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

Percentage Accurate: 74.0% → 81.2%

Time: 28.1s

Alternatives: 21

Speedup: 0.5×

• 57.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 74.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 81.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;t_1 \leq 10^{+277}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;\left(t \cdot \left(b \cdot i - x \cdot a\right) - \left(j \cdot \left(y \cdot i - a \cdot c\right) - x \cdot \left(y \cdot z\right)\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (+ (* x (- (* y z) (* t a))) (* b (- (* t i) (* z c))))
          (* j (- (* a c) (* y i))))))
   (if (<= t_1 1e+277)
     t_1
     (if (<= t_1 INFINITY)
       (-
        (-
         (* t (- (* b i) (* x a)))
         (- (* j (- (* y i) (* a c))) (* x (* y z))))
        (* b (* z c)))
       (* 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 * ((t * i) - (z * c)))) + (j * ((a * c) - (y * i)));
	double tmp;
	if (t_1 <= 1e+277) {
		tmp = t_1;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = ((t * ((b * i) - (x * a))) - ((j * ((y * i) - (a * c))) - (x * (y * z)))) - (b * (z * c));
	} 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 * ((t * i) - (z * c)))) + (j * ((a * c) - (y * i)));
	double tmp;
	if (t_1 <= 1e+277) {
		tmp = t_1;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = ((t * ((b * i) - (x * a))) - ((j * ((y * i) - (a * c))) - (x * (y * z)))) - (b * (z * c));
	} 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 * ((t * i) - (z * c)))) + (j * ((a * c) - (y * i)))
	tmp = 0
	if t_1 <= 1e+277:
		tmp = t_1
	elif t_1 <= math.inf:
		tmp = ((t * ((b * i) - (x * a))) - ((j * ((y * i) - (a * c))) - (x * (y * z)))) - (b * (z * c))
	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(t * i) - Float64(z * c)))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))))
	tmp = 0.0
	if (t_1 <= 1e+277)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(Float64(t * Float64(Float64(b * i) - Float64(x * a))) - Float64(Float64(j * Float64(Float64(y * i) - Float64(a * c))) - Float64(x * Float64(y * z)))) - Float64(b * Float64(z * c)));
	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 * ((t * i) - (z * c)))) + (j * ((a * c) - (y * i)));
	tmp = 0.0;
	if (t_1 <= 1e+277)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = ((t * ((b * i) - (x * a))) - ((j * ((y * i) - (a * c))) - (x * (y * z)))) - (b * (z * c));
	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[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+277], t$95$1, If[LessEqual[t$95$1, Infinity], N[(N[(N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(j * N[(N[(y * i), $MachinePrecision] - N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))) < 1e277

   1. Initial program 93.4%

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

   if 1e277 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))) < +inf.0

   1. Initial program 72.2%

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

   2. Taylor expanded in t around -inf 80.8%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in y around inf 42.2%

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

      1. +-commutative 42.2%

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

      2. mul-1-neg 42.2%

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

      3. unsub-neg 42.2%

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

      4. *-commutative 42.2%

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

   4. Simplified 42.2%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right) \leq 10^{+277}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right) \leq \infty:\\ \;\;\;\;\left(t \cdot \left(b \cdot i - x \cdot a\right) - \left(j \cdot \left(y \cdot i - a \cdot c\right) - x \cdot \left(y \cdot z\right)\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]

Alternative 2: 82.2% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (+ (* x (- (* y z) (* t a))) (* b (- (* t i) (* z c))))
          (* j (- (* a 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 * ((t * i) - (z * c)))) + (j * ((a * 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 * ((t * i) - (z * c)))) + (j * ((a * 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 * ((t * i) - (z * c)))) + (j * ((a * 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(t * i) - Float64(z * c)))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(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 * ((t * i) - (z * c)))) + (j * ((a * 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[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(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 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))) < +inf.0

   1. Initial program 86.9%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in y around inf 42.2%

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

      1. +-commutative 42.2%

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

      2. mul-1-neg 42.2%

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

      3. unsub-neg 42.2%

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

      4. *-commutative 42.2%

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

   4. Simplified 42.2%

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

4. Final simplification 78.9%

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

Alternative 3: 60.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;a \leq 2.2 \cdot 10^{-204}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-163}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq 2.65 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* j (- (* a c) (* y i))) (* b (- (* t i) (* z c))))))
   (if (<= a 2.2e-204)
     t_1
     (if (<= a 3.1e-163)
       (* z (- (* x y) (* b c)))
       (if (<= a 2.65e+38) t_1 (* a (- (* c j) (* x t))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((a * c) - (y * i))) + (b * ((t * i) - (z * c)));
	double tmp;
	if (a <= 2.2e-204) {
		tmp = t_1;
	} else if (a <= 3.1e-163) {
		tmp = z * ((x * y) - (b * c));
	} else if (a <= 2.65e+38) {
		tmp = t_1;
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (j * ((a * c) - (y * i))) + (b * ((t * i) - (z * c)))
    if (a <= 2.2d-204) then
        tmp = t_1
    else if (a <= 3.1d-163) then
        tmp = z * ((x * y) - (b * c))
    else if (a <= 2.65d+38) then
        tmp = t_1
    else
        tmp = a * ((c * j) - (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((a * c) - (y * i))) + (b * ((t * i) - (z * c)));
	double tmp;
	if (a <= 2.2e-204) {
		tmp = t_1;
	} else if (a <= 3.1e-163) {
		tmp = z * ((x * y) - (b * c));
	} else if (a <= 2.65e+38) {
		tmp = t_1;
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((a * c) - (y * i))) + (b * ((t * i) - (z * c)))
	tmp = 0
	if a <= 2.2e-204:
		tmp = t_1
	elif a <= 3.1e-163:
		tmp = z * ((x * y) - (b * c))
	elif a <= 2.65e+38:
		tmp = t_1
	else:
		tmp = a * ((c * j) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))))
	tmp = 0.0
	if (a <= 2.2e-204)
		tmp = t_1;
	elseif (a <= 3.1e-163)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (a <= 2.65e+38)
		tmp = t_1;
	else
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (j * ((a * c) - (y * i))) + (b * ((t * i) - (z * c)));
	tmp = 0.0;
	if (a <= 2.2e-204)
		tmp = t_1;
	elseif (a <= 3.1e-163)
		tmp = z * ((x * y) - (b * c));
	elseif (a <= 2.65e+38)
		tmp = t_1;
	else
		tmp = a * ((c * j) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, 2.2e-204], t$95$1, If[LessEqual[a, 3.1e-163], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.65e+38], t$95$1, N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < 2.1999999999999998e-204 or 3.09999999999999975e-163 < a < 2.65000000000000012e38

   1. Initial program 77.9%

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

   2. Taylor expanded in x around 0 66.1%

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

      1. *-commutative 66.1%

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

   4. Simplified 66.1%

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

   if 2.1999999999999998e-204 < a < 3.09999999999999975e-163

   1. Initial program 70.2%

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

   2. Taylor expanded in z around inf 70.7%

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

   if 2.65000000000000012e38 < a

   1. Initial program 48.7%

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

   2. Taylor expanded in a around inf 67.1%

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

      1. +-commutative 67.1%

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

      2. mul-1-neg 67.1%

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

      3. unsub-neg 67.1%

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

   4. Simplified 67.1%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 2.2 \cdot 10^{-204}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-163}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq 2.65 \cdot 10^{+38}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]

Alternative 4: 62.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -5.4 \cdot 10^{+97}:\\ \;\;\;\;t_2 - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;j \leq 4.9 \cdot 10^{-160}:\\ \;\;\;\;\left(a \cdot \left(c \cdot j\right) - a \cdot \left(x \cdot t\right)\right) + t_1\\ \mathbf{elif}\;j \leq 9.5 \cdot 10^{-73}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_2 + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* j (- (* a c) (* y i)))))
   (if (<= j -5.4e+97)
     (- t_2 (* b (* z c)))
     (if (<= j 4.9e-160)
       (+ (- (* a (* c j)) (* a (* x t))) t_1)
       (if (<= j 9.5e-73) (* y (- (* x z) (* i j))) (+ t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -5.4e+97) {
		tmp = t_2 - (b * (z * c));
	} else if (j <= 4.9e-160) {
		tmp = ((a * (c * j)) - (a * (x * t))) + t_1;
	} else if (j <= 9.5e-73) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_2 + 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) :: t_2
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = j * ((a * c) - (y * i))
    if (j <= (-5.4d+97)) then
        tmp = t_2 - (b * (z * c))
    else if (j <= 4.9d-160) then
        tmp = ((a * (c * j)) - (a * (x * t))) + t_1
    else if (j <= 9.5d-73) then
        tmp = y * ((x * z) - (i * j))
    else
        tmp = t_2 + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -5.4e+97) {
		tmp = t_2 - (b * (z * c));
	} else if (j <= 4.9e-160) {
		tmp = ((a * (c * j)) - (a * (x * t))) + t_1;
	} else if (j <= 9.5e-73) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_2 + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -5.4e+97:
		tmp = t_2 - (b * (z * c))
	elif j <= 4.9e-160:
		tmp = ((a * (c * j)) - (a * (x * t))) + t_1
	elif j <= 9.5e-73:
		tmp = y * ((x * z) - (i * j))
	else:
		tmp = t_2 + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -5.4e+97)
		tmp = Float64(t_2 - Float64(b * Float64(z * c)));
	elseif (j <= 4.9e-160)
		tmp = Float64(Float64(Float64(a * Float64(c * j)) - Float64(a * Float64(x * t))) + t_1);
	elseif (j <= 9.5e-73)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	else
		tmp = Float64(t_2 + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -5.4e+97)
		tmp = t_2 - (b * (z * c));
	elseif (j <= 4.9e-160)
		tmp = ((a * (c * j)) - (a * (x * t))) + t_1;
	elseif (j <= 9.5e-73)
		tmp = y * ((x * z) - (i * j));
	else
		tmp = t_2 + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -5.4e+97], N[(t$95$2 - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.9e-160], N[(N[(N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[j, 9.5e-73], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$2 + t$95$1), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -5.39999999999999987e97

   1. Initial program 69.6%

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

   2. Taylor expanded in x around 0 69.5%

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

      1. *-commutative 69.5%

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

   4. Simplified 69.5%

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

   5. Taylor expanded in c around inf 72.2%

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

   if -5.39999999999999987e97 < j < 4.8999999999999999e-160

   1. Initial program 71.4%

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

   2. Taylor expanded in y around 0 68.3%

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

   if 4.8999999999999999e-160 < j < 9.50000000000000005e-73

   1. Initial program 47.1%

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

   2. Taylor expanded in y around inf 62.0%

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

      1. +-commutative 62.0%

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

      2. mul-1-neg 62.0%

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

      3. unsub-neg 62.0%

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

      4. *-commutative 62.0%

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

   4. Simplified 62.0%

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

   if 9.50000000000000005e-73 < j

   1. Initial program 78.6%

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

   2. Taylor expanded in x around 0 75.0%

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

      1. *-commutative 75.0%

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

   4. Simplified 75.0%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -5.4 \cdot 10^{+97}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;j \leq 4.9 \cdot 10^{-160}:\\ \;\;\;\;\left(a \cdot \left(c \cdot j\right) - a \cdot \left(x \cdot t\right)\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 9.5 \cdot 10^{-73}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 5: 51.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_3 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -5.5 \cdot 10^{+45}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -5.7 \cdot 10^{-238}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-272}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-208}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-163}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{+33}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j))))
        (t_2 (* b (- (* t i) (* z c))))
        (t_3 (* a (- (* c j) (* x t)))))
   (if (<= a -5.5e+45)
     t_3
     (if (<= a -5.7e-238)
       t_2
       (if (<= a 5e-272)
         t_1
         (if (<= a 1.25e-208)
           t_2
           (if (<= a 2.8e-163)
             (* y (- (* x z) (* i j)))
             (if (<= a 9e-96)
               t_1
               (if (<= a 4.9e+33) (* c (- (* a j) (* z b))) 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 = i * ((t * b) - (y * j));
	double t_2 = b * ((t * i) - (z * c));
	double t_3 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -5.5e+45) {
		tmp = t_3;
	} else if (a <= -5.7e-238) {
		tmp = t_2;
	} else if (a <= 5e-272) {
		tmp = t_1;
	} else if (a <= 1.25e-208) {
		tmp = t_2;
	} else if (a <= 2.8e-163) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= 9e-96) {
		tmp = t_1;
	} else if (a <= 4.9e+33) {
		tmp = c * ((a * j) - (z * b));
	} 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 = i * ((t * b) - (y * j))
    t_2 = b * ((t * i) - (z * c))
    t_3 = a * ((c * j) - (x * t))
    if (a <= (-5.5d+45)) then
        tmp = t_3
    else if (a <= (-5.7d-238)) then
        tmp = t_2
    else if (a <= 5d-272) then
        tmp = t_1
    else if (a <= 1.25d-208) then
        tmp = t_2
    else if (a <= 2.8d-163) then
        tmp = y * ((x * z) - (i * j))
    else if (a <= 9d-96) then
        tmp = t_1
    else if (a <= 4.9d+33) then
        tmp = c * ((a * j) - (z * b))
    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 = i * ((t * b) - (y * j));
	double t_2 = b * ((t * i) - (z * c));
	double t_3 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -5.5e+45) {
		tmp = t_3;
	} else if (a <= -5.7e-238) {
		tmp = t_2;
	} else if (a <= 5e-272) {
		tmp = t_1;
	} else if (a <= 1.25e-208) {
		tmp = t_2;
	} else if (a <= 2.8e-163) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= 9e-96) {
		tmp = t_1;
	} else if (a <= 4.9e+33) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	t_2 = b * ((t * i) - (z * c))
	t_3 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -5.5e+45:
		tmp = t_3
	elif a <= -5.7e-238:
		tmp = t_2
	elif a <= 5e-272:
		tmp = t_1
	elif a <= 1.25e-208:
		tmp = t_2
	elif a <= 2.8e-163:
		tmp = y * ((x * z) - (i * j))
	elif a <= 9e-96:
		tmp = t_1
	elif a <= 4.9e+33:
		tmp = c * ((a * j) - (z * b))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_3 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -5.5e+45)
		tmp = t_3;
	elseif (a <= -5.7e-238)
		tmp = t_2;
	elseif (a <= 5e-272)
		tmp = t_1;
	elseif (a <= 1.25e-208)
		tmp = t_2;
	elseif (a <= 2.8e-163)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (a <= 9e-96)
		tmp = t_1;
	elseif (a <= 4.9e+33)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((t * b) - (y * j));
	t_2 = b * ((t * i) - (z * c));
	t_3 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -5.5e+45)
		tmp = t_3;
	elseif (a <= -5.7e-238)
		tmp = t_2;
	elseif (a <= 5e-272)
		tmp = t_1;
	elseif (a <= 1.25e-208)
		tmp = t_2;
	elseif (a <= 2.8e-163)
		tmp = y * ((x * z) - (i * j));
	elseif (a <= 9e-96)
		tmp = t_1;
	elseif (a <= 4.9e+33)
		tmp = c * ((a * j) - (z * b));
	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[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.5e+45], t$95$3, If[LessEqual[a, -5.7e-238], t$95$2, If[LessEqual[a, 5e-272], t$95$1, If[LessEqual[a, 1.25e-208], t$95$2, If[LessEqual[a, 2.8e-163], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9e-96], t$95$1, If[LessEqual[a, 4.9e+33], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -5.5000000000000001e45 or 4.90000000000000014e33 < a

   1. Initial program 55.3%

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

   2. Taylor expanded in a around inf 61.9%

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

      1. +-commutative 61.9%

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

      2. mul-1-neg 61.9%

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

      3. unsub-neg 61.9%

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

   4. Simplified 61.9%

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

   if -5.5000000000000001e45 < a < -5.70000000000000022e-238 or 4.99999999999999982e-272 < a < 1.24999999999999991e-208

   1. Initial program 84.8%

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

   2. Taylor expanded in b around inf 58.8%

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

   if -5.70000000000000022e-238 < a < 4.99999999999999982e-272 or 2.8e-163 < a < 9e-96

   1. Initial program 90.7%

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

   2. Taylor expanded in i around inf 73.3%

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

      1. distribute-lft-out-- 73.3%

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

      2. *-commutative 73.3%

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

   4. Simplified 73.3%

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

   5. Taylor expanded in i around 0 73.3%

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

      1. mul-1-neg 73.3%

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

      2. distribute-rgt-neg-in 73.3%

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

      3. neg-sub0 73.3%

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

      4. associate-+l- 73.3%

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

      5. neg-sub0 73.3%

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

      6. +-commutative 73.3%

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

      7. unsub-neg 73.3%

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

   7. Simplified 73.3%

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

   if 1.24999999999999991e-208 < a < 2.8e-163

   1. Initial program 69.4%

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

   2. Taylor expanded in y around inf 62.6%

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

      1. +-commutative 62.6%

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

      2. mul-1-neg 62.6%

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

      3. unsub-neg 62.6%

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

      4. *-commutative 62.6%

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

   4. Simplified 62.6%

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

   if 9e-96 < a < 4.90000000000000014e33

   1. Initial program 74.6%

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

   2. Taylor expanded in c around inf 52.7%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{+45}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -5.7 \cdot 10^{-238}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-272}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-208}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-163}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-96}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{+33}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]

Alternative 6: 51.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_3 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -2.9 \cdot 10^{+45}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-237}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-273}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-209}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-163}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+43}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j))))
        (t_2 (* b (- (* t i) (* z c))))
        (t_3 (* a (- (* c j) (* x t)))))
   (if (<= a -2.9e+45)
     t_3
     (if (<= a -9e-237)
       t_2
       (if (<= a 9e-273)
         t_1
         (if (<= a 6.2e-209)
           t_2
           (if (<= a 3.1e-163)
             (* y (- (* x z) (* i j)))
             (if (<= a 3.4e-96)
               t_1
               (if (<= a 5.5e+43) (* z (- (* x y) (* b c))) 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 = i * ((t * b) - (y * j));
	double t_2 = b * ((t * i) - (z * c));
	double t_3 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -2.9e+45) {
		tmp = t_3;
	} else if (a <= -9e-237) {
		tmp = t_2;
	} else if (a <= 9e-273) {
		tmp = t_1;
	} else if (a <= 6.2e-209) {
		tmp = t_2;
	} else if (a <= 3.1e-163) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= 3.4e-96) {
		tmp = t_1;
	} else if (a <= 5.5e+43) {
		tmp = z * ((x * y) - (b * c));
	} 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 = i * ((t * b) - (y * j))
    t_2 = b * ((t * i) - (z * c))
    t_3 = a * ((c * j) - (x * t))
    if (a <= (-2.9d+45)) then
        tmp = t_3
    else if (a <= (-9d-237)) then
        tmp = t_2
    else if (a <= 9d-273) then
        tmp = t_1
    else if (a <= 6.2d-209) then
        tmp = t_2
    else if (a <= 3.1d-163) then
        tmp = y * ((x * z) - (i * j))
    else if (a <= 3.4d-96) then
        tmp = t_1
    else if (a <= 5.5d+43) then
        tmp = z * ((x * y) - (b * c))
    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 = i * ((t * b) - (y * j));
	double t_2 = b * ((t * i) - (z * c));
	double t_3 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -2.9e+45) {
		tmp = t_3;
	} else if (a <= -9e-237) {
		tmp = t_2;
	} else if (a <= 9e-273) {
		tmp = t_1;
	} else if (a <= 6.2e-209) {
		tmp = t_2;
	} else if (a <= 3.1e-163) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= 3.4e-96) {
		tmp = t_1;
	} else if (a <= 5.5e+43) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	t_2 = b * ((t * i) - (z * c))
	t_3 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -2.9e+45:
		tmp = t_3
	elif a <= -9e-237:
		tmp = t_2
	elif a <= 9e-273:
		tmp = t_1
	elif a <= 6.2e-209:
		tmp = t_2
	elif a <= 3.1e-163:
		tmp = y * ((x * z) - (i * j))
	elif a <= 3.4e-96:
		tmp = t_1
	elif a <= 5.5e+43:
		tmp = z * ((x * y) - (b * c))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_3 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -2.9e+45)
		tmp = t_3;
	elseif (a <= -9e-237)
		tmp = t_2;
	elseif (a <= 9e-273)
		tmp = t_1;
	elseif (a <= 6.2e-209)
		tmp = t_2;
	elseif (a <= 3.1e-163)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (a <= 3.4e-96)
		tmp = t_1;
	elseif (a <= 5.5e+43)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((t * b) - (y * j));
	t_2 = b * ((t * i) - (z * c));
	t_3 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -2.9e+45)
		tmp = t_3;
	elseif (a <= -9e-237)
		tmp = t_2;
	elseif (a <= 9e-273)
		tmp = t_1;
	elseif (a <= 6.2e-209)
		tmp = t_2;
	elseif (a <= 3.1e-163)
		tmp = y * ((x * z) - (i * j));
	elseif (a <= 3.4e-96)
		tmp = t_1;
	elseif (a <= 5.5e+43)
		tmp = z * ((x * y) - (b * c));
	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[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.9e+45], t$95$3, If[LessEqual[a, -9e-237], t$95$2, If[LessEqual[a, 9e-273], t$95$1, If[LessEqual[a, 6.2e-209], t$95$2, If[LessEqual[a, 3.1e-163], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.4e-96], t$95$1, If[LessEqual[a, 5.5e+43], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.8999999999999997e45 or 5.49999999999999989e43 < a

   1. Initial program 55.9%

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

   2. Taylor expanded in a around inf 62.7%

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

      1. +-commutative 62.7%

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

      2. mul-1-neg 62.7%

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

      3. unsub-neg 62.7%

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

   4. Simplified 62.7%

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

   if -2.8999999999999997e45 < a < -9.00000000000000019e-237 or 8.99999999999999921e-273 < a < 6.2e-209

   1. Initial program 84.8%

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

   2. Taylor expanded in b around inf 58.8%

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

   if -9.00000000000000019e-237 < a < 8.99999999999999921e-273 or 3.09999999999999975e-163 < a < 3.4000000000000001e-96

   1. Initial program 90.7%

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

   2. Taylor expanded in i around inf 73.3%

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

      1. distribute-lft-out-- 73.3%

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

      2. *-commutative 73.3%

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

   4. Simplified 73.3%

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

   5. Taylor expanded in i around 0 73.3%

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

      1. mul-1-neg 73.3%

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

      2. distribute-rgt-neg-in 73.3%

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

      3. neg-sub0 73.3%

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

      4. associate-+l- 73.3%

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

      5. neg-sub0 73.3%

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

      6. +-commutative 73.3%

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

      7. unsub-neg 73.3%

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

   7. Simplified 73.3%

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

   if 6.2e-209 < a < 3.09999999999999975e-163

   1. Initial program 69.4%

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

   2. Taylor expanded in y around inf 62.6%

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

      1. +-commutative 62.6%

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

      2. mul-1-neg 62.6%

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

      3. unsub-neg 62.6%

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

      4. *-commutative 62.6%

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

   4. Simplified 62.6%

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

   if 3.4000000000000001e-96 < a < 5.49999999999999989e43

   1. Initial program 70.1%

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

   2. Taylor expanded in z around inf 55.5%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{+45}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-237}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-273}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-209}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-163}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-96}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+43}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]

Alternative 7: 51.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_3 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -9.2 \cdot 10^{+82}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -1.46 \cdot 10^{-44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{-150}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;t \leq -3.15 \cdot 10^{-180}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-146}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+64}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j))))
        (t_2 (* c (- (* a j) (* z b))))
        (t_3 (* t (- (* b i) (* x a)))))
   (if (<= t -9.2e+82)
     t_3
     (if (<= t -1.46e-44)
       t_2
       (if (<= t -3.5e-110)
         t_1
         (if (<= t -2.15e-150)
           (* a (- (* c j) (* x t)))
           (if (<= t -3.15e-180)
             t_1
             (if (<= t 1.5e-146)
               (* z (- (* x y) (* b c)))
               (if (<= t 8.2e+64) 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 = y * ((x * z) - (i * j));
	double t_2 = c * ((a * j) - (z * b));
	double t_3 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -9.2e+82) {
		tmp = t_3;
	} else if (t <= -1.46e-44) {
		tmp = t_2;
	} else if (t <= -3.5e-110) {
		tmp = t_1;
	} else if (t <= -2.15e-150) {
		tmp = a * ((c * j) - (x * t));
	} else if (t <= -3.15e-180) {
		tmp = t_1;
	} else if (t <= 1.5e-146) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 8.2e+64) {
		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 = y * ((x * z) - (i * j))
    t_2 = c * ((a * j) - (z * b))
    t_3 = t * ((b * i) - (x * a))
    if (t <= (-9.2d+82)) then
        tmp = t_3
    else if (t <= (-1.46d-44)) then
        tmp = t_2
    else if (t <= (-3.5d-110)) then
        tmp = t_1
    else if (t <= (-2.15d-150)) then
        tmp = a * ((c * j) - (x * t))
    else if (t <= (-3.15d-180)) then
        tmp = t_1
    else if (t <= 1.5d-146) then
        tmp = z * ((x * y) - (b * c))
    else if (t <= 8.2d+64) 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 = y * ((x * z) - (i * j));
	double t_2 = c * ((a * j) - (z * b));
	double t_3 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -9.2e+82) {
		tmp = t_3;
	} else if (t <= -1.46e-44) {
		tmp = t_2;
	} else if (t <= -3.5e-110) {
		tmp = t_1;
	} else if (t <= -2.15e-150) {
		tmp = a * ((c * j) - (x * t));
	} else if (t <= -3.15e-180) {
		tmp = t_1;
	} else if (t <= 1.5e-146) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 8.2e+64) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	t_2 = c * ((a * j) - (z * b))
	t_3 = t * ((b * i) - (x * a))
	tmp = 0
	if t <= -9.2e+82:
		tmp = t_3
	elif t <= -1.46e-44:
		tmp = t_2
	elif t <= -3.5e-110:
		tmp = t_1
	elif t <= -2.15e-150:
		tmp = a * ((c * j) - (x * t))
	elif t <= -3.15e-180:
		tmp = t_1
	elif t <= 1.5e-146:
		tmp = z * ((x * y) - (b * c))
	elif t <= 8.2e+64:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_2 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	t_3 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	tmp = 0.0
	if (t <= -9.2e+82)
		tmp = t_3;
	elseif (t <= -1.46e-44)
		tmp = t_2;
	elseif (t <= -3.5e-110)
		tmp = t_1;
	elseif (t <= -2.15e-150)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (t <= -3.15e-180)
		tmp = t_1;
	elseif (t <= 1.5e-146)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (t <= 8.2e+64)
		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 = y * ((x * z) - (i * j));
	t_2 = c * ((a * j) - (z * b));
	t_3 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -9.2e+82)
		tmp = t_3;
	elseif (t <= -1.46e-44)
		tmp = t_2;
	elseif (t <= -3.5e-110)
		tmp = t_1;
	elseif (t <= -2.15e-150)
		tmp = a * ((c * j) - (x * t));
	elseif (t <= -3.15e-180)
		tmp = t_1;
	elseif (t <= 1.5e-146)
		tmp = z * ((x * y) - (b * c));
	elseif (t <= 8.2e+64)
		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[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.2e+82], t$95$3, If[LessEqual[t, -1.46e-44], t$95$2, If[LessEqual[t, -3.5e-110], t$95$1, If[LessEqual[t, -2.15e-150], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.15e-180], t$95$1, If[LessEqual[t, 1.5e-146], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.2e+64], t$95$2, t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -9.19999999999999953e82 or 8.19999999999999956e64 < t

   1. Initial program 69.7%

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

   2. Taylor expanded in t around inf 68.1%

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

      1. distribute-lft-out-- 68.1%

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

      2. *-commutative 68.1%

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

   4. Simplified 68.1%

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

   5. Taylor expanded in t around 0 68.1%

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

      1. mul-1-neg 68.1%

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

      2. *-commutative 68.1%

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

      3. *-commutative 68.1%

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

      4. distribute-rgt-neg-in 68.1%

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

   7. Simplified 68.1%

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

   if -9.19999999999999953e82 < t < -1.46000000000000012e-44 or 1.50000000000000009e-146 < t < 8.19999999999999956e64

   1. Initial program 65.4%

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

   2. Taylor expanded in c around inf 61.4%

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

   if -1.46000000000000012e-44 < t < -3.49999999999999974e-110 or -2.15000000000000002e-150 < t < -3.1499999999999998e-180

   1. Initial program 83.7%

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

   2. Taylor expanded in y around inf 63.8%

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

      1. +-commutative 63.8%

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

      2. mul-1-neg 63.8%

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

      3. unsub-neg 63.8%

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

      4. *-commutative 63.8%

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

   4. Simplified 63.8%

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

   if -3.49999999999999974e-110 < t < -2.15000000000000002e-150

   1. Initial program 85.7%

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

   2. Taylor expanded in a around inf 79.9%

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

      1. +-commutative 79.9%

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

      2. mul-1-neg 79.9%

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

      3. unsub-neg 79.9%

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

   4. Simplified 79.9%

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

   if -3.1499999999999998e-180 < t < 1.50000000000000009e-146

   1. Initial program 72.5%

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

   2. Taylor expanded in z around inf 53.3%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{+82}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -1.46 \cdot 10^{-44}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-110}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{-150}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;t \leq -3.15 \cdot 10^{-180}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-146}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+64}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]

Alternative 8: 59.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ t_2 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -2.7 \cdot 10^{+82}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-265}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-277}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{+65}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* j (- (* a c) (* y i))) (* b (* z c))))
        (t_2 (* t (- (* b i) (* x a)))))
   (if (<= t -2.7e+82)
     t_2
     (if (<= t -3.2e-265)
       t_1
       (if (<= t 6.5e-277)
         (* z (- (* x y) (* b c)))
         (if (<= t 9.6e+65) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((a * c) - (y * i))) - (b * (z * c));
	double t_2 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -2.7e+82) {
		tmp = t_2;
	} else if (t <= -3.2e-265) {
		tmp = t_1;
	} else if (t <= 6.5e-277) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 9.6e+65) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (j * ((a * c) - (y * i))) - (b * (z * c))
    t_2 = t * ((b * i) - (x * a))
    if (t <= (-2.7d+82)) then
        tmp = t_2
    else if (t <= (-3.2d-265)) then
        tmp = t_1
    else if (t <= 6.5d-277) then
        tmp = z * ((x * y) - (b * c))
    else if (t <= 9.6d+65) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((a * c) - (y * i))) - (b * (z * c));
	double t_2 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -2.7e+82) {
		tmp = t_2;
	} else if (t <= -3.2e-265) {
		tmp = t_1;
	} else if (t <= 6.5e-277) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 9.6e+65) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((a * c) - (y * i))) - (b * (z * c))
	t_2 = t * ((b * i) - (x * a))
	tmp = 0
	if t <= -2.7e+82:
		tmp = t_2
	elif t <= -3.2e-265:
		tmp = t_1
	elif t <= 6.5e-277:
		tmp = z * ((x * y) - (b * c))
	elif t <= 9.6e+65:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) - Float64(b * Float64(z * c)))
	t_2 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	tmp = 0.0
	if (t <= -2.7e+82)
		tmp = t_2;
	elseif (t <= -3.2e-265)
		tmp = t_1;
	elseif (t <= 6.5e-277)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (t <= 9.6e+65)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (j * ((a * c) - (y * i))) - (b * (z * c));
	t_2 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -2.7e+82)
		tmp = t_2;
	elseif (t <= -3.2e-265)
		tmp = t_1;
	elseif (t <= 6.5e-277)
		tmp = z * ((x * y) - (b * c));
	elseif (t <= 9.6e+65)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.7e+82], t$95$2, If[LessEqual[t, -3.2e-265], t$95$1, If[LessEqual[t, 6.5e-277], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.6e+65], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.6999999999999999e82 or 9.6000000000000007e65 < t

   1. Initial program 69.7%

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

   2. Taylor expanded in t around inf 68.1%

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

      1. distribute-lft-out-- 68.1%

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

      2. *-commutative 68.1%

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

   4. Simplified 68.1%

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

   5. Taylor expanded in t around 0 68.1%

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

      1. mul-1-neg 68.1%

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

      2. *-commutative 68.1%

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

      3. *-commutative 68.1%

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

      4. distribute-rgt-neg-in 68.1%

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

   7. Simplified 68.1%

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

   if -2.6999999999999999e82 < t < -3.2e-265 or 6.49999999999999961e-277 < t < 9.6000000000000007e65

   1. Initial program 73.2%

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

   2. Taylor expanded in x around 0 63.4%

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

      1. *-commutative 63.4%

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

   4. Simplified 63.4%

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

   5. Taylor expanded in c around inf 58.6%

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

   if -3.2e-265 < t < 6.49999999999999961e-277

   1. Initial program 67.4%

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

   2. Taylor expanded in z around inf 73.3%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+82}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-265}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-277}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{+65}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]

Alternative 9: 29.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(z \cdot \left(-b\right)\right)\\ t_2 := i \cdot \left(t \cdot b\right)\\ \mathbf{if}\;a \leq -2.65 \cdot 10^{+45}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{-233}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-268}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-163}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-96}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+167}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* z (- b)))) (t_2 (* i (* t b))))
   (if (<= a -2.65e+45)
     (* a (* c j))
     (if (<= a -5.4e-233)
       t_1
       (if (<= a 7.5e-268)
         t_2
         (if (<= a 9e-163)
           (* y (* x z))
           (if (<= a 4e-96)
             t_2
             (if (<= a 2.6e+45)
               t_1
               (if (<= a 5.8e+167) (* c (* a j)) (* a (* x (- t))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (z * -b);
	double t_2 = i * (t * b);
	double tmp;
	if (a <= -2.65e+45) {
		tmp = a * (c * j);
	} else if (a <= -5.4e-233) {
		tmp = t_1;
	} else if (a <= 7.5e-268) {
		tmp = t_2;
	} else if (a <= 9e-163) {
		tmp = y * (x * z);
	} else if (a <= 4e-96) {
		tmp = t_2;
	} else if (a <= 2.6e+45) {
		tmp = t_1;
	} else if (a <= 5.8e+167) {
		tmp = c * (a * j);
	} else {
		tmp = a * (x * -t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * (z * -b)
    t_2 = i * (t * b)
    if (a <= (-2.65d+45)) then
        tmp = a * (c * j)
    else if (a <= (-5.4d-233)) then
        tmp = t_1
    else if (a <= 7.5d-268) then
        tmp = t_2
    else if (a <= 9d-163) then
        tmp = y * (x * z)
    else if (a <= 4d-96) then
        tmp = t_2
    else if (a <= 2.6d+45) then
        tmp = t_1
    else if (a <= 5.8d+167) then
        tmp = c * (a * j)
    else
        tmp = a * (x * -t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (z * -b);
	double t_2 = i * (t * b);
	double tmp;
	if (a <= -2.65e+45) {
		tmp = a * (c * j);
	} else if (a <= -5.4e-233) {
		tmp = t_1;
	} else if (a <= 7.5e-268) {
		tmp = t_2;
	} else if (a <= 9e-163) {
		tmp = y * (x * z);
	} else if (a <= 4e-96) {
		tmp = t_2;
	} else if (a <= 2.6e+45) {
		tmp = t_1;
	} else if (a <= 5.8e+167) {
		tmp = c * (a * j);
	} else {
		tmp = a * (x * -t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (z * -b)
	t_2 = i * (t * b)
	tmp = 0
	if a <= -2.65e+45:
		tmp = a * (c * j)
	elif a <= -5.4e-233:
		tmp = t_1
	elif a <= 7.5e-268:
		tmp = t_2
	elif a <= 9e-163:
		tmp = y * (x * z)
	elif a <= 4e-96:
		tmp = t_2
	elif a <= 2.6e+45:
		tmp = t_1
	elif a <= 5.8e+167:
		tmp = c * (a * j)
	else:
		tmp = a * (x * -t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(z * Float64(-b)))
	t_2 = Float64(i * Float64(t * b))
	tmp = 0.0
	if (a <= -2.65e+45)
		tmp = Float64(a * Float64(c * j));
	elseif (a <= -5.4e-233)
		tmp = t_1;
	elseif (a <= 7.5e-268)
		tmp = t_2;
	elseif (a <= 9e-163)
		tmp = Float64(y * Float64(x * z));
	elseif (a <= 4e-96)
		tmp = t_2;
	elseif (a <= 2.6e+45)
		tmp = t_1;
	elseif (a <= 5.8e+167)
		tmp = Float64(c * Float64(a * j));
	else
		tmp = Float64(a * Float64(x * Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (z * -b);
	t_2 = i * (t * b);
	tmp = 0.0;
	if (a <= -2.65e+45)
		tmp = a * (c * j);
	elseif (a <= -5.4e-233)
		tmp = t_1;
	elseif (a <= 7.5e-268)
		tmp = t_2;
	elseif (a <= 9e-163)
		tmp = y * (x * z);
	elseif (a <= 4e-96)
		tmp = t_2;
	elseif (a <= 2.6e+45)
		tmp = t_1;
	elseif (a <= 5.8e+167)
		tmp = c * (a * j);
	else
		tmp = a * (x * -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.65e+45], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5.4e-233], t$95$1, If[LessEqual[a, 7.5e-268], t$95$2, If[LessEqual[a, 9e-163], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4e-96], t$95$2, If[LessEqual[a, 2.6e+45], t$95$1, If[LessEqual[a, 5.8e+167], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -2.64999999999999996e45

   1. Initial program 62.1%

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

   2. Taylor expanded in a around inf 56.6%

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

      1. +-commutative 56.6%

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

      2. mul-1-neg 56.6%

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

      3. unsub-neg 56.6%

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

   4. Simplified 56.6%

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

   5. Taylor expanded in c around inf 36.3%

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

      1. *-commutative 36.3%

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

   7. Simplified 36.3%

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

   if -2.64999999999999996e45 < a < -5.3999999999999999e-233 or 3.9999999999999996e-96 < a < 2.60000000000000007e45

   1. Initial program 79.3%

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

   2. Taylor expanded in c around inf 46.1%

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

   3. Taylor expanded in a around 0 41.4%

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

      1. neg-mul-1 41.4%

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

      2. distribute-lft-neg-in 41.4%

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

      3. *-commutative 41.4%

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

   5. Simplified 41.4%

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

   if -5.3999999999999999e-233 < a < 7.4999999999999999e-268 or 8.9999999999999995e-163 < a < 3.9999999999999996e-96

   1. Initial program 89.5%

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

   2. Taylor expanded in t around inf 47.5%

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

      1. distribute-lft-out-- 47.5%

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

      2. *-commutative 47.5%

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

   4. Simplified 47.5%

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

   5. Taylor expanded in x around 0 44.8%

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

      1. associate-*r* 42.4%

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

      2. *-commutative 42.4%

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

      3. associate-*l* 47.3%

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

   7. Simplified 47.3%

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

   if 7.4999999999999999e-268 < a < 8.9999999999999995e-163

   1. Initial program 80.8%

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

   2. Taylor expanded in z around inf 55.0%

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

   3. Taylor expanded in x around inf 32.6%

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

      1. associate-*r* 36.1%

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

      2. *-commutative 36.1%

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

      3. associate-*l* 36.2%

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

   5. Simplified 36.2%

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

   if 2.60000000000000007e45 < a < 5.79999999999999949e167

   1. Initial program 53.8%

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

   2. Taylor expanded in c around inf 56.7%

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

   3. Taylor expanded in a around inf 49.5%

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

      1. *-commutative 49.5%

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

   5. Simplified 49.5%

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

   if 5.79999999999999949e167 < a

   1. Initial program 44.8%

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

   2. Taylor expanded in a around inf 74.6%

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

      1. +-commutative 74.6%

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

      2. mul-1-neg 74.6%

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

      3. unsub-neg 74.6%

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

   4. Simplified 74.6%

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

   5. Taylor expanded in c around 0 53.0%

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

      1. mul-1-neg 53.0%

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

      2. *-commutative 53.0%

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

      3. distribute-lft-neg-in 53.0%

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

   7. Simplified 53.0%

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

4. Final simplification 42.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.65 \cdot 10^{+45}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{-233}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-268}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-163}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-96}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+45}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+167}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \end{array} \]

Alternative 10: 29.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{if}\;a \leq -3.6 \cdot 10^{+45}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq -1.42 \cdot 10^{-232}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-302}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-113}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+167}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* z (- b)))))
   (if (<= a -3.6e+45)
     (* a (* c j))
     (if (<= a -1.42e-232)
       t_1
       (if (<= a 3.5e-302)
         (* i (* t b))
         (if (<= a 6.5e-113)
           (* i (* y (- j)))
           (if (<= a 2.7e+44)
             t_1
             (if (<= a 1.7e+167) (* c (* a j)) (* a (* x (- t)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (z * -b);
	double tmp;
	if (a <= -3.6e+45) {
		tmp = a * (c * j);
	} else if (a <= -1.42e-232) {
		tmp = t_1;
	} else if (a <= 3.5e-302) {
		tmp = i * (t * b);
	} else if (a <= 6.5e-113) {
		tmp = i * (y * -j);
	} else if (a <= 2.7e+44) {
		tmp = t_1;
	} else if (a <= 1.7e+167) {
		tmp = c * (a * j);
	} else {
		tmp = a * (x * -t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (z * -b)
    if (a <= (-3.6d+45)) then
        tmp = a * (c * j)
    else if (a <= (-1.42d-232)) then
        tmp = t_1
    else if (a <= 3.5d-302) then
        tmp = i * (t * b)
    else if (a <= 6.5d-113) then
        tmp = i * (y * -j)
    else if (a <= 2.7d+44) then
        tmp = t_1
    else if (a <= 1.7d+167) then
        tmp = c * (a * j)
    else
        tmp = a * (x * -t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (z * -b);
	double tmp;
	if (a <= -3.6e+45) {
		tmp = a * (c * j);
	} else if (a <= -1.42e-232) {
		tmp = t_1;
	} else if (a <= 3.5e-302) {
		tmp = i * (t * b);
	} else if (a <= 6.5e-113) {
		tmp = i * (y * -j);
	} else if (a <= 2.7e+44) {
		tmp = t_1;
	} else if (a <= 1.7e+167) {
		tmp = c * (a * j);
	} else {
		tmp = a * (x * -t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (z * -b)
	tmp = 0
	if a <= -3.6e+45:
		tmp = a * (c * j)
	elif a <= -1.42e-232:
		tmp = t_1
	elif a <= 3.5e-302:
		tmp = i * (t * b)
	elif a <= 6.5e-113:
		tmp = i * (y * -j)
	elif a <= 2.7e+44:
		tmp = t_1
	elif a <= 1.7e+167:
		tmp = c * (a * j)
	else:
		tmp = a * (x * -t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(z * Float64(-b)))
	tmp = 0.0
	if (a <= -3.6e+45)
		tmp = Float64(a * Float64(c * j));
	elseif (a <= -1.42e-232)
		tmp = t_1;
	elseif (a <= 3.5e-302)
		tmp = Float64(i * Float64(t * b));
	elseif (a <= 6.5e-113)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (a <= 2.7e+44)
		tmp = t_1;
	elseif (a <= 1.7e+167)
		tmp = Float64(c * Float64(a * j));
	else
		tmp = Float64(a * Float64(x * Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (z * -b);
	tmp = 0.0;
	if (a <= -3.6e+45)
		tmp = a * (c * j);
	elseif (a <= -1.42e-232)
		tmp = t_1;
	elseif (a <= 3.5e-302)
		tmp = i * (t * b);
	elseif (a <= 6.5e-113)
		tmp = i * (y * -j);
	elseif (a <= 2.7e+44)
		tmp = t_1;
	elseif (a <= 1.7e+167)
		tmp = c * (a * j);
	else
		tmp = a * (x * -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.6e+45], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.42e-232], t$95$1, If[LessEqual[a, 3.5e-302], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.5e-113], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.7e+44], t$95$1, If[LessEqual[a, 1.7e+167], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -3.6e45

   1. Initial program 62.1%

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

   2. Taylor expanded in a around inf 56.6%

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

      1. +-commutative 56.6%

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

      2. mul-1-neg 56.6%

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

      3. unsub-neg 56.6%

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

   4. Simplified 56.6%

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

   5. Taylor expanded in c around inf 36.3%

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

      1. *-commutative 36.3%

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

   7. Simplified 36.3%

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

   if -3.6e45 < a < -1.42e-232 or 6.49999999999999979e-113 < a < 2.7e44

   1. Initial program 80.0%

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

   2. Taylor expanded in c around inf 44.6%

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

   3. Taylor expanded in a around 0 40.1%

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

      1. neg-mul-1 40.1%

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

      2. distribute-lft-neg-in 40.1%

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

      3. *-commutative 40.1%

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

   5. Simplified 40.1%

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

   if -1.42e-232 < a < 3.5000000000000001e-302

   1. Initial program 82.1%

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

   2. Taylor expanded in t around inf 54.2%

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

      1. distribute-lft-out-- 54.2%

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

      2. *-commutative 54.2%

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

   4. Simplified 54.2%

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

   5. Taylor expanded in x around 0 54.2%

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

      1. associate-*r* 48.6%

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

      2. *-commutative 48.6%

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

      3. associate-*l* 59.8%

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

   7. Simplified 59.8%

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

   if 3.5000000000000001e-302 < a < 6.49999999999999979e-113

   1. Initial program 86.6%

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

   2. Taylor expanded in i around inf 45.9%

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

      1. distribute-lft-out-- 45.9%

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

      2. *-commutative 45.9%

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

   4. Simplified 45.9%

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

   5. Taylor expanded in y around inf 34.8%

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

      1. mul-1-neg 34.8%

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

      2. distribute-rgt-neg-in 34.8%

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

      3. distribute-rgt-neg-in 34.8%

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

   7. Simplified 34.8%

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

   if 2.7e44 < a < 1.7e167

   1. Initial program 53.8%

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

   2. Taylor expanded in c around inf 56.7%

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

   3. Taylor expanded in a around inf 49.5%

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

      1. *-commutative 49.5%

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

   5. Simplified 49.5%

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

   if 1.7e167 < a

   1. Initial program 44.8%

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

   2. Taylor expanded in a around inf 74.6%

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

      1. +-commutative 74.6%

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

      2. mul-1-neg 74.6%

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

      3. unsub-neg 74.6%

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

   4. Simplified 74.6%

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

   5. Taylor expanded in c around 0 53.0%

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

      1. mul-1-neg 53.0%

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

      2. *-commutative 53.0%

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

      3. distribute-lft-neg-in 53.0%

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

   7. Simplified 53.0%

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

4. Final simplification 41.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{+45}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq -1.42 \cdot 10^{-232}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-302}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-113}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+44}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+167}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \end{array} \]

Alternative 11: 29.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{if}\;a \leq -1.4 \cdot 10^{+24}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-231}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.36 \cdot 10^{-301}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-112}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{+163}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* b (- c)))))
   (if (<= a -1.4e+24)
     (* a (* c j))
     (if (<= a -1.25e-231)
       t_1
       (if (<= a 1.36e-301)
         (* i (* t b))
         (if (<= a 1.65e-112)
           (* i (* y (- j)))
           (if (<= a 6e+43)
             t_1
             (if (<= a 2.45e+163) (* c (* a j)) (* a (* x (- t)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (b * -c);
	double tmp;
	if (a <= -1.4e+24) {
		tmp = a * (c * j);
	} else if (a <= -1.25e-231) {
		tmp = t_1;
	} else if (a <= 1.36e-301) {
		tmp = i * (t * b);
	} else if (a <= 1.65e-112) {
		tmp = i * (y * -j);
	} else if (a <= 6e+43) {
		tmp = t_1;
	} else if (a <= 2.45e+163) {
		tmp = c * (a * j);
	} else {
		tmp = a * (x * -t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (b * -c)
    if (a <= (-1.4d+24)) then
        tmp = a * (c * j)
    else if (a <= (-1.25d-231)) then
        tmp = t_1
    else if (a <= 1.36d-301) then
        tmp = i * (t * b)
    else if (a <= 1.65d-112) then
        tmp = i * (y * -j)
    else if (a <= 6d+43) then
        tmp = t_1
    else if (a <= 2.45d+163) then
        tmp = c * (a * j)
    else
        tmp = a * (x * -t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (b * -c);
	double tmp;
	if (a <= -1.4e+24) {
		tmp = a * (c * j);
	} else if (a <= -1.25e-231) {
		tmp = t_1;
	} else if (a <= 1.36e-301) {
		tmp = i * (t * b);
	} else if (a <= 1.65e-112) {
		tmp = i * (y * -j);
	} else if (a <= 6e+43) {
		tmp = t_1;
	} else if (a <= 2.45e+163) {
		tmp = c * (a * j);
	} else {
		tmp = a * (x * -t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (b * -c)
	tmp = 0
	if a <= -1.4e+24:
		tmp = a * (c * j)
	elif a <= -1.25e-231:
		tmp = t_1
	elif a <= 1.36e-301:
		tmp = i * (t * b)
	elif a <= 1.65e-112:
		tmp = i * (y * -j)
	elif a <= 6e+43:
		tmp = t_1
	elif a <= 2.45e+163:
		tmp = c * (a * j)
	else:
		tmp = a * (x * -t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(b * Float64(-c)))
	tmp = 0.0
	if (a <= -1.4e+24)
		tmp = Float64(a * Float64(c * j));
	elseif (a <= -1.25e-231)
		tmp = t_1;
	elseif (a <= 1.36e-301)
		tmp = Float64(i * Float64(t * b));
	elseif (a <= 1.65e-112)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (a <= 6e+43)
		tmp = t_1;
	elseif (a <= 2.45e+163)
		tmp = Float64(c * Float64(a * j));
	else
		tmp = Float64(a * Float64(x * Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * (b * -c);
	tmp = 0.0;
	if (a <= -1.4e+24)
		tmp = a * (c * j);
	elseif (a <= -1.25e-231)
		tmp = t_1;
	elseif (a <= 1.36e-301)
		tmp = i * (t * b);
	elseif (a <= 1.65e-112)
		tmp = i * (y * -j);
	elseif (a <= 6e+43)
		tmp = t_1;
	elseif (a <= 2.45e+163)
		tmp = c * (a * j);
	else
		tmp = a * (x * -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.4e+24], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.25e-231], t$95$1, If[LessEqual[a, 1.36e-301], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.65e-112], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6e+43], t$95$1, If[LessEqual[a, 2.45e+163], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -1.4000000000000001e24

   1. Initial program 64.1%

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

   2. Taylor expanded in a around inf 54.4%

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

      1. +-commutative 54.4%

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

      2. mul-1-neg 54.4%

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

      3. unsub-neg 54.4%

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

   4. Simplified 54.4%

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

   5. Taylor expanded in c around inf 36.1%

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

      1. *-commutative 36.1%

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

   7. Simplified 36.1%

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

   if -1.4000000000000001e24 < a < -1.25000000000000006e-231 or 1.65e-112 < a < 6.00000000000000033e43

   1. Initial program 79.8%

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

   2. Taylor expanded in z around inf 49.2%

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

   3. Taylor expanded in x around 0 41.7%

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

      1. mul-1-neg 41.7%

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

      2. distribute-lft-neg-out 41.7%

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

      3. *-commutative 41.7%

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

   5. Simplified 41.7%

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

   if -1.25000000000000006e-231 < a < 1.36e-301

   1. Initial program 82.1%

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

   2. Taylor expanded in t around inf 54.2%

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

      1. distribute-lft-out-- 54.2%

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

      2. *-commutative 54.2%

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

   4. Simplified 54.2%

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

   5. Taylor expanded in x around 0 54.2%

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

      1. associate-*r* 48.6%

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

      2. *-commutative 48.6%

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

      3. associate-*l* 59.8%

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

   7. Simplified 59.8%

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

   if 1.36e-301 < a < 1.65e-112

   1. Initial program 86.6%

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

   2. Taylor expanded in i around inf 45.9%

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

      1. distribute-lft-out-- 45.9%

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

      2. *-commutative 45.9%

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

   4. Simplified 45.9%

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

   5. Taylor expanded in y around inf 34.8%

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

      1. mul-1-neg 34.8%

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

      2. distribute-rgt-neg-in 34.8%

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

      3. distribute-rgt-neg-in 34.8%

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

   7. Simplified 34.8%

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

   if 6.00000000000000033e43 < a < 2.45e163

   1. Initial program 53.8%

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

   2. Taylor expanded in c around inf 56.7%

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

   3. Taylor expanded in a around inf 49.5%

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

      1. *-commutative 49.5%

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

   5. Simplified 49.5%

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

   if 2.45e163 < a

   1. Initial program 44.8%

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

   2. Taylor expanded in a around inf 74.6%

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

      1. +-commutative 74.6%

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

      2. mul-1-neg 74.6%

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

      3. unsub-neg 74.6%

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

   4. Simplified 74.6%

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

   5. Taylor expanded in c around 0 53.0%

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

      1. mul-1-neg 53.0%

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

      2. *-commutative 53.0%

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

      3. distribute-lft-neg-in 53.0%

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

   7. Simplified 53.0%

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

4. Final simplification 42.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{+24}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-231}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq 1.36 \cdot 10^{-301}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-112}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+43}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{+163}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \end{array} \]

Alternative 12: 51.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -2.6 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-235}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-96}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+36}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -2.6e+45)
     t_1
     (if (<= a -6.2e-235)
       (* b (- (* t i) (* z c)))
       (if (<= a 5e-96)
         (* i (- (* t b) (* y j)))
         (if (<= a 2.7e+36) (* c (- (* a j) (* z b))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -2.6e+45) {
		tmp = t_1;
	} else if (a <= -6.2e-235) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 5e-96) {
		tmp = i * ((t * b) - (y * j));
	} else if (a <= 2.7e+36) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (a <= (-2.6d+45)) then
        tmp = t_1
    else if (a <= (-6.2d-235)) then
        tmp = b * ((t * i) - (z * c))
    else if (a <= 5d-96) then
        tmp = i * ((t * b) - (y * j))
    else if (a <= 2.7d+36) then
        tmp = c * ((a * j) - (z * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -2.6e+45) {
		tmp = t_1;
	} else if (a <= -6.2e-235) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 5e-96) {
		tmp = i * ((t * b) - (y * j));
	} else if (a <= 2.7e+36) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -2.6e+45:
		tmp = t_1
	elif a <= -6.2e-235:
		tmp = b * ((t * i) - (z * c))
	elif a <= 5e-96:
		tmp = i * ((t * b) - (y * j))
	elif a <= 2.7e+36:
		tmp = c * ((a * j) - (z * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -2.6e+45)
		tmp = t_1;
	elseif (a <= -6.2e-235)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (a <= 5e-96)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (a <= 2.7e+36)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -2.6e+45)
		tmp = t_1;
	elseif (a <= -6.2e-235)
		tmp = b * ((t * i) - (z * c));
	elseif (a <= 5e-96)
		tmp = i * ((t * b) - (y * j));
	elseif (a <= 2.7e+36)
		tmp = c * ((a * j) - (z * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.6e+45], t$95$1, If[LessEqual[a, -6.2e-235], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5e-96], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.7e+36], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.60000000000000007e45 or 2.7000000000000001e36 < a

   1. Initial program 55.3%

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

   2. Taylor expanded in a around inf 61.9%

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

      1. +-commutative 61.9%

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

      2. mul-1-neg 61.9%

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

      3. unsub-neg 61.9%

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

   4. Simplified 61.9%

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

   if -2.60000000000000007e45 < a < -6.2e-235

   1. Initial program 82.5%

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

   2. Taylor expanded in b around inf 57.7%

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

   if -6.2e-235 < a < 4.99999999999999995e-96

   1. Initial program 87.0%

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

   2. Taylor expanded in i around inf 54.6%

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

      1. distribute-lft-out-- 54.6%

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

      2. *-commutative 54.6%

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

   4. Simplified 54.6%

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

   5. Taylor expanded in i around 0 54.6%

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

      1. mul-1-neg 54.6%

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

      2. distribute-rgt-neg-in 54.6%

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

      3. neg-sub0 54.6%

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

      4. associate-+l- 54.6%

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

      5. neg-sub0 54.6%

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

      6. +-commutative 54.6%

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

      7. unsub-neg 54.6%

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

   7. Simplified 54.6%

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

   if 4.99999999999999995e-96 < a < 2.7000000000000001e36

   1. Initial program 74.6%

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

   2. Taylor expanded in c around inf 52.7%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{+45}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-235}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-96}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+36}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]

Alternative 13: 28.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b\right)\\ \mathbf{if}\;a \leq -9.5 \cdot 10^{-15}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq 10^{-267}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-163}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-66}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* t b))))
   (if (<= a -9.5e-15)
     (* a (* c j))
     (if (<= a 1e-267)
       t_1
       (if (<= a 3.1e-163)
         (* y (* x z))
         (if (<= a 2.6e-66) t_1 (* a (* x (- t)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (t * b);
	double tmp;
	if (a <= -9.5e-15) {
		tmp = a * (c * j);
	} else if (a <= 1e-267) {
		tmp = t_1;
	} else if (a <= 3.1e-163) {
		tmp = y * (x * z);
	} else if (a <= 2.6e-66) {
		tmp = t_1;
	} else {
		tmp = a * (x * -t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * (t * b)
    if (a <= (-9.5d-15)) then
        tmp = a * (c * j)
    else if (a <= 1d-267) then
        tmp = t_1
    else if (a <= 3.1d-163) then
        tmp = y * (x * z)
    else if (a <= 2.6d-66) then
        tmp = t_1
    else
        tmp = a * (x * -t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (t * b);
	double tmp;
	if (a <= -9.5e-15) {
		tmp = a * (c * j);
	} else if (a <= 1e-267) {
		tmp = t_1;
	} else if (a <= 3.1e-163) {
		tmp = y * (x * z);
	} else if (a <= 2.6e-66) {
		tmp = t_1;
	} else {
		tmp = a * (x * -t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (t * b)
	tmp = 0
	if a <= -9.5e-15:
		tmp = a * (c * j)
	elif a <= 1e-267:
		tmp = t_1
	elif a <= 3.1e-163:
		tmp = y * (x * z)
	elif a <= 2.6e-66:
		tmp = t_1
	else:
		tmp = a * (x * -t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(t * b))
	tmp = 0.0
	if (a <= -9.5e-15)
		tmp = Float64(a * Float64(c * j));
	elseif (a <= 1e-267)
		tmp = t_1;
	elseif (a <= 3.1e-163)
		tmp = Float64(y * Float64(x * z));
	elseif (a <= 2.6e-66)
		tmp = t_1;
	else
		tmp = Float64(a * Float64(x * Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * (t * b);
	tmp = 0.0;
	if (a <= -9.5e-15)
		tmp = a * (c * j);
	elseif (a <= 1e-267)
		tmp = t_1;
	elseif (a <= 3.1e-163)
		tmp = y * (x * z);
	elseif (a <= 2.6e-66)
		tmp = t_1;
	else
		tmp = a * (x * -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9.5e-15], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1e-267], t$95$1, If[LessEqual[a, 3.1e-163], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.6e-66], t$95$1, N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -9.5000000000000005e-15

   1. Initial program 64.1%

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

   2. Taylor expanded in a around inf 52.0%

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

      1. +-commutative 52.0%

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

      2. mul-1-neg 52.0%

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

      3. unsub-neg 52.0%

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

   4. Simplified 52.0%

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

   5. Taylor expanded in c around inf 33.6%

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

      1. *-commutative 33.6%

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

   7. Simplified 33.6%

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

   if -9.5000000000000005e-15 < a < 9.9999999999999998e-268 or 3.09999999999999975e-163 < a < 2.5999999999999999e-66

   1. Initial program 85.0%

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

   2. Taylor expanded in t around inf 40.5%

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

      1. distribute-lft-out-- 40.5%

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

      2. *-commutative 40.5%

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

   4. Simplified 40.5%

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

   5. Taylor expanded in x around 0 32.5%

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

      1. associate-*r* 34.3%

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

      2. *-commutative 34.3%

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

      3. associate-*l* 38.3%

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

   7. Simplified 38.3%

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

   if 9.9999999999999998e-268 < a < 3.09999999999999975e-163

   1. Initial program 80.8%

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

   2. Taylor expanded in z around inf 55.0%

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

   3. Taylor expanded in x around inf 32.6%

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

      1. associate-*r* 36.1%

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

      2. *-commutative 36.1%

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

      3. associate-*l* 36.2%

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

   5. Simplified 36.2%

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

   if 2.5999999999999999e-66 < a

   1. Initial program 56.7%

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

   2. Taylor expanded in a around inf 57.4%

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

      1. +-commutative 57.4%

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

      2. mul-1-neg 57.4%

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

      3. unsub-neg 57.4%

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

   4. Simplified 57.4%

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

   5. Taylor expanded in c around 0 37.4%

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

      1. mul-1-neg 37.4%

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

      2. *-commutative 37.4%

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

      3. distribute-lft-neg-in 37.4%

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

   7. Simplified 37.4%

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

4. Final simplification 36.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{-15}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq 10^{-267}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-163}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-66}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \end{array} \]

Alternative 14: 51.7% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.4 \cdot 10^{+45} \lor \neg \left(a \leq 1.4 \cdot 10^{+45}\right):\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -6.4e+45) (not (<= a 1.4e+45)))
   (* a (- (* c j) (* x t)))
   (* b (- (* t i) (* z c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -6.4e+45) || !(a <= 1.4e+45)) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = b * ((t * i) - (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((a <= (-6.4d+45)) .or. (.not. (a <= 1.4d+45))) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = b * ((t * i) - (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -6.4e+45) || !(a <= 1.4e+45)) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = b * ((t * i) - (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (a <= -6.4e+45) or not (a <= 1.4e+45):
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = b * ((t * i) - (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -6.4e+45) || !(a <= 1.4e+45))
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((a <= -6.4e+45) || ~((a <= 1.4e+45)))
		tmp = a * ((c * j) - (x * t));
	else
		tmp = b * ((t * i) - (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -6.4e+45], N[Not[LessEqual[a, 1.4e+45]], $MachinePrecision]], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -6.4000000000000006e45 or 1.4e45 < a

   1. Initial program 55.9%

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

   2. Taylor expanded in a around inf 62.7%

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

      1. +-commutative 62.7%

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

      2. mul-1-neg 62.7%

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

      3. unsub-neg 62.7%

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

   4. Simplified 62.7%

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

   if -6.4000000000000006e45 < a < 1.4e45

   1. Initial program 82.2%

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

   2. Taylor expanded in b around inf 50.4%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.4 \cdot 10^{+45} \lor \neg \left(a \leq 1.4 \cdot 10^{+45}\right):\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 15: 41.1% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.25 \cdot 10^{+211}:\\ \;\;\;\;j \cdot \left(-y \cdot i\right)\\ \mathbf{elif}\;i \leq 1.32 \cdot 10^{+79}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -1.25e+211)
   (* j (- (* y i)))
   (if (<= i 1.32e+79) (* a (- (* c j) (* x t))) (* b (* t i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -1.25e+211) {
		tmp = j * -(y * i);
	} else if (i <= 1.32e+79) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (i <= (-1.25d+211)) then
        tmp = j * -(y * i)
    else if (i <= 1.32d+79) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -1.25e+211) {
		tmp = j * -(y * i);
	} else if (i <= 1.32e+79) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -1.25e+211:
		tmp = j * -(y * i)
	elif i <= 1.32e+79:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -1.25e+211)
		tmp = Float64(j * Float64(-Float64(y * i)));
	elseif (i <= 1.32e+79)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -1.25e+211)
		tmp = j * -(y * i);
	elseif (i <= 1.32e+79)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -1.25e+211], N[(j * (-N[(y * i), $MachinePrecision])), $MachinePrecision], If[LessEqual[i, 1.32e+79], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if i < -1.2499999999999999e211

   1. Initial program 71.3%

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

   2. Taylor expanded in i around inf 88.7%

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

      1. distribute-lft-out-- 88.7%

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

      2. *-commutative 88.7%

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

   4. Simplified 88.7%

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

   5. Taylor expanded in y around inf 54.1%

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

      1. mul-1-neg 54.1%

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

      2. *-commutative 54.1%

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

      3. associate-*l* 54.6%

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

      4. distribute-lft-neg-in 54.6%

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

   7. Simplified 54.6%

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

   if -1.2499999999999999e211 < i < 1.32e79

   1. Initial program 74.1%

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

   2. Taylor expanded in a around inf 44.7%

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

      1. +-commutative 44.7%

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

      2. mul-1-neg 44.7%

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

      3. unsub-neg 44.7%

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

   4. Simplified 44.7%

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

   if 1.32e79 < i

   1. Initial program 59.7%

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

   2. Taylor expanded in t around inf 50.8%

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

      1. distribute-lft-out-- 50.8%

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

      2. *-commutative 50.8%

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

   4. Simplified 50.8%

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

   5. Taylor expanded in x around 0 50.9%

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

4. Final simplification 46.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.25 \cdot 10^{+211}:\\ \;\;\;\;j \cdot \left(-y \cdot i\right)\\ \mathbf{elif}\;i \leq 1.32 \cdot 10^{+79}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]

Alternative 16: 29.2% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b\right)\\ \mathbf{if}\;b \leq -7.4 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -9.6 \cdot 10^{-120}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 7.4 \cdot 10^{-6}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* t b))))
   (if (<= b -7.4e-7)
     t_1
     (if (<= b -9.6e-120)
       (* x (* y z))
       (if (<= b 7.4e-6) (* c (* a j)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (t * b);
	double tmp;
	if (b <= -7.4e-7) {
		tmp = t_1;
	} else if (b <= -9.6e-120) {
		tmp = x * (y * z);
	} else if (b <= 7.4e-6) {
		tmp = c * (a * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * (t * b)
    if (b <= (-7.4d-7)) then
        tmp = t_1
    else if (b <= (-9.6d-120)) then
        tmp = x * (y * z)
    else if (b <= 7.4d-6) then
        tmp = c * (a * j)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (t * b);
	double tmp;
	if (b <= -7.4e-7) {
		tmp = t_1;
	} else if (b <= -9.6e-120) {
		tmp = x * (y * z);
	} else if (b <= 7.4e-6) {
		tmp = c * (a * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (t * b)
	tmp = 0
	if b <= -7.4e-7:
		tmp = t_1
	elif b <= -9.6e-120:
		tmp = x * (y * z)
	elif b <= 7.4e-6:
		tmp = c * (a * j)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(t * b))
	tmp = 0.0
	if (b <= -7.4e-7)
		tmp = t_1;
	elseif (b <= -9.6e-120)
		tmp = Float64(x * Float64(y * z));
	elseif (b <= 7.4e-6)
		tmp = Float64(c * Float64(a * j));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * (t * b);
	tmp = 0.0;
	if (b <= -7.4e-7)
		tmp = t_1;
	elseif (b <= -9.6e-120)
		tmp = x * (y * z);
	elseif (b <= 7.4e-6)
		tmp = c * (a * j);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.4e-7], t$95$1, If[LessEqual[b, -9.6e-120], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.4e-6], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.40000000000000009e-7 or 7.4000000000000003e-6 < b

   1. Initial program 73.9%

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

   2. Taylor expanded in t around inf 43.8%

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

      1. distribute-lft-out-- 43.8%

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

      2. *-commutative 43.8%

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

   4. Simplified 43.8%

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

   5. Taylor expanded in x around 0 30.8%

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

      1. associate-*r* 30.9%

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

      2. *-commutative 30.9%

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

      3. associate-*l* 34.5%

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

   7. Simplified 34.5%

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

   if -7.40000000000000009e-7 < b < -9.5999999999999998e-120

   1. Initial program 76.4%

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

   2. Taylor expanded in z around inf 55.3%

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

   3. Taylor expanded in x around inf 45.2%

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

   if -9.5999999999999998e-120 < b < 7.4000000000000003e-6

   1. Initial program 66.6%

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

   2. Taylor expanded in c around inf 40.6%

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

   3. Taylor expanded in a around inf 31.9%

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

      1. *-commutative 31.9%

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

   5. Simplified 31.9%

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

4. Final simplification 34.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.4 \cdot 10^{-7}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;b \leq -9.6 \cdot 10^{-120}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 7.4 \cdot 10^{-6}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \]

Alternative 17: 29.4% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b\right)\\ \mathbf{if}\;b \leq -9 \cdot 10^{+27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-120}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{-6}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* t b))))
   (if (<= b -9e+27)
     t_1
     (if (<= b -2.4e-120)
       (* y (* x z))
       (if (<= b 3.7e-6) (* c (* a j)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (t * b);
	double tmp;
	if (b <= -9e+27) {
		tmp = t_1;
	} else if (b <= -2.4e-120) {
		tmp = y * (x * z);
	} else if (b <= 3.7e-6) {
		tmp = c * (a * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * (t * b)
    if (b <= (-9d+27)) then
        tmp = t_1
    else if (b <= (-2.4d-120)) then
        tmp = y * (x * z)
    else if (b <= 3.7d-6) then
        tmp = c * (a * j)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (t * b);
	double tmp;
	if (b <= -9e+27) {
		tmp = t_1;
	} else if (b <= -2.4e-120) {
		tmp = y * (x * z);
	} else if (b <= 3.7e-6) {
		tmp = c * (a * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (t * b)
	tmp = 0
	if b <= -9e+27:
		tmp = t_1
	elif b <= -2.4e-120:
		tmp = y * (x * z)
	elif b <= 3.7e-6:
		tmp = c * (a * j)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(t * b))
	tmp = 0.0
	if (b <= -9e+27)
		tmp = t_1;
	elseif (b <= -2.4e-120)
		tmp = Float64(y * Float64(x * z));
	elseif (b <= 3.7e-6)
		tmp = Float64(c * Float64(a * j));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * (t * b);
	tmp = 0.0;
	if (b <= -9e+27)
		tmp = t_1;
	elseif (b <= -2.4e-120)
		tmp = y * (x * z);
	elseif (b <= 3.7e-6)
		tmp = c * (a * j);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9e+27], t$95$1, If[LessEqual[b, -2.4e-120], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.7e-6], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.9999999999999998e27 or 3.7000000000000002e-6 < b

   1. Initial program 72.8%

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

   2. Taylor expanded in t around inf 43.1%

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

      1. distribute-lft-out-- 43.1%

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

      2. *-commutative 43.1%

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

   4. Simplified 43.1%

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

   5. Taylor expanded in x around 0 31.2%

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

      1. associate-*r* 31.3%

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

      2. *-commutative 31.3%

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

      3. associate-*l* 35.1%

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

   7. Simplified 35.1%

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

   if -8.9999999999999998e27 < b < -2.3999999999999999e-120

   1. Initial program 79.9%

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

   2. Taylor expanded in z around inf 50.6%

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

   3. Taylor expanded in x around inf 39.1%

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

      1. associate-*r* 39.4%

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

      2. *-commutative 39.4%

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

      3. associate-*l* 41.8%

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

   5. Simplified 41.8%

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

   if -2.3999999999999999e-120 < b < 3.7000000000000002e-6

   1. Initial program 66.6%

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

   2. Taylor expanded in c around inf 40.6%

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

   3. Taylor expanded in a around inf 31.9%

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

      1. *-commutative 31.9%

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

   5. Simplified 31.9%

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

4. Final simplification 34.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{+27}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-120}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{-6}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \]

Alternative 18: 29.3% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b\right)\\ \mathbf{if}\;b \leq -9 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-121}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-7}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* t b))))
   (if (<= b -9e-5)
     t_1
     (if (<= b -2.1e-121)
       (* z (* x y))
       (if (<= b 1.6e-7) (* c (* a j)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (t * b);
	double tmp;
	if (b <= -9e-5) {
		tmp = t_1;
	} else if (b <= -2.1e-121) {
		tmp = z * (x * y);
	} else if (b <= 1.6e-7) {
		tmp = c * (a * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * (t * b)
    if (b <= (-9d-5)) then
        tmp = t_1
    else if (b <= (-2.1d-121)) then
        tmp = z * (x * y)
    else if (b <= 1.6d-7) then
        tmp = c * (a * j)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (t * b);
	double tmp;
	if (b <= -9e-5) {
		tmp = t_1;
	} else if (b <= -2.1e-121) {
		tmp = z * (x * y);
	} else if (b <= 1.6e-7) {
		tmp = c * (a * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (t * b)
	tmp = 0
	if b <= -9e-5:
		tmp = t_1
	elif b <= -2.1e-121:
		tmp = z * (x * y)
	elif b <= 1.6e-7:
		tmp = c * (a * j)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(t * b))
	tmp = 0.0
	if (b <= -9e-5)
		tmp = t_1;
	elseif (b <= -2.1e-121)
		tmp = Float64(z * Float64(x * y));
	elseif (b <= 1.6e-7)
		tmp = Float64(c * Float64(a * j));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * (t * b);
	tmp = 0.0;
	if (b <= -9e-5)
		tmp = t_1;
	elseif (b <= -2.1e-121)
		tmp = z * (x * y);
	elseif (b <= 1.6e-7)
		tmp = c * (a * j);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9e-5], t$95$1, If[LessEqual[b, -2.1e-121], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.6e-7], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.00000000000000057e-5 or 1.6e-7 < b

   1. Initial program 73.9%

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

   2. Taylor expanded in t around inf 43.8%

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

      1. distribute-lft-out-- 43.8%

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

      2. *-commutative 43.8%

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

   4. Simplified 43.8%

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

   5. Taylor expanded in x around 0 30.8%

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

      1. associate-*r* 30.9%

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

      2. *-commutative 30.9%

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

      3. associate-*l* 34.5%

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

   7. Simplified 34.5%

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

   if -9.00000000000000057e-5 < b < -2.0999999999999999e-121

   1. Initial program 76.4%

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

   2. Taylor expanded in z around inf 55.3%

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

   3. Taylor expanded in x around inf 45.5%

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

      1. *-commutative 45.5%

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

   5. Simplified 45.5%

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

   if -2.0999999999999999e-121 < b < 1.6e-7

   1. Initial program 66.6%

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

   2. Taylor expanded in c around inf 40.6%

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

   3. Taylor expanded in a around inf 31.9%

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

      1. *-commutative 31.9%

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

   5. Simplified 31.9%

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

4. Final simplification 34.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{-5}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-121}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-7}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \]

Alternative 19: 26.7% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -2.05 \cdot 10^{+211} \lor \neg \left(i \leq 7 \cdot 10^{-16}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -2.05e+211) (not (<= i 7e-16))) (* b (* t i)) (* a (* c j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -2.05e+211) || !(i <= 7e-16)) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((i <= (-2.05d+211)) .or. (.not. (i <= 7d-16))) then
        tmp = b * (t * i)
    else
        tmp = a * (c * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -2.05e+211) || !(i <= 7e-16)) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (i <= -2.05e+211) or not (i <= 7e-16):
		tmp = b * (t * i)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((i <= -2.05e+211) || !(i <= 7e-16))
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(a * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((i <= -2.05e+211) || ~((i <= 7e-16)))
		tmp = b * (t * i);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[i, -2.05e+211], N[Not[LessEqual[i, 7e-16]], $MachinePrecision]], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -2.0499999999999999e211 or 7.00000000000000035e-16 < i

   1. Initial program 67.0%

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

   2. Taylor expanded in t around inf 49.7%

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

      1. distribute-lft-out-- 49.7%

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

      2. *-commutative 49.7%

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

   4. Simplified 49.7%

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

   5. Taylor expanded in x around 0 43.2%

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

   if -2.0499999999999999e211 < i < 7.00000000000000035e-16

   1. Initial program 73.5%

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

   2. Taylor expanded in a around inf 46.8%

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

      1. +-commutative 46.8%

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

      2. mul-1-neg 46.8%

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

      3. unsub-neg 46.8%

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

   4. Simplified 46.8%

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

   5. Taylor expanded in c around inf 26.4%

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

      1. *-commutative 26.4%

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

   7. Simplified 26.4%

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

4. Final simplification 32.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.05 \cdot 10^{+211} \lor \neg \left(i \leq 7 \cdot 10^{-16}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 20: 29.1% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.22 \cdot 10^{-15}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+45}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -1.22e-15)
   (* a (* c j))
   (if (<= a 1.85e+45) (* i (* t b)) (* c (* a j)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -1.22e-15) {
		tmp = a * (c * j);
	} else if (a <= 1.85e+45) {
		tmp = i * (t * b);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (a <= (-1.22d-15)) then
        tmp = a * (c * j)
    else if (a <= 1.85d+45) then
        tmp = i * (t * b)
    else
        tmp = c * (a * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -1.22e-15) {
		tmp = a * (c * j);
	} else if (a <= 1.85e+45) {
		tmp = i * (t * b);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -1.22e-15:
		tmp = a * (c * j)
	elif a <= 1.85e+45:
		tmp = i * (t * b)
	else:
		tmp = c * (a * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -1.22e-15)
		tmp = Float64(a * Float64(c * j));
	elseif (a <= 1.85e+45)
		tmp = Float64(i * Float64(t * b));
	else
		tmp = Float64(c * Float64(a * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -1.22e-15)
		tmp = a * (c * j);
	elseif (a <= 1.85e+45)
		tmp = i * (t * b);
	else
		tmp = c * (a * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -1.22e-15], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.85e+45], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.21999999999999991e-15

   1. Initial program 64.1%

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

   2. Taylor expanded in a around inf 52.0%

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

      1. +-commutative 52.0%

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

      2. mul-1-neg 52.0%

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

      3. unsub-neg 52.0%

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

   4. Simplified 52.0%

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

   5. Taylor expanded in c around inf 33.6%

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

      1. *-commutative 33.6%

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

   7. Simplified 33.6%

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

   if -1.21999999999999991e-15 < a < 1.84999999999999989e45

   1. Initial program 82.8%

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

   2. Taylor expanded in t around inf 37.9%

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

      1. distribute-lft-out-- 37.9%

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

      2. *-commutative 37.9%

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

   4. Simplified 37.9%

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

   5. Taylor expanded in x around 0 25.7%

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

      1. associate-*r* 26.9%

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

      2. *-commutative 26.9%

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

      3. associate-*l* 30.3%

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

   7. Simplified 30.3%

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

   if 1.84999999999999989e45 < a

   1. Initial program 49.5%

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

   2. Taylor expanded in c around inf 48.3%

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

   3. Taylor expanded in a around inf 38.9%

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

      1. *-commutative 38.9%

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

   5. Simplified 38.9%

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

4. Final simplification 32.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.22 \cdot 10^{-15}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+45}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]

Alternative 21: 21.7% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(c \cdot j\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 71.3%

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

2. Taylor expanded in a around inf 38.9%

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

   1. +-commutative 38.9%

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

   2. mul-1-neg 38.9%

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

   3. unsub-neg 38.9%

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

4. Simplified 38.9%

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

5. Taylor expanded in c around inf 21.6%

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

   1. *-commutative 21.6%

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

7. Simplified 21.6%

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

8. Final simplification 21.6%

   \[\leadsto a \cdot \left(c \cdot j\right) \]

Developer target: 60.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right)\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + t_1\\ \mathbf{if}\;x < -1.469694296777705 \cdot 10^{-64}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x < 3.2113527362226803 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - t_1\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* c a) (* y i))))
        (t_2
         (+
          (-
           (* x (- (* y z) (* t a)))
           (/
            (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0)))
            (+ (* c z) (* t i))))
          t_1)))
   (if (< x -1.469694296777705e-64)
     t_2
     (if (< x 3.2113527362226803e-147)
       (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) t_1))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (pow((c * z), 2.0) - pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((c * a) - (y * i))
    t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ** 2.0d0) - ((t * i) ** 2.0d0))) / ((c * z) + (t * i)))) + t_1
    if (x < (-1.469694296777705d-64)) then
        tmp = t_2
    else if (x < 3.2113527362226803d-147) then
        tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (Math.pow((c * z), 2.0) - Math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((c * a) - (y * i))
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (math.pow((c * z), 2.0) - math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1
	tmp = 0
	if x < -1.469694296777705e-64:
		tmp = t_2
	elif x < 3.2113527362226803e-147:
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(c * a) - Float64(y * i)))
	t_2 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(Float64(b * Float64((Float64(c * z) ^ 2.0) - (Float64(t * i) ^ 2.0))) / Float64(Float64(c * z) + Float64(t * i)))) + t_1)
	tmp = 0.0
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = Float64(Float64(Float64(Float64(b * i) - Float64(x * a)) * t) - Float64(Float64(z * Float64(c * b)) - t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((c * a) - (y * i));
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ^ 2.0) - ((t * i) ^ 2.0))) / ((c * z) + (t * i)))) + t_1;
	tmp = 0.0;
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[Power[N[(c * z), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(t * i), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * z), $MachinePrecision] + N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[Less[x, -1.469694296777705e-64], t$95$2, If[Less[x, 3.2113527362226803e-147], N[(N[(N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] - N[(N[(z * N[(c * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2023340 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (if (< x -1.469694296777705e-64) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 3.2113527362226803e-147) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i))))))

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