Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.9% → 82.5%

Time: 25.8s

Alternatives: 20

Speedup: 0.5×

• 58.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

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) - (i * a)))) + (j * ((c * t) - (i * y)));
}

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) - (i * a)))) + (j * ((c * t) - (i * y)))
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) - (i * a)))) + (j * ((c * t) - (i * y)));
}

Python

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

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(i * a)))) + Float64(j * Float64(Float64(c * t) - Float64(i * y))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
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[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 73.9% accurate, 1.0× speedup

Math

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

FPCore

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

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) - (i * a)))) + (j * ((c * t) - (i * y)));
}

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) - (i * a)))) + (j * ((c * t) - (i * y)))
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) - (i * a)))) + (j * ((c * t) - (i * y)));
}

Python

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

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(i * a)))) + Float64(j * Float64(Float64(c * t) - Float64(i * y))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
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[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 82.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := y \cdot z - t \cdot a\\ \mathbf{if}\;\left(x \cdot t_2 + b \cdot \left(a \cdot i - z \cdot c\right)\right) + t_1 \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(t_2, x, t_1 - b \cdot \left(z \cdot c - a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))) (t_2 (- (* y z) (* t a))))
   (if (<= (+ (+ (* x t_2) (* b (- (* a i) (* z c)))) t_1) INFINITY)
     (fma t_2 x (- t_1 (* b (- (* z c) (* a i)))))
     (* y (- (* x z) (* i j))))))

C

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

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(Float64(y * z) - Float64(t * a))
	tmp = 0.0
	if (Float64(Float64(Float64(x * t_2) + Float64(b * Float64(Float64(a * i) - Float64(z * c)))) + t_1) <= Inf)
		tmp = fma(t_2, x, Float64(t_1 - Float64(b * Float64(Float64(z * c) - Float64(a * i)))));
	else
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(N[(x * t$95$2), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], Infinity], N[(t$95$2 * x + N[(t$95$1 - N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $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 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))) < +inf.0

   1. Initial program 93.8%

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

      1. associate-+l- 93.8%

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

      2. *-commutative 93.8%

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

      3. fma-neg 93.8%

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

   3. Applied egg-rr 93.8%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in y around inf 48.8%

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

      1. +-commutative 48.8%

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

      2. mul-1-neg 48.8%

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

      3. unsub-neg 48.8%

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

      4. *-commutative 48.8%

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

   4. Simplified 48.8%

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

4. Final simplification 84.3%

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

Alternative 2: 82.5% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $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 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))) < +inf.0

   1. Initial program 93.8%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in y around inf 48.8%

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

      1. +-commutative 48.8%

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

      2. mul-1-neg 48.8%

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

      3. unsub-neg 48.8%

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

      4. *-commutative 48.8%

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

   4. Simplified 48.8%

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

4. Final simplification 84.3%

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

Alternative 3: 66.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.6 \cdot 10^{+112} \lor \neg \left(b \leq 3 \cdot 10^{+14} \lor \neg \left(b \leq 1.42 \cdot 10^{+50}\right) \land \left(b \leq 1.65 \cdot 10^{+106} \lor \neg \left(b \leq 2 \cdot 10^{+207}\right) \land b \leq 1.72 \cdot 10^{+227}\right)\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -7.6e+112)
         (not
          (or (<= b 3e+14)
              (and (not (<= b 1.42e+50))
                   (or (<= b 1.65e+106)
                       (and (not (<= b 2e+207)) (<= b 1.72e+227)))))))
   (* b (- (* a i) (* z c)))
   (+ (* x (- (* y z) (* t a))) (* j (- (* t c) (* y 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 <= -7.6e+112) || !((b <= 3e+14) || (!(b <= 1.42e+50) && ((b <= 1.65e+106) || (!(b <= 2e+207) && (b <= 1.72e+227)))))) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * 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 <= (-7.6d+112)) .or. (.not. (b <= 3d+14) .or. (.not. (b <= 1.42d+50)) .and. (b <= 1.65d+106) .or. (.not. (b <= 2d+207)) .and. (b <= 1.72d+227))) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * 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 <= -7.6e+112) || !((b <= 3e+14) || (!(b <= 1.42e+50) && ((b <= 1.65e+106) || (!(b <= 2e+207) && (b <= 1.72e+227)))))) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -7.6e+112) or not ((b <= 3e+14) or (not (b <= 1.42e+50) and ((b <= 1.65e+106) or (not (b <= 2e+207) and (b <= 1.72e+227))))):
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -7.6e+112) || !((b <= 3e+14) || (!(b <= 1.42e+50) && ((b <= 1.65e+106) || (!(b <= 2e+207) && (b <= 1.72e+227))))))
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -7.6e+112) || ~(((b <= 3e+14) || (~((b <= 1.42e+50)) && ((b <= 1.65e+106) || (~((b <= 2e+207)) && (b <= 1.72e+227)))))))
		tmp = b * ((a * i) - (z * c));
	else
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -7.6e+112], N[Not[Or[LessEqual[b, 3e+14], And[N[Not[LessEqual[b, 1.42e+50]], $MachinePrecision], Or[LessEqual[b, 1.65e+106], And[N[Not[LessEqual[b, 2e+207]], $MachinePrecision], LessEqual[b, 1.72e+227]]]]]], $MachinePrecision]], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -7.60000000000000015e112 or 3e14 < b < 1.41999999999999994e50 or 1.65000000000000004e106 < b < 2.0000000000000001e207 or 1.71999999999999995e227 < b

   1. Initial program 74.2%

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

   2. Taylor expanded in b around inf 82.0%

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

      1. *-commutative 82.0%

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

   4. Simplified 82.0%

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

   if -7.60000000000000015e112 < b < 3e14 or 1.41999999999999994e50 < b < 1.65000000000000004e106 or 2.0000000000000001e207 < b < 1.71999999999999995e227

   1. Initial program 73.9%

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

   2. Taylor expanded in b around 0 73.4%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.6 \cdot 10^{+112} \lor \neg \left(b \leq 3 \cdot 10^{+14} \lor \neg \left(b \leq 1.42 \cdot 10^{+50}\right) \land \left(b \leq 1.65 \cdot 10^{+106} \lor \neg \left(b \leq 2 \cdot 10^{+207}\right) \land b \leq 1.72 \cdot 10^{+227}\right)\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 4: 67.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -4.1 \cdot 10^{+111}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{+14}:\\ \;\;\;\;t_2 + t_1\\ \mathbf{elif}\;b \leq 2.55 \cdot 10^{+50}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{+87}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1 - b \cdot \left(z \cdot c - a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i))))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (* b (- (* a i) (* z c)))))
   (if (<= b -4.1e+111)
     t_3
     (if (<= b 2.8e+14)
       (+ t_2 t_1)
       (if (<= b 2.55e+50)
         t_3
         (if (<= b 1.55e+87) t_2 (- t_1 (* b (- (* z c) (* a 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 = j * ((t * c) - (y * i));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -4.1e+111) {
		tmp = t_3;
	} else if (b <= 2.8e+14) {
		tmp = t_2 + t_1;
	} else if (b <= 2.55e+50) {
		tmp = t_3;
	} else if (b <= 1.55e+87) {
		tmp = t_2;
	} else {
		tmp = t_1 - (b * ((z * c) - (a * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = x * ((y * z) - (t * a))
    t_3 = b * ((a * i) - (z * c))
    if (b <= (-4.1d+111)) then
        tmp = t_3
    else if (b <= 2.8d+14) then
        tmp = t_2 + t_1
    else if (b <= 2.55d+50) then
        tmp = t_3
    else if (b <= 1.55d+87) then
        tmp = t_2
    else
        tmp = t_1 - (b * ((z * c) - (a * 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 = j * ((t * c) - (y * i));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -4.1e+111) {
		tmp = t_3;
	} else if (b <= 2.8e+14) {
		tmp = t_2 + t_1;
	} else if (b <= 2.55e+50) {
		tmp = t_3;
	} else if (b <= 1.55e+87) {
		tmp = t_2;
	} else {
		tmp = t_1 - (b * ((z * c) - (a * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = x * ((y * z) - (t * a))
	t_3 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -4.1e+111:
		tmp = t_3
	elif b <= 2.8e+14:
		tmp = t_2 + t_1
	elif b <= 2.55e+50:
		tmp = t_3
	elif b <= 1.55e+87:
		tmp = t_2
	else:
		tmp = t_1 - (b * ((z * c) - (a * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_3 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -4.1e+111)
		tmp = t_3;
	elseif (b <= 2.8e+14)
		tmp = Float64(t_2 + t_1);
	elseif (b <= 2.55e+50)
		tmp = t_3;
	elseif (b <= 1.55e+87)
		tmp = t_2;
	else
		tmp = Float64(t_1 - Float64(b * Float64(Float64(z * c) - Float64(a * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = x * ((y * z) - (t * a));
	t_3 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -4.1e+111)
		tmp = t_3;
	elseif (b <= 2.8e+14)
		tmp = t_2 + t_1;
	elseif (b <= 2.55e+50)
		tmp = t_3;
	elseif (b <= 1.55e+87)
		tmp = t_2;
	else
		tmp = t_1 - (b * ((z * c) - (a * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.1e+111], t$95$3, If[LessEqual[b, 2.8e+14], N[(t$95$2 + t$95$1), $MachinePrecision], If[LessEqual[b, 2.55e+50], t$95$3, If[LessEqual[b, 1.55e+87], t$95$2, N[(t$95$1 - N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -4.09999999999999986e111 or 2.8e14 < b < 2.5499999999999999e50

   1. Initial program 67.6%

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

   2. Taylor expanded in b around inf 82.5%

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

      1. *-commutative 82.5%

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

   4. Simplified 82.5%

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

   if -4.09999999999999986e111 < b < 2.8e14

   1. Initial program 74.0%

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

   2. Taylor expanded in b around 0 73.1%

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

   if 2.5499999999999999e50 < b < 1.55e87

   1. Initial program 73.3%

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

   2. Taylor expanded in x around inf 74.2%

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

      1. *-commutative 74.2%

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

   4. Simplified 74.2%

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

   if 1.55e87 < b

   1. Initial program 81.3%

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

   2. Taylor expanded in x around 0 74.5%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.1 \cdot 10^{+111}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 2.55 \cdot 10^{+50}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{+87}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c - a \cdot i\right)\\ \end{array} \]

Alternative 5: 51.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_3 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_4 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -9.6 \cdot 10^{+62}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-37}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-157}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-44}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{-11}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{+48}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+91}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c))))
        (t_2 (* y (- (* x z) (* i j))))
        (t_3 (* j (- (* t c) (* y i))))
        (t_4 (* x (- (* y z) (* t a)))))
   (if (<= x -9.6e+62)
     t_4
     (if (<= x -1.05e-37)
       t_2
       (if (<= x 1.25e-157)
         t_1
         (if (<= x 8e-44)
           t_3
           (if (<= x 8.5e-20)
             t_1
             (if (<= x 5.6e-11)
               t_2
               (if (<= x 1.08e+48)
                 (* a (- (* b i) (* x t)))
                 (if (<= x 3.1e+91) t_3 t_4))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = j * ((t * c) - (y * i));
	double t_4 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -9.6e+62) {
		tmp = t_4;
	} else if (x <= -1.05e-37) {
		tmp = t_2;
	} else if (x <= 1.25e-157) {
		tmp = t_1;
	} else if (x <= 8e-44) {
		tmp = t_3;
	} else if (x <= 8.5e-20) {
		tmp = t_1;
	} else if (x <= 5.6e-11) {
		tmp = t_2;
	} else if (x <= 1.08e+48) {
		tmp = a * ((b * i) - (x * t));
	} else if (x <= 3.1e+91) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = y * ((x * z) - (i * j))
    t_3 = j * ((t * c) - (y * i))
    t_4 = x * ((y * z) - (t * a))
    if (x <= (-9.6d+62)) then
        tmp = t_4
    else if (x <= (-1.05d-37)) then
        tmp = t_2
    else if (x <= 1.25d-157) then
        tmp = t_1
    else if (x <= 8d-44) then
        tmp = t_3
    else if (x <= 8.5d-20) then
        tmp = t_1
    else if (x <= 5.6d-11) then
        tmp = t_2
    else if (x <= 1.08d+48) then
        tmp = a * ((b * i) - (x * t))
    else if (x <= 3.1d+91) then
        tmp = t_3
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = j * ((t * c) - (y * i));
	double t_4 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -9.6e+62) {
		tmp = t_4;
	} else if (x <= -1.05e-37) {
		tmp = t_2;
	} else if (x <= 1.25e-157) {
		tmp = t_1;
	} else if (x <= 8e-44) {
		tmp = t_3;
	} else if (x <= 8.5e-20) {
		tmp = t_1;
	} else if (x <= 5.6e-11) {
		tmp = t_2;
	} else if (x <= 1.08e+48) {
		tmp = a * ((b * i) - (x * t));
	} else if (x <= 3.1e+91) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = y * ((x * z) - (i * j))
	t_3 = j * ((t * c) - (y * i))
	t_4 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -9.6e+62:
		tmp = t_4
	elif x <= -1.05e-37:
		tmp = t_2
	elif x <= 1.25e-157:
		tmp = t_1
	elif x <= 8e-44:
		tmp = t_3
	elif x <= 8.5e-20:
		tmp = t_1
	elif x <= 5.6e-11:
		tmp = t_2
	elif x <= 1.08e+48:
		tmp = a * ((b * i) - (x * t))
	elif x <= 3.1e+91:
		tmp = t_3
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_3 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_4 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -9.6e+62)
		tmp = t_4;
	elseif (x <= -1.05e-37)
		tmp = t_2;
	elseif (x <= 1.25e-157)
		tmp = t_1;
	elseif (x <= 8e-44)
		tmp = t_3;
	elseif (x <= 8.5e-20)
		tmp = t_1;
	elseif (x <= 5.6e-11)
		tmp = t_2;
	elseif (x <= 1.08e+48)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (x <= 3.1e+91)
		tmp = t_3;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = y * ((x * z) - (i * j));
	t_3 = j * ((t * c) - (y * i));
	t_4 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -9.6e+62)
		tmp = t_4;
	elseif (x <= -1.05e-37)
		tmp = t_2;
	elseif (x <= 1.25e-157)
		tmp = t_1;
	elseif (x <= 8e-44)
		tmp = t_3;
	elseif (x <= 8.5e-20)
		tmp = t_1;
	elseif (x <= 5.6e-11)
		tmp = t_2;
	elseif (x <= 1.08e+48)
		tmp = a * ((b * i) - (x * t));
	elseif (x <= 3.1e+91)
		tmp = t_3;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * 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]}, Block[{t$95$3 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9.6e+62], t$95$4, If[LessEqual[x, -1.05e-37], t$95$2, If[LessEqual[x, 1.25e-157], t$95$1, If[LessEqual[x, 8e-44], t$95$3, If[LessEqual[x, 8.5e-20], t$95$1, If[LessEqual[x, 5.6e-11], t$95$2, If[LessEqual[x, 1.08e+48], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.1e+91], t$95$3, t$95$4]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -9.6e62 or 3.09999999999999998e91 < x

   1. Initial program 72.6%

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

   2. Taylor expanded in x around inf 70.3%

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

      1. *-commutative 70.3%

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

   4. Simplified 70.3%

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

   if -9.6e62 < x < -1.05e-37 or 8.5000000000000005e-20 < x < 5.6e-11

   1. Initial program 79.8%

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

   2. Taylor expanded in y around inf 68.3%

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

      1. +-commutative 68.3%

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

      2. mul-1-neg 68.3%

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

      3. unsub-neg 68.3%

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

      4. *-commutative 68.3%

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

   4. Simplified 68.3%

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

   if -1.05e-37 < x < 1.25000000000000005e-157 or 7.99999999999999962e-44 < x < 8.5000000000000005e-20

   1. Initial program 76.4%

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

   2. Taylor expanded in b around inf 65.0%

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

      1. *-commutative 65.0%

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

   4. Simplified 65.0%

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

   if 1.25000000000000005e-157 < x < 7.99999999999999962e-44 or 1.07999999999999998e48 < x < 3.09999999999999998e91

   1. Initial program 67.7%

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

   2. Taylor expanded in j around inf 63.0%

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

   if 5.6e-11 < x < 1.07999999999999998e48

   1. Initial program 69.8%

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

   2. Taylor expanded in a around inf 71.2%

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

      1. distribute-lft-out-- 71.2%

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

      2. *-commutative 71.2%

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

   4. Simplified 71.2%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.6 \cdot 10^{+62}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-37}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-157}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-44}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-20}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{-11}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{+48}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+91}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]

Alternative 6: 52.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -9.6 \cdot 10^{+26}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-76}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-164}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+39}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+91}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i))))
        (t_2 (* b (- (* a i) (* z c))))
        (t_3 (* x (- (* y z) (* t a)))))
   (if (<= x -9.6e+26)
     t_3
     (if (<= x -2.6e-39)
       t_1
       (if (<= x -9e-76)
         (* t (- (* c j) (* x a)))
         (if (<= x 6.5e-164)
           t_2
           (if (<= x 5e-44)
             t_1
             (if (<= x 7e+39) t_2 (if (<= x 2.4e+91) t_1 t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -9.6e+26) {
		tmp = t_3;
	} else if (x <= -2.6e-39) {
		tmp = t_1;
	} else if (x <= -9e-76) {
		tmp = t * ((c * j) - (x * a));
	} else if (x <= 6.5e-164) {
		tmp = t_2;
	} else if (x <= 5e-44) {
		tmp = t_1;
	} else if (x <= 7e+39) {
		tmp = t_2;
	} else if (x <= 2.4e+91) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = b * ((a * i) - (z * c))
    t_3 = x * ((y * z) - (t * a))
    if (x <= (-9.6d+26)) then
        tmp = t_3
    else if (x <= (-2.6d-39)) then
        tmp = t_1
    else if (x <= (-9d-76)) then
        tmp = t * ((c * j) - (x * a))
    else if (x <= 6.5d-164) then
        tmp = t_2
    else if (x <= 5d-44) then
        tmp = t_1
    else if (x <= 7d+39) then
        tmp = t_2
    else if (x <= 2.4d+91) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -9.6e+26) {
		tmp = t_3;
	} else if (x <= -2.6e-39) {
		tmp = t_1;
	} else if (x <= -9e-76) {
		tmp = t * ((c * j) - (x * a));
	} else if (x <= 6.5e-164) {
		tmp = t_2;
	} else if (x <= 5e-44) {
		tmp = t_1;
	} else if (x <= 7e+39) {
		tmp = t_2;
	} else if (x <= 2.4e+91) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = b * ((a * i) - (z * c))
	t_3 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -9.6e+26:
		tmp = t_3
	elif x <= -2.6e-39:
		tmp = t_1
	elif x <= -9e-76:
		tmp = t * ((c * j) - (x * a))
	elif x <= 6.5e-164:
		tmp = t_2
	elif x <= 5e-44:
		tmp = t_1
	elif x <= 7e+39:
		tmp = t_2
	elif x <= 2.4e+91:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_3 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -9.6e+26)
		tmp = t_3;
	elseif (x <= -2.6e-39)
		tmp = t_1;
	elseif (x <= -9e-76)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (x <= 6.5e-164)
		tmp = t_2;
	elseif (x <= 5e-44)
		tmp = t_1;
	elseif (x <= 7e+39)
		tmp = t_2;
	elseif (x <= 2.4e+91)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = b * ((a * i) - (z * c));
	t_3 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -9.6e+26)
		tmp = t_3;
	elseif (x <= -2.6e-39)
		tmp = t_1;
	elseif (x <= -9e-76)
		tmp = t * ((c * j) - (x * a));
	elseif (x <= 6.5e-164)
		tmp = t_2;
	elseif (x <= 5e-44)
		tmp = t_1;
	elseif (x <= 7e+39)
		tmp = t_2;
	elseif (x <= 2.4e+91)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9.6e+26], t$95$3, If[LessEqual[x, -2.6e-39], t$95$1, If[LessEqual[x, -9e-76], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.5e-164], t$95$2, If[LessEqual[x, 5e-44], t$95$1, If[LessEqual[x, 7e+39], t$95$2, If[LessEqual[x, 2.4e+91], t$95$1, t$95$3]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -9.60000000000000018e26 or 2.39999999999999983e91 < x

   1. Initial program 71.6%

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

   2. Taylor expanded in x around inf 70.4%

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

      1. *-commutative 70.4%

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

   4. Simplified 70.4%

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

   if -9.60000000000000018e26 < x < -2.6e-39 or 6.50000000000000004e-164 < x < 5.00000000000000039e-44 or 7.0000000000000003e39 < x < 2.39999999999999983e91

   1. Initial program 72.1%

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

   2. Taylor expanded in j around inf 59.1%

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

   if -2.6e-39 < x < -9.0000000000000001e-76

   1. Initial program 99.7%

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

      1. associate-+l- 99.7%

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

      2. *-commutative 99.7%

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

      3. fma-neg 99.7%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in t around inf 56.1%

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

      1. neg-mul-1 56.1%

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

      2. +-commutative 56.1%

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

      3. unsub-neg 56.1%

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

   6. Simplified 56.1%

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

   if -9.0000000000000001e-76 < x < 6.50000000000000004e-164 or 5.00000000000000039e-44 < x < 7.0000000000000003e39

   1. Initial program 74.9%

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

   2. Taylor expanded in b around inf 64.0%

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

      1. *-commutative 64.0%

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

   4. Simplified 64.0%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.6 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-39}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-76}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-164}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-44}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+39}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+91}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]

Alternative 7: 56.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right) + i \cdot \left(a \cdot b\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -2.4 \cdot 10^{+29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -8.8 \cdot 10^{-33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-224}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 1.16 \cdot 10^{+92}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* j (- (* t c) (* y i))) (* i (* a b))))
        (t_2 (* x (- (* y z) (* t a)))))
   (if (<= x -2.4e+29)
     t_2
     (if (<= x -8.8e-33)
       t_1
       (if (<= x 4.5e-224)
         (* b (- (* a i) (* z c)))
         (if (<= x 1.16e+92) 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 * ((t * c) - (y * i))) + (i * (a * b));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -2.4e+29) {
		tmp = t_2;
	} else if (x <= -8.8e-33) {
		tmp = t_1;
	} else if (x <= 4.5e-224) {
		tmp = b * ((a * i) - (z * c));
	} else if (x <= 1.16e+92) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (j * ((t * c) - (y * i))) + (i * (a * b))
    t_2 = x * ((y * z) - (t * a))
    if (x <= (-2.4d+29)) then
        tmp = t_2
    else if (x <= (-8.8d-33)) then
        tmp = t_1
    else if (x <= 4.5d-224) then
        tmp = b * ((a * i) - (z * c))
    else if (x <= 1.16d+92) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((t * c) - (y * i))) + (i * (a * b));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -2.4e+29) {
		tmp = t_2;
	} else if (x <= -8.8e-33) {
		tmp = t_1;
	} else if (x <= 4.5e-224) {
		tmp = b * ((a * i) - (z * c));
	} else if (x <= 1.16e+92) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((t * c) - (y * i))) + (i * (a * b))
	t_2 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -2.4e+29:
		tmp = t_2
	elif x <= -8.8e-33:
		tmp = t_1
	elif x <= 4.5e-224:
		tmp = b * ((a * i) - (z * c))
	elif x <= 1.16e+92:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(i * Float64(a * b)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -2.4e+29)
		tmp = t_2;
	elseif (x <= -8.8e-33)
		tmp = t_1;
	elseif (x <= 4.5e-224)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (x <= 1.16e+92)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (j * ((t * c) - (y * i))) + (i * (a * b));
	t_2 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -2.4e+29)
		tmp = t_2;
	elseif (x <= -8.8e-33)
		tmp = t_1;
	elseif (x <= 4.5e-224)
		tmp = b * ((a * i) - (z * c));
	elseif (x <= 1.16e+92)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.4e+29], t$95$2, If[LessEqual[x, -8.8e-33], t$95$1, If[LessEqual[x, 4.5e-224], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.16e+92], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.4000000000000001e29 or 1.16000000000000006e92 < x

   1. Initial program 71.6%

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

   2. Taylor expanded in x around inf 70.4%

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

      1. *-commutative 70.4%

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

   4. Simplified 70.4%

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

   if -2.4000000000000001e29 < x < -8.80000000000000022e-33 or 4.5000000000000004e-224 < x < 1.16000000000000006e92

   1. Initial program 76.4%

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

      1. associate-+l- 76.4%

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

      2. *-commutative 76.4%

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

      3. fma-neg 77.6%

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

   3. Applied egg-rr 77.6%

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

   4. Taylor expanded in x around 0 68.1%

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

      1. fma-neg 68.1%

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

      2. *-commutative 68.1%

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

      3. *-commutative 68.1%

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

      4. *-rgt-identity 68.1%

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

      5. fma-neg 68.1%

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

      6. *-rgt-identity 68.1%

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

      7. *-commutative 68.1%

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

   6. Simplified 68.1%

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

   7. Taylor expanded in c around 0 64.8%

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

      1. mul-1-neg 64.8%

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

      2. associate-*r* 69.4%

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

      3. distribute-lft-neg-in 69.4%

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

      4. *-commutative 69.4%

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

      5. distribute-rgt-neg-in 69.4%

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

   9. Simplified 69.4%

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

   if -8.80000000000000022e-33 < x < 4.5000000000000004e-224

   1. Initial program 74.8%

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

   2. Taylor expanded in b around inf 61.9%

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

      1. *-commutative 61.9%

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

   4. Simplified 61.9%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -8.8 \cdot 10^{-33}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-224}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 1.16 \cdot 10^{+92}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]

Alternative 8: 56.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -8 \cdot 10^{+29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.18 \cdot 10^{-32}:\\ \;\;\;\;t_1 + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 6.3 \cdot 10^{-226}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+92}:\\ \;\;\;\;t_1 + i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))) (t_2 (* x (- (* y z) (* t a)))))
   (if (<= x -8e+29)
     t_2
     (if (<= x -1.18e-32)
       (+ t_1 (* a (* b i)))
       (if (<= x 6.3e-226)
         (* b (- (* a i) (* z c)))
         (if (<= x 2.2e+92) (+ t_1 (* i (* a b))) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -8e+29) {
		tmp = t_2;
	} else if (x <= -1.18e-32) {
		tmp = t_1 + (a * (b * i));
	} else if (x <= 6.3e-226) {
		tmp = b * ((a * i) - (z * c));
	} else if (x <= 2.2e+92) {
		tmp = t_1 + (i * (a * b));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = x * ((y * z) - (t * a))
    if (x <= (-8d+29)) then
        tmp = t_2
    else if (x <= (-1.18d-32)) then
        tmp = t_1 + (a * (b * i))
    else if (x <= 6.3d-226) then
        tmp = b * ((a * i) - (z * c))
    else if (x <= 2.2d+92) then
        tmp = t_1 + (i * (a * b))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -8e+29) {
		tmp = t_2;
	} else if (x <= -1.18e-32) {
		tmp = t_1 + (a * (b * i));
	} else if (x <= 6.3e-226) {
		tmp = b * ((a * i) - (z * c));
	} else if (x <= 2.2e+92) {
		tmp = t_1 + (i * (a * b));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -8e+29:
		tmp = t_2
	elif x <= -1.18e-32:
		tmp = t_1 + (a * (b * i))
	elif x <= 6.3e-226:
		tmp = b * ((a * i) - (z * c))
	elif x <= 2.2e+92:
		tmp = t_1 + (i * (a * b))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -8e+29)
		tmp = t_2;
	elseif (x <= -1.18e-32)
		tmp = Float64(t_1 + Float64(a * Float64(b * i)));
	elseif (x <= 6.3e-226)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (x <= 2.2e+92)
		tmp = Float64(t_1 + Float64(i * Float64(a * b)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -8e+29)
		tmp = t_2;
	elseif (x <= -1.18e-32)
		tmp = t_1 + (a * (b * i));
	elseif (x <= 6.3e-226)
		tmp = b * ((a * i) - (z * c));
	elseif (x <= 2.2e+92)
		tmp = t_1 + (i * (a * b));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8e+29], t$95$2, If[LessEqual[x, -1.18e-32], N[(t$95$1 + N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.3e-226], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.2e+92], N[(t$95$1 + N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -7.99999999999999931e29 or 2.19999999999999992e92 < x

   1. Initial program 71.6%

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

   2. Taylor expanded in x around inf 70.4%

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

      1. *-commutative 70.4%

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

   4. Simplified 70.4%

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

   if -7.99999999999999931e29 < x < -1.17999999999999997e-32

   1. Initial program 84.7%

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

   2. Taylor expanded in z around 0 64.1%

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

   3. Taylor expanded in x around 0 64.7%

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

   if -1.17999999999999997e-32 < x < 6.2999999999999997e-226

   1. Initial program 74.8%

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

   2. Taylor expanded in b around inf 61.9%

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

      1. *-commutative 61.9%

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

   4. Simplified 61.9%

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

   if 6.2999999999999997e-226 < x < 2.19999999999999992e92

   1. Initial program 73.8%

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

      1. associate-+l- 73.8%

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

      2. *-commutative 73.8%

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

      3. fma-neg 75.4%

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

   3. Applied egg-rr 75.4%

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

   4. Taylor expanded in x around 0 69.3%

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

      1. fma-neg 69.3%

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

      2. *-commutative 69.3%

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

      3. *-commutative 69.3%

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

      4. *-rgt-identity 69.3%

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

      5. fma-neg 69.3%

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

      6. *-rgt-identity 69.3%

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

      7. *-commutative 69.3%

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

   6. Simplified 69.3%

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

   7. Taylor expanded in c around 0 64.8%

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

      1. mul-1-neg 64.8%

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

      2. associate-*r* 70.9%

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

      3. distribute-lft-neg-in 70.9%

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

      4. *-commutative 70.9%

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

      5. distribute-rgt-neg-in 70.9%

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

   9. Simplified 70.9%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -1.18 \cdot 10^{-32}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;x \leq 6.3 \cdot 10^{-226}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+92}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]

Alternative 9: 39.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;j \leq -5.2 \cdot 10^{+198}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;j \leq -58000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -6.5 \cdot 10^{-47}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq -7.5 \cdot 10^{-205}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -6.5 \cdot 10^{-287}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;j \leq 4 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(i \cdot \left(-y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= j -5.2e+198)
     (* i (* y (- j)))
     (if (<= j -58000000000.0)
       t_1
       (if (<= j -6.5e-47)
         (* x (* y z))
         (if (<= j -7.5e-205)
           t_1
           (if (<= j -6.5e-287)
             (* x (* t (- a)))
             (if (<= j 4e+66) t_1 (* j (* i (- y)))))))))))

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 * ((a * i) - (z * c));
	double tmp;
	if (j <= -5.2e+198) {
		tmp = i * (y * -j);
	} else if (j <= -58000000000.0) {
		tmp = t_1;
	} else if (j <= -6.5e-47) {
		tmp = x * (y * z);
	} else if (j <= -7.5e-205) {
		tmp = t_1;
	} else if (j <= -6.5e-287) {
		tmp = x * (t * -a);
	} else if (j <= 4e+66) {
		tmp = t_1;
	} else {
		tmp = j * (i * -y);
	}
	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 * ((a * i) - (z * c))
    if (j <= (-5.2d+198)) then
        tmp = i * (y * -j)
    else if (j <= (-58000000000.0d0)) then
        tmp = t_1
    else if (j <= (-6.5d-47)) then
        tmp = x * (y * z)
    else if (j <= (-7.5d-205)) then
        tmp = t_1
    else if (j <= (-6.5d-287)) then
        tmp = x * (t * -a)
    else if (j <= 4d+66) then
        tmp = t_1
    else
        tmp = j * (i * -y)
    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 * ((a * i) - (z * c));
	double tmp;
	if (j <= -5.2e+198) {
		tmp = i * (y * -j);
	} else if (j <= -58000000000.0) {
		tmp = t_1;
	} else if (j <= -6.5e-47) {
		tmp = x * (y * z);
	} else if (j <= -7.5e-205) {
		tmp = t_1;
	} else if (j <= -6.5e-287) {
		tmp = x * (t * -a);
	} else if (j <= 4e+66) {
		tmp = t_1;
	} else {
		tmp = j * (i * -y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	tmp = 0
	if j <= -5.2e+198:
		tmp = i * (y * -j)
	elif j <= -58000000000.0:
		tmp = t_1
	elif j <= -6.5e-47:
		tmp = x * (y * z)
	elif j <= -7.5e-205:
		tmp = t_1
	elif j <= -6.5e-287:
		tmp = x * (t * -a)
	elif j <= 4e+66:
		tmp = t_1
	else:
		tmp = j * (i * -y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (j <= -5.2e+198)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (j <= -58000000000.0)
		tmp = t_1;
	elseif (j <= -6.5e-47)
		tmp = Float64(x * Float64(y * z));
	elseif (j <= -7.5e-205)
		tmp = t_1;
	elseif (j <= -6.5e-287)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (j <= 4e+66)
		tmp = t_1;
	else
		tmp = Float64(j * Float64(i * Float64(-y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (j <= -5.2e+198)
		tmp = i * (y * -j);
	elseif (j <= -58000000000.0)
		tmp = t_1;
	elseif (j <= -6.5e-47)
		tmp = x * (y * z);
	elseif (j <= -7.5e-205)
		tmp = t_1;
	elseif (j <= -6.5e-287)
		tmp = x * (t * -a);
	elseif (j <= 4e+66)
		tmp = t_1;
	else
		tmp = j * (i * -y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -5.2e+198], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -58000000000.0], t$95$1, If[LessEqual[j, -6.5e-47], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -7.5e-205], t$95$1, If[LessEqual[j, -6.5e-287], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4e+66], t$95$1, N[(j * N[(i * (-y)), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -5.19999999999999961e198

   1. Initial program 60.4%

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

   2. Taylor expanded in y around inf 42.1%

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

      1. +-commutative 42.1%

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

      2. mul-1-neg 42.1%

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

      3. unsub-neg 42.1%

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

      4. *-commutative 42.1%

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

   4. Simplified 42.1%

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

   5. Taylor expanded in z around 0 53.1%

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

      1. associate-*r* 53.1%

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

      2. neg-mul-1 53.1%

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

   7. Simplified 53.1%

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

   if -5.19999999999999961e198 < j < -5.8e10 or -6.5000000000000004e-47 < j < -7.4999999999999996e-205 or -6.4999999999999999e-287 < j < 3.99999999999999978e66

   1. Initial program 76.7%

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

   2. Taylor expanded in b around inf 53.8%

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

      1. *-commutative 53.8%

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

   4. Simplified 53.8%

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

   if -5.8e10 < j < -6.5000000000000004e-47

   1. Initial program 71.9%

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

   2. Taylor expanded in y around inf 72.0%

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

      1. +-commutative 72.0%

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

      2. mul-1-neg 72.0%

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

      3. unsub-neg 72.0%

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

      4. *-commutative 72.0%

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

   4. Simplified 72.0%

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

   5. Taylor expanded in z around inf 71.9%

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

      1. *-commutative 71.9%

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

   7. Simplified 71.9%

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

   if -7.4999999999999996e-205 < j < -6.4999999999999999e-287

   1. Initial program 80.3%

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

      1. associate-+l- 80.3%

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

      2. *-commutative 80.3%

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

      3. fma-neg 80.3%

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

   3. Applied egg-rr 80.3%

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

   4. Taylor expanded in x around inf 67.8%

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

      1. *-commutative 67.8%

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

   6. Simplified 67.8%

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

   7. Taylor expanded in z around 0 48.7%

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

      1. mul-1-neg 48.7%

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

      2. associate-*r* 55.1%

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

      3. distribute-lft-neg-in 55.1%

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

      4. distribute-rgt-neg-out 55.1%

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

      5. *-commutative 55.1%

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

   9. Simplified 55.1%

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

   if 3.99999999999999978e66 < j

   1. Initial program 70.5%

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

   2. Taylor expanded in y around inf 64.4%

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

      1. +-commutative 64.4%

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

      2. mul-1-neg 64.4%

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

      3. unsub-neg 64.4%

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

      4. *-commutative 64.4%

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

   4. Simplified 64.4%

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

   5. Taylor expanded in z around 0 49.3%

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

      1. mul-1-neg 49.3%

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

      2. distribute-lft-neg-in 49.3%

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

      3. associate-*r* 53.5%

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

      4. *-commutative 53.5%

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

      5. associate-*l* 51.3%

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

      6. distribute-lft-neg-in 51.3%

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

      7. distribute-rgt-neg-in 51.3%

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

   7. Simplified 51.3%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -5.2 \cdot 10^{+198}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;j \leq -58000000000:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -6.5 \cdot 10^{-47}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq -7.5 \cdot 10^{-205}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -6.5 \cdot 10^{-287}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;j \leq 4 \cdot 10^{+66}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(i \cdot \left(-y\right)\right)\\ \end{array} \]

Alternative 10: 42.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;j \leq -4800000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -2.2 \cdot 10^{-47}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq -3.3 \cdot 10^{-204}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -5.5 \cdot 10^{-287}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;j \leq 4.4 \cdot 10^{-55}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 1.02 \cdot 10^{+239}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(i \cdot \left(-y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))) (t_2 (* b (- (* a i) (* z c)))))
   (if (<= j -4800000.0)
     t_1
     (if (<= j -2.2e-47)
       (* x (* y z))
       (if (<= j -3.3e-204)
         t_2
         (if (<= j -5.5e-287)
           (* x (* t (- a)))
           (if (<= j 4.4e-55)
             t_2
             (if (<= j 1.02e+239) t_1 (* j (* i (- y)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (j <= -4800000.0) {
		tmp = t_1;
	} else if (j <= -2.2e-47) {
		tmp = x * (y * z);
	} else if (j <= -3.3e-204) {
		tmp = t_2;
	} else if (j <= -5.5e-287) {
		tmp = x * (t * -a);
	} else if (j <= 4.4e-55) {
		tmp = t_2;
	} else if (j <= 1.02e+239) {
		tmp = t_1;
	} else {
		tmp = j * (i * -y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * ((t * j) - (z * b))
    t_2 = b * ((a * i) - (z * c))
    if (j <= (-4800000.0d0)) then
        tmp = t_1
    else if (j <= (-2.2d-47)) then
        tmp = x * (y * z)
    else if (j <= (-3.3d-204)) then
        tmp = t_2
    else if (j <= (-5.5d-287)) then
        tmp = x * (t * -a)
    else if (j <= 4.4d-55) then
        tmp = t_2
    else if (j <= 1.02d+239) then
        tmp = t_1
    else
        tmp = j * (i * -y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (j <= -4800000.0) {
		tmp = t_1;
	} else if (j <= -2.2e-47) {
		tmp = x * (y * z);
	} else if (j <= -3.3e-204) {
		tmp = t_2;
	} else if (j <= -5.5e-287) {
		tmp = x * (t * -a);
	} else if (j <= 4.4e-55) {
		tmp = t_2;
	} else if (j <= 1.02e+239) {
		tmp = t_1;
	} else {
		tmp = j * (i * -y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if j <= -4800000.0:
		tmp = t_1
	elif j <= -2.2e-47:
		tmp = x * (y * z)
	elif j <= -3.3e-204:
		tmp = t_2
	elif j <= -5.5e-287:
		tmp = x * (t * -a)
	elif j <= 4.4e-55:
		tmp = t_2
	elif j <= 1.02e+239:
		tmp = t_1
	else:
		tmp = j * (i * -y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (j <= -4800000.0)
		tmp = t_1;
	elseif (j <= -2.2e-47)
		tmp = Float64(x * Float64(y * z));
	elseif (j <= -3.3e-204)
		tmp = t_2;
	elseif (j <= -5.5e-287)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (j <= 4.4e-55)
		tmp = t_2;
	elseif (j <= 1.02e+239)
		tmp = t_1;
	else
		tmp = Float64(j * Float64(i * Float64(-y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((t * j) - (z * b));
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (j <= -4800000.0)
		tmp = t_1;
	elseif (j <= -2.2e-47)
		tmp = x * (y * z);
	elseif (j <= -3.3e-204)
		tmp = t_2;
	elseif (j <= -5.5e-287)
		tmp = x * (t * -a);
	elseif (j <= 4.4e-55)
		tmp = t_2;
	elseif (j <= 1.02e+239)
		tmp = t_1;
	else
		tmp = j * (i * -y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -4800000.0], t$95$1, If[LessEqual[j, -2.2e-47], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3.3e-204], t$95$2, If[LessEqual[j, -5.5e-287], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.4e-55], t$95$2, If[LessEqual[j, 1.02e+239], t$95$1, N[(j * N[(i * (-y)), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -4.8e6 or 4.3999999999999999e-55 < j < 1.02e239

   1. Initial program 74.6%

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

   2. Taylor expanded in c around inf 49.6%

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

   if -4.8e6 < j < -2.20000000000000019e-47

   1. Initial program 71.9%

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

   2. Taylor expanded in y around inf 72.0%

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

      1. +-commutative 72.0%

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

      2. mul-1-neg 72.0%

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

      3. unsub-neg 72.0%

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

      4. *-commutative 72.0%

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

   4. Simplified 72.0%

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

   5. Taylor expanded in z around inf 71.9%

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

      1. *-commutative 71.9%

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

   7. Simplified 71.9%

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

   if -2.20000000000000019e-47 < j < -3.30000000000000009e-204 or -5.4999999999999998e-287 < j < 4.3999999999999999e-55

   1. Initial program 75.0%

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

   2. Taylor expanded in b around inf 56.8%

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

      1. *-commutative 56.8%

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

   4. Simplified 56.8%

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

   if -3.30000000000000009e-204 < j < -5.4999999999999998e-287

   1. Initial program 80.3%

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

      1. associate-+l- 80.3%

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

      2. *-commutative 80.3%

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

      3. fma-neg 80.3%

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

   3. Applied egg-rr 80.3%

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

   4. Taylor expanded in x around inf 67.8%

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

      1. *-commutative 67.8%

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

   6. Simplified 67.8%

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

   7. Taylor expanded in z around 0 48.7%

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

      1. mul-1-neg 48.7%

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

      2. associate-*r* 55.1%

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

      3. distribute-lft-neg-in 55.1%

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

      4. distribute-rgt-neg-out 55.1%

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

      5. *-commutative 55.1%

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

   9. Simplified 55.1%

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

   if 1.02e239 < j

   1. Initial program 60.9%

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

   2. Taylor expanded in y around inf 77.6%

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

      1. +-commutative 77.6%

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

      2. mul-1-neg 77.6%

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

      3. unsub-neg 77.6%

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

      4. *-commutative 77.6%

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

   4. Simplified 77.6%

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

   5. Taylor expanded in z around 0 57.1%

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

      1. mul-1-neg 57.1%

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

      2. distribute-lft-neg-in 57.1%

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

      3. associate-*r* 67.4%

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

      4. *-commutative 67.4%

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

      5. associate-*l* 61.8%

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

      6. distribute-lft-neg-in 61.8%

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

      7. distribute-rgt-neg-in 61.8%

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

   7. Simplified 61.8%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4800000:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq -2.2 \cdot 10^{-47}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq -3.3 \cdot 10^{-204}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -5.5 \cdot 10^{-287}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;j \leq 4.4 \cdot 10^{-55}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.02 \cdot 10^{+239}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(i \cdot \left(-y\right)\right)\\ \end{array} \]

Alternative 11: 49.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -9.5 \cdot 10^{+62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -58000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -4 \cdot 10^{-47}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq -2.1 \cdot 10^{-207}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -5.5 \cdot 10^{-287}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;j \leq 18500:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))) (t_2 (* j (- (* t c) (* y i)))))
   (if (<= j -9.5e+62)
     t_2
     (if (<= j -58000000000.0)
       t_1
       (if (<= j -4e-47)
         (* x (* y z))
         (if (<= j -2.1e-207)
           t_1
           (if (<= j -5.5e-287)
             (* x (* t (- a)))
             (if (<= j 18500.0) 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 * ((a * i) - (z * c));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -9.5e+62) {
		tmp = t_2;
	} else if (j <= -58000000000.0) {
		tmp = t_1;
	} else if (j <= -4e-47) {
		tmp = x * (y * z);
	} else if (j <= -2.1e-207) {
		tmp = t_1;
	} else if (j <= -5.5e-287) {
		tmp = x * (t * -a);
	} else if (j <= 18500.0) {
		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 = b * ((a * i) - (z * c))
    t_2 = j * ((t * c) - (y * i))
    if (j <= (-9.5d+62)) then
        tmp = t_2
    else if (j <= (-58000000000.0d0)) then
        tmp = t_1
    else if (j <= (-4d-47)) then
        tmp = x * (y * z)
    else if (j <= (-2.1d-207)) then
        tmp = t_1
    else if (j <= (-5.5d-287)) then
        tmp = x * (t * -a)
    else if (j <= 18500.0d0) 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 * ((a * i) - (z * c));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -9.5e+62) {
		tmp = t_2;
	} else if (j <= -58000000000.0) {
		tmp = t_1;
	} else if (j <= -4e-47) {
		tmp = x * (y * z);
	} else if (j <= -2.1e-207) {
		tmp = t_1;
	} else if (j <= -5.5e-287) {
		tmp = x * (t * -a);
	} else if (j <= 18500.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -9.5e+62:
		tmp = t_2
	elif j <= -58000000000.0:
		tmp = t_1
	elif j <= -4e-47:
		tmp = x * (y * z)
	elif j <= -2.1e-207:
		tmp = t_1
	elif j <= -5.5e-287:
		tmp = x * (t * -a)
	elif j <= 18500.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -9.5e+62)
		tmp = t_2;
	elseif (j <= -58000000000.0)
		tmp = t_1;
	elseif (j <= -4e-47)
		tmp = Float64(x * Float64(y * z));
	elseif (j <= -2.1e-207)
		tmp = t_1;
	elseif (j <= -5.5e-287)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (j <= 18500.0)
		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 * ((a * i) - (z * c));
	t_2 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -9.5e+62)
		tmp = t_2;
	elseif (j <= -58000000000.0)
		tmp = t_1;
	elseif (j <= -4e-47)
		tmp = x * (y * z);
	elseif (j <= -2.1e-207)
		tmp = t_1;
	elseif (j <= -5.5e-287)
		tmp = x * (t * -a);
	elseif (j <= 18500.0)
		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[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -9.5e+62], t$95$2, If[LessEqual[j, -58000000000.0], t$95$1, If[LessEqual[j, -4e-47], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.1e-207], t$95$1, If[LessEqual[j, -5.5e-287], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 18500.0], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -9.5000000000000003e62 or 18500 < j

   1. Initial program 72.9%

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

   2. Taylor expanded in j around inf 66.1%

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

   if -9.5000000000000003e62 < j < -5.8e10 or -3.9999999999999999e-47 < j < -2.10000000000000003e-207 or -5.4999999999999998e-287 < j < 18500

   1. Initial program 74.4%

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

   2. Taylor expanded in b around inf 58.2%

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

      1. *-commutative 58.2%

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

   4. Simplified 58.2%

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

   if -5.8e10 < j < -3.9999999999999999e-47

   1. Initial program 71.9%

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

   2. Taylor expanded in y around inf 72.0%

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

      1. +-commutative 72.0%

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

      2. mul-1-neg 72.0%

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

      3. unsub-neg 72.0%

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

      4. *-commutative 72.0%

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

   4. Simplified 72.0%

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

   5. Taylor expanded in z around inf 71.9%

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

      1. *-commutative 71.9%

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

   7. Simplified 71.9%

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

   if -2.10000000000000003e-207 < j < -5.4999999999999998e-287

   1. Initial program 80.3%

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

      1. associate-+l- 80.3%

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

      2. *-commutative 80.3%

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

      3. fma-neg 80.3%

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

   3. Applied egg-rr 80.3%

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

   4. Taylor expanded in x around inf 67.8%

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

      1. *-commutative 67.8%

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

   6. Simplified 67.8%

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

   7. Taylor expanded in z around 0 48.7%

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

      1. mul-1-neg 48.7%

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

      2. associate-*r* 55.1%

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

      3. distribute-lft-neg-in 55.1%

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

      4. distribute-rgt-neg-out 55.1%

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

      5. *-commutative 55.1%

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

   9. Simplified 55.1%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -9.5 \cdot 10^{+62}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -58000000000:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -4 \cdot 10^{-47}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq -2.1 \cdot 10^{-207}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -5.5 \cdot 10^{-287}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;j \leq 18500:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 12: 51.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -1.25 \cdot 10^{+64}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.48 \cdot 10^{-36}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+91}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c))))
        (t_2 (* j (- (* t c) (* y i))))
        (t_3 (* x (- (* y z) (* t a)))))
   (if (<= x -1.25e+64)
     t_3
     (if (<= x -1.48e-36)
       (* y (- (* x z) (* i j)))
       (if (<= x 7.8e-153)
         t_1
         (if (<= x 4.5e-44)
           t_2
           (if (<= x 5.2e+39) t_1 (if (<= x 2.7e+91) 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 = b * ((a * i) - (z * c));
	double t_2 = j * ((t * c) - (y * i));
	double t_3 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.25e+64) {
		tmp = t_3;
	} else if (x <= -1.48e-36) {
		tmp = y * ((x * z) - (i * j));
	} else if (x <= 7.8e-153) {
		tmp = t_1;
	} else if (x <= 4.5e-44) {
		tmp = t_2;
	} else if (x <= 5.2e+39) {
		tmp = t_1;
	} else if (x <= 2.7e+91) {
		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 = b * ((a * i) - (z * c))
    t_2 = j * ((t * c) - (y * i))
    t_3 = x * ((y * z) - (t * a))
    if (x <= (-1.25d+64)) then
        tmp = t_3
    else if (x <= (-1.48d-36)) then
        tmp = y * ((x * z) - (i * j))
    else if (x <= 7.8d-153) then
        tmp = t_1
    else if (x <= 4.5d-44) then
        tmp = t_2
    else if (x <= 5.2d+39) then
        tmp = t_1
    else if (x <= 2.7d+91) 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 = b * ((a * i) - (z * c));
	double t_2 = j * ((t * c) - (y * i));
	double t_3 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.25e+64) {
		tmp = t_3;
	} else if (x <= -1.48e-36) {
		tmp = y * ((x * z) - (i * j));
	} else if (x <= 7.8e-153) {
		tmp = t_1;
	} else if (x <= 4.5e-44) {
		tmp = t_2;
	} else if (x <= 5.2e+39) {
		tmp = t_1;
	} else if (x <= 2.7e+91) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = j * ((t * c) - (y * i))
	t_3 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -1.25e+64:
		tmp = t_3
	elif x <= -1.48e-36:
		tmp = y * ((x * z) - (i * j))
	elif x <= 7.8e-153:
		tmp = t_1
	elif x <= 4.5e-44:
		tmp = t_2
	elif x <= 5.2e+39:
		tmp = t_1
	elif x <= 2.7e+91:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_3 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -1.25e+64)
		tmp = t_3;
	elseif (x <= -1.48e-36)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (x <= 7.8e-153)
		tmp = t_1;
	elseif (x <= 4.5e-44)
		tmp = t_2;
	elseif (x <= 5.2e+39)
		tmp = t_1;
	elseif (x <= 2.7e+91)
		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 = b * ((a * i) - (z * c));
	t_2 = j * ((t * c) - (y * i));
	t_3 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -1.25e+64)
		tmp = t_3;
	elseif (x <= -1.48e-36)
		tmp = y * ((x * z) - (i * j));
	elseif (x <= 7.8e-153)
		tmp = t_1;
	elseif (x <= 4.5e-44)
		tmp = t_2;
	elseif (x <= 5.2e+39)
		tmp = t_1;
	elseif (x <= 2.7e+91)
		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[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.25e+64], t$95$3, If[LessEqual[x, -1.48e-36], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.8e-153], t$95$1, If[LessEqual[x, 4.5e-44], t$95$2, If[LessEqual[x, 5.2e+39], t$95$1, If[LessEqual[x, 2.7e+91], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.25e64 or 2.7e91 < x

   1. Initial program 72.6%

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

   2. Taylor expanded in x around inf 70.3%

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

      1. *-commutative 70.3%

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

   4. Simplified 70.3%

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

   if -1.25e64 < x < -1.48e-36

   1. Initial program 75.6%

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

   2. Taylor expanded in y around inf 65.0%

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

      1. +-commutative 65.0%

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

      2. mul-1-neg 65.0%

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

      3. unsub-neg 65.0%

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

      4. *-commutative 65.0%

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

   4. Simplified 65.0%

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

   if -1.48e-36 < x < 7.8000000000000004e-153 or 4.4999999999999999e-44 < x < 5.2e39

   1. Initial program 77.8%

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

   2. Taylor expanded in b around inf 63.0%

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

      1. *-commutative 63.0%

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

   4. Simplified 63.0%

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

   if 7.8000000000000004e-153 < x < 4.4999999999999999e-44 or 5.2e39 < x < 2.7e91

   1. Initial program 66.7%

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

   2. Taylor expanded in j around inf 62.4%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+64}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -1.48 \cdot 10^{-36}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-153}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-44}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+39}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+91}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]

Alternative 13: 29.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ t_2 := i \cdot \left(a \cdot b\right)\\ \mathbf{if}\;b \leq -4.05 \cdot 10^{+211}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{+123}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;b \leq -1 \cdot 10^{+110}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{+28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{-233}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{-74}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j))) (t_2 (* i (* a b))))
   (if (<= b -4.05e+211)
     t_2
     (if (<= b -1.5e+123)
       (* (* z c) (- b))
       (if (<= b -1e+110)
         (* b (* a i))
         (if (<= b -1.15e+28)
           t_1
           (if (<= b 3.7e-233) (* x (* y z)) (if (<= b 8.2e-74) 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 = c * (t * j);
	double t_2 = i * (a * b);
	double tmp;
	if (b <= -4.05e+211) {
		tmp = t_2;
	} else if (b <= -1.5e+123) {
		tmp = (z * c) * -b;
	} else if (b <= -1e+110) {
		tmp = b * (a * i);
	} else if (b <= -1.15e+28) {
		tmp = t_1;
	} else if (b <= 3.7e-233) {
		tmp = x * (y * z);
	} else if (b <= 8.2e-74) {
		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 = c * (t * j)
    t_2 = i * (a * b)
    if (b <= (-4.05d+211)) then
        tmp = t_2
    else if (b <= (-1.5d+123)) then
        tmp = (z * c) * -b
    else if (b <= (-1d+110)) then
        tmp = b * (a * i)
    else if (b <= (-1.15d+28)) then
        tmp = t_1
    else if (b <= 3.7d-233) then
        tmp = x * (y * z)
    else if (b <= 8.2d-74) 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 = c * (t * j);
	double t_2 = i * (a * b);
	double tmp;
	if (b <= -4.05e+211) {
		tmp = t_2;
	} else if (b <= -1.5e+123) {
		tmp = (z * c) * -b;
	} else if (b <= -1e+110) {
		tmp = b * (a * i);
	} else if (b <= -1.15e+28) {
		tmp = t_1;
	} else if (b <= 3.7e-233) {
		tmp = x * (y * z);
	} else if (b <= 8.2e-74) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (t * j)
	t_2 = i * (a * b)
	tmp = 0
	if b <= -4.05e+211:
		tmp = t_2
	elif b <= -1.5e+123:
		tmp = (z * c) * -b
	elif b <= -1e+110:
		tmp = b * (a * i)
	elif b <= -1.15e+28:
		tmp = t_1
	elif b <= 3.7e-233:
		tmp = x * (y * z)
	elif b <= 8.2e-74:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(t * j))
	t_2 = Float64(i * Float64(a * b))
	tmp = 0.0
	if (b <= -4.05e+211)
		tmp = t_2;
	elseif (b <= -1.5e+123)
		tmp = Float64(Float64(z * c) * Float64(-b));
	elseif (b <= -1e+110)
		tmp = Float64(b * Float64(a * i));
	elseif (b <= -1.15e+28)
		tmp = t_1;
	elseif (b <= 3.7e-233)
		tmp = Float64(x * Float64(y * z));
	elseif (b <= 8.2e-74)
		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 = c * (t * j);
	t_2 = i * (a * b);
	tmp = 0.0;
	if (b <= -4.05e+211)
		tmp = t_2;
	elseif (b <= -1.5e+123)
		tmp = (z * c) * -b;
	elseif (b <= -1e+110)
		tmp = b * (a * i);
	elseif (b <= -1.15e+28)
		tmp = t_1;
	elseif (b <= 3.7e-233)
		tmp = x * (y * z);
	elseif (b <= 8.2e-74)
		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[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.05e+211], t$95$2, If[LessEqual[b, -1.5e+123], N[(N[(z * c), $MachinePrecision] * (-b)), $MachinePrecision], If[LessEqual[b, -1e+110], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.15e+28], t$95$1, If[LessEqual[b, 3.7e-233], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.2e-74], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -4.04999999999999986e211 or 8.20000000000000063e-74 < b

   1. Initial program 73.6%

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

   2. Taylor expanded in b around inf 59.9%

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

      1. *-commutative 59.9%

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

   4. Simplified 59.9%

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

   5. Taylor expanded in i around inf 38.2%

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

   6. Taylor expanded in b around 0 36.4%

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

      1. *-commutative 36.4%

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

      2. *-commutative 36.4%

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

      3. associate-*l* 40.9%

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

      4. *-commutative 40.9%

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

   8. Simplified 40.9%

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

   if -4.04999999999999986e211 < b < -1.50000000000000004e123

   1. Initial program 81.3%

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

   2. Taylor expanded in b around inf 87.8%

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

      1. *-commutative 87.8%

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

   4. Simplified 87.8%

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

   5. Taylor expanded in i around 0 69.2%

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

      1. mul-1-neg 69.2%

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

      2. distribute-lft-neg-out 69.2%

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

      3. *-commutative 69.2%

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

   7. Simplified 69.2%

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

   if -1.50000000000000004e123 < b < -1e110

   1. Initial program 99.5%

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

   2. Taylor expanded in b around inf 99.5%

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

      1. *-commutative 99.5%

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

   4. Simplified 99.5%

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

   5. Taylor expanded in i around inf 99.5%

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

   if -1e110 < b < -1.14999999999999992e28 or 3.6999999999999998e-233 < b < 8.20000000000000063e-74

   1. Initial program 69.9%

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

   2. Taylor expanded in t around inf 58.0%

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

   3. Taylor expanded in a around 0 45.6%

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

      1. *-commutative 45.6%

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

   5. Simplified 45.6%

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

   if -1.14999999999999992e28 < b < 3.6999999999999998e-233

   1. Initial program 74.7%

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

   2. Taylor expanded in y around inf 53.0%

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

      1. +-commutative 53.0%

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

      2. mul-1-neg 53.0%

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

      3. unsub-neg 53.0%

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

      4. *-commutative 53.0%

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

   4. Simplified 53.0%

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

   5. Taylor expanded in z around inf 37.2%

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

      1. *-commutative 37.2%

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

   7. Simplified 37.2%

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

4. Final simplification 43.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.05 \cdot 10^{+211}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{+123}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;b \leq -1 \cdot 10^{+110}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{+28}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{-233}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{-74}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 14: 29.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ t_2 := i \cdot \left(a \cdot b\right)\\ \mathbf{if}\;b \leq -2.4 \cdot 10^{+211}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{+121}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{+109}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;b \leq -1.1 \cdot 10^{+28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{-233}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-79}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j))) (t_2 (* i (* a b))))
   (if (<= b -2.4e+211)
     t_2
     (if (<= b -1.15e+121)
       (* c (* z (- b)))
       (if (<= b -6.5e+109)
         (* b (* a i))
         (if (<= b -1.1e+28)
           t_1
           (if (<= b 3.5e-233) (* x (* y z)) (if (<= b 1.4e-79) 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 = c * (t * j);
	double t_2 = i * (a * b);
	double tmp;
	if (b <= -2.4e+211) {
		tmp = t_2;
	} else if (b <= -1.15e+121) {
		tmp = c * (z * -b);
	} else if (b <= -6.5e+109) {
		tmp = b * (a * i);
	} else if (b <= -1.1e+28) {
		tmp = t_1;
	} else if (b <= 3.5e-233) {
		tmp = x * (y * z);
	} else if (b <= 1.4e-79) {
		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 = c * (t * j)
    t_2 = i * (a * b)
    if (b <= (-2.4d+211)) then
        tmp = t_2
    else if (b <= (-1.15d+121)) then
        tmp = c * (z * -b)
    else if (b <= (-6.5d+109)) then
        tmp = b * (a * i)
    else if (b <= (-1.1d+28)) then
        tmp = t_1
    else if (b <= 3.5d-233) then
        tmp = x * (y * z)
    else if (b <= 1.4d-79) 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 = c * (t * j);
	double t_2 = i * (a * b);
	double tmp;
	if (b <= -2.4e+211) {
		tmp = t_2;
	} else if (b <= -1.15e+121) {
		tmp = c * (z * -b);
	} else if (b <= -6.5e+109) {
		tmp = b * (a * i);
	} else if (b <= -1.1e+28) {
		tmp = t_1;
	} else if (b <= 3.5e-233) {
		tmp = x * (y * z);
	} else if (b <= 1.4e-79) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (t * j)
	t_2 = i * (a * b)
	tmp = 0
	if b <= -2.4e+211:
		tmp = t_2
	elif b <= -1.15e+121:
		tmp = c * (z * -b)
	elif b <= -6.5e+109:
		tmp = b * (a * i)
	elif b <= -1.1e+28:
		tmp = t_1
	elif b <= 3.5e-233:
		tmp = x * (y * z)
	elif b <= 1.4e-79:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(t * j))
	t_2 = Float64(i * Float64(a * b))
	tmp = 0.0
	if (b <= -2.4e+211)
		tmp = t_2;
	elseif (b <= -1.15e+121)
		tmp = Float64(c * Float64(z * Float64(-b)));
	elseif (b <= -6.5e+109)
		tmp = Float64(b * Float64(a * i));
	elseif (b <= -1.1e+28)
		tmp = t_1;
	elseif (b <= 3.5e-233)
		tmp = Float64(x * Float64(y * z));
	elseif (b <= 1.4e-79)
		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 = c * (t * j);
	t_2 = i * (a * b);
	tmp = 0.0;
	if (b <= -2.4e+211)
		tmp = t_2;
	elseif (b <= -1.15e+121)
		tmp = c * (z * -b);
	elseif (b <= -6.5e+109)
		tmp = b * (a * i);
	elseif (b <= -1.1e+28)
		tmp = t_1;
	elseif (b <= 3.5e-233)
		tmp = x * (y * z);
	elseif (b <= 1.4e-79)
		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[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.4e+211], t$95$2, If[LessEqual[b, -1.15e+121], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -6.5e+109], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.1e+28], t$95$1, If[LessEqual[b, 3.5e-233], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.4e-79], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -2.40000000000000018e211 or 1.40000000000000006e-79 < b

   1. Initial program 73.6%

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

   2. Taylor expanded in b around inf 59.9%

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

      1. *-commutative 59.9%

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

   4. Simplified 59.9%

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

   5. Taylor expanded in i around inf 38.2%

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

   6. Taylor expanded in b around 0 36.4%

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

      1. *-commutative 36.4%

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

      2. *-commutative 36.4%

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

      3. associate-*l* 40.9%

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

      4. *-commutative 40.9%

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

   8. Simplified 40.9%

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

   if -2.40000000000000018e211 < b < -1.1499999999999999e121

   1. Initial program 81.3%

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

      1. associate-+l- 81.3%

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

      2. *-commutative 81.3%

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

      3. fma-neg 81.3%

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

   3. Applied egg-rr 81.3%

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

   4. Taylor expanded in c around inf 69.3%

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

      1. *-commutative 69.3%

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

   6. Simplified 69.3%

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

   7. Taylor expanded in t around 0 69.2%

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

      1. mul-1-neg 69.2%

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

      2. distribute-rgt-neg-out 69.2%

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

   9. Simplified 69.2%

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

   if -1.1499999999999999e121 < b < -6.5e109

   1. Initial program 99.5%

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

   2. Taylor expanded in b around inf 99.5%

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

      1. *-commutative 99.5%

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

   4. Simplified 99.5%

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

   5. Taylor expanded in i around inf 99.5%

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

   if -6.5e109 < b < -1.09999999999999993e28 or 3.49999999999999991e-233 < b < 1.40000000000000006e-79

   1. Initial program 69.9%

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

   2. Taylor expanded in t around inf 58.0%

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

   3. Taylor expanded in a around 0 45.6%

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

      1. *-commutative 45.6%

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

   5. Simplified 45.6%

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

   if -1.09999999999999993e28 < b < 3.49999999999999991e-233

   1. Initial program 74.7%

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

   2. Taylor expanded in y around inf 53.0%

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

      1. +-commutative 53.0%

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

      2. mul-1-neg 53.0%

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

      3. unsub-neg 53.0%

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

      4. *-commutative 53.0%

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

   4. Simplified 53.0%

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

   5. Taylor expanded in z around inf 37.2%

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

      1. *-commutative 37.2%

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

   7. Simplified 37.2%

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

4. Final simplification 43.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.4 \cdot 10^{+211}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{+121}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{+109}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;b \leq -1.1 \cdot 10^{+28}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{-233}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-79}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 15: 29.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b\right)\\ \mathbf{if}\;b \leq -4.5 \cdot 10^{+110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.1 \cdot 10^{+28}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-233}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{-168}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{+14}:\\ \;\;\;\;j \cdot \left(i \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* a b))))
   (if (<= b -4.5e+110)
     t_1
     (if (<= b -1.1e+28)
       (* c (* t j))
       (if (<= b 3.1e-233)
         (* x (* y z))
         (if (<= b 5.8e-168)
           (* t (* c j))
           (if (<= b 4.4e+14) (* j (* i (- y))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (a * b);
	double tmp;
	if (b <= -4.5e+110) {
		tmp = t_1;
	} else if (b <= -1.1e+28) {
		tmp = c * (t * j);
	} else if (b <= 3.1e-233) {
		tmp = x * (y * z);
	} else if (b <= 5.8e-168) {
		tmp = t * (c * j);
	} else if (b <= 4.4e+14) {
		tmp = j * (i * -y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * (a * b)
    if (b <= (-4.5d+110)) then
        tmp = t_1
    else if (b <= (-1.1d+28)) then
        tmp = c * (t * j)
    else if (b <= 3.1d-233) then
        tmp = x * (y * z)
    else if (b <= 5.8d-168) then
        tmp = t * (c * j)
    else if (b <= 4.4d+14) then
        tmp = j * (i * -y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (a * b);
	double tmp;
	if (b <= -4.5e+110) {
		tmp = t_1;
	} else if (b <= -1.1e+28) {
		tmp = c * (t * j);
	} else if (b <= 3.1e-233) {
		tmp = x * (y * z);
	} else if (b <= 5.8e-168) {
		tmp = t * (c * j);
	} else if (b <= 4.4e+14) {
		tmp = j * (i * -y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (a * b)
	tmp = 0
	if b <= -4.5e+110:
		tmp = t_1
	elif b <= -1.1e+28:
		tmp = c * (t * j)
	elif b <= 3.1e-233:
		tmp = x * (y * z)
	elif b <= 5.8e-168:
		tmp = t * (c * j)
	elif b <= 4.4e+14:
		tmp = j * (i * -y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(a * b))
	tmp = 0.0
	if (b <= -4.5e+110)
		tmp = t_1;
	elseif (b <= -1.1e+28)
		tmp = Float64(c * Float64(t * j));
	elseif (b <= 3.1e-233)
		tmp = Float64(x * Float64(y * z));
	elseif (b <= 5.8e-168)
		tmp = Float64(t * Float64(c * j));
	elseif (b <= 4.4e+14)
		tmp = Float64(j * Float64(i * Float64(-y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * (a * b);
	tmp = 0.0;
	if (b <= -4.5e+110)
		tmp = t_1;
	elseif (b <= -1.1e+28)
		tmp = c * (t * j);
	elseif (b <= 3.1e-233)
		tmp = x * (y * z);
	elseif (b <= 5.8e-168)
		tmp = t * (c * j);
	elseif (b <= 4.4e+14)
		tmp = j * (i * -y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.5e+110], t$95$1, If[LessEqual[b, -1.1e+28], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.1e-233], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.8e-168], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.4e+14], N[(j * N[(i * (-y)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -4.5000000000000003e110 or 4.4e14 < b

   1. Initial program 73.9%

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

   2. Taylor expanded in b around inf 69.1%

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

      1. *-commutative 69.1%

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

   4. Simplified 69.1%

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

   5. Taylor expanded in i around inf 42.0%

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

   6. Taylor expanded in b around 0 40.0%

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

      1. *-commutative 40.0%

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

      2. *-commutative 40.0%

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

      3. associate-*l* 44.3%

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

      4. *-commutative 44.3%

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

   8. Simplified 44.3%

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

   if -4.5000000000000003e110 < b < -1.09999999999999993e28

   1. Initial program 77.9%

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

   2. Taylor expanded in t around inf 58.2%

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

   3. Taylor expanded in a around 0 49.1%

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

      1. *-commutative 49.1%

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

   5. Simplified 49.1%

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

   if -1.09999999999999993e28 < b < 3.10000000000000015e-233

   1. Initial program 74.7%

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

   2. Taylor expanded in y around inf 53.0%

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

      1. +-commutative 53.0%

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

      2. mul-1-neg 53.0%

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

      3. unsub-neg 53.0%

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

      4. *-commutative 53.0%

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

   4. Simplified 53.0%

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

   5. Taylor expanded in z around inf 37.2%

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

      1. *-commutative 37.2%

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

   7. Simplified 37.2%

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

   if 3.10000000000000015e-233 < b < 5.7999999999999997e-168

   1. Initial program 62.0%

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

   2. Taylor expanded in t around inf 78.4%

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

   3. Taylor expanded in a around 0 55.5%

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

   if 5.7999999999999997e-168 < b < 4.4e14

   1. Initial program 74.4%

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

   2. Taylor expanded in y around inf 50.2%

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

      1. +-commutative 50.2%

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

      2. mul-1-neg 50.2%

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

      3. unsub-neg 50.2%

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

      4. *-commutative 50.2%

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

   4. Simplified 50.2%

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

   5. Taylor expanded in z around 0 40.8%

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

      1. mul-1-neg 40.8%

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

      2. distribute-lft-neg-in 40.8%

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

      3. associate-*r* 34.6%

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

      4. *-commutative 34.6%

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

      5. associate-*l* 43.6%

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

      6. distribute-lft-neg-in 43.6%

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

      7. distribute-rgt-neg-in 43.6%

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

   7. Simplified 43.6%

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

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{+110}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq -1.1 \cdot 10^{+28}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-233}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{-168}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{+14}:\\ \;\;\;\;j \cdot \left(i \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 16: 29.2% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ t_2 := i \cdot \left(a \cdot b\right)\\ \mathbf{if}\;b \leq -2.4 \cdot 10^{+110}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -9.2 \cdot 10^{+27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{-233}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-75}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j))) (t_2 (* i (* a b))))
   (if (<= b -2.4e+110)
     t_2
     (if (<= b -9.2e+27)
       t_1
       (if (<= b 4.3e-233) (* x (* y z)) (if (<= b 1.7e-75) 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 = c * (t * j);
	double t_2 = i * (a * b);
	double tmp;
	if (b <= -2.4e+110) {
		tmp = t_2;
	} else if (b <= -9.2e+27) {
		tmp = t_1;
	} else if (b <= 4.3e-233) {
		tmp = x * (y * z);
	} else if (b <= 1.7e-75) {
		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 = c * (t * j)
    t_2 = i * (a * b)
    if (b <= (-2.4d+110)) then
        tmp = t_2
    else if (b <= (-9.2d+27)) then
        tmp = t_1
    else if (b <= 4.3d-233) then
        tmp = x * (y * z)
    else if (b <= 1.7d-75) 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 = c * (t * j);
	double t_2 = i * (a * b);
	double tmp;
	if (b <= -2.4e+110) {
		tmp = t_2;
	} else if (b <= -9.2e+27) {
		tmp = t_1;
	} else if (b <= 4.3e-233) {
		tmp = x * (y * z);
	} else if (b <= 1.7e-75) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (t * j)
	t_2 = i * (a * b)
	tmp = 0
	if b <= -2.4e+110:
		tmp = t_2
	elif b <= -9.2e+27:
		tmp = t_1
	elif b <= 4.3e-233:
		tmp = x * (y * z)
	elif b <= 1.7e-75:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(t * j))
	t_2 = Float64(i * Float64(a * b))
	tmp = 0.0
	if (b <= -2.4e+110)
		tmp = t_2;
	elseif (b <= -9.2e+27)
		tmp = t_1;
	elseif (b <= 4.3e-233)
		tmp = Float64(x * Float64(y * z));
	elseif (b <= 1.7e-75)
		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 = c * (t * j);
	t_2 = i * (a * b);
	tmp = 0.0;
	if (b <= -2.4e+110)
		tmp = t_2;
	elseif (b <= -9.2e+27)
		tmp = t_1;
	elseif (b <= 4.3e-233)
		tmp = x * (y * z);
	elseif (b <= 1.7e-75)
		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[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.4e+110], t$95$2, If[LessEqual[b, -9.2e+27], t$95$1, If[LessEqual[b, 4.3e-233], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.7e-75], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.40000000000000012e110 or 1.70000000000000008e-75 < b

   1. Initial program 75.2%

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

   2. Taylor expanded in b around inf 64.6%

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

      1. *-commutative 64.6%

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

   4. Simplified 64.6%

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

   5. Taylor expanded in i around inf 39.9%

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

   6. Taylor expanded in b around 0 38.2%

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

      1. *-commutative 38.2%

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

      2. *-commutative 38.2%

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

      3. associate-*l* 41.9%

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

      4. *-commutative 41.9%

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

   8. Simplified 41.9%

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

   if -2.40000000000000012e110 < b < -9.2000000000000002e27 or 4.29999999999999988e-233 < b < 1.70000000000000008e-75

   1. Initial program 69.9%

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

   2. Taylor expanded in t around inf 58.0%

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

   3. Taylor expanded in a around 0 45.6%

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

      1. *-commutative 45.6%

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

   5. Simplified 45.6%

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

   if -9.2000000000000002e27 < b < 4.29999999999999988e-233

   1. Initial program 74.7%

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

   2. Taylor expanded in y around inf 53.0%

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

      1. +-commutative 53.0%

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

      2. mul-1-neg 53.0%

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

      3. unsub-neg 53.0%

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

      4. *-commutative 53.0%

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

   4. Simplified 53.0%

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

   5. Taylor expanded in z around inf 37.2%

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

      1. *-commutative 37.2%

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

   7. Simplified 37.2%

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

4. Final simplification 41.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.4 \cdot 10^{+110}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq -9.2 \cdot 10^{+27}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{-233}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-75}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 17: 28.2% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -6.5 \cdot 10^{+197} \lor \neg \left(j \leq 2 \cdot 10^{-44}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -6.5e+197) (not (<= j 2e-44))) (* c (* t j)) (* b (* a 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 ((j <= -6.5e+197) || !(j <= 2e-44)) {
		tmp = c * (t * j);
	} else {
		tmp = b * (a * 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 ((j <= (-6.5d+197)) .or. (.not. (j <= 2d-44))) then
        tmp = c * (t * j)
    else
        tmp = b * (a * 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 ((j <= -6.5e+197) || !(j <= 2e-44)) {
		tmp = c * (t * j);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -6.5e+197) or not (j <= 2e-44):
		tmp = c * (t * j)
	else:
		tmp = b * (a * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -6.5e+197) || !(j <= 2e-44))
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(b * Float64(a * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -6.5e+197) || ~((j <= 2e-44)))
		tmp = c * (t * j);
	else
		tmp = b * (a * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -6.5e+197], N[Not[LessEqual[j, 2e-44]], $MachinePrecision]], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -6.49999999999999952e197 or 1.99999999999999991e-44 < j

   1. Initial program 70.6%

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

   2. Taylor expanded in t around inf 42.2%

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

   3. Taylor expanded in a around 0 42.9%

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

      1. *-commutative 42.9%

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

   5. Simplified 42.9%

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

   if -6.49999999999999952e197 < j < 1.99999999999999991e-44

   1. Initial program 75.8%

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

   2. Taylor expanded in b around inf 49.0%

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

      1. *-commutative 49.0%

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

   4. Simplified 49.0%

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

   5. Taylor expanded in i around inf 30.5%

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

4. Final simplification 34.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -6.5 \cdot 10^{+197} \lor \neg \left(j \leq 2 \cdot 10^{-44}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]

Alternative 18: 29.3% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.6 \cdot 10^{+112} \lor \neg \left(b \leq 1.6 \cdot 10^{-72}\right):\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -2.6e+112) (not (<= b 1.6e-72))) (* i (* a b)) (* c (* t 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 <= -2.6e+112) || !(b <= 1.6e-72)) {
		tmp = i * (a * b);
	} else {
		tmp = c * (t * 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 <= (-2.6d+112)) .or. (.not. (b <= 1.6d-72))) then
        tmp = i * (a * b)
    else
        tmp = c * (t * 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 <= -2.6e+112) || !(b <= 1.6e-72)) {
		tmp = i * (a * b);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -2.6e+112) or not (b <= 1.6e-72):
		tmp = i * (a * b)
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -2.6e+112) || !(b <= 1.6e-72))
		tmp = Float64(i * Float64(a * b));
	else
		tmp = Float64(c * Float64(t * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -2.6e+112) || ~((b <= 1.6e-72)))
		tmp = i * (a * b);
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -2.6e+112], N[Not[LessEqual[b, 1.6e-72]], $MachinePrecision]], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.6000000000000001e112 or 1.6e-72 < b

   1. Initial program 75.2%

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

   2. Taylor expanded in b around inf 64.6%

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

      1. *-commutative 64.6%

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

   4. Simplified 64.6%

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

   5. Taylor expanded in i around inf 39.9%

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

   6. Taylor expanded in b around 0 38.2%

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

      1. *-commutative 38.2%

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

      2. *-commutative 38.2%

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

      3. associate-*l* 41.9%

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

      4. *-commutative 41.9%

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

   8. Simplified 41.9%

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

   if -2.6000000000000001e112 < b < 1.6e-72

   1. Initial program 72.9%

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

   2. Taylor expanded in t around inf 44.6%

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

   3. Taylor expanded in a around 0 29.5%

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

      1. *-commutative 29.5%

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

   5. Simplified 29.5%

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

4. Final simplification 35.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.6 \cdot 10^{+112} \lor \neg \left(b \leq 1.6 \cdot 10^{-72}\right):\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]

Alternative 19: 21.8% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(b \cdot i\right) \end{array} \]

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 74.0%

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

2. Taylor expanded in b around inf 40.5%

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

   1. *-commutative 40.5%

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

4. Simplified 40.5%

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

5. Taylor expanded in i around inf 23.4%

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

6. Final simplification 23.4%

   \[\leadsto a \cdot \left(b \cdot i\right) \]

Alternative 20: 21.9% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ b \cdot \left(a \cdot i\right) \end{array} \]

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 74.0%

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

2. Taylor expanded in b around inf 40.5%

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

   1. *-commutative 40.5%

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

4. Simplified 40.5%

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

5. Taylor expanded in i around inf 25.3%

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

6. Final simplification 25.3%

   \[\leadsto b \cdot \left(a \cdot i\right) \]

Developer target: 69.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ t_2 := x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{if}\;t < -8.120978919195912 \cdot 10^{-33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t < -4.712553818218485 \cdot 10^{-169}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t < -7.633533346031584 \cdot 10^{-308}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t < 1.0535888557455487 \cdot 10^{-139}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
          (/
           (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0)))
           (+ (* c t) (* i y)))))
        (t_2
         (-
          (* x (- (* z y) (* a t)))
          (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))
   (if (< t -8.120978919195912e-33)
     t_2
     (if (< t -4.712553818218485e-169)
       t_1
       (if (< t -7.633533346031584e-308)
         t_2
         (if (< t 1.0535888557455487e-139) 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 * ((c * z) - (i * a)))) + ((j * (pow((c * t), 2.0) - pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		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 * ((c * z) - (i * a)))) + ((j * (((c * t) ** 2.0d0) - ((i * y) ** 2.0d0))) / ((c * t) + (i * y)))
    t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
    if (t < (-8.120978919195912d-33)) then
        tmp = t_2
    else if (t < (-4.712553818218485d-169)) then
        tmp = t_1
    else if (t < (-7.633533346031584d-308)) then
        tmp = t_2
    else if (t < 1.0535888557455487d-139) 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 * ((c * z) - (i * a)))) + ((j * (Math.pow((c * t), 2.0) - Math.pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		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 * ((c * z) - (i * a)))) + ((j * (math.pow((c * t), 2.0) - math.pow((i * y), 2.0))) / ((c * t) + (i * y)))
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
	tmp = 0
	if t < -8.120978919195912e-33:
		tmp = t_2
	elif t < -4.712553818218485e-169:
		tmp = t_1
	elif t < -7.633533346031584e-308:
		tmp = t_2
	elif t < 1.0535888557455487e-139:
		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(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(Float64(j * Float64((Float64(c * t) ^ 2.0) - (Float64(i * y) ^ 2.0))) / Float64(Float64(c * t) + Float64(i * y))))
	t_2 = Float64(Float64(x * Float64(Float64(z * y) - Float64(a * t))) - Float64(Float64(b * Float64(Float64(z * c) - Float64(a * i))) - Float64(Float64(Float64(c * t) - Float64(y * i)) * j)))
	tmp = 0.0
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		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 * ((c * z) - (i * a)))) + ((j * (((c * t) ^ 2.0) - ((i * y) ^ 2.0))) / ((c * t) + (i * y)));
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	tmp = 0.0;
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		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[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[Power[N[(c * t), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(i * y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * t), $MachinePrecision] + N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(c * t), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -8.120978919195912e-33], t$95$2, If[Less[t, -4.712553818218485e-169], t$95$1, If[Less[t, -7.633533346031584e-308], t$95$2, If[Less[t, 1.0535888557455487e-139], t$95$1, t$95$2]]]]]]

Reproduce

herbie shell --seed 2023308 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< t -8.120978919195912e-33) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -4.712553818218485e-169) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (if (< t -7.633533346031584e-308) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 1.0535888557455487e-139) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))