);
	} else if (y <= -1.36e-55) {
		tmp = y * (x * z);
	} else if (y <= -9.8e-265) {
		tmp = j * (a * c);
	} else if (y <= 1.35e-203) {
		tmp = z * (b * -c);
	} else if (y <= 2.7e-17) {
		tmp = t * (x * -a);
	} else if (y <= 5.2e+171) {
		tmp = t * (b * i);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-3.2d+205)) then
        tmp = i * (y * -j)
    else if (y <= (-1.36d-55)) then
        tmp = y * (x * z)
    else if (y <= (-9.8d-265)) then
        tmp = j * (a * c)
    else if (y <= 1.35d-203) then
        tmp = z * (b * -c)
    else if (y <= 2.7d-17) then
        tmp = t * (x * -a)
    else if (y <= 5.2d+171) then
        tmp = t * (b * i)
    else
        tmp = x * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -3.2e+205) {
		tmp = i * (y * -j);
	} else if (y <= -1.36e-55) {
		tmp = y * (x * z);
	} else if (y <= -9.8e-265) {
		tmp = j * (a * c);
	} else if (y <= 1.35e-203) {
		tmp = z * (b * -c);
	} else if (y <= 2.7e-17) {
		tmp = t * (x * -a);
	} else if (y <= 5.2e+171) {
		tmp = t * (b * i);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -3.2e+205:
		tmp = i * (y * -j)
	elif y <= -1.36e-55:
		tmp = y * (x * z)
	elif y <= -9.8e-265:
		tmp = j * (a * c)
	elif y <= 1.35e-203:
		tmp = z * (b * -c)
	elif y <= 2.7e-17:
		tmp = t * (x * -a)
	elif y <= 5.2e+171:
		tmp = t * (b * i)
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -3.2e+205)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (y <= -1.36e-55)
		tmp = Float64(y * Float64(x * z));
	elseif (y <= -9.8e-265)
		tmp = Float64(j * Float64(a * c));
	elseif (y <= 1.35e-203)
		tmp = Float64(z * Float64(b * Float64(-c)));
	elseif (y <= 2.7e-17)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (y <= 5.2e+171)
		tmp = Float64(t * Float64(b * i));
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -3.2e+205)
		tmp = i * (y * -j);
	elseif (y <= -1.36e-55)
		tmp = y * (x * z);
	elseif (y <= -9.8e-265)
		tmp = j * (a * c);
	elseif (y <= 1.35e-203)
		tmp = z * (b * -c);
	elseif (y <= 2.7e-17)
		tmp = t * (x * -a);
	elseif (y <= 5.2e+171)
		tmp = t * (b * i);
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -3.2e+205], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.36e-55], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -9.8e-265], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.35e-203], N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e-17], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.2e+171], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -3.19999999999999996e205

   1. Initial program 46.0%

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

      1. sub-neg 46.0%

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

      2. distribute-rgt-in 41.4%

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

      3. distribute-rgt-neg-in 41.4%

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

   4. Applied egg-rr 41.4%

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

   5. Taylor expanded in i around inf 59.8%

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

      1. associate-*r* 59.8%

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

      2. neg-mul-1 59.8%

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

      3. cancel-sign-sub 59.8%

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

      4. +-commutative 59.8%

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

      5. mul-1-neg 59.8%

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

      6. unsub-neg 59.8%

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

      7. *-commutative 59.8%

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

   7. Simplified 59.8%

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

   8. Taylor expanded in t around 0 64.0%

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

      1. mul-1-neg 64.0%

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

      2. *-commutative 64.0%

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

      3. distribute-rgt-neg-in 64.0%

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

      4. distribute-lft-neg-in 64.0%

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

   10. Simplified 64.0%

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

   if -3.19999999999999996e205 < y < -1.35999999999999993e-55

   1. Initial program 71.7%

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

   3. Taylor expanded in z around inf 55.7%

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

      1. *-commutative 55.7%

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

      2. *-commutative 55.7%

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

   5. Simplified 55.7%

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

   6. Taylor expanded in y around inf 35.3%

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

      1. *-commutative 35.3%

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

      2. associate-*r* 38.6%

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

   8. Simplified 38.6%

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

   if -1.35999999999999993e-55 < y < -9.79999999999999999e-265

   1. Initial program 82.7%

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

   3. Taylor expanded in a around inf 61.8%

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

      1. +-commutative 61.8%

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

      2. mul-1-neg 61.8%

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

      3. unsub-neg 61.8%

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

      4. *-commutative 61.8%

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

   5. Simplified 61.8%

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

   6. Taylor expanded in j around inf 40.4%

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

      1. associate-*r* 48.7%

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

   8. Simplified 48.7%

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

   if -9.79999999999999999e-265 < y < 1.34999999999999999e-203

   1. Initial program 74.8%

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

   3. Taylor expanded in z around inf 45.5%

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

      1. *-commutative 45.5%

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

      2. *-commutative 45.5%

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

   5. Simplified 45.5%

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

   6. Taylor expanded in y around 0 45.0%

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

      1. mul-1-neg 45.0%

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

      2. *-commutative 45.0%

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

      3. distribute-rgt-neg-in 45.0%

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

   8. Simplified 45.0%

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

   if 1.34999999999999999e-203 < y < 2.7000000000000001e-17

   1. Initial program 81.8%

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

   3. Taylor expanded in t around inf 52.6%

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

      1. distribute-lft-out-- 52.6%

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

      2. *-commutative 52.6%

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

   5. Simplified 52.6%

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

   6. Taylor expanded in a around inf 41.6%

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

   if 2.7000000000000001e-17 < y < 5.2e171

   1. Initial program 69.5%

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

   3. Taylor expanded in t around inf 39.5%

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

      1. distribute-lft-out-- 39.5%

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

      2. *-commutative 39.5%

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

   5. Simplified 39.5%

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

   6. Taylor expanded in a around 0 37.3%

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

      1. neg-mul-1 37.3%

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

      2. distribute-rgt-neg-in 37.3%

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

   8. Simplified 37.3%

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

   if 5.2e171 < y

   1. Initial program 50.1%

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

   3. Taylor expanded in x around inf 68.6%

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

   4. Taylor expanded in y around inf 73.3%

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

      1. *-commutative 73.3%

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

   6. Simplified 73.3%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 46.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+205}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq -1.36 \cdot 10^{-55}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq -9.8 \cdot 10^{-265}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-203}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-17}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+171}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 28.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{+206}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-54}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-265}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;y \leq 10^{-203}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-18}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+177}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -1.06e+206)
   (* i (* y (- j)))
   (if (<= y -2.3e-54)
     (* y (* x z))
     (if (<= y -4.4e-265)
       (* j (* a c))
       (if (<= y 1e-203)
         (* z (* b (- c)))
         (if (<= y 3.6e-18)
           (* t (* x (- a)))
           (if (<= y 3.8e+177) (* t (* b i)) (* x (* y z)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -1.06e+206) {
		tmp = i * (y * -j);
	} else if (y <= -2.3e-54) {
		tmp = y * (x * z);
	} else if (y <= -4.4e-265) {
		tmp = j * (a * c);
	} else if (y <= 1e-203) {
		tmp = z * (b * -c);
	} else if (y <= 3.6e-18) {
		tmp = t * (x * -a);
	} else if (y <= 3.8e+177) {
		tmp = t * (b * i);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-1.06d+206)) then
        tmp = i * (y * -j)
    else if (y <= (-2.3d-54)) then
        tmp = y * (x * z)
    else if (y <= (-4.4d-265)) then
        tmp = j * (a * c)
    else if (y <= 1d-203) then
        tmp = z * (b * -c)
    else if (y <= 3.6d-18) then
        tmp = t * (x * -a)
    else if (y <= 3.8d+177) then
        tmp = t * (b * i)
    else
        tmp = x * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -1.06e+206) {
		tmp = i * (y * -j);
	} else if (y <= -2.3e-54) {
		tmp = y * (x * z);
	} else if (y <= -4.4e-265) {
		tmp = j * (a * c);
	} else if (y <= 1e-203) {
		tmp = z * (b * -c);
	} else if (y <= 3.6e-18) {
		tmp = t * (x * -a);
	} else if (y <= 3.8e+177) {
		tmp = t * (b * i);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -1.06e+206:
		tmp = i * (y * -j)
	elif y <= -2.3e-54:
		tmp = y * (x * z)
	elif y <= -4.4e-265:
		tmp = j * (a * c)
	elif y <= 1e-203:
		tmp = z * (b * -c)
	elif y <= 3.6e-18:
		tmp = t * (x * -a)
	elif y <= 3.8e+177:
		tmp = t * (b * i)
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -1.06e+206)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (y <= -2.3e-54)
		tmp = Float64(y * Float64(x * z));
	elseif (y <= -4.4e-265)
		tmp = Float64(j * Float64(a * c));
	elseif (y <= 1e-203)
		tmp = Float64(z * Float64(b * Float64(-c)));
	elseif (y <= 3.6e-18)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (y <= 3.8e+177)
		tmp = Float64(t * Float64(b * i));
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -1.06e+206)
		tmp = i * (y * -j);
	elseif (y <= -2.3e-54)
		tmp = y * (x * z);
	elseif (y <= -4.4e-265)
		tmp = j * (a * c);
	elseif (y <= 1e-203)
		tmp = z * (b * -c);
	elseif (y <= 3.6e-18)
		tmp = t * (x * -a);
	elseif (y <= 3.8e+177)
		tmp = t * (b * i);
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -1.06e+206], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.3e-54], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.4e-265], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e-203], N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e-18], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.8e+177], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -1.0599999999999999e206

   1. Initial program 46.0%

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

      1. sub-neg 46.0%

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

      2. distribute-rgt-in 41.4%

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

      3. distribute-rgt-neg-in 41.4%

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

   4. Applied egg-rr 41.4%

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

   5. Taylor expanded in i around inf 59.8%

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

      1. associate-*r* 59.8%

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

      2. neg-mul-1 59.8%

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

      3. cancel-sign-sub 59.8%

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

      4. +-commutative 59.8%

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

      5. mul-1-neg 59.8%

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

      6. unsub-neg 59.8%

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

      7. *-commutative 59.8%

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

   7. Simplified 59.8%

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

   8. Taylor expanded in t around 0 64.0%

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

      1. mul-1-neg 64.0%

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

      2. *-commutative 64.0%

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

      3. distribute-rgt-neg-in 64.0%

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

      4. distribute-lft-neg-in 64.0%

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

   10. Simplified 64.0%

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

   if -1.0599999999999999e206 < y < -2.2999999999999999e-54

   1. Initial program 71.7%

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

   3. Taylor expanded in z around inf 55.7%

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

      1. *-commutative 55.7%

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

      2. *-commutative 55.7%

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

   5. Simplified 55.7%

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

   6. Taylor expanded in y around inf 35.3%

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

      1. *-commutative 35.3%

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

      2. associate-*r* 38.6%

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

   8. Simplified 38.6%

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

   if -2.2999999999999999e-54 < y < -4.40000000000000021e-265

   1. Initial program 82.7%

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

   3. Taylor expanded in a around inf 61.8%

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

      1. +-commutative 61.8%

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

      2. mul-1-neg 61.8%

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

      3. unsub-neg 61.8%

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

      4. *-commutative 61.8%

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

   5. Simplified 61.8%

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

   6. Taylor expanded in j around inf 40.4%

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

      1. associate-*r* 48.7%

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

   8. Simplified 48.7%

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

   if -4.40000000000000021e-265 < y < 1e-203

   1. Initial program 74.8%

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

   3. Taylor expanded in z around inf 45.5%

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

      1. *-commutative 45.5%

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

      2. *-commutative 45.5%

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

   5. Simplified 45.5%

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

   6. Taylor expanded in y around 0 45.0%

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

      1. mul-1-neg 45.0%

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

      2. *-commutative 45.0%

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

      3. distribute-rgt-neg-in 45.0%

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

   8. Simplified 45.0%

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

   if 1e-203 < y < 3.6000000000000001e-18

   1. Initial program 81.8%

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

   3. Taylor expanded in t around inf 52.6%

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

      1. distribute-lft-out-- 52.6%

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

      2. *-commutative 52.6%

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

   5. Simplified 52.6%

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

   6. Taylor expanded in a around inf 41.6%

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

   if 3.6000000000000001e-18 < y < 3.7999999999999998e177

   1. Initial program 69.5%

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

      1. sub-neg 69.5%

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

      2. distribute-rgt-in 69.5%

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

      3. distribute-rgt-neg-in 69.5%

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

   4. Applied egg-rr 69.5%

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

   5. Taylor expanded in j around 0 54.4%

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

      1. mul-1-neg 54.4%

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

      2. associate-*r* 52.1%

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

      3. distribute-lft-neg-in 52.1%

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

      4. mul-1-neg 52.1%

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

      5. *-commutative 52.1%

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

      6. distribute-rgt-in 52.1%

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

      7. +-commutative 52.1%

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

      8. mul-1-neg 52.1%

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

      9. unsub-neg 52.1%

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

      10. *-commutative 52.1%

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

      11. *-commutative 52.1%

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

      12. *-commutative 52.1%

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

      13. *-commutative 52.1%

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

   7. Simplified 52.1%

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

   8. Taylor expanded in i around inf 37.2%

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

      1. *-commutative 37.2%

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

      2. associate-*r* 37.1%

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

      3. *-commutative 37.1%

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

      4. associate-*r* 37.3%

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

   10. Simplified 37.3%

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

   if 3.7999999999999998e177 < y

   1. Initial program 50.1%

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

   3. Taylor expanded in x around inf 68.6%

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

   4. Taylor expanded in y around inf 73.3%

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

      1. *-commutative 73.3%

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

   6. Simplified 73.3%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 46.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{+206}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-54}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-265}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;y \leq 10^{-203}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-18}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+177}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 28.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+206}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-55}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-265}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-204}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-17}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+171}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -8e+206)
   (* i (* y (- j)))
   (if (<= y -2.15e-55)
     (* y (* x z))
     (if (<= y -1.02e-265)
       (* j (* a c))
       (if (<= y 8e-204)
         (* z (* b (- c)))
         (if (<= y 2.2e-17)
           (* t (* x (- a)))
           (if (<= y 6.4e+171) (* t (* b i)) (* x (* y z)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -8e+206) {
		tmp = i * (y * -j);
	} else if (y <= -2.15e-55) {
		tmp = y * (x * z);
	} else if (y <= -1.02e-265) {
		tmp = j * (a * c);
	} else if (y <= 8e-204) {
		tmp = z * (b * -c);
	} else if (y <= 2.2e-17) {
		tmp = t * (x * -a);
	} else if (y <= 6.4e+171) {
		tmp = t * (b * i);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-8d+206)) then
        tmp = i * (y * -j)
    else if (y <= (-2.15d-55)) then
        tmp = y * (x * z)
    else if (y <= (-1.02d-265)) then
        tmp = j * (a * c)
    else if (y <= 8d-204) then
        tmp = z * (b * -c)
    else if (y <= 2.2d-17) then
        tmp = t * (x * -a)
    else if (y <= 6.4d+171) then
        tmp = t * (b * i)
    else
        tmp = x * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -8e+206) {
		tmp = i * (y * -j);
	} else if (y <= -2.15e-55) {
		tmp = y * (x * z);
	} else if (y <= -1.02e-265) {
		tmp = j * (a * c);
	} else if (y <= 8e-204) {
		tmp = z * (b * -c);
	} else if (y <= 2.2e-17) {
		tmp = t * (x * -a);
	} else if (y <= 6.4e+171) {
		tmp = t * (b * i);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -8e+206:
		tmp = i * (y * -j)
	elif y <= -2.15e-55:
		tmp = y * (x * z)
	elif y <= -1.02e-265:
		tmp = j * (a * c)
	elif y <= 8e-204:
		tmp = z * (b * -c)
	elif y <= 2.2e-17:
		tmp = t * (x * -a)
	elif y <= 6.4e+171:
		tmp = t * (b * i)
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -8e+206)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (y <= -2.15e-55)
		tmp = Float64(y * Float64(x * z));
	elseif (y <= -1.02e-265)
		tmp = Float64(j * Float64(a * c));
	elseif (y <= 8e-204)
		tmp = Float64(z * Float64(b * Float64(-c)));
	elseif (y <= 2.2e-17)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (y <= 6.4e+171)
		tmp = Float64(t * Float64(b * i));
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -8e+206)
		tmp = i * (y * -j);
	elseif (y <= -2.15e-55)
		tmp = y * (x * z);
	elseif (y <= -1.02e-265)
		tmp = j * (a * c);
	elseif (y <= 8e-204)
		tmp = z * (b * -c);
	elseif (y <= 2.2e-17)
		tmp = t * (x * -a);
	elseif (y <= 6.4e+171)
		tmp = t * (b * i);
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -8e+206], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.15e-55], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.02e-265], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8e-204], N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.2e-17], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.4e+171], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -8.0000000000000003e206

   1. Initial program 46.0%

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

      1. sub-neg 46.0%

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

      2. distribute-rgt-in 41.4%

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

      3. distribute-rgt-neg-in 41.4%

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

   4. Applied egg-rr 41.4%

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

   5. Taylor expanded in i around inf 59.8%

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

      1. associate-*r* 59.8%

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

      2. neg-mul-1 59.8%

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

      3. cancel-sign-sub 59.8%

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

      4. +-commutative 59.8%

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

      5. mul-1-neg 59.8%

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

      6. unsub-neg 59.8%

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

      7. *-commutative 59.8%

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

   7. Simplified 59.8%

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

   8. Taylor expanded in t around 0 64.0%

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

      1. mul-1-neg 64.0%

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

      2. *-commutative 64.0%

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

      3. distribute-rgt-neg-in 64.0%

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

      4. distribute-lft-neg-in 64.0%

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

   10. Simplified 64.0%

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

   if -8.0000000000000003e206 < y < -2.15000000000000005e-55

   1. Initial program 71.7%

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

   3. Taylor expanded in z around inf 55.7%

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

      1. *-commutative 55.7%

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

      2. *-commutative 55.7%

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

   5. Simplified 55.7%

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

   6. Taylor expanded in y around inf 35.3%

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

      1. *-commutative 35.3%

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

      2. associate-*r* 38.6%

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

   8. Simplified 38.6%

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

   if -2.15000000000000005e-55 < y < -1.02000000000000005e-265

   1. Initial program 82.7%

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

   3. Taylor expanded in a around inf 61.8%

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

      1. +-commutative 61.8%

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

      2. mul-1-neg 61.8%

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

      3. unsub-neg 61.8%

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

      4. *-commutative 61.8%

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

   5. Simplified 61.8%

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

   6. Taylor expanded in j around inf 40.4%

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

      1. associate-*r* 48.7%

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

   8. Simplified 48.7%

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

   if -1.02000000000000005e-265 < y < 8.00000000000000001e-204

   1. Initial program 74.8%

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

   3. Taylor expanded in z around inf 45.5%

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

      1. *-commutative 45.5%

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

      2. *-commutative 45.5%

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

   5. Simplified 45.5%

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

   6. Taylor expanded in y around 0 45.0%

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

      1. mul-1-neg 45.0%

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

      2. *-commutative 45.0%

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

      3. distribute-rgt-neg-in 45.0%

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

   8. Simplified 45.0%

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

   if 8.00000000000000001e-204 < y < 2.2e-17

   1. Initial program 81.8%

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

   3. Taylor expanded in t around inf 52.6%

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

      1. distribute-lft-out-- 52.6%

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

      2. *-commutative 52.6%

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

   5. Simplified 52.6%

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

   6. Taylor expanded in a around inf 41.6%

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

   7. Taylor expanded in t around 0 41.6%

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

      1. mul-1-neg 41.6%

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

      2. *-commutative 41.6%

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

      3. distribute-rgt-neg-in 41.6%

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

      4. neg-mul-1 41.6%

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

      5. associate-*r* 41.6%

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

      6. neg-mul-1 41.6%

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

   9. Simplified 41.6%

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

   if 2.2e-17 < y < 6.40000000000000022e171

   1. Initial program 69.5%

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

      1. sub-neg 69.5%

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

      2. distribute-rgt-in 69.5%

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

      3. distribute-rgt-neg-in 69.5%

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

   4. Applied egg-rr 69.5%

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

   5. Taylor expanded in j around 0 54.4%

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

      1. mul-1-neg 54.4%

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

      2. associate-*r* 52.1%

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

      3. distribute-lft-neg-in 52.1%

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

      4. mul-1-neg 52.1%

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

      5. *-commutative 52.1%

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

      6. distribute-rgt-in 52.1%

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

      7. +-commutative 52.1%

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

      8. mul-1-neg 52.1%

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

      9. unsub-neg 52.1%

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

      10. *-commutative 52.1%

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

      11. *-commutative 52.1%

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

      12. *-commutative 52.1%

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

      13. *-commutative 52.1%

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

   7. Simplified 52.1%

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

   8. Taylor expanded in i around inf 37.2%

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

      1. *-commutative 37.2%

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

      2. associate-*r* 37.1%

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

      3. *-commutative 37.1%

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

      4. associate-*r* 37.3%

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

   10. Simplified 37.3%

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

   if 6.40000000000000022e171 < y

   1. Initial program 50.1%

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

   3. Taylor expanded in x around inf 68.6%

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

   4. Taylor expanded in y around inf 73.3%

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

      1. *-commutative 73.3%

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

   6. Simplified 73.3%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 46.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+206}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-55}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-265}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-204}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-17}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+171}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 58.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -2.5 \cdot 10^{+48}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 1.12 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 1.05 \cdot 10^{+77}:\\ \;\;\;\;z \cdot \left(b \cdot \left(i \cdot \frac{t}{z} - c\right)\right)\\ \mathbf{elif}\;j \leq 1.3 \cdot 10^{+180}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* x (- (* y z) (* t a))) (* b (* z c))))
        (t_2 (* j (- (* a c) (* y i)))))
   (if (<= j -2.5e+48)
     t_2
     (if (<= j 1.12e+18)
       t_1
       (if (<= j 1.05e+77)
         (* z (* b (- (* i (/ t z)) c)))
         (if (<= j 1.3e+180) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * ((y * z) - (t * a))) - (b * (z * c));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -2.5e+48) {
		tmp = t_2;
	} else if (j <= 1.12e+18) {
		tmp = t_1;
	} else if (j <= 1.05e+77) {
		tmp = z * (b * ((i * (t / z)) - c));
	} else if (j <= 1.3e+180) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * ((y * z) - (t * a))) - (b * (z * c))
    t_2 = j * ((a * c) - (y * i))
    if (j <= (-2.5d+48)) then
        tmp = t_2
    else if (j <= 1.12d+18) then
        tmp = t_1
    else if (j <= 1.05d+77) then
        tmp = z * (b * ((i * (t / z)) - c))
    else if (j <= 1.3d+180) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * ((y * z) - (t * a))) - (b * (z * c));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -2.5e+48) {
		tmp = t_2;
	} else if (j <= 1.12e+18) {
		tmp = t_1;
	} else if (j <= 1.05e+77) {
		tmp = z * (b * ((i * (t / z)) - c));
	} else if (j <= 1.3e+180) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (x * ((y * z) - (t * a))) - (b * (z * c))
	t_2 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -2.5e+48:
		tmp = t_2
	elif j <= 1.12e+18:
		tmp = t_1
	elif j <= 1.05e+77:
		tmp = z * (b * ((i * (t / z)) - c))
	elif j <= 1.3e+180:
		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(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(z * c)))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -2.5e+48)
		tmp = t_2;
	elseif (j <= 1.12e+18)
		tmp = t_1;
	elseif (j <= 1.05e+77)
		tmp = Float64(z * Float64(b * Float64(Float64(i * Float64(t / z)) - c)));
	elseif (j <= 1.3e+180)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (x * ((y * z) - (t * a))) - (b * (z * c));
	t_2 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -2.5e+48)
		tmp = t_2;
	elseif (j <= 1.12e+18)
		tmp = t_1;
	elseif (j <= 1.05e+77)
		tmp = z * (b * ((i * (t / z)) - c));
	elseif (j <= 1.3e+180)
		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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.5e+48], t$95$2, If[LessEqual[j, 1.12e+18], t$95$1, If[LessEqual[j, 1.05e+77], N[(z * N[(b * N[(N[(i * N[(t / z), $MachinePrecision]), $MachinePrecision] - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.3e+180], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -2.49999999999999987e48 or 1.3000000000000001e180 < j

   1. Initial program 61.6%

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

   3. Taylor expanded in j around inf 72.1%

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

   if -2.49999999999999987e48 < j < 1.12e18 or 1.0499999999999999e77 < j < 1.3000000000000001e180

   1. Initial program 73.6%

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

      1. sub-neg 73.6%

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

      2. distribute-rgt-in 73.0%

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

      3. distribute-rgt-neg-in 73.0%

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

   4. Applied egg-rr 73.0%

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

   5. Taylor expanded in j around 0 71.3%

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

      1. mul-1-neg 71.3%

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

      2. associate-*r* 72.5%

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

      3. distribute-lft-neg-in 72.5%

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

      4. mul-1-neg 72.5%

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

      5. *-commutative 72.5%

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

      6. distribute-rgt-in 74.2%

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

      7. +-commutative 74.2%

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

      8. mul-1-neg 74.2%

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

      9. unsub-neg 74.2%

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

      10. *-commutative 74.2%

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

      11. *-commutative 74.2%

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

      12. *-commutative 74.2%

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

      13. *-commutative 74.2%

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

   7. Simplified 74.2%

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

   8. Taylor expanded in c around inf 65.6%

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

   if 1.12e18 < j < 1.0499999999999999e77

   1. Initial program 83.1%

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

   3. Taylor expanded in a around -inf 91.3%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in b around inf 67.0%

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

      1. mul-1-neg 67.0%

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

      2. distribute-rgt-neg-in 67.0%

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

      3. distribute-lft-neg-in 67.0%

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

      4. div-sub 67.0%

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

      5. *-commutative 67.0%

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

   8. Simplified 67.0%

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

   9. Taylor expanded in z around inf 59.6%

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

       1. +-commutative 59.6%

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

       2. associate-/l* 59.6%

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

       3. mul-1-neg 59.6%

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

       4. distribute-rgt-neg-in 59.6%

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

       5. distribute-lft-out 67.9%

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

       6. unsub-neg 67.9%

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

       7. associate-/l* 68.1%

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

   11. Simplified 68.1%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.5 \cdot 10^{+48}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 1.12 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.05 \cdot 10^{+77}:\\ \;\;\;\;z \cdot \left(b \cdot \left(i \cdot \frac{t}{z} - c\right)\right)\\ \mathbf{elif}\;j \leq 1.3 \cdot 10^{+180}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 28.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -4.05 \cdot 10^{+155}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -6000:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq -1.25 \cdot 10^{-272}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;i \leq 3.4 \cdot 10^{-18}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 1.4 \cdot 10^{+276}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(j \cdot \left(-i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -4.05e+155)
   (* t (* b i))
   (if (<= i -6000.0)
     (* z (* x y))
     (if (<= i -1.25e-272)
       (* j (* a c))
       (if (<= i 3.4e-18)
         (* y (* x z))
         (if (<= i 1.4e+276) (* b (* t i)) (* y (* j (- i)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -4.05e+155) {
		tmp = t * (b * i);
	} else if (i <= -6000.0) {
		tmp = z * (x * y);
	} else if (i <= -1.25e-272) {
		tmp = j * (a * c);
	} else if (i <= 3.4e-18) {
		tmp = y * (x * z);
	} else if (i <= 1.4e+276) {
		tmp = b * (t * i);
	} else {
		tmp = y * (j * -i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (i <= (-4.05d+155)) then
        tmp = t * (b * i)
    else if (i <= (-6000.0d0)) then
        tmp = z * (x * y)
    else if (i <= (-1.25d-272)) then
        tmp = j * (a * c)
    else if (i <= 3.4d-18) then
        tmp = y * (x * z)
    else if (i <= 1.4d+276) then
        tmp = b * (t * i)
    else
        tmp = y * (j * -i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -4.05e+155) {
		tmp = t * (b * i);
	} else if (i <= -6000.0) {
		tmp = z * (x * y);
	} else if (i <= -1.25e-272) {
		tmp = j * (a * c);
	} else if (i <= 3.4e-18) {
		tmp = y * (x * z);
	} else if (i <= 1.4e+276) {
		tmp = b * (t * i);
	} else {
		tmp = y * (j * -i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -4.05e+155:
		tmp = t * (b * i)
	elif i <= -6000.0:
		tmp = z * (x * y)
	elif i <= -1.25e-272:
		tmp = j * (a * c)
	elif i <= 3.4e-18:
		tmp = y * (x * z)
	elif i <= 1.4e+276:
		tmp = b * (t * i)
	else:
		tmp = y * (j * -i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -4.05e+155)
		tmp = Float64(t * Float64(b * i));
	elseif (i <= -6000.0)
		tmp = Float64(z * Float64(x * y));
	elseif (i <= -1.25e-272)
		tmp = Float64(j * Float64(a * c));
	elseif (i <= 3.4e-18)
		tmp = Float64(y * Float64(x * z));
	elseif (i <= 1.4e+276)
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(y * Float64(j * Float64(-i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -4.05e+155)
		tmp = t * (b * i);
	elseif (i <= -6000.0)
		tmp = z * (x * y);
	elseif (i <= -1.25e-272)
		tmp = j * (a * c);
	elseif (i <= 3.4e-18)
		tmp = y * (x * z);
	elseif (i <= 1.4e+276)
		tmp = b * (t * i);
	else
		tmp = y * (j * -i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -4.05e+155], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -6000.0], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.25e-272], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.4e-18], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.4e+276], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(y * N[(j * (-i)), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -4.05000000000000014e155

   1. Initial program 68.1%

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

      1. sub-neg 68.1%

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

      2. distribute-rgt-in 68.1%

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

      3. distribute-rgt-neg-in 68.1%

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

   4. Applied egg-rr 68.1%

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

   5. Taylor expanded in j around 0 58.9%

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

      1. mul-1-neg 58.9%

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

      2. associate-*r* 61.8%

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

      3. distribute-lft-neg-in 61.8%

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

      4. mul-1-neg 61.8%

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

      5. *-commutative 61.8%

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

      6. distribute-rgt-in 61.8%

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

      7. +-commutative 61.8%

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

      8. mul-1-neg 61.8%

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

      9. unsub-neg 61.8%

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

      10. *-commutative 61.8%

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

      11. *-commutative 61.8%

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

      12. *-commutative 61.8%

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

      13. *-commutative 61.8%

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

   7. Simplified 61.8%

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

   8. Taylor expanded in i around inf 41.3%

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

      1. *-commutative 41.3%

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

      2. associate-*r* 47.3%

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

      3. *-commutative 47.3%

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

      4. associate-*r* 53.4%

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

   10. Simplified 53.4%

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

   if -4.05000000000000014e155 < i < -6e3

   1. Initial program 71.8%

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

   3. Taylor expanded in z around inf 40.7%

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

      1. *-commutative 40.7%

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

      2. *-commutative 40.7%

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

   5. Simplified 40.7%

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

   6. Taylor expanded in y around inf 33.4%

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

      1. *-commutative 33.4%

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

   8. Simplified 33.4%

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

   if -6e3 < i < -1.24999999999999995e-272

   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 51.3%

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

      1. +-commutative 51.3%

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

      2. mul-1-neg 51.3%

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

      3. unsub-neg 51.3%

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

      4. *-commutative 51.3%

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

   5. Simplified 51.3%

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

   6. Taylor expanded in j around inf 29.3%

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

      1. associate-*r* 40.2%

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

   8. Simplified 40.2%

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

   if -1.24999999999999995e-272 < i < 3.40000000000000001e-18

   1. Initial program 74.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 49.9%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 49.9%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

      2. *-commutative 49.9%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) \]

   5. Simplified 49.9%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   6. Taylor expanded in y around inf 28.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-commutative 28.1%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

      2. associate-*r* 32.3%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   8. Simplified 32.3%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if 3.40000000000000001e-18 < i < 1.39999999999999997e276

   1. Initial program 66.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 44.0%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 44.0%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x - b \cdot i\right)\right)} \]

      2. *-commutative 44.0%

         \[\leadsto t \cdot \left(-1 \cdot \left(a \cdot x - \color{blue}{i \cdot b}\right)\right) \]

   5. Simplified 44.0%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x - i \cdot b\right)\right)} \]

   6. Taylor expanded in a around 0 45.2%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 45.2%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   8. Simplified 45.2%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]

   if 1.39999999999999997e276 < 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. Step-by-step derivation

      1. sub-neg 0.0%

         \[\leadsto \left(x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. distribute-rgt-in 0.0%

         \[\leadsto \left(\color{blue}{\left(\left(y \cdot z\right) \cdot x + \left(-t \cdot a\right) \cdot x\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. distribute-rgt-neg-in 0.0%

         \[\leadsto \left(\left(\left(y \cdot z\right) \cdot x + \color{blue}{\left(t \cdot \left(-a\right)\right)} \cdot x\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 0.0%

      \[\leadsto \left(\color{blue}{\left(\left(y \cdot z\right) \cdot x + \left(t \cdot \left(-a\right)\right) \cdot x\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in i around inf 57.1%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 57.1%

         \[\leadsto i \cdot \left(-1 \cdot \left(j \cdot y\right) - \color{blue}{\left(-1 \cdot b\right) \cdot t}\right) \]

      2. neg-mul-1 57.1%

         \[\leadsto i \cdot \left(-1 \cdot \left(j \cdot y\right) - \color{blue}{\left(-b\right)} \cdot t\right) \]

      3. cancel-sign-sub 57.1%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]

      4. +-commutative 57.1%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      5. mul-1-neg 57.1%

         \[\leadsto i \cdot \left(b \cdot t + \color{blue}{\left(-j \cdot y\right)}\right) \]

      6. unsub-neg 57.1%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t - j \cdot y\right)} \]

      7. *-commutative 57.1%

         \[\leadsto i \cdot \left(\color{blue}{t \cdot b} - j \cdot y\right) \]

   7. Simplified 57.1%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b - j \cdot y\right)} \]

   8. Taylor expanded in t around 0 57.9%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 57.9%

         \[\leadsto \color{blue}{-i \cdot \left(j \cdot y\right)} \]

      2. associate-*r* 71.6%

         \[\leadsto -\color{blue}{\left(i \cdot j\right) \cdot y} \]

   10. Simplified 71.6%

       \[\leadsto \color{blue}{-\left(i \cdot j\right) \cdot y} \]
3. Recombined 6 regimes into one program.

4. Final simplification 40.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4.05 \cdot 10^{+155}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -6000:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq -1.25 \cdot 10^{-272}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;i \leq 3.4 \cdot 10^{-18}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 1.4 \cdot 10^{+276}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(j \cdot \left(-i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 65.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -6.5 \cdot 10^{+109}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 9 \cdot 10^{+45}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+197}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y - b \cdot \frac{c}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot \left(i \cdot \frac{t}{z} - c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))))
   (if (<= b -6.5e+109)
     t_1
     (if (<= b 9e+45)
       (- (* j (- (* a c) (* y i))) (* x (- (* t a) (* y z))))
       (if (<= b 1.25e+78)
         t_1
         (if (<= b 1.5e+197)
           (* z (* x (- y (* b (/ c x)))))
           (* z (* b (- (* i (/ t z)) c)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -6.5e+109) {
		tmp = t_1;
	} else if (b <= 9e+45) {
		tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)));
	} else if (b <= 1.25e+78) {
		tmp = t_1;
	} else if (b <= 1.5e+197) {
		tmp = z * (x * (y - (b * (c / x))));
	} else {
		tmp = z * (b * ((i * (t / z)) - c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    if (b <= (-6.5d+109)) then
        tmp = t_1
    else if (b <= 9d+45) then
        tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)))
    else if (b <= 1.25d+78) then
        tmp = t_1
    else if (b <= 1.5d+197) then
        tmp = z * (x * (y - (b * (c / x))))
    else
        tmp = z * (b * ((i * (t / z)) - c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -6.5e+109) {
		tmp = t_1;
	} else if (b <= 9e+45) {
		tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)));
	} else if (b <= 1.25e+78) {
		tmp = t_1;
	} else if (b <= 1.5e+197) {
		tmp = z * (x * (y - (b * (c / x))));
	} else {
		tmp = z * (b * ((i * (t / z)) - 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 b <= -6.5e+109:
		tmp = t_1
	elif b <= 9e+45:
		tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)))
	elif b <= 1.25e+78:
		tmp = t_1
	elif b <= 1.5e+197:
		tmp = z * (x * (y - (b * (c / x))))
	else:
		tmp = z * (b * ((i * (t / z)) - 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 (b <= -6.5e+109)
		tmp = t_1;
	elseif (b <= 9e+45)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) - Float64(x * Float64(Float64(t * a) - Float64(y * z))));
	elseif (b <= 1.25e+78)
		tmp = t_1;
	elseif (b <= 1.5e+197)
		tmp = Float64(z * Float64(x * Float64(y - Float64(b * Float64(c / x)))));
	else
		tmp = Float64(z * Float64(b * Float64(Float64(i * Float64(t / z)) - 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 (b <= -6.5e+109)
		tmp = t_1;
	elseif (b <= 9e+45)
		tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)));
	elseif (b <= 1.25e+78)
		tmp = t_1;
	elseif (b <= 1.5e+197)
		tmp = z * (x * (y - (b * (c / x))));
	else
		tmp = z * (b * ((i * (t / z)) - 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[b, -6.5e+109], t$95$1, If[LessEqual[b, 9e+45], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.25e+78], t$95$1, If[LessEqual[b, 1.5e+197], N[(z * N[(x * N[(y - N[(b * N[(c / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(b * N[(N[(i * N[(t / z), $MachinePrecision]), $MachinePrecision] - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -6.5e109

   1. Initial program 68.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 67.0%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]

   if -6.5e109 < b < 8.9999999999999997e45

   1. Initial program 72.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 68.5%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   if 8.9999999999999997e45 < b < 1.24999999999999996e78

   1. Initial program 67.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg 67.1%

         \[\leadsto \left(x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. distribute-rgt-in 67.1%

         \[\leadsto \left(\color{blue}{\left(\left(y \cdot z\right) \cdot x + \left(-t \cdot a\right) \cdot x\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. distribute-rgt-neg-in 67.1%

         \[\leadsto \left(\left(\left(y \cdot z\right) \cdot x + \color{blue}{\left(t \cdot \left(-a\right)\right)} \cdot x\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 67.1%

      \[\leadsto \left(\color{blue}{\left(\left(y \cdot z\right) \cdot x + \left(t \cdot \left(-a\right)\right) \cdot x\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in j around 0 66.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 66.7%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      2. associate-*r* 67.1%

         \[\leadsto \left(\left(-\color{blue}{\left(a \cdot t\right) \cdot x}\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      3. distribute-lft-neg-in 67.1%

         \[\leadsto \left(\color{blue}{\left(-a \cdot t\right) \cdot x} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      4. mul-1-neg 67.1%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(a \cdot t\right)\right)} \cdot x + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      5. *-commutative 67.1%

         \[\leadsto \left(\left(-1 \cdot \left(a \cdot t\right)\right) \cdot x + \color{blue}{\left(y \cdot z\right) \cdot x}\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      6. distribute-rgt-in 67.1%

         \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)} - b \cdot \left(c \cdot z - i \cdot t\right) \]

      7. +-commutative 67.1%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z + -1 \cdot \left(a \cdot t\right)\right)} - b \cdot \left(c \cdot z - i \cdot t\right) \]

      8. mul-1-neg 67.1%

         \[\leadsto x \cdot \left(y \cdot z + \color{blue}{\left(-a \cdot t\right)}\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      9. unsub-neg 67.1%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z - a \cdot t\right)} - b \cdot \left(c \cdot z - i \cdot t\right) \]

      10. *-commutative 67.1%

          \[\leadsto x \cdot \left(\color{blue}{z \cdot y} - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      11. *-commutative 67.1%

          \[\leadsto x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right) \]

      12. *-commutative 67.1%

          \[\leadsto x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right) \]

      13. *-commutative 67.1%

          \[\leadsto x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(\color{blue}{c \cdot z} - t \cdot i\right) \]

   7. Simplified 67.1%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

   8. Taylor expanded in x around 0 89.4%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 89.4%

         \[\leadsto \color{blue}{\left(-1 \cdot b\right) \cdot \left(c \cdot z - i \cdot t\right)} \]

      2. *-commutative 89.4%

         \[\leadsto \color{blue}{\left(b \cdot -1\right)} \cdot \left(c \cdot z - i \cdot t\right) \]

      3. associate-*r* 89.4%

         \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \left(c \cdot z - i \cdot t\right)\right)} \]

      4. mul-1-neg 89.4%

         \[\leadsto b \cdot \color{blue}{\left(-\left(c \cdot z - i \cdot t\right)\right)} \]

      5. neg-sub0 89.4%

         \[\leadsto b \cdot \color{blue}{\left(0 - \left(c \cdot z - i \cdot t\right)\right)} \]

      6. associate--r- 89.4%

         \[\leadsto b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)} \]

      7. neg-sub0 89.4%

         \[\leadsto b \cdot \left(\color{blue}{\left(-c \cdot z\right)} + i \cdot t\right) \]

      8. +-commutative 89.4%

         \[\leadsto b \cdot \color{blue}{\left(i \cdot t + \left(-c \cdot z\right)\right)} \]

      9. sub-neg 89.4%

         \[\leadsto b \cdot \color{blue}{\left(i \cdot t - c \cdot z\right)} \]

      10. *-commutative 89.4%

          \[\leadsto b \cdot \left(\color{blue}{t \cdot i} - c \cdot z\right) \]

      11. *-commutative 89.4%

          \[\leadsto b \cdot \left(t \cdot i - \color{blue}{z \cdot c}\right) \]

   10. Simplified 89.4%

       \[\leadsto \color{blue}{b \cdot \left(t \cdot i - z \cdot c\right)} \]

   if 1.24999999999999996e78 < b < 1.5000000000000001e197

   1. Initial program 62.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 70.4%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 70.4%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

      2. *-commutative 70.4%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) \]

   5. Simplified 70.4%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   6. Taylor expanded in x around inf 74.5%

      \[\leadsto z \cdot \color{blue}{\left(x \cdot \left(y + -1 \cdot \frac{b \cdot c}{x}\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 74.5%

         \[\leadsto z \cdot \left(x \cdot \left(y + \color{blue}{\left(-\frac{b \cdot c}{x}\right)}\right)\right) \]

      2. unsub-neg 74.5%

         \[\leadsto z \cdot \left(x \cdot \color{blue}{\left(y - \frac{b \cdot c}{x}\right)}\right) \]

      3. associate-/l* 74.5%

         \[\leadsto z \cdot \left(x \cdot \left(y - \color{blue}{b \cdot \frac{c}{x}}\right)\right) \]

   8. Simplified 74.5%

      \[\leadsto z \cdot \color{blue}{\left(x \cdot \left(y - b \cdot \frac{c}{x}\right)\right)} \]

   if 1.5000000000000001e197 < b

   1. Initial program 69.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf 70.0%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(-1 \cdot \left(c \cdot j\right) + \left(-1 \cdot \frac{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}{a} + t \cdot x\right)\right)\right)} \]

   5. Simplified 66.4%

      \[\leadsto \color{blue}{\left(\left(t \cdot x - \frac{y \cdot \left(z \cdot x - j \cdot i\right) + b \cdot \left(i \cdot t - c \cdot z\right)}{a}\right) - j \cdot c\right) \cdot \left(-a\right)} \]

   6. Taylor expanded in b around inf 70.2%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(b \cdot \left(\frac{c \cdot z}{a} - \frac{i \cdot t}{a}\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 70.2%

         \[\leadsto \color{blue}{-a \cdot \left(b \cdot \left(\frac{c \cdot z}{a} - \frac{i \cdot t}{a}\right)\right)} \]

      2. distribute-rgt-neg-in 70.2%

         \[\leadsto \color{blue}{a \cdot \left(-b \cdot \left(\frac{c \cdot z}{a} - \frac{i \cdot t}{a}\right)\right)} \]

      3. distribute-lft-neg-in 70.2%

         \[\leadsto a \cdot \color{blue}{\left(\left(-b\right) \cdot \left(\frac{c \cdot z}{a} - \frac{i \cdot t}{a}\right)\right)} \]

      4. div-sub 70.2%

         \[\leadsto a \cdot \left(\left(-b\right) \cdot \color{blue}{\frac{c \cdot z - i \cdot t}{a}}\right) \]

      5. *-commutative 70.2%

         \[\leadsto a \cdot \left(\left(-b\right) \cdot \frac{c \cdot z - \color{blue}{t \cdot i}}{a}\right) \]

   8. Simplified 70.2%

      \[\leadsto \color{blue}{a \cdot \left(\left(-b\right) \cdot \frac{c \cdot z - t \cdot i}{a}\right)} \]

   9. Taylor expanded in z around inf 61.7%

      \[\leadsto \color{blue}{z \cdot \left(-1 \cdot \left(b \cdot c\right) + \frac{b \cdot \left(i \cdot t\right)}{z}\right)} \]
   10. Step-by-step derivation

       1. +-commutative 61.7%

          \[\leadsto z \cdot \color{blue}{\left(\frac{b \cdot \left(i \cdot t\right)}{z} + -1 \cdot \left(b \cdot c\right)\right)} \]

       2. associate-/l* 65.6%

          \[\leadsto z \cdot \left(\color{blue}{b \cdot \frac{i \cdot t}{z}} + -1 \cdot \left(b \cdot c\right)\right) \]

       3. mul-1-neg 65.6%

          \[\leadsto z \cdot \left(b \cdot \frac{i \cdot t}{z} + \color{blue}{\left(-b \cdot c\right)}\right) \]

       4. distribute-rgt-neg-in 65.6%

          \[\leadsto z \cdot \left(b \cdot \frac{i \cdot t}{z} + \color{blue}{b \cdot \left(-c\right)}\right) \]

       5. distribute-lft-out 84.8%

          \[\leadsto z \cdot \color{blue}{\left(b \cdot \left(\frac{i \cdot t}{z} + \left(-c\right)\right)\right)} \]

       6. unsub-neg 84.8%

          \[\leadsto z \cdot \left(b \cdot \color{blue}{\left(\frac{i \cdot t}{z} - c\right)}\right) \]

       7. associate-/l* 84.8%

          \[\leadsto z \cdot \left(b \cdot \left(\color{blue}{i \cdot \frac{t}{z}} - c\right)\right) \]

   11. Simplified 84.8%

       \[\leadsto \color{blue}{z \cdot \left(b \cdot \left(i \cdot \frac{t}{z} - c\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.5 \cdot 10^{+109}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 9 \cdot 10^{+45}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{+78}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+197}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y - b \cdot \frac{c}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot \left(i \cdot \frac{t}{z} - c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 28.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+206}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq -1.26 \cdot 10^{-55}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{-279}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;y \leq 3.75 \cdot 10^{-17}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+171}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -1.25e+206)
   (* i (* y (- j)))
   (if (<= y -1.26e-55)
     (* y (* x z))
     (if (<= y 1.16e-279)
       (* j (* a c))
       (if (<= y 3.75e-17)
         (* a (* t (- x)))
         (if (<= y 3.3e+171) (* t (* b i)) (* x (* y z))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -1.25e+206) {
		tmp = i * (y * -j);
	} else if (y <= -1.26e-55) {
		tmp = y * (x * z);
	} else if (y <= 1.16e-279) {
		tmp = j * (a * c);
	} else if (y <= 3.75e-17) {
		tmp = a * (t * -x);
	} else if (y <= 3.3e+171) {
		tmp = t * (b * i);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-1.25d+206)) then
        tmp = i * (y * -j)
    else if (y <= (-1.26d-55)) then
        tmp = y * (x * z)
    else if (y <= 1.16d-279) then
        tmp = j * (a * c)
    else if (y <= 3.75d-17) then
        tmp = a * (t * -x)
    else if (y <= 3.3d+171) then
        tmp = t * (b * i)
    else
        tmp = x * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -1.25e+206) {
		tmp = i * (y * -j);
	} else if (y <= -1.26e-55) {
		tmp = y * (x * z);
	} else if (y <= 1.16e-279) {
		tmp = j * (a * c);
	} else if (y <= 3.75e-17) {
		tmp = a * (t * -x);
	} else if (y <= 3.3e+171) {
		tmp = t * (b * i);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -1.25e+206:
		tmp = i * (y * -j)
	elif y <= -1.26e-55:
		tmp = y * (x * z)
	elif y <= 1.16e-279:
		tmp = j * (a * c)
	elif y <= 3.75e-17:
		tmp = a * (t * -x)
	elif y <= 3.3e+171:
		tmp = t * (b * i)
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -1.25e+206)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (y <= -1.26e-55)
		tmp = Float64(y * Float64(x * z));
	elseif (y <= 1.16e-279)
		tmp = Float64(j * Float64(a * c));
	elseif (y <= 3.75e-17)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (y <= 3.3e+171)
		tmp = Float64(t * Float64(b * i));
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -1.25e+206)
		tmp = i * (y * -j);
	elseif (y <= -1.26e-55)
		tmp = y * (x * z);
	elseif (y <= 1.16e-279)
		tmp = j * (a * c);
	elseif (y <= 3.75e-17)
		tmp = a * (t * -x);
	elseif (y <= 3.3e+171)
		tmp = t * (b * i);
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -1.25e+206], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.26e-55], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.16e-279], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.75e-17], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.3e+171], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -1.25e206

   1. Initial program 46.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg 46.0%

         \[\leadsto \left(x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. distribute-rgt-in 41.4%

         \[\leadsto \left(\color{blue}{\left(\left(y \cdot z\right) \cdot x + \left(-t \cdot a\right) \cdot x\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. distribute-rgt-neg-in 41.4%

         \[\leadsto \left(\left(\left(y \cdot z\right) \cdot x + \color{blue}{\left(t \cdot \left(-a\right)\right)} \cdot x\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 41.4%

      \[\leadsto \left(\color{blue}{\left(\left(y \cdot z\right) \cdot x + \left(t \cdot \left(-a\right)\right) \cdot x\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in i around inf 59.8%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 59.8%

         \[\leadsto i \cdot \left(-1 \cdot \left(j \cdot y\right) - \color{blue}{\left(-1 \cdot b\right) \cdot t}\right) \]

      2. neg-mul-1 59.8%

         \[\leadsto i \cdot \left(-1 \cdot \left(j \cdot y\right) - \color{blue}{\left(-b\right)} \cdot t\right) \]

      3. cancel-sign-sub 59.8%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]

      4. +-commutative 59.8%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      5. mul-1-neg 59.8%

         \[\leadsto i \cdot \left(b \cdot t + \color{blue}{\left(-j \cdot y\right)}\right) \]

      6. unsub-neg 59.8%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t - j \cdot y\right)} \]

      7. *-commutative 59.8%

         \[\leadsto i \cdot \left(\color{blue}{t \cdot b} - j \cdot y\right) \]

   7. Simplified 59.8%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b - j \cdot y\right)} \]

   8. Taylor expanded in t around 0 64.0%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 64.0%

         \[\leadsto \color{blue}{-i \cdot \left(j \cdot y\right)} \]

      2. *-commutative 64.0%

         \[\leadsto -i \cdot \color{blue}{\left(y \cdot j\right)} \]

      3. distribute-rgt-neg-in 64.0%

         \[\leadsto \color{blue}{i \cdot \left(-y \cdot j\right)} \]

      4. distribute-lft-neg-in 64.0%

         \[\leadsto i \cdot \color{blue}{\left(\left(-y\right) \cdot j\right)} \]

   10. Simplified 64.0%

       \[\leadsto \color{blue}{i \cdot \left(\left(-y\right) \cdot j\right)} \]

   if -1.25e206 < y < -1.2599999999999999e-55

   1. Initial program 71.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 55.7%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 55.7%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

      2. *-commutative 55.7%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) \]

   5. Simplified 55.7%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   6. Taylor expanded in y around inf 35.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-commutative 35.3%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

      2. associate-*r* 38.6%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   8. Simplified 38.6%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if -1.2599999999999999e-55 < y < 1.16e-279

   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 a around inf 48.1%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 48.1%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 48.1%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 48.1%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 48.1%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 48.1%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around inf 34.6%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 38.9%

         \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]

   8. Simplified 38.9%

      \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]

   if 1.16e-279 < y < 3.74999999999999992e-17

   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 50.7%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 50.7%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 50.7%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 50.7%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 50.7%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 50.7%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around 0 37.4%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 37.4%

         \[\leadsto a \cdot \color{blue}{\left(-t \cdot x\right)} \]

      2. distribute-lft-neg-out 37.4%

         \[\leadsto a \cdot \color{blue}{\left(\left(-t\right) \cdot x\right)} \]

      3. *-commutative 37.4%

         \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   8. Simplified 37.4%

      \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   if 3.74999999999999992e-17 < y < 3.29999999999999991e171

   1. Initial program 69.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg 69.5%

         \[\leadsto \left(x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. distribute-rgt-in 69.5%

         \[\leadsto \left(\color{blue}{\left(\left(y \cdot z\right) \cdot x + \left(-t \cdot a\right) \cdot x\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. distribute-rgt-neg-in 69.5%

         \[\leadsto \left(\left(\left(y \cdot z\right) \cdot x + \color{blue}{\left(t \cdot \left(-a\right)\right)} \cdot x\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 69.5%

      \[\leadsto \left(\color{blue}{\left(\left(y \cdot z\right) \cdot x + \left(t \cdot \left(-a\right)\right) \cdot x\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in j around 0 54.4%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 54.4%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      2. associate-*r* 52.1%

         \[\leadsto \left(\left(-\color{blue}{\left(a \cdot t\right) \cdot x}\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      3. distribute-lft-neg-in 52.1%

         \[\leadsto \left(\color{blue}{\left(-a \cdot t\right) \cdot x} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      4. mul-1-neg 52.1%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(a \cdot t\right)\right)} \cdot x + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      5. *-commutative 52.1%

         \[\leadsto \left(\left(-1 \cdot \left(a \cdot t\right)\right) \cdot x + \color{blue}{\left(y \cdot z\right) \cdot x}\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      6. distribute-rgt-in 52.1%

         \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)} - b \cdot \left(c \cdot z - i \cdot t\right) \]

      7. +-commutative 52.1%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z + -1 \cdot \left(a \cdot t\right)\right)} - b \cdot \left(c \cdot z - i \cdot t\right) \]

      8. mul-1-neg 52.1%

         \[\leadsto x \cdot \left(y \cdot z + \color{blue}{\left(-a \cdot t\right)}\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      9. unsub-neg 52.1%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z - a \cdot t\right)} - b \cdot \left(c \cdot z - i \cdot t\right) \]

      10. *-commutative 52.1%

          \[\leadsto x \cdot \left(\color{blue}{z \cdot y} - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      11. *-commutative 52.1%

          \[\leadsto x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right) \]

      12. *-commutative 52.1%

          \[\leadsto x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right) \]

      13. *-commutative 52.1%

          \[\leadsto x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(\color{blue}{c \cdot z} - t \cdot i\right) \]

   7. Simplified 52.1%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

   8. Taylor expanded in i around inf 37.2%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   9. Step-by-step derivation

      1. *-commutative 37.2%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

      2. associate-*r* 37.1%

         \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot i} \]

      3. *-commutative 37.1%

         \[\leadsto \color{blue}{\left(t \cdot b\right)} \cdot i \]

      4. associate-*r* 37.3%

         \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]

   10. Simplified 37.3%

       \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]

   if 3.29999999999999991e171 < y

   1. Initial program 50.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 68.6%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]

   4. Taylor expanded in y around inf 73.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   5. Step-by-step derivation

      1. *-commutative 73.3%

         \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

   6. Simplified 73.3%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+206}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq -1.26 \cdot 10^{-55}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{-279}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;y \leq 3.75 \cdot 10^{-17}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+171}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 28.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+206}:\\ \;\;\;\;y \cdot \left(j \cdot \left(-i\right)\right)\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-56}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-279}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-18}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+171}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -1.1e+206)
   (* y (* j (- i)))
   (if (<= y -3.4e-56)
     (* y (* x z))
     (if (<= y 1.22e-279)
       (* j (* a c))
       (if (<= y 1.7e-18)
         (* a (* t (- x)))
         (if (<= y 3.3e+171) (* t (* b i)) (* x (* y z))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -1.1e+206) {
		tmp = y * (j * -i);
	} else if (y <= -3.4e-56) {
		tmp = y * (x * z);
	} else if (y <= 1.22e-279) {
		tmp = j * (a * c);
	} else if (y <= 1.7e-18) {
		tmp = a * (t * -x);
	} else if (y <= 3.3e+171) {
		tmp = t * (b * i);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-1.1d+206)) then
        tmp = y * (j * -i)
    else if (y <= (-3.4d-56)) then
        tmp = y * (x * z)
    else if (y <= 1.22d-279) then
        tmp = j * (a * c)
    else if (y <= 1.7d-18) then
        tmp = a * (t * -x)
    else if (y <= 3.3d+171) then
        tmp = t * (b * i)
    else
        tmp = x * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -1.1e+206) {
		tmp = y * (j * -i);
	} else if (y <= -3.4e-56) {
		tmp = y * (x * z);
	} else if (y <= 1.22e-279) {
		tmp = j * (a * c);
	} else if (y <= 1.7e-18) {
		tmp = a * (t * -x);
	} else if (y <= 3.3e+171) {
		tmp = t * (b * i);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -1.1e+206:
		tmp = y * (j * -i)
	elif y <= -3.4e-56:
		tmp = y * (x * z)
	elif y <= 1.22e-279:
		tmp = j * (a * c)
	elif y <= 1.7e-18:
		tmp = a * (t * -x)
	elif y <= 3.3e+171:
		tmp = t * (b * i)
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -1.1e+206)
		tmp = Float64(y * Float64(j * Float64(-i)));
	elseif (y <= -3.4e-56)
		tmp = Float64(y * Float64(x * z));
	elseif (y <= 1.22e-279)
		tmp = Float64(j * Float64(a * c));
	elseif (y <= 1.7e-18)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (y <= 3.3e+171)
		tmp = Float64(t * Float64(b * i));
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -1.1e+206)
		tmp = y * (j * -i);
	elseif (y <= -3.4e-56)
		tmp = y * (x * z);
	elseif (y <= 1.22e-279)
		tmp = j * (a * c);
	elseif (y <= 1.7e-18)
		tmp = a * (t * -x);
	elseif (y <= 3.3e+171)
		tmp = t * (b * i);
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -1.1e+206], N[(y * N[(j * (-i)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.4e-56], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.22e-279], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e-18], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.3e+171], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -1.10000000000000001e206

   1. Initial program 46.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg 46.0%

         \[\leadsto \left(x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. distribute-rgt-in 41.4%

         \[\leadsto \left(\color{blue}{\left(\left(y \cdot z\right) \cdot x + \left(-t \cdot a\right) \cdot x\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. distribute-rgt-neg-in 41.4%

         \[\leadsto \left(\left(\left(y \cdot z\right) \cdot x + \color{blue}{\left(t \cdot \left(-a\right)\right)} \cdot x\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 41.4%

      \[\leadsto \left(\color{blue}{\left(\left(y \cdot z\right) \cdot x + \left(t \cdot \left(-a\right)\right) \cdot x\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in i around inf 59.8%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 59.8%

         \[\leadsto i \cdot \left(-1 \cdot \left(j \cdot y\right) - \color{blue}{\left(-1 \cdot b\right) \cdot t}\right) \]

      2. neg-mul-1 59.8%

         \[\leadsto i \cdot \left(-1 \cdot \left(j \cdot y\right) - \color{blue}{\left(-b\right)} \cdot t\right) \]

      3. cancel-sign-sub 59.8%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]

      4. +-commutative 59.8%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      5. mul-1-neg 59.8%

         \[\leadsto i \cdot \left(b \cdot t + \color{blue}{\left(-j \cdot y\right)}\right) \]

      6. unsub-neg 59.8%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t - j \cdot y\right)} \]

      7. *-commutative 59.8%

         \[\leadsto i \cdot \left(\color{blue}{t \cdot b} - j \cdot y\right) \]

   7. Simplified 59.8%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b - j \cdot y\right)} \]

   8. Taylor expanded in t around 0 64.0%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 64.0%

         \[\leadsto \color{blue}{-i \cdot \left(j \cdot y\right)} \]

      2. associate-*r* 59.6%

         \[\leadsto -\color{blue}{\left(i \cdot j\right) \cdot y} \]

   10. Simplified 59.6%

       \[\leadsto \color{blue}{-\left(i \cdot j\right) \cdot y} \]

   if -1.10000000000000001e206 < y < -3.39999999999999982e-56

   1. Initial program 71.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 55.7%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 55.7%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

      2. *-commutative 55.7%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) \]

   5. Simplified 55.7%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   6. Taylor expanded in y around inf 35.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-commutative 35.3%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

      2. associate-*r* 38.6%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   8. Simplified 38.6%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if -3.39999999999999982e-56 < y < 1.22000000000000002e-279

   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 a around inf 48.1%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 48.1%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 48.1%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 48.1%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 48.1%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 48.1%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around inf 34.6%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 38.9%

         \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]

   8. Simplified 38.9%

      \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]

   if 1.22000000000000002e-279 < y < 1.70000000000000001e-18

   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 50.7%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 50.7%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 50.7%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 50.7%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 50.7%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 50.7%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around 0 37.4%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 37.4%

         \[\leadsto a \cdot \color{blue}{\left(-t \cdot x\right)} \]

      2. distribute-lft-neg-out 37.4%

         \[\leadsto a \cdot \color{blue}{\left(\left(-t\right) \cdot x\right)} \]

      3. *-commutative 37.4%

         \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   8. Simplified 37.4%

      \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   if 1.70000000000000001e-18 < y < 3.29999999999999991e171

   1. Initial program 69.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg 69.5%

         \[\leadsto \left(x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. distribute-rgt-in 69.5%

         \[\leadsto \left(\color{blue}{\left(\left(y \cdot z\right) \cdot x + \left(-t \cdot a\right) \cdot x\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. distribute-rgt-neg-in 69.5%

         \[\leadsto \left(\left(\left(y \cdot z\right) \cdot x + \color{blue}{\left(t \cdot \left(-a\right)\right)} \cdot x\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 69.5%

      \[\leadsto \left(\color{blue}{\left(\left(y \cdot z\right) \cdot x + \left(t \cdot \left(-a\right)\right) \cdot x\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in j around 0 54.4%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 54.4%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      2. associate-*r* 52.1%

         \[\leadsto \left(\left(-\color{blue}{\left(a \cdot t\right) \cdot x}\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      3. distribute-lft-neg-in 52.1%

         \[\leadsto \left(\color{blue}{\left(-a \cdot t\right) \cdot x} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      4. mul-1-neg 52.1%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(a \cdot t\right)\right)} \cdot x + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      5. *-commutative 52.1%

         \[\leadsto \left(\left(-1 \cdot \left(a \cdot t\right)\right) \cdot x + \color{blue}{\left(y \cdot z\right) \cdot x}\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      6. distribute-rgt-in 52.1%

         \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)} - b \cdot \left(c \cdot z - i \cdot t\right) \]

      7. +-commutative 52.1%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z + -1 \cdot \left(a \cdot t\right)\right)} - b \cdot \left(c \cdot z - i \cdot t\right) \]

      8. mul-1-neg 52.1%

         \[\leadsto x \cdot \left(y \cdot z + \color{blue}{\left(-a \cdot t\right)}\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      9. unsub-neg 52.1%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z - a \cdot t\right)} - b \cdot \left(c \cdot z - i \cdot t\right) \]

      10. *-commutative 52.1%

          \[\leadsto x \cdot \left(\color{blue}{z \cdot y} - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      11. *-commutative 52.1%

          \[\leadsto x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right) \]

      12. *-commutative 52.1%

          \[\leadsto x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right) \]

      13. *-commutative 52.1%

          \[\leadsto x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(\color{blue}{c \cdot z} - t \cdot i\right) \]

   7. Simplified 52.1%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

   8. Taylor expanded in i around inf 37.2%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   9. Step-by-step derivation

      1. *-commutative 37.2%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

      2. associate-*r* 37.1%

         \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot i} \]

      3. *-commutative 37.1%

         \[\leadsto \color{blue}{\left(t \cdot b\right)} \cdot i \]

      4. associate-*r* 37.3%

         \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]

   10. Simplified 37.3%

       \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]

   if 3.29999999999999991e171 < y

   1. Initial program 50.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 68.6%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]

   4. Taylor expanded in y around inf 73.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   5. Step-by-step derivation

      1. *-commutative 73.3%

         \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

   6. Simplified 73.3%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+206}:\\ \;\;\;\;y \cdot \left(j \cdot \left(-i\right)\right)\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-56}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-279}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-18}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+171}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 27.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{+242}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{+199}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-288}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+170}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* x z))))
   (if (<= y -3.2e+242)
     t_1
     (if (<= y -5.4e+199)
       (* b (* t i))
       (if (<= y -2.9e-55)
         t_1
         (if (<= y -7.5e-288)
           (* a (* c j))
           (if (<= y 4.9e+170) (* i (* t b)) (* x (* y z)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (x * z);
	double tmp;
	if (y <= -3.2e+242) {
		tmp = t_1;
	} else if (y <= -5.4e+199) {
		tmp = b * (t * i);
	} else if (y <= -2.9e-55) {
		tmp = t_1;
	} else if (y <= -7.5e-288) {
		tmp = a * (c * j);
	} else if (y <= 4.9e+170) {
		tmp = i * (t * b);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (x * z)
    if (y <= (-3.2d+242)) then
        tmp = t_1
    else if (y <= (-5.4d+199)) then
        tmp = b * (t * i)
    else if (y <= (-2.9d-55)) then
        tmp = t_1
    else if (y <= (-7.5d-288)) then
        tmp = a * (c * j)
    else if (y <= 4.9d+170) then
        tmp = i * (t * b)
    else
        tmp = x * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (x * z);
	double tmp;
	if (y <= -3.2e+242) {
		tmp = t_1;
	} else if (y <= -5.4e+199) {
		tmp = b * (t * i);
	} else if (y <= -2.9e-55) {
		tmp = t_1;
	} else if (y <= -7.5e-288) {
		tmp = a * (c * j);
	} else if (y <= 4.9e+170) {
		tmp = i * (t * b);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (x * z)
	tmp = 0
	if y <= -3.2e+242:
		tmp = t_1
	elif y <= -5.4e+199:
		tmp = b * (t * i)
	elif y <= -2.9e-55:
		tmp = t_1
	elif y <= -7.5e-288:
		tmp = a * (c * j)
	elif y <= 4.9e+170:
		tmp = i * (t * b)
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(x * z))
	tmp = 0.0
	if (y <= -3.2e+242)
		tmp = t_1;
	elseif (y <= -5.4e+199)
		tmp = Float64(b * Float64(t * i));
	elseif (y <= -2.9e-55)
		tmp = t_1;
	elseif (y <= -7.5e-288)
		tmp = Float64(a * Float64(c * j));
	elseif (y <= 4.9e+170)
		tmp = Float64(i * Float64(t * b));
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * (x * z);
	tmp = 0.0;
	if (y <= -3.2e+242)
		tmp = t_1;
	elseif (y <= -5.4e+199)
		tmp = b * (t * i);
	elseif (y <= -2.9e-55)
		tmp = t_1;
	elseif (y <= -7.5e-288)
		tmp = a * (c * j);
	elseif (y <= 4.9e+170)
		tmp = i * (t * b);
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.2e+242], t$95$1, If[LessEqual[y, -5.4e+199], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.9e-55], t$95$1, If[LessEqual[y, -7.5e-288], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.9e+170], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.2000000000000002e242 or -5.3999999999999998e199 < y < -2.9e-55

   1. Initial program 66.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 56.3%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 56.3%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

      2. *-commutative 56.3%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) \]

   5. Simplified 56.3%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   6. Taylor expanded in y around inf 38.7%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-commutative 38.7%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

      2. associate-*r* 41.6%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   8. Simplified 41.6%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if -3.2000000000000002e242 < y < -5.3999999999999998e199

   1. Initial program 54.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 25.6%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 25.6%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x - b \cdot i\right)\right)} \]

      2. *-commutative 25.6%

         \[\leadsto t \cdot \left(-1 \cdot \left(a \cdot x - \color{blue}{i \cdot b}\right)\right) \]

   5. Simplified 25.6%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x - i \cdot b\right)\right)} \]

   6. Taylor expanded in a around 0 39.0%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 39.0%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   8. Simplified 39.0%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]

   if -2.9e-55 < y < -7.4999999999999998e-288

   1. Initial program 82.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 59.6%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 59.6%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 59.6%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 59.6%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 59.6%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 59.6%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around inf 39.1%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

   if -7.4999999999999998e-288 < y < 4.9000000000000004e170

   1. Initial program 75.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg 75.8%

         \[\leadsto \left(x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. distribute-rgt-in 75.8%

         \[\leadsto \left(\color{blue}{\left(\left(y \cdot z\right) \cdot x + \left(-t \cdot a\right) \cdot x\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. distribute-rgt-neg-in 75.8%

         \[\leadsto \left(\left(\left(y \cdot z\right) \cdot x + \color{blue}{\left(t \cdot \left(-a\right)\right)} \cdot x\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 75.8%

      \[\leadsto \left(\color{blue}{\left(\left(y \cdot z\right) \cdot x + \left(t \cdot \left(-a\right)\right) \cdot x\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in i around inf 38.3%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 38.3%

         \[\leadsto i \cdot \left(-1 \cdot \left(j \cdot y\right) - \color{blue}{\left(-1 \cdot b\right) \cdot t}\right) \]

      2. neg-mul-1 38.3%

         \[\leadsto i \cdot \left(-1 \cdot \left(j \cdot y\right) - \color{blue}{\left(-b\right)} \cdot t\right) \]

      3. cancel-sign-sub 38.3%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]

      4. +-commutative 38.3%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      5. mul-1-neg 38.3%

         \[\leadsto i \cdot \left(b \cdot t + \color{blue}{\left(-j \cdot y\right)}\right) \]

      6. unsub-neg 38.3%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t - j \cdot y\right)} \]

      7. *-commutative 38.3%

         \[\leadsto i \cdot \left(\color{blue}{t \cdot b} - j \cdot y\right) \]

   7. Simplified 38.3%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b - j \cdot y\right)} \]

   8. Taylor expanded in t around inf 31.3%

      \[\leadsto i \cdot \color{blue}{\left(b \cdot t\right)} \]
   9. Step-by-step derivation

      1. *-commutative 31.3%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b\right)} \]

   10. Simplified 31.3%

       \[\leadsto i \cdot \color{blue}{\left(t \cdot b\right)} \]

   if 4.9000000000000004e170 < y

   1. Initial program 47.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 65.6%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]

   4. Taylor expanded in y around inf 70.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   5. Step-by-step derivation

      1. *-commutative 70.1%

         \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

   6. Simplified 70.1%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 38.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+242}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{+199}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-55}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-288}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+170}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 59.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -6.2 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 8 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.4 \cdot 10^{+154}:\\ \;\;\;\;b \cdot \left(t \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (<= j -6.2e+48)
     t_1
     (if (<= j 8e-10)
       (- (* x (- (* y z) (* t a))) (* b (* z c)))
       (if (<= j 1.4e+154) (- (* b (* t i)) (* x (- (* t a) (* y z)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -6.2e+48) {
		tmp = t_1;
	} else if (j <= 8e-10) {
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c));
	} else if (j <= 1.4e+154) {
		tmp = (b * (t * i)) - (x * ((t * a) - (y * z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    if (j <= (-6.2d+48)) then
        tmp = t_1
    else if (j <= 8d-10) then
        tmp = (x * ((y * z) - (t * a))) - (b * (z * c))
    else if (j <= 1.4d+154) then
        tmp = (b * (t * i)) - (x * ((t * a) - (y * z)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -6.2e+48) {
		tmp = t_1;
	} else if (j <= 8e-10) {
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c));
	} else if (j <= 1.4e+154) {
		tmp = (b * (t * i)) - (x * ((t * a) - (y * z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -6.2e+48:
		tmp = t_1
	elif j <= 8e-10:
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c))
	elif j <= 1.4e+154:
		tmp = (b * (t * i)) - (x * ((t * a) - (y * z)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -6.2e+48)
		tmp = t_1;
	elseif (j <= 8e-10)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(z * c)));
	elseif (j <= 1.4e+154)
		tmp = Float64(Float64(b * Float64(t * i)) - Float64(x * Float64(Float64(t * a) - Float64(y * z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -6.2e+48)
		tmp = t_1;
	elseif (j <= 8e-10)
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c));
	elseif (j <= 1.4e+154)
		tmp = (b * (t * i)) - (x * ((t * a) - (y * z)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -6.2e+48], t$95$1, If[LessEqual[j, 8e-10], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.4e+154], N[(N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if j < -6.20000000000000011e48 or 1.4e154 < j

   1. Initial program 60.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 70.1%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]

   if -6.20000000000000011e48 < j < 8.00000000000000029e-10

   1. Initial program 72.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg 72.9%

         \[\leadsto \left(x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. distribute-rgt-in 72.3%

         \[\leadsto \left(\color{blue}{\left(\left(y \cdot z\right) \cdot x + \left(-t \cdot a\right) \cdot x\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. distribute-rgt-neg-in 72.3%

         \[\leadsto \left(\left(\left(y \cdot z\right) \cdot x + \color{blue}{\left(t \cdot \left(-a\right)\right)} \cdot x\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 72.3%

      \[\leadsto \left(\color{blue}{\left(\left(y \cdot z\right) \cdot x + \left(t \cdot \left(-a\right)\right) \cdot x\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in j around 0 74.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 74.2%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      2. associate-*r* 75.0%

         \[\leadsto \left(\left(-\color{blue}{\left(a \cdot t\right) \cdot x}\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      3. distribute-lft-neg-in 75.0%

         \[\leadsto \left(\color{blue}{\left(-a \cdot t\right) \cdot x} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      4. mul-1-neg 75.0%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(a \cdot t\right)\right)} \cdot x + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      5. *-commutative 75.0%

         \[\leadsto \left(\left(-1 \cdot \left(a \cdot t\right)\right) \cdot x + \color{blue}{\left(y \cdot z\right) \cdot x}\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      6. distribute-rgt-in 76.4%

         \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)} - b \cdot \left(c \cdot z - i \cdot t\right) \]

      7. +-commutative 76.4%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z + -1 \cdot \left(a \cdot t\right)\right)} - b \cdot \left(c \cdot z - i \cdot t\right) \]

      8. mul-1-neg 76.4%

         \[\leadsto x \cdot \left(y \cdot z + \color{blue}{\left(-a \cdot t\right)}\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      9. unsub-neg 76.4%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z - a \cdot t\right)} - b \cdot \left(c \cdot z - i \cdot t\right) \]

      10. *-commutative 76.4%

          \[\leadsto x \cdot \left(\color{blue}{z \cdot y} - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      11. *-commutative 76.4%

          \[\leadsto x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right) \]

      12. *-commutative 76.4%

          \[\leadsto x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right) \]

      13. *-commutative 76.4%

          \[\leadsto x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(\color{blue}{c \cdot z} - t \cdot i\right) \]

   7. Simplified 76.4%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

   8. Taylor expanded in c around inf 67.3%

      \[\leadsto x \cdot \left(z \cdot y - a \cdot t\right) - \color{blue}{b \cdot \left(c \cdot z\right)} \]

   if 8.00000000000000029e-10 < j < 1.4e154

   1. Initial program 83.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg 83.5%

         \[\leadsto \left(x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. distribute-rgt-in 83.5%

         \[\leadsto \left(\color{blue}{\left(\left(y \cdot z\right) \cdot x + \left(-t \cdot a\right) \cdot x\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. distribute-rgt-neg-in 83.5%

         \[\leadsto \left(\left(\left(y \cdot z\right) \cdot x + \color{blue}{\left(t \cdot \left(-a\right)\right)} \cdot x\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 83.5%

      \[\leadsto \left(\color{blue}{\left(\left(y \cdot z\right) \cdot x + \left(t \cdot \left(-a\right)\right) \cdot x\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in j around 0 63.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 63.0%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      2. associate-*r* 65.4%

         \[\leadsto \left(\left(-\color{blue}{\left(a \cdot t\right) \cdot x}\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      3. distribute-lft-neg-in 65.4%

         \[\leadsto \left(\color{blue}{\left(-a \cdot t\right) \cdot x} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      4. mul-1-neg 65.4%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(a \cdot t\right)\right)} \cdot x + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      5. *-commutative 65.4%

         \[\leadsto \left(\left(-1 \cdot \left(a \cdot t\right)\right) \cdot x + \color{blue}{\left(y \cdot z\right) \cdot x}\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      6. distribute-rgt-in 65.4%

         \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)} - b \cdot \left(c \cdot z - i \cdot t\right) \]

      7. +-commutative 65.4%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z + -1 \cdot \left(a \cdot t\right)\right)} - b \cdot \left(c \cdot z - i \cdot t\right) \]

      8. mul-1-neg 65.4%

         \[\leadsto x \cdot \left(y \cdot z + \color{blue}{\left(-a \cdot t\right)}\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      9. unsub-neg 65.4%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z - a \cdot t\right)} - b \cdot \left(c \cdot z - i \cdot t\right) \]

      10. *-commutative 65.4%

          \[\leadsto x \cdot \left(\color{blue}{z \cdot y} - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      11. *-commutative 65.4%

          \[\leadsto x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right) \]

      12. *-commutative 65.4%

          \[\leadsto x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right) \]

      13. *-commutative 65.4%

          \[\leadsto x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(\color{blue}{c \cdot z} - t \cdot i\right) \]

   7. Simplified 65.4%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

   8. Taylor expanded in c around 0 60.4%

      \[\leadsto x \cdot \left(z \cdot y - a \cdot t\right) - \color{blue}{-1 \cdot \left(b \cdot \left(i \cdot t\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 60.4%

         \[\leadsto x \cdot \left(z \cdot y - a \cdot t\right) - \color{blue}{\left(-1 \cdot b\right) \cdot \left(i \cdot t\right)} \]

      2. neg-mul-1 60.4%

         \[\leadsto x \cdot \left(z \cdot y - a \cdot t\right) - \color{blue}{\left(-b\right)} \cdot \left(i \cdot t\right) \]

   10. Simplified 60.4%

       \[\leadsto x \cdot \left(z \cdot y - a \cdot t\right) - \color{blue}{\left(-b\right) \cdot \left(i \cdot t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -6.2 \cdot 10^{+48}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 8 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.4 \cdot 10^{+154}:\\ \;\;\;\;b \cdot \left(t \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 40.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b\right)\\ \mathbf{if}\;b \leq -1060000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{+46}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{+77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+129}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* t b))))
   (if (<= b -1060000000000.0)
     t_1
     (if (<= b 1.35e+46)
       (* a (- (* c j) (* x t)))
       (if (<= b 3.6e+77)
         t_1
         (if (<= b 5.5e+129) (* a (* t (- x))) (* 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 t_1 = i * (t * b);
	double tmp;
	if (b <= -1060000000000.0) {
		tmp = t_1;
	} else if (b <= 1.35e+46) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= 3.6e+77) {
		tmp = t_1;
	} else if (b <= 5.5e+129) {
		tmp = a * (t * -x);
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = i * (t * b)
    if (b <= (-1060000000000.0d0)) then
        tmp = t_1
    else if (b <= 1.35d+46) then
        tmp = a * ((c * j) - (x * t))
    else if (b <= 3.6d+77) then
        tmp = t_1
    else if (b <= 5.5d+129) then
        tmp = a * (t * -x)
    else
        tmp = 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 t_1 = i * (t * b);
	double tmp;
	if (b <= -1060000000000.0) {
		tmp = t_1;
	} else if (b <= 1.35e+46) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= 3.6e+77) {
		tmp = t_1;
	} else if (b <= 5.5e+129) {
		tmp = a * (t * -x);
	} else {
		tmp = z * (b * -c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (t * b)
	tmp = 0
	if b <= -1060000000000.0:
		tmp = t_1
	elif b <= 1.35e+46:
		tmp = a * ((c * j) - (x * t))
	elif b <= 3.6e+77:
		tmp = t_1
	elif b <= 5.5e+129:
		tmp = a * (t * -x)
	else:
		tmp = z * (b * -c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(t * b))
	tmp = 0.0
	if (b <= -1060000000000.0)
		tmp = t_1;
	elseif (b <= 1.35e+46)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (b <= 3.6e+77)
		tmp = t_1;
	elseif (b <= 5.5e+129)
		tmp = Float64(a * Float64(t * Float64(-x)));
	else
		tmp = Float64(z * Float64(b * Float64(-c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * (t * b);
	tmp = 0.0;
	if (b <= -1060000000000.0)
		tmp = t_1;
	elseif (b <= 1.35e+46)
		tmp = a * ((c * j) - (x * t));
	elseif (b <= 3.6e+77)
		tmp = t_1;
	elseif (b <= 5.5e+129)
		tmp = a * (t * -x);
	else
		tmp = z * (b * -c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1060000000000.0], t$95$1, If[LessEqual[b, 1.35e+46], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.6e+77], t$95$1, If[LessEqual[b, 5.5e+129], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.06e12

   1. Initial program 69.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf 59.7%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(-1 \cdot \left(c \cdot j\right) + \left(-1 \cdot \frac{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}{a} + t \cdot x\right)\right)\right)} \]

   5. Simplified 59.5%

      \[\leadsto \color{blue}{\left(\left(t \cdot x - \frac{y \cdot \left(z \cdot x - j \cdot i\right) + b \cdot \left(i \cdot t - c \cdot z\right)}{a}\right) - j \cdot c\right) \cdot \left(-a\right)} \]

   6. Taylor expanded in b around inf 54.1%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(b \cdot \left(\frac{c \cdot z}{a} - \frac{i \cdot t}{a}\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 54.1%

         \[\leadsto \color{blue}{-a \cdot \left(b \cdot \left(\frac{c \cdot z}{a} - \frac{i \cdot t}{a}\right)\right)} \]

      2. distribute-rgt-neg-in 54.1%

         \[\leadsto \color{blue}{a \cdot \left(-b \cdot \left(\frac{c \cdot z}{a} - \frac{i \cdot t}{a}\right)\right)} \]

      3. distribute-lft-neg-in 54.1%

         \[\leadsto a \cdot \color{blue}{\left(\left(-b\right) \cdot \left(\frac{c \cdot z}{a} - \frac{i \cdot t}{a}\right)\right)} \]

      4. div-sub 54.1%

         \[\leadsto a \cdot \left(\left(-b\right) \cdot \color{blue}{\frac{c \cdot z - i \cdot t}{a}}\right) \]

      5. *-commutative 54.1%

         \[\leadsto a \cdot \left(\left(-b\right) \cdot \frac{c \cdot z - \color{blue}{t \cdot i}}{a}\right) \]

   8. Simplified 54.1%

      \[\leadsto \color{blue}{a \cdot \left(\left(-b\right) \cdot \frac{c \cdot z - t \cdot i}{a}\right)} \]

   9. Taylor expanded in c around 0 37.3%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 35.6%

          \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot t} \]

       2. *-commutative 35.6%

          \[\leadsto \color{blue}{\left(i \cdot b\right)} \cdot t \]

       3. associate-*r* 39.0%

          \[\leadsto \color{blue}{i \cdot \left(b \cdot t\right)} \]

   11. Simplified 39.0%

       \[\leadsto \color{blue}{i \cdot \left(b \cdot t\right)} \]

   if -1.06e12 < b < 1.3500000000000001e46

   1. Initial program 72.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 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%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 49.2%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 49.2%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   if 1.3500000000000001e46 < b < 3.5999999999999998e77

   1. Initial program 67.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg 67.1%

         \[\leadsto \left(x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. distribute-rgt-in 67.1%

         \[\leadsto \left(\color{blue}{\left(\left(y \cdot z\right) \cdot x + \left(-t \cdot a\right) \cdot x\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. distribute-rgt-neg-in 67.1%

         \[\leadsto \left(\left(\left(y \cdot z\right) \cdot x + \color{blue}{\left(t \cdot \left(-a\right)\right)} \cdot x\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 67.1%

      \[\leadsto \left(\color{blue}{\left(\left(y \cdot z\right) \cdot x + \left(t \cdot \left(-a\right)\right) \cdot x\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in i around inf 78.1%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 78.1%

         \[\leadsto i \cdot \left(-1 \cdot \left(j \cdot y\right) - \color{blue}{\left(-1 \cdot b\right) \cdot t}\right) \]

      2. neg-mul-1 78.1%

         \[\leadsto i \cdot \left(-1 \cdot \left(j \cdot y\right) - \color{blue}{\left(-b\right)} \cdot t\right) \]

      3. cancel-sign-sub 78.1%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]

      4. +-commutative 78.1%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      5. mul-1-neg 78.1%

         \[\leadsto i \cdot \left(b \cdot t + \color{blue}{\left(-j \cdot y\right)}\right) \]

      6. unsub-neg 78.1%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t - j \cdot y\right)} \]

      7. *-commutative 78.1%

         \[\leadsto i \cdot \left(\color{blue}{t \cdot b} - j \cdot y\right) \]

   7. Simplified 78.1%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b - j \cdot y\right)} \]

   8. Taylor expanded in t around inf 78.1%

      \[\leadsto i \cdot \color{blue}{\left(b \cdot t\right)} \]
   9. Step-by-step derivation

      1. *-commutative 78.1%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b\right)} \]

   10. Simplified 78.1%

       \[\leadsto i \cdot \color{blue}{\left(t \cdot b\right)} \]

   if 3.5999999999999998e77 < b < 5.49999999999999984e129

   1. Initial program 62.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 75.3%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 75.3%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 75.3%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 75.3%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 75.3%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 75.3%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around 0 75.4%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 75.4%

         \[\leadsto a \cdot \color{blue}{\left(-t \cdot x\right)} \]

      2. distribute-lft-neg-out 75.4%

         \[\leadsto a \cdot \color{blue}{\left(\left(-t\right) \cdot x\right)} \]

      3. *-commutative 75.4%

         \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   8. Simplified 75.4%

      \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   if 5.49999999999999984e129 < b

   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 67.6%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 67.6%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

      2. *-commutative 67.6%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) \]

   5. Simplified 67.6%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   6. Taylor expanded in y around 0 62.9%

      \[\leadsto z \cdot \color{blue}{\left(-1 \cdot \left(b \cdot c\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 62.9%

         \[\leadsto z \cdot \color{blue}{\left(-b \cdot c\right)} \]

      2. *-commutative 62.9%

         \[\leadsto z \cdot \left(-\color{blue}{c \cdot b}\right) \]

      3. distribute-rgt-neg-in 62.9%

         \[\leadsto z \cdot \color{blue}{\left(c \cdot \left(-b\right)\right)} \]

   8. Simplified 62.9%

      \[\leadsto z \cdot \color{blue}{\left(c \cdot \left(-b\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 51.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1060000000000:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{+46}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{+77}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+129}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 28.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.32 \cdot 10^{+156}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -62000:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq -6.2 \cdot 10^{-275}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;i \leq 2.7 \cdot 10^{-18}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -1.32e+156)
   (* t (* b i))
   (if (<= i -62000.0)
     (* z (* x y))
     (if (<= i -6.2e-275)
       (* j (* a c))
       (if (<= i 2.7e-18) (* y (* x 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 tmp;
	if (i <= -1.32e+156) {
		tmp = t * (b * i);
	} else if (i <= -62000.0) {
		tmp = z * (x * y);
	} else if (i <= -6.2e-275) {
		tmp = j * (a * c);
	} else if (i <= 2.7e-18) {
		tmp = y * (x * 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) :: tmp
    if (i <= (-1.32d+156)) then
        tmp = t * (b * i)
    else if (i <= (-62000.0d0)) then
        tmp = z * (x * y)
    else if (i <= (-6.2d-275)) then
        tmp = j * (a * c)
    else if (i <= 2.7d-18) then
        tmp = y * (x * 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 tmp;
	if (i <= -1.32e+156) {
		tmp = t * (b * i);
	} else if (i <= -62000.0) {
		tmp = z * (x * y);
	} else if (i <= -6.2e-275) {
		tmp = j * (a * c);
	} else if (i <= 2.7e-18) {
		tmp = y * (x * z);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -1.32e+156:
		tmp = t * (b * i)
	elif i <= -62000.0:
		tmp = z * (x * y)
	elif i <= -6.2e-275:
		tmp = j * (a * c)
	elif i <= 2.7e-18:
		tmp = y * (x * z)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -1.32e+156)
		tmp = Float64(t * Float64(b * i));
	elseif (i <= -62000.0)
		tmp = Float64(z * Float64(x * y));
	elseif (i <= -6.2e-275)
		tmp = Float64(j * Float64(a * c));
	elseif (i <= 2.7e-18)
		tmp = Float64(y * Float64(x * 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)
	tmp = 0.0;
	if (i <= -1.32e+156)
		tmp = t * (b * i);
	elseif (i <= -62000.0)
		tmp = z * (x * y);
	elseif (i <= -6.2e-275)
		tmp = j * (a * c);
	elseif (i <= 2.7e-18)
		tmp = y * (x * z);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -1.32e+156], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -62000.0], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -6.2e-275], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.7e-18], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -1.3199999999999999e156

   1. Initial program 68.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg 68.1%

         \[\leadsto \left(x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. distribute-rgt-in 68.1%

         \[\leadsto \left(\color{blue}{\left(\left(y \cdot z\right) \cdot x + \left(-t \cdot a\right) \cdot x\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. distribute-rgt-neg-in 68.1%

         \[\leadsto \left(\left(\left(y \cdot z\right) \cdot x + \color{blue}{\left(t \cdot \left(-a\right)\right)} \cdot x\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 68.1%

      \[\leadsto \left(\color{blue}{\left(\left(y \cdot z\right) \cdot x + \left(t \cdot \left(-a\right)\right) \cdot x\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in j around 0 58.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 58.9%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      2. associate-*r* 61.8%

         \[\leadsto \left(\left(-\color{blue}{\left(a \cdot t\right) \cdot x}\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      3. distribute-lft-neg-in 61.8%

         \[\leadsto \left(\color{blue}{\left(-a \cdot t\right) \cdot x} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      4. mul-1-neg 61.8%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(a \cdot t\right)\right)} \cdot x + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      5. *-commutative 61.8%

         \[\leadsto \left(\left(-1 \cdot \left(a \cdot t\right)\right) \cdot x + \color{blue}{\left(y \cdot z\right) \cdot x}\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      6. distribute-rgt-in 61.8%

         \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)} - b \cdot \left(c \cdot z - i \cdot t\right) \]

      7. +-commutative 61.8%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z + -1 \cdot \left(a \cdot t\right)\right)} - b \cdot \left(c \cdot z - i \cdot t\right) \]

      8. mul-1-neg 61.8%

         \[\leadsto x \cdot \left(y \cdot z + \color{blue}{\left(-a \cdot t\right)}\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      9. unsub-neg 61.8%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z - a \cdot t\right)} - b \cdot \left(c \cdot z - i \cdot t\right) \]

      10. *-commutative 61.8%

          \[\leadsto x \cdot \left(\color{blue}{z \cdot y} - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      11. *-commutative 61.8%

          \[\leadsto x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right) \]

      12. *-commutative 61.8%

          \[\leadsto x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right) \]

      13. *-commutative 61.8%

          \[\leadsto x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(\color{blue}{c \cdot z} - t \cdot i\right) \]

   7. Simplified 61.8%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

   8. Taylor expanded in i around inf 41.3%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   9. Step-by-step derivation

      1. *-commutative 41.3%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

      2. associate-*r* 47.3%

         \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot i} \]

      3. *-commutative 47.3%

         \[\leadsto \color{blue}{\left(t \cdot b\right)} \cdot i \]

      4. associate-*r* 53.4%

         \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]

   10. Simplified 53.4%

       \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]

   if -1.3199999999999999e156 < i < -62000

   1. Initial program 71.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 40.7%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 40.7%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

      2. *-commutative 40.7%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) \]

   5. Simplified 40.7%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   6. Taylor expanded in y around inf 33.4%

      \[\leadsto z \cdot \color{blue}{\left(x \cdot y\right)} \]
   7. Step-by-step derivation

      1. *-commutative 33.4%

         \[\leadsto z \cdot \color{blue}{\left(y \cdot x\right)} \]

   8. Simplified 33.4%

      \[\leadsto z \cdot \color{blue}{\left(y \cdot x\right)} \]

   if -62000 < i < -6.200000000000001e-275

   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 51.3%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 51.3%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 51.3%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 51.3%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 51.3%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 51.3%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around inf 29.3%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 40.2%

         \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]

   8. Simplified 40.2%

      \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]

   if -6.200000000000001e-275 < i < 2.69999999999999989e-18

   1. Initial program 74.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 49.9%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 49.9%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

      2. *-commutative 49.9%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) \]

   5. Simplified 49.9%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   6. Taylor expanded in y around inf 28.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-commutative 28.1%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

      2. associate-*r* 32.3%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   8. Simplified 32.3%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if 2.69999999999999989e-18 < i

   1. Initial program 59.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 41.0%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 41.0%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x - b \cdot i\right)\right)} \]

      2. *-commutative 41.0%

         \[\leadsto t \cdot \left(-1 \cdot \left(a \cdot x - \color{blue}{i \cdot b}\right)\right) \]

   5. Simplified 41.0%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x - i \cdot b\right)\right)} \]

   6. Taylor expanded in a around 0 42.0%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 42.0%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   8. Simplified 42.0%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 39.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.32 \cdot 10^{+156}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -62000:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq -6.2 \cdot 10^{-275}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;i \leq 2.7 \cdot 10^{-18}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 28.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -6.8 \cdot 10^{+155}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -3.5 \cdot 10^{-24}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq -1.75 \cdot 10^{-181}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 8 \cdot 10^{-19}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -6.8e+155)
   (* t (* b i))
   (if (<= i -3.5e-24)
     (* z (* x y))
     (if (<= i -1.75e-181)
       (* a (* c j))
       (if (<= i 8e-19) (* y (* x 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 tmp;
	if (i <= -6.8e+155) {
		tmp = t * (b * i);
	} else if (i <= -3.5e-24) {
		tmp = z * (x * y);
	} else if (i <= -1.75e-181) {
		tmp = a * (c * j);
	} else if (i <= 8e-19) {
		tmp = y * (x * 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) :: tmp
    if (i <= (-6.8d+155)) then
        tmp = t * (b * i)
    else if (i <= (-3.5d-24)) then
        tmp = z * (x * y)
    else if (i <= (-1.75d-181)) then
        tmp = a * (c * j)
    else if (i <= 8d-19) then
        tmp = y * (x * 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 tmp;
	if (i <= -6.8e+155) {
		tmp = t * (b * i);
	} else if (i <= -3.5e-24) {
		tmp = z * (x * y);
	} else if (i <= -1.75e-181) {
		tmp = a * (c * j);
	} else if (i <= 8e-19) {
		tmp = y * (x * z);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -6.8e+155:
		tmp = t * (b * i)
	elif i <= -3.5e-24:
		tmp = z * (x * y)
	elif i <= -1.75e-181:
		tmp = a * (c * j)
	elif i <= 8e-19:
		tmp = y * (x * z)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -6.8e+155)
		tmp = Float64(t * Float64(b * i));
	elseif (i <= -3.5e-24)
		tmp = Float64(z * Float64(x * y));
	elseif (i <= -1.75e-181)
		tmp = Float64(a * Float64(c * j));
	elseif (i <= 8e-19)
		tmp = Float64(y * Float64(x * 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)
	tmp = 0.0;
	if (i <= -6.8e+155)
		tmp = t * (b * i);
	elseif (i <= -3.5e-24)
		tmp = z * (x * y);
	elseif (i <= -1.75e-181)
		tmp = a * (c * j);
	elseif (i <= 8e-19)
		tmp = y * (x * z);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -6.8e+155], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -3.5e-24], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.75e-181], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 8e-19], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -6.8000000000000002e155

   1. Initial program 68.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg 68.1%

         \[\leadsto \left(x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. distribute-rgt-in 68.1%

         \[\leadsto \left(\color{blue}{\left(\left(y \cdot z\right) \cdot x + \left(-t \cdot a\right) \cdot x\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. distribute-rgt-neg-in 68.1%

         \[\leadsto \left(\left(\left(y \cdot z\right) \cdot x + \color{blue}{\left(t \cdot \left(-a\right)\right)} \cdot x\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 68.1%

      \[\leadsto \left(\color{blue}{\left(\left(y \cdot z\right) \cdot x + \left(t \cdot \left(-a\right)\right) \cdot x\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in j around 0 58.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 58.9%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      2. associate-*r* 61.8%

         \[\leadsto \left(\left(-\color{blue}{\left(a \cdot t\right) \cdot x}\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      3. distribute-lft-neg-in 61.8%

         \[\leadsto \left(\color{blue}{\left(-a \cdot t\right) \cdot x} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      4. mul-1-neg 61.8%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(a \cdot t\right)\right)} \cdot x + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      5. *-commutative 61.8%

         \[\leadsto \left(\left(-1 \cdot \left(a \cdot t\right)\right) \cdot x + \color{blue}{\left(y \cdot z\right) \cdot x}\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      6. distribute-rgt-in 61.8%

         \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)} - b \cdot \left(c \cdot z - i \cdot t\right) \]

      7. +-commutative 61.8%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z + -1 \cdot \left(a \cdot t\right)\right)} - b \cdot \left(c \cdot z - i \cdot t\right) \]

      8. mul-1-neg 61.8%

         \[\leadsto x \cdot \left(y \cdot z + \color{blue}{\left(-a \cdot t\right)}\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      9. unsub-neg 61.8%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z - a \cdot t\right)} - b \cdot \left(c \cdot z - i \cdot t\right) \]

      10. *-commutative 61.8%

          \[\leadsto x \cdot \left(\color{blue}{z \cdot y} - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      11. *-commutative 61.8%

          \[\leadsto x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right) \]

      12. *-commutative 61.8%

          \[\leadsto x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right) \]

      13. *-commutative 61.8%

          \[\leadsto x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(\color{blue}{c \cdot z} - t \cdot i\right) \]

   7. Simplified 61.8%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

   8. Taylor expanded in i around inf 41.3%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   9. Step-by-step derivation

      1. *-commutative 41.3%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

      2. associate-*r* 47.3%

         \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot i} \]

      3. *-commutative 47.3%

         \[\leadsto \color{blue}{\left(t \cdot b\right)} \cdot i \]

      4. associate-*r* 53.4%

         \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]

   10. Simplified 53.4%

       \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]

   if -6.8000000000000002e155 < i < -3.4999999999999996e-24

   1. Initial program 72.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 41.7%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 41.7%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

      2. *-commutative 41.7%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) \]

   5. Simplified 41.7%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   6. Taylor expanded in y around inf 32.7%

      \[\leadsto z \cdot \color{blue}{\left(x \cdot y\right)} \]
   7. Step-by-step derivation

      1. *-commutative 32.7%

         \[\leadsto z \cdot \color{blue}{\left(y \cdot x\right)} \]

   8. Simplified 32.7%

      \[\leadsto z \cdot \color{blue}{\left(y \cdot x\right)} \]

   if -3.4999999999999996e-24 < i < -1.74999999999999998e-181

   1. Initial program 79.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. 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%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 53.9%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 53.9%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around inf 37.9%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

   if -1.74999999999999998e-181 < i < 7.9999999999999998e-19

   1. Initial program 76.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 49.8%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 49.8%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

      2. *-commutative 49.8%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) \]

   5. Simplified 49.8%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   6. Taylor expanded in y around inf 26.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-commutative 26.1%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

      2. associate-*r* 29.5%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   8. Simplified 29.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if 7.9999999999999998e-19 < i

   1. Initial program 59.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 41.0%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 41.0%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x - b \cdot i\right)\right)} \]

      2. *-commutative 41.0%

         \[\leadsto t \cdot \left(-1 \cdot \left(a \cdot x - \color{blue}{i \cdot b}\right)\right) \]

   5. Simplified 41.0%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x - i \cdot b\right)\right)} \]

   6. Taylor expanded in a around 0 42.0%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 42.0%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   8. Simplified 42.0%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 37.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -6.8 \cdot 10^{+155}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -3.5 \cdot 10^{-24}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq -1.75 \cdot 10^{-181}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 8 \cdot 10^{-19}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 29.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;b \leq -3.9 \cdot 10^{-14}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-147}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-81}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))))
   (if (<= b -3.9e-14)
     (* i (* t b))
     (if (<= b -2e-147)
       t_1
       (if (<= b 8.5e-81)
         (* x (* y z))
         (if (<= b 8.5e+40) t_1 (* t (* b i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double tmp;
	if (b <= -3.9e-14) {
		tmp = i * (t * b);
	} else if (b <= -2e-147) {
		tmp = t_1;
	} else if (b <= 8.5e-81) {
		tmp = x * (y * z);
	} else if (b <= 8.5e+40) {
		tmp = t_1;
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (c * j)
    if (b <= (-3.9d-14)) then
        tmp = i * (t * b)
    else if (b <= (-2d-147)) then
        tmp = t_1
    else if (b <= 8.5d-81) then
        tmp = x * (y * z)
    else if (b <= 8.5d+40) then
        tmp = t_1
    else
        tmp = t * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double tmp;
	if (b <= -3.9e-14) {
		tmp = i * (t * b);
	} else if (b <= -2e-147) {
		tmp = t_1;
	} else if (b <= 8.5e-81) {
		tmp = x * (y * z);
	} else if (b <= 8.5e+40) {
		tmp = t_1;
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	tmp = 0
	if b <= -3.9e-14:
		tmp = i * (t * b)
	elif b <= -2e-147:
		tmp = t_1
	elif b <= 8.5e-81:
		tmp = x * (y * z)
	elif b <= 8.5e+40:
		tmp = t_1
	else:
		tmp = t * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	tmp = 0.0
	if (b <= -3.9e-14)
		tmp = Float64(i * Float64(t * b));
	elseif (b <= -2e-147)
		tmp = t_1;
	elseif (b <= 8.5e-81)
		tmp = Float64(x * Float64(y * z));
	elseif (b <= 8.5e+40)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (c * j);
	tmp = 0.0;
	if (b <= -3.9e-14)
		tmp = i * (t * b);
	elseif (b <= -2e-147)
		tmp = t_1;
	elseif (b <= 8.5e-81)
		tmp = x * (y * z);
	elseif (b <= 8.5e+40)
		tmp = t_1;
	else
		tmp = t * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.9e-14], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2e-147], t$95$1, If[LessEqual[b, 8.5e-81], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.5e+40], t$95$1, N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.8999999999999998e-14

   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 59.7%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(-1 \cdot \left(c \cdot j\right) + \left(-1 \cdot \frac{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}{a} + t \cdot x\right)\right)\right)} \]

   5. Simplified 58.0%

      \[\leadsto \color{blue}{\left(\left(t \cdot x - \frac{y \cdot \left(z \cdot x - j \cdot i\right) + b \cdot \left(i \cdot t - c \cdot z\right)}{a}\right) - j \cdot c\right) \cdot \left(-a\right)} \]

   6. Taylor expanded in b around inf 52.2%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(b \cdot \left(\frac{c \cdot z}{a} - \frac{i \cdot t}{a}\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 52.2%

         \[\leadsto \color{blue}{-a \cdot \left(b \cdot \left(\frac{c \cdot z}{a} - \frac{i \cdot t}{a}\right)\right)} \]

      2. distribute-rgt-neg-in 52.2%

         \[\leadsto \color{blue}{a \cdot \left(-b \cdot \left(\frac{c \cdot z}{a} - \frac{i \cdot t}{a}\right)\right)} \]

      3. distribute-lft-neg-in 52.2%

         \[\leadsto a \cdot \color{blue}{\left(\left(-b\right) \cdot \left(\frac{c \cdot z}{a} - \frac{i \cdot t}{a}\right)\right)} \]

      4. div-sub 52.2%

         \[\leadsto a \cdot \left(\left(-b\right) \cdot \color{blue}{\frac{c \cdot z - i \cdot t}{a}}\right) \]

      5. *-commutative 52.2%

         \[\leadsto a \cdot \left(\left(-b\right) \cdot \frac{c \cdot z - \color{blue}{t \cdot i}}{a}\right) \]

   8. Simplified 52.2%

      \[\leadsto \color{blue}{a \cdot \left(\left(-b\right) \cdot \frac{c \cdot z - t \cdot i}{a}\right)} \]

   9. Taylor expanded in c around 0 36.1%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 34.6%

          \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot t} \]

       2. *-commutative 34.6%

          \[\leadsto \color{blue}{\left(i \cdot b\right)} \cdot t \]

       3. associate-*r* 37.7%

          \[\leadsto \color{blue}{i \cdot \left(b \cdot t\right)} \]

   11. Simplified 37.7%

       \[\leadsto \color{blue}{i \cdot \left(b \cdot t\right)} \]

   if -3.8999999999999998e-14 < b < -1.9999999999999999e-147 or 8.5000000000000001e-81 < b < 8.49999999999999996e40

   1. Initial program 69.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 51.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 51.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 51.2%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 51.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 51.2%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 51.2%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around inf 36.2%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

   if -1.9999999999999999e-147 < b < 8.5000000000000001e-81

   1. Initial program 73.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 59.6%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]

   4. Taylor expanded in y around inf 35.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   5. Step-by-step derivation

      1. *-commutative 35.1%

         \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

   6. Simplified 35.1%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y\right)} \]

   if 8.49999999999999996e40 < b

   1. Initial program 66.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg 66.3%

         \[\leadsto \left(x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. distribute-rgt-in 66.3%

         \[\leadsto \left(\color{blue}{\left(\left(y \cdot z\right) \cdot x + \left(-t \cdot a\right) \cdot x\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. distribute-rgt-neg-in 66.3%

         \[\leadsto \left(\left(\left(y \cdot z\right) \cdot x + \color{blue}{\left(t \cdot \left(-a\right)\right)} \cdot x\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 66.3%

      \[\leadsto \left(\color{blue}{\left(\left(y \cdot z\right) \cdot x + \left(t \cdot \left(-a\right)\right) \cdot x\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in j around 0 66.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 66.7%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      2. associate-*r* 66.8%

         \[\leadsto \left(\left(-\color{blue}{\left(a \cdot t\right) \cdot x}\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      3. distribute-lft-neg-in 66.8%

         \[\leadsto \left(\color{blue}{\left(-a \cdot t\right) \cdot x} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      4. mul-1-neg 66.8%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(a \cdot t\right)\right)} \cdot x + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      5. *-commutative 66.8%

         \[\leadsto \left(\left(-1 \cdot \left(a \cdot t\right)\right) \cdot x + \color{blue}{\left(y \cdot z\right) \cdot x}\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      6. distribute-rgt-in 66.8%

         \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)} - b \cdot \left(c \cdot z - i \cdot t\right) \]

      7. +-commutative 66.8%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z + -1 \cdot \left(a \cdot t\right)\right)} - b \cdot \left(c \cdot z - i \cdot t\right) \]

      8. mul-1-neg 66.8%

         \[\leadsto x \cdot \left(y \cdot z + \color{blue}{\left(-a \cdot t\right)}\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      9. unsub-neg 66.8%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z - a \cdot t\right)} - b \cdot \left(c \cdot z - i \cdot t\right) \]

      10. *-commutative 66.8%

          \[\leadsto x \cdot \left(\color{blue}{z \cdot y} - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      11. *-commutative 66.8%

          \[\leadsto x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right) \]

      12. *-commutative 66.8%

          \[\leadsto x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right) \]

      13. *-commutative 66.8%

          \[\leadsto x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(\color{blue}{c \cdot z} - t \cdot i\right) \]

   7. Simplified 66.8%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

   8. Taylor expanded in i around inf 36.9%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   9. Step-by-step derivation

      1. *-commutative 36.9%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

      2. associate-*r* 36.9%

         \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot i} \]

      3. *-commutative 36.9%

         \[\leadsto \color{blue}{\left(t \cdot b\right)} \cdot i \]

      4. associate-*r* 40.2%

         \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]

   10. Simplified 40.2%

       \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 37.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.9 \cdot 10^{-14}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-147}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-81}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+40}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 52.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -420000 \lor \neg \left(b \leq 2.45 \cdot 10^{+34}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -420000.0) (not (<= b 2.45e+34)))
   (* b (- (* t i) (* z c)))
   (* a (- (* c j) (* x t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -420000.0) || !(b <= 2.45e+34)) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-420000.0d0)) .or. (.not. (b <= 2.45d+34))) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = a * ((c * j) - (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -420000.0) || !(b <= 2.45e+34)) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -420000.0) or not (b <= 2.45e+34):
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = a * ((c * j) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -420000.0) || !(b <= 2.45e+34))
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -420000.0) || ~((b <= 2.45e+34)))
		tmp = b * ((t * i) - (z * c));
	else
		tmp = a * ((c * j) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -420000.0], N[Not[LessEqual[b, 2.45e+34]], $MachinePrecision]], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if b < -4.2e5

   1. Initial program 70.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 59.1%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]

   if -4.2e5 < b < 2.4500000000000001e34

   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 50.9%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 50.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 50.9%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 50.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 50.9%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 50.9%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   if 2.4500000000000001e34 < b

   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. Step-by-step derivation

      1. sub-neg 66.8%

         \[\leadsto \left(x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. distribute-rgt-in 66.8%

         \[\leadsto \left(\color{blue}{\left(\left(y \cdot z\right) \cdot x + \left(-t \cdot a\right) \cdot x\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. distribute-rgt-neg-in 66.8%

         \[\leadsto \left(\left(\left(y \cdot z\right) \cdot x + \color{blue}{\left(t \cdot \left(-a\right)\right)} \cdot x\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 66.8%

      \[\leadsto \left(\color{blue}{\left(\left(y \cdot z\right) \cdot x + \left(t \cdot \left(-a\right)\right) \cdot x\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in j around 0 65.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 65.7%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      2. associate-*r* 65.8%

         \[\leadsto \left(\left(-\color{blue}{\left(a \cdot t\right) \cdot x}\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      3. distribute-lft-neg-in 65.8%

         \[\leadsto \left(\color{blue}{\left(-a \cdot t\right) \cdot x} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      4. mul-1-neg 65.8%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(a \cdot t\right)\right)} \cdot x + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      5. *-commutative 65.8%

         \[\leadsto \left(\left(-1 \cdot \left(a \cdot t\right)\right) \cdot x + \color{blue}{\left(y \cdot z\right) \cdot x}\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      6. distribute-rgt-in 65.8%

         \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)} - b \cdot \left(c \cdot z - i \cdot t\right) \]

      7. +-commutative 65.8%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z + -1 \cdot \left(a \cdot t\right)\right)} - b \cdot \left(c \cdot z - i \cdot t\right) \]

      8. mul-1-neg 65.8%

         \[\leadsto x \cdot \left(y \cdot z + \color{blue}{\left(-a \cdot t\right)}\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      9. unsub-neg 65.8%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z - a \cdot t\right)} - b \cdot \left(c \cdot z - i \cdot t\right) \]

      10. *-commutative 65.8%

          \[\leadsto x \cdot \left(\color{blue}{z \cdot y} - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      11. *-commutative 65.8%

          \[\leadsto x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right) \]

      12. *-commutative 65.8%

          \[\leadsto x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right) \]

      13. *-commutative 65.8%

          \[\leadsto x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(\color{blue}{c \cdot z} - t \cdot i\right) \]

   7. Simplified 65.8%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

   8. Taylor expanded in x around 0 70.2%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 70.2%

         \[\leadsto \color{blue}{\left(-1 \cdot b\right) \cdot \left(c \cdot z - i \cdot t\right)} \]

      2. *-commutative 70.2%

         \[\leadsto \color{blue}{\left(b \cdot -1\right)} \cdot \left(c \cdot z - i \cdot t\right) \]

      3. associate-*r* 70.2%

         \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \left(c \cdot z - i \cdot t\right)\right)} \]

      4. mul-1-neg 70.2%

         \[\leadsto b \cdot \color{blue}{\left(-\left(c \cdot z - i \cdot t\right)\right)} \]

      5. neg-sub0 70.2%

         \[\leadsto b \cdot \color{blue}{\left(0 - \left(c \cdot z - i \cdot t\right)\right)} \]

      6. associate--r- 70.2%

         \[\leadsto b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)} \]

      7. neg-sub0 70.2%

         \[\leadsto b \cdot \left(\color{blue}{\left(-c \cdot z\right)} + i \cdot t\right) \]

      8. +-commutative 70.2%

         \[\leadsto b \cdot \color{blue}{\left(i \cdot t + \left(-c \cdot z\right)\right)} \]

      9. sub-neg 70.2%

         \[\leadsto b \cdot \color{blue}{\left(i \cdot t - c \cdot z\right)} \]

      10. *-commutative 70.2%

          \[\leadsto b \cdot \left(\color{blue}{t \cdot i} - c \cdot z\right) \]

      11. *-commutative 70.2%

          \[\leadsto b \cdot \left(t \cdot i - \color{blue}{z \cdot c}\right) \]

   10. Simplified 70.2%

       \[\leadsto \color{blue}{b \cdot \left(t \cdot i - z \cdot c\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -420000 \lor \neg \left(b \leq 2.45 \cdot 10^{+34}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 52.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -700000 \lor \neg \left(b \leq 2.2 \cdot 10^{+35}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -700000.0) (not (<= b 2.2e+35)))
   (* b (- (* t i) (* z c)))
   (* a (- (* c j) (* x t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -700000.0) || !(b <= 2.2e+35)) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-700000.0d0)) .or. (.not. (b <= 2.2d+35))) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = a * ((c * j) - (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -700000.0) || !(b <= 2.2e+35)) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -700000.0) or not (b <= 2.2e+35):
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = a * ((c * j) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -700000.0) || !(b <= 2.2e+35))
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -700000.0) || ~((b <= 2.2e+35)))
		tmp = b * ((t * i) - (z * c));
	else
		tmp = a * ((c * j) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -700000.0], N[Not[LessEqual[b, 2.2e+35]], $MachinePrecision]], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if b < -7e5

   1. Initial program 70.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 59.1%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]

   if -7e5 < b < 2.1999999999999999e35

   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 50.9%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 50.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 50.9%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 50.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 50.9%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 50.9%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   if 2.1999999999999999e35 < b

   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. Step-by-step derivation

      1. sub-neg 66.8%

         \[\leadsto \left(x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. distribute-rgt-in 66.8%

         \[\leadsto \left(\color{blue}{\left(\left(y \cdot z\right) \cdot x + \left(-t \cdot a\right) \cdot x\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. distribute-rgt-neg-in 66.8%

         \[\leadsto \left(\left(\left(y \cdot z\right) \cdot x + \color{blue}{\left(t \cdot \left(-a\right)\right)} \cdot x\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 66.8%

      \[\leadsto \left(\color{blue}{\left(\left(y \cdot z\right) \cdot x + \left(t \cdot \left(-a\right)\right) \cdot x\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in b around inf 70.2%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 70.2%

         \[\leadsto b \cdot \left(\color{blue}{t \cdot i} - c \cdot z\right) \]

      2. *-commutative 70.2%

         \[\leadsto b \cdot \left(t \cdot i - \color{blue}{z \cdot c}\right) \]

      3. *-commutative 70.2%

         \[\leadsto b \cdot \left(t \cdot i - \color{blue}{c \cdot z}\right) \]

   7. Simplified 70.2%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i - c \cdot z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -700000 \lor \neg \left(b \leq 2.2 \cdot 10^{+35}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 52.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -350000 \lor \neg \left(b \leq 2.2 \cdot 10^{+33}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -350000.0) (not (<= b 2.2e+33)))
   (* b (- (* t i) (* z c)))
   (* a (- (* c j) (* x t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -350000.0) || !(b <= 2.2e+33)) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-350000.0d0)) .or. (.not. (b <= 2.2d+33))) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = a * ((c * j) - (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -350000.0) || !(b <= 2.2e+33)) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -350000.0) or not (b <= 2.2e+33):
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = a * ((c * j) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -350000.0) || !(b <= 2.2e+33))
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -350000.0) || ~((b <= 2.2e+33)))
		tmp = b * ((t * i) - (z * c));
	else
		tmp = a * ((c * j) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -350000.0], N[Not[LessEqual[b, 2.2e+33]], $MachinePrecision]], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.5e5 or 2.19999999999999994e33 < b

   1. Initial program 68.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 64.9%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]

   if -3.5e5 < b < 2.19999999999999994e33

   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 50.9%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 50.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 50.9%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 50.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 50.9%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 50.9%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -350000 \lor \neg \left(b \leq 2.2 \cdot 10^{+33}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 29.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{-14} \lor \neg \left(b \leq 5.5 \cdot 10^{+44}\right):\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -1.1e-14) (not (<= b 5.5e+44))) (* i (* t b)) (* a (* c j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -1.1e-14) || !(b <= 5.5e+44)) {
		tmp = i * (t * b);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-1.1d-14)) .or. (.not. (b <= 5.5d+44))) then
        tmp = i * (t * b)
    else
        tmp = a * (c * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -1.1e-14) || !(b <= 5.5e+44)) {
		tmp = i * (t * b);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -1.1e-14) or not (b <= 5.5e+44):
		tmp = i * (t * b)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -1.1e-14) || !(b <= 5.5e+44))
		tmp = Float64(i * Float64(t * b));
	else
		tmp = Float64(a * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -1.1e-14) || ~((b <= 5.5e+44)))
		tmp = i * (t * b);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -1.1e-14], N[Not[LessEqual[b, 5.5e+44]], $MachinePrecision]], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if b < -1.1e-14

   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 59.7%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(-1 \cdot \left(c \cdot j\right) + \left(-1 \cdot \frac{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}{a} + t \cdot x\right)\right)\right)} \]

   5. Simplified 58.0%

      \[\leadsto \color{blue}{\left(\left(t \cdot x - \frac{y \cdot \left(z \cdot x - j \cdot i\right) + b \cdot \left(i \cdot t - c \cdot z\right)}{a}\right) - j \cdot c\right) \cdot \left(-a\right)} \]

   6. Taylor expanded in b around inf 52.2%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(b \cdot \left(\frac{c \cdot z}{a} - \frac{i \cdot t}{a}\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 52.2%

         \[\leadsto \color{blue}{-a \cdot \left(b \cdot \left(\frac{c \cdot z}{a} - \frac{i \cdot t}{a}\right)\right)} \]

      2. distribute-rgt-neg-in 52.2%

         \[\leadsto \color{blue}{a \cdot \left(-b \cdot \left(\frac{c \cdot z}{a} - \frac{i \cdot t}{a}\right)\right)} \]

      3. distribute-lft-neg-in 52.2%

         \[\leadsto a \cdot \color{blue}{\left(\left(-b\right) \cdot \left(\frac{c \cdot z}{a} - \frac{i \cdot t}{a}\right)\right)} \]

      4. div-sub 52.2%

         \[\leadsto a \cdot \left(\left(-b\right) \cdot \color{blue}{\frac{c \cdot z - i \cdot t}{a}}\right) \]

      5. *-commutative 52.2%

         \[\leadsto a \cdot \left(\left(-b\right) \cdot \frac{c \cdot z - \color{blue}{t \cdot i}}{a}\right) \]

   8. Simplified 52.2%

      \[\leadsto \color{blue}{a \cdot \left(\left(-b\right) \cdot \frac{c \cdot z - t \cdot i}{a}\right)} \]

   9. Taylor expanded in c around 0 36.1%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 34.6%

          \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot t} \]

       2. *-commutative 34.6%

          \[\leadsto \color{blue}{\left(i \cdot b\right)} \cdot t \]

       3. associate-*r* 37.7%

          \[\leadsto \color{blue}{i \cdot \left(b \cdot t\right)} \]

   11. Simplified 37.7%

       \[\leadsto \color{blue}{i \cdot \left(b \cdot t\right)} \]

   if -1.1e-14 < b < 5.5000000000000001e44

   1. Initial program 71.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 48.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 48.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 48.8%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 48.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 48.8%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 48.8%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around inf 27.4%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

   if 5.5000000000000001e44 < b

   1. Initial program 66.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg 66.3%

         \[\leadsto \left(x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. distribute-rgt-in 66.3%

         \[\leadsto \left(\color{blue}{\left(\left(y \cdot z\right) \cdot x + \left(-t \cdot a\right) \cdot x\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. distribute-rgt-neg-in 66.3%

         \[\leadsto \left(\left(\left(y \cdot z\right) \cdot x + \color{blue}{\left(t \cdot \left(-a\right)\right)} \cdot x\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 66.3%

      \[\leadsto \left(\color{blue}{\left(\left(y \cdot z\right) \cdot x + \left(t \cdot \left(-a\right)\right) \cdot x\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in i around inf 45.2%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 45.2%

         \[\leadsto i \cdot \left(-1 \cdot \left(j \cdot y\right) - \color{blue}{\left(-1 \cdot b\right) \cdot t}\right) \]

      2. neg-mul-1 45.2%

         \[\leadsto i \cdot \left(-1 \cdot \left(j \cdot y\right) - \color{blue}{\left(-b\right)} \cdot t\right) \]

      3. cancel-sign-sub 45.2%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]

      4. +-commutative 45.2%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      5. mul-1-neg 45.2%

         \[\leadsto i \cdot \left(b \cdot t + \color{blue}{\left(-j \cdot y\right)}\right) \]

      6. unsub-neg 45.2%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t - j \cdot y\right)} \]

      7. *-commutative 45.2%

         \[\leadsto i \cdot \left(\color{blue}{t \cdot b} - j \cdot y\right) \]

   7. Simplified 45.2%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b - j \cdot y\right)} \]

   8. Taylor expanded in t around inf 36.9%

      \[\leadsto i \cdot \color{blue}{\left(b \cdot t\right)} \]
   9. Step-by-step derivation

      1. *-commutative 36.9%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b\right)} \]

   10. Simplified 36.9%

       \[\leadsto i \cdot \color{blue}{\left(t \cdot b\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 32.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{-14} \lor \neg \left(b \leq 5.5 \cdot 10^{+44}\right):\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 29.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8.8 \cdot 10^{-15} \lor \neg \left(b \leq 4.8 \cdot 10^{+41}\right):\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -8.8e-15) (not (<= b 4.8e+41))) (* i (* t b)) (* a (* c j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -8.8e-15) || !(b <= 4.8e+41)) {
		tmp = i * (t * b);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-8.8d-15)) .or. (.not. (b <= 4.8d+41))) then
        tmp = i * (t * b)
    else
        tmp = a * (c * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -8.8e-15) || !(b <= 4.8e+41)) {
		tmp = i * (t * b);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -8.8e-15) or not (b <= 4.8e+41):
		tmp = i * (t * b)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -8.8e-15) || !(b <= 4.8e+41))
		tmp = Float64(i * Float64(t * b));
	else
		tmp = Float64(a * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -8.8e-15) || ~((b <= 4.8e+41)))
		tmp = i * (t * b);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -8.8e-15], N[Not[LessEqual[b, 4.8e+41]], $MachinePrecision]], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -8.79999999999999942e-15 or 4.8000000000000003e41 < b

   1. Initial program 69.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf 63.2%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(-1 \cdot \left(c \cdot j\right) + \left(-1 \cdot \frac{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}{a} + t \cdot x\right)\right)\right)} \]

   5. Simplified 62.4%

      \[\leadsto \color{blue}{\left(\left(t \cdot x - \frac{y \cdot \left(z \cdot x - j \cdot i\right) + b \cdot \left(i \cdot t - c \cdot z\right)}{a}\right) - j \cdot c\right) \cdot \left(-a\right)} \]

   6. Taylor expanded in b around inf 55.3%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(b \cdot \left(\frac{c \cdot z}{a} - \frac{i \cdot t}{a}\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 55.3%

         \[\leadsto \color{blue}{-a \cdot \left(b \cdot \left(\frac{c \cdot z}{a} - \frac{i \cdot t}{a}\right)\right)} \]

      2. distribute-rgt-neg-in 55.3%

         \[\leadsto \color{blue}{a \cdot \left(-b \cdot \left(\frac{c \cdot z}{a} - \frac{i \cdot t}{a}\right)\right)} \]

      3. distribute-lft-neg-in 55.3%

         \[\leadsto a \cdot \color{blue}{\left(\left(-b\right) \cdot \left(\frac{c \cdot z}{a} - \frac{i \cdot t}{a}\right)\right)} \]

      4. div-sub 56.2%

         \[\leadsto a \cdot \left(\left(-b\right) \cdot \color{blue}{\frac{c \cdot z - i \cdot t}{a}}\right) \]

      5. *-commutative 56.2%

         \[\leadsto a \cdot \left(\left(-b\right) \cdot \frac{c \cdot z - \color{blue}{t \cdot i}}{a}\right) \]

   8. Simplified 56.2%

      \[\leadsto \color{blue}{a \cdot \left(\left(-b\right) \cdot \frac{c \cdot z - t \cdot i}{a}\right)} \]

   9. Taylor expanded in c around 0 36.5%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 37.3%

          \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot t} \]

       2. *-commutative 37.3%

          \[\leadsto \color{blue}{\left(i \cdot b\right)} \cdot t \]

       3. associate-*r* 37.3%

          \[\leadsto \color{blue}{i \cdot \left(b \cdot t\right)} \]

   11. Simplified 37.3%

       \[\leadsto \color{blue}{i \cdot \left(b \cdot t\right)} \]

   if -8.79999999999999942e-15 < b < 4.8000000000000003e41

   1. Initial program 71.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 48.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 48.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 48.8%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 48.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 48.8%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 48.8%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around inf 27.4%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 32.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.8 \cdot 10^{-15} \lor \neg \left(b \leq 4.8 \cdot 10^{+41}\right):\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 29.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.02 \cdot 10^{-13} \lor \neg \left(b \leq 5.2 \cdot 10^{+42}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -2.02e-13) (not (<= b 5.2e+42))) (* b (* t i)) (* a (* c j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -2.02e-13) || !(b <= 5.2e+42)) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-2.02d-13)) .or. (.not. (b <= 5.2d+42))) then
        tmp = b * (t * i)
    else
        tmp = a * (c * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -2.02e-13) || !(b <= 5.2e+42)) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -2.02e-13) or not (b <= 5.2e+42):
		tmp = b * (t * i)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -2.02e-13) || !(b <= 5.2e+42))
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(a * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -2.02e-13) || ~((b <= 5.2e+42)))
		tmp = b * (t * i);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -2.02e-13], N[Not[LessEqual[b, 5.2e+42]], $MachinePrecision]], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.02e-13 or 5.1999999999999998e42 < b

   1. Initial program 69.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 43.8%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 43.8%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x - b \cdot i\right)\right)} \]

      2. *-commutative 43.8%

         \[\leadsto t \cdot \left(-1 \cdot \left(a \cdot x - \color{blue}{i \cdot b}\right)\right) \]

   5. Simplified 43.8%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x - i \cdot b\right)\right)} \]

   6. Taylor expanded in a around 0 36.5%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 36.5%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   8. Simplified 36.5%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]

   if -2.02e-13 < b < 5.1999999999999998e42

   1. Initial program 71.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 48.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 48.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 48.8%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 48.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 48.8%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 48.8%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around inf 27.4%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 31.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.02 \cdot 10^{-13} \lor \neg \left(b \leq 5.2 \cdot 10^{+42}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 31: 29.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.8 \cdot 10^{-14}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;b \leq 9 \cdot 10^{+40}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -5.8e-14)
   (* i (* t b))
   (if (<= b 9e+40) (* a (* c j)) (* t (* b i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -5.8e-14) {
		tmp = i * (t * b);
	} else if (b <= 9e+40) {
		tmp = a * (c * j);
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-5.8d-14)) then
        tmp = i * (t * b)
    else if (b <= 9d+40) then
        tmp = a * (c * j)
    else
        tmp = t * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -5.8e-14) {
		tmp = i * (t * b);
	} else if (b <= 9e+40) {
		tmp = a * (c * j);
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -5.8e-14:
		tmp = i * (t * b)
	elif b <= 9e+40:
		tmp = a * (c * j)
	else:
		tmp = t * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -5.8e-14)
		tmp = Float64(i * Float64(t * b));
	elseif (b <= 9e+40)
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(t * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -5.8e-14)
		tmp = i * (t * b);
	elseif (b <= 9e+40)
		tmp = a * (c * j);
	else
		tmp = t * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -5.8e-14], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9e+40], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.8000000000000005e-14

   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 59.7%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(-1 \cdot \left(c \cdot j\right) + \left(-1 \cdot \frac{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}{a} + t \cdot x\right)\right)\right)} \]

   5. Simplified 58.0%

      \[\leadsto \color{blue}{\left(\left(t \cdot x - \frac{y \cdot \left(z \cdot x - j \cdot i\right) + b \cdot \left(i \cdot t - c \cdot z\right)}{a}\right) - j \cdot c\right) \cdot \left(-a\right)} \]

   6. Taylor expanded in b around inf 52.2%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(b \cdot \left(\frac{c \cdot z}{a} - \frac{i \cdot t}{a}\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 52.2%

         \[\leadsto \color{blue}{-a \cdot \left(b \cdot \left(\frac{c \cdot z}{a} - \frac{i \cdot t}{a}\right)\right)} \]

      2. distribute-rgt-neg-in 52.2%

         \[\leadsto \color{blue}{a \cdot \left(-b \cdot \left(\frac{c \cdot z}{a} - \frac{i \cdot t}{a}\right)\right)} \]

      3. distribute-lft-neg-in 52.2%

         \[\leadsto a \cdot \color{blue}{\left(\left(-b\right) \cdot \left(\frac{c \cdot z}{a} - \frac{i \cdot t}{a}\right)\right)} \]

      4. div-sub 52.2%

         \[\leadsto a \cdot \left(\left(-b\right) \cdot \color{blue}{\frac{c \cdot z - i \cdot t}{a}}\right) \]

      5. *-commutative 52.2%

         \[\leadsto a \cdot \left(\left(-b\right) \cdot \frac{c \cdot z - \color{blue}{t \cdot i}}{a}\right) \]

   8. Simplified 52.2%

      \[\leadsto \color{blue}{a \cdot \left(\left(-b\right) \cdot \frac{c \cdot z - t \cdot i}{a}\right)} \]

   9. Taylor expanded in c around 0 36.1%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 34.6%

          \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot t} \]

       2. *-commutative 34.6%

          \[\leadsto \color{blue}{\left(i \cdot b\right)} \cdot t \]

       3. associate-*r* 37.7%

          \[\leadsto \color{blue}{i \cdot \left(b \cdot t\right)} \]

   11. Simplified 37.7%

       \[\leadsto \color{blue}{i \cdot \left(b \cdot t\right)} \]

   if -5.8000000000000005e-14 < b < 9.00000000000000064e40

   1. Initial program 71.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 48.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 48.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 48.8%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 48.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 48.8%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 48.8%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around inf 27.4%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

   if 9.00000000000000064e40 < b

   1. Initial program 66.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg 66.3%

         \[\leadsto \left(x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. distribute-rgt-in 66.3%

         \[\leadsto \left(\color{blue}{\left(\left(y \cdot z\right) \cdot x + \left(-t \cdot a\right) \cdot x\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. distribute-rgt-neg-in 66.3%

         \[\leadsto \left(\left(\left(y \cdot z\right) \cdot x + \color{blue}{\left(t \cdot \left(-a\right)\right)} \cdot x\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 66.3%

      \[\leadsto \left(\color{blue}{\left(\left(y \cdot z\right) \cdot x + \left(t \cdot \left(-a\right)\right) \cdot x\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in j around 0 66.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 66.7%

         \[\leadsto \left(\color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      2. associate-*r* 66.8%

         \[\leadsto \left(\left(-\color{blue}{\left(a \cdot t\right) \cdot x}\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      3. distribute-lft-neg-in 66.8%

         \[\leadsto \left(\color{blue}{\left(-a \cdot t\right) \cdot x} + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      4. mul-1-neg 66.8%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(a \cdot t\right)\right)} \cdot x + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      5. *-commutative 66.8%

         \[\leadsto \left(\left(-1 \cdot \left(a \cdot t\right)\right) \cdot x + \color{blue}{\left(y \cdot z\right) \cdot x}\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      6. distribute-rgt-in 66.8%

         \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)} - b \cdot \left(c \cdot z - i \cdot t\right) \]

      7. +-commutative 66.8%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z + -1 \cdot \left(a \cdot t\right)\right)} - b \cdot \left(c \cdot z - i \cdot t\right) \]

      8. mul-1-neg 66.8%

         \[\leadsto x \cdot \left(y \cdot z + \color{blue}{\left(-a \cdot t\right)}\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      9. unsub-neg 66.8%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z - a \cdot t\right)} - b \cdot \left(c \cdot z - i \cdot t\right) \]

      10. *-commutative 66.8%

          \[\leadsto x \cdot \left(\color{blue}{z \cdot y} - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right) \]

      11. *-commutative 66.8%

          \[\leadsto x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right) \]

      12. *-commutative 66.8%

          \[\leadsto x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right) \]

      13. *-commutative 66.8%

          \[\leadsto x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(\color{blue}{c \cdot z} - t \cdot i\right) \]

   7. Simplified 66.8%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(c \cdot z - t \cdot i\right)} \]

   8. Taylor expanded in i around inf 36.9%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   9. Step-by-step derivation

      1. *-commutative 36.9%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

      2. associate-*r* 36.9%

         \[\leadsto \color{blue}{\left(b \cdot t\right) \cdot i} \]

      3. *-commutative 36.9%

         \[\leadsto \color{blue}{\left(t \cdot b\right)} \cdot i \]

      4. associate-*r* 40.2%

         \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]

   10. Simplified 40.2%

       \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 32.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.8 \cdot 10^{-14}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;b \leq 9 \cdot 10^{+40}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 32: 22.4% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(c \cdot j\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* c j)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = a * (c * j)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (c * j)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(c * j))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (c * j);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 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 a around inf 36.9%

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
4. Step-by-step derivation

   1. +-commutative 36.9%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

   2. mul-1-neg 36.9%

      \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

   3. unsub-neg 36.9%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. *-commutative 36.9%

      \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

5. Simplified 36.9%

   \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

6. Taylor expanded in j around inf 19.0%

   \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
7. Add Preprocessing

Developer target: 60.0% 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 2024103 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :alt
  (if (< x -1.469694296777705e-64) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 3.2113527362226803e-147) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i)))))