Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.1% → 81.3%

Time: 37.5s

Alternatives: 25

Speedup: 0.5×

• 58.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 81.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_3 := \left(x \cdot \left(y \cdot z - t \cdot a\right) + t_1\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;\left(y \cdot \left(x \cdot z - i \cdot j\right) + t_2\right) + t_1\\ \mathbf{elif}\;t_3 \leq \infty:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c))))
        (t_2 (* t (- (* c j) (* x a))))
        (t_3 (+ (+ (* x (- (* y z) (* t a))) t_1) (* j (- (* t c) (* y i))))))
   (if (<= t_3 (- INFINITY))
     (+ (+ (* y (- (* x z) (* i j))) t_2) t_1)
     (if (<= t_3 INFINITY) t_3 t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = t * ((c * j) - (x * a));
	double t_3 = ((x * ((y * z) - (t * a))) + t_1) + (j * ((t * c) - (y * i)));
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = ((y * ((x * z) - (i * j))) + t_2) + t_1;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	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 = b * ((a * i) - (z * c));
	double t_2 = t * ((c * j) - (x * a));
	double t_3 = ((x * ((y * z) - (t * a))) + t_1) + (j * ((t * c) - (y * i)));
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = ((y * ((x * z) - (i * j))) + t_2) + t_1;
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = t * ((c * j) - (x * a))
	t_3 = ((x * ((y * z) - (t * a))) + t_1) + (j * ((t * c) - (y * i)))
	tmp = 0
	if t_3 <= -math.inf:
		tmp = ((y * ((x * z) - (i * j))) + t_2) + t_1
	elif t_3 <= math.inf:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_3 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_1) + Float64(j * Float64(Float64(t * c) - Float64(y * i))))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + t_2) + t_1);
	elseif (t_3 <= Inf)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = t * ((c * j) - (x * a));
	t_3 = ((x * ((y * z) - (t * a))) + t_1) + (j * ((t * c) - (y * i)));
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = ((y * ((x * z) - (i * j))) + t_2) + t_1;
	elseif (t_3 <= Inf)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

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

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 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))) < -inf.0

   1. Initial program 85.0%

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

   3. Taylor expanded in t around -inf 88.8%

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

   5. Simplified 92.8%

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

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

   1. Initial program 94.3%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in t around -inf 16.3%

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

   5. Simplified 20.4%

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

   6. Taylor expanded in t around inf 53.5%

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

4. Final simplification 86.1%

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

Alternative 2: 81.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 91.2%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in t around -inf 16.3%

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

   5. Simplified 20.4%

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

   6. Taylor expanded in t around inf 53.5%

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

4. Final simplification 84.0%

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

Alternative 3: 52.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := t_1 + x \cdot \left(y \cdot z\right)\\ t_3 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -9.2 \cdot 10^{+28}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -2300000000000:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq -1.9 \cdot 10^{-115}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -4.2 \cdot 10^{-228}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq -5.4 \cdot 10^{-271}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 8.8 \cdot 10^{-134}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.75 \cdot 10^{+97}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;c \leq 6.5 \cdot 10^{+128}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t))))
        (t_2 (+ t_1 (* x (* y z))))
        (t_3 (* c (- (* t j) (* z b)))))
   (if (<= c -9.2e+28)
     t_3
     (if (<= c -2300000000000.0)
       (* z (* x y))
       (if (<= c -1.9e-115)
         t_3
         (if (<= c -4.2e-228)
           (* y (- (* x z) (* i j)))
           (if (<= c -5.4e-271)
             t_1
             (if (<= c 8.8e-134)
               t_2
               (if (<= c 1.75e+97)
                 (* t (- (* c j) (* x a)))
                 (if (<= c 6.5e+128) t_2 t_3))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double t_2 = t_1 + (x * (y * z));
	double t_3 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -9.2e+28) {
		tmp = t_3;
	} else if (c <= -2300000000000.0) {
		tmp = z * (x * y);
	} else if (c <= -1.9e-115) {
		tmp = t_3;
	} else if (c <= -4.2e-228) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= -5.4e-271) {
		tmp = t_1;
	} else if (c <= 8.8e-134) {
		tmp = t_2;
	} else if (c <= 1.75e+97) {
		tmp = t * ((c * j) - (x * a));
	} else if (c <= 6.5e+128) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a * ((b * i) - (x * t))
    t_2 = t_1 + (x * (y * z))
    t_3 = c * ((t * j) - (z * b))
    if (c <= (-9.2d+28)) then
        tmp = t_3
    else if (c <= (-2300000000000.0d0)) then
        tmp = z * (x * y)
    else if (c <= (-1.9d-115)) then
        tmp = t_3
    else if (c <= (-4.2d-228)) then
        tmp = y * ((x * z) - (i * j))
    else if (c <= (-5.4d-271)) then
        tmp = t_1
    else if (c <= 8.8d-134) then
        tmp = t_2
    else if (c <= 1.75d+97) then
        tmp = t * ((c * j) - (x * a))
    else if (c <= 6.5d+128) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double t_2 = t_1 + (x * (y * z));
	double t_3 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -9.2e+28) {
		tmp = t_3;
	} else if (c <= -2300000000000.0) {
		tmp = z * (x * y);
	} else if (c <= -1.9e-115) {
		tmp = t_3;
	} else if (c <= -4.2e-228) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= -5.4e-271) {
		tmp = t_1;
	} else if (c <= 8.8e-134) {
		tmp = t_2;
	} else if (c <= 1.75e+97) {
		tmp = t * ((c * j) - (x * a));
	} else if (c <= 6.5e+128) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	t_2 = t_1 + (x * (y * z))
	t_3 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -9.2e+28:
		tmp = t_3
	elif c <= -2300000000000.0:
		tmp = z * (x * y)
	elif c <= -1.9e-115:
		tmp = t_3
	elif c <= -4.2e-228:
		tmp = y * ((x * z) - (i * j))
	elif c <= -5.4e-271:
		tmp = t_1
	elif c <= 8.8e-134:
		tmp = t_2
	elif c <= 1.75e+97:
		tmp = t * ((c * j) - (x * a))
	elif c <= 6.5e+128:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	t_2 = Float64(t_1 + Float64(x * Float64(y * z)))
	t_3 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -9.2e+28)
		tmp = t_3;
	elseif (c <= -2300000000000.0)
		tmp = Float64(z * Float64(x * y));
	elseif (c <= -1.9e-115)
		tmp = t_3;
	elseif (c <= -4.2e-228)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (c <= -5.4e-271)
		tmp = t_1;
	elseif (c <= 8.8e-134)
		tmp = t_2;
	elseif (c <= 1.75e+97)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (c <= 6.5e+128)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((b * i) - (x * t));
	t_2 = t_1 + (x * (y * z));
	t_3 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -9.2e+28)
		tmp = t_3;
	elseif (c <= -2300000000000.0)
		tmp = z * (x * y);
	elseif (c <= -1.9e-115)
		tmp = t_3;
	elseif (c <= -4.2e-228)
		tmp = y * ((x * z) - (i * j));
	elseif (c <= -5.4e-271)
		tmp = t_1;
	elseif (c <= 8.8e-134)
		tmp = t_2;
	elseif (c <= 1.75e+97)
		tmp = t * ((c * j) - (x * a));
	elseif (c <= 6.5e+128)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -9.2e+28], t$95$3, If[LessEqual[c, -2300000000000.0], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.9e-115], t$95$3, If[LessEqual[c, -4.2e-228], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -5.4e-271], t$95$1, If[LessEqual[c, 8.8e-134], t$95$2, If[LessEqual[c, 1.75e+97], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.5e+128], t$95$2, t$95$3]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -9.19999999999999935e28 or -2.3e12 < c < -1.89999999999999996e-115 or 6.5000000000000003e128 < c

   1. Initial program 64.1%

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

   3. Taylor expanded in c around inf 65.1%

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

      1. *-commutative 65.1%

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

      2. *-commutative 65.1%

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

   5. Simplified 65.1%

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

   if -9.19999999999999935e28 < c < -2.3e12

   1. Initial program 79.7%

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

   3. Taylor expanded in z around inf 100.0%

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

      1. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around inf 100.0%

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

   if -1.89999999999999996e-115 < c < -4.19999999999999982e-228

   1. Initial program 71.3%

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

   3. Taylor expanded in y around inf 75.5%

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

      1. +-commutative 75.5%

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

      2. mul-1-neg 75.5%

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

      3. unsub-neg 75.5%

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

      4. *-commutative 75.5%

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

   5. Simplified 75.5%

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

   if -4.19999999999999982e-228 < c < -5.3999999999999997e-271

   1. Initial program 85.5%

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

   3. Taylor expanded in a around inf 73.0%

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

      1. distribute-lft-out-- 73.0%

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

      2. *-commutative 73.0%

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

      3. *-commutative 73.0%

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

   5. Simplified 73.0%

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

   if -5.3999999999999997e-271 < c < 8.7999999999999999e-134 or 1.75e97 < c < 6.5000000000000003e128

   1. Initial program 84.7%

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

   3. Taylor expanded in t around -inf 84.7%

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

   5. Simplified 82.0%

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

   6. Taylor expanded in c around 0 80.8%

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

      1. sub-neg 80.8%

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

      2. +-commutative 80.8%

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

      3. associate-+l+ 80.8%

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

      4. sub-neg 80.8%

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

      5. *-commutative 80.8%

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

      6. sub-neg 80.8%

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

      7. associate-*r* 80.8%

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

      8. *-commutative 80.8%

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

      9. associate-*r* 80.8%

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

      10. *-commutative 80.8%

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

      11. distribute-rgt-neg-in 80.8%

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

      12. distribute-lft-in 80.8%

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

      13. neg-mul-1 80.8%

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

      14. sub-neg 80.8%

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

   8. Simplified 80.8%

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

   9. Taylor expanded in x around inf 72.7%

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

       1. *-commutative 72.7%

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

   11. Simplified 72.7%

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

   if 8.7999999999999999e-134 < c < 1.75e97

   1. Initial program 82.4%

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

   3. Taylor expanded in t around -inf 74.0%

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

   5. Simplified 73.9%

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

   6. Taylor expanded in t around inf 57.1%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -9.2 \cdot 10^{+28}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -2300000000000:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq -1.9 \cdot 10^{-115}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -4.2 \cdot 10^{-228}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq -5.4 \cdot 10^{-271}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 8.8 \cdot 10^{-134}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 1.75 \cdot 10^{+97}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;c \leq 6.5 \cdot 10^{+128}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 62.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := y \cdot \left(x \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := y \cdot \left(x \cdot z - i \cdot j\right) + a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;b \leq -1.75 \cdot 10^{-6}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.8 \cdot 10^{-171}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -9.2 \cdot 10^{-204}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.35 \cdot 10^{-181}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-145}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{+47}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i))))
        (t_2 (+ (* y (* x z)) (* b (- (* a i) (* z c)))))
        (t_3 (+ (* y (- (* x z) (* i j))) (* a (- (* b i) (* x t))))))
   (if (<= b -1.75e-6)
     t_2
     (if (<= b -1.8e-171)
       t_3
       (if (<= b -9.2e-204)
         t_1
         (if (<= b 2.35e-181)
           t_3
           (if (<= b 3.4e-145) t_1 (if (<= b 3.1e+47) t_3 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = (y * (x * z)) + (b * ((a * i) - (z * c)));
	double t_3 = (y * ((x * z) - (i * j))) + (a * ((b * i) - (x * t)));
	double tmp;
	if (b <= -1.75e-6) {
		tmp = t_2;
	} else if (b <= -1.8e-171) {
		tmp = t_3;
	} else if (b <= -9.2e-204) {
		tmp = t_1;
	} else if (b <= 2.35e-181) {
		tmp = t_3;
	} else if (b <= 3.4e-145) {
		tmp = t_1;
	} else if (b <= 3.1e+47) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = (y * (x * z)) + (b * ((a * i) - (z * c)))
    t_3 = (y * ((x * z) - (i * j))) + (a * ((b * i) - (x * t)))
    if (b <= (-1.75d-6)) then
        tmp = t_2
    else if (b <= (-1.8d-171)) then
        tmp = t_3
    else if (b <= (-9.2d-204)) then
        tmp = t_1
    else if (b <= 2.35d-181) then
        tmp = t_3
    else if (b <= 3.4d-145) then
        tmp = t_1
    else if (b <= 3.1d+47) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = (y * (x * z)) + (b * ((a * i) - (z * c)));
	double t_3 = (y * ((x * z) - (i * j))) + (a * ((b * i) - (x * t)));
	double tmp;
	if (b <= -1.75e-6) {
		tmp = t_2;
	} else if (b <= -1.8e-171) {
		tmp = t_3;
	} else if (b <= -9.2e-204) {
		tmp = t_1;
	} else if (b <= 2.35e-181) {
		tmp = t_3;
	} else if (b <= 3.4e-145) {
		tmp = t_1;
	} else if (b <= 3.1e+47) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = (y * (x * z)) + (b * ((a * i) - (z * c)))
	t_3 = (y * ((x * z) - (i * j))) + (a * ((b * i) - (x * t)))
	tmp = 0
	if b <= -1.75e-6:
		tmp = t_2
	elif b <= -1.8e-171:
		tmp = t_3
	elif b <= -9.2e-204:
		tmp = t_1
	elif b <= 2.35e-181:
		tmp = t_3
	elif b <= 3.4e-145:
		tmp = t_1
	elif b <= 3.1e+47:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(Float64(y * Float64(x * z)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))))
	t_3 = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(a * Float64(Float64(b * i) - Float64(x * t))))
	tmp = 0.0
	if (b <= -1.75e-6)
		tmp = t_2;
	elseif (b <= -1.8e-171)
		tmp = t_3;
	elseif (b <= -9.2e-204)
		tmp = t_1;
	elseif (b <= 2.35e-181)
		tmp = t_3;
	elseif (b <= 3.4e-145)
		tmp = t_1;
	elseif (b <= 3.1e+47)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = (y * (x * z)) + (b * ((a * i) - (z * c)));
	t_3 = (y * ((x * z) - (i * j))) + (a * ((b * i) - (x * t)));
	tmp = 0.0;
	if (b <= -1.75e-6)
		tmp = t_2;
	elseif (b <= -1.8e-171)
		tmp = t_3;
	elseif (b <= -9.2e-204)
		tmp = t_1;
	elseif (b <= 2.35e-181)
		tmp = t_3;
	elseif (b <= 3.4e-145)
		tmp = t_1;
	elseif (b <= 3.1e+47)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.75e-6], t$95$2, If[LessEqual[b, -1.8e-171], t$95$3, If[LessEqual[b, -9.2e-204], t$95$1, If[LessEqual[b, 2.35e-181], t$95$3, If[LessEqual[b, 3.4e-145], t$95$1, If[LessEqual[b, 3.1e+47], t$95$3, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.74999999999999997e-6 or 3.1000000000000001e47 < b

   1. Initial program 75.0%

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

   3. Taylor expanded in t around 0 68.1%

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

      1. *-commutative 68.1%

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

      2. associate-*r* 68.8%

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

      3. associate-*r* 68.1%

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

      4. associate-*r* 68.1%

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

      5. distribute-rgt-in 68.8%

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

      6. +-commutative 68.8%

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

      7. mul-1-neg 68.8%

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

      8. unsub-neg 68.8%

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

      9. *-commutative 68.8%

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

      10. *-commutative 68.8%

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

   5. Simplified 68.8%

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

   6. Taylor expanded in x around inf 70.0%

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

      1. *-commutative 21.7%

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

   8. Simplified 70.0%

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

   if -1.74999999999999997e-6 < b < -1.80000000000000002e-171 or -9.1999999999999997e-204 < b < 2.3499999999999999e-181 or 3.3999999999999999e-145 < b < 3.1000000000000001e47

   1. Initial program 70.4%

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

   3. Taylor expanded in t around -inf 74.5%

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

   5. Simplified 74.4%

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

   6. Taylor expanded in c around 0 69.5%

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

      1. sub-neg 69.5%

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

      2. +-commutative 69.5%

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

      3. associate-+l+ 69.5%

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

      4. sub-neg 69.5%

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

      5. *-commutative 69.5%

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

      6. sub-neg 69.5%

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

      7. associate-*r* 69.5%

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

      8. *-commutative 69.5%

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

      9. associate-*r* 69.5%

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

      10. *-commutative 69.5%

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

      11. distribute-rgt-neg-in 69.5%

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

      12. distribute-lft-in 69.5%

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

      13. neg-mul-1 69.5%

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

      14. sub-neg 69.5%

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

   8. Simplified 69.5%

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

   if -1.80000000000000002e-171 < b < -9.1999999999999997e-204 or 2.3499999999999999e-181 < b < 3.3999999999999999e-145

   1. Initial program 79.6%

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

   3. Taylor expanded in j around inf 83.0%

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

      1. sub-neg 83.0%

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

      2. *-commutative 83.0%

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

      3. *-commutative 83.0%

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

      4. sub-neg 83.0%

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

   5. Simplified 83.0%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.75 \cdot 10^{-6}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.8 \cdot 10^{-171}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;b \leq -9.2 \cdot 10^{-204}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 2.35 \cdot 10^{-181}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-145}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 29.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c\right)\\ \mathbf{if}\;i \leq -62000000000:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;i \leq 4 \cdot 10^{-308}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 7.4 \cdot 10^{-153}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;i \leq 1.16 \cdot 10^{-94}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{+73}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 3.7 \cdot 10^{+132}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 1.1 \cdot 10^{+161}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;i \leq 1.12 \cdot 10^{+214}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (* t c))))
   (if (<= i -62000000000.0)
     (* b (* a i))
     (if (<= i 4e-308)
       t_1
       (if (<= i 7.4e-153)
         (* b (* z (- c)))
         (if (<= i 1.16e-94)
           (* t (* x (- a)))
           (if (<= i 4.8e+73)
             (* x (* y z))
             (if (<= i 3.7e+132)
               t_1
               (if (<= i 1.1e+161)
                 (* i (* a b))
                 (if (<= i 1.12e+214) (* j (* y (- i))) (* a (* b i))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (t * c);
	double tmp;
	if (i <= -62000000000.0) {
		tmp = b * (a * i);
	} else if (i <= 4e-308) {
		tmp = t_1;
	} else if (i <= 7.4e-153) {
		tmp = b * (z * -c);
	} else if (i <= 1.16e-94) {
		tmp = t * (x * -a);
	} else if (i <= 4.8e+73) {
		tmp = x * (y * z);
	} else if (i <= 3.7e+132) {
		tmp = t_1;
	} else if (i <= 1.1e+161) {
		tmp = i * (a * b);
	} else if (i <= 1.12e+214) {
		tmp = j * (y * -i);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (t * c)
    if (i <= (-62000000000.0d0)) then
        tmp = b * (a * i)
    else if (i <= 4d-308) then
        tmp = t_1
    else if (i <= 7.4d-153) then
        tmp = b * (z * -c)
    else if (i <= 1.16d-94) then
        tmp = t * (x * -a)
    else if (i <= 4.8d+73) then
        tmp = x * (y * z)
    else if (i <= 3.7d+132) then
        tmp = t_1
    else if (i <= 1.1d+161) then
        tmp = i * (a * b)
    else if (i <= 1.12d+214) then
        tmp = j * (y * -i)
    else
        tmp = a * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (t * c);
	double tmp;
	if (i <= -62000000000.0) {
		tmp = b * (a * i);
	} else if (i <= 4e-308) {
		tmp = t_1;
	} else if (i <= 7.4e-153) {
		tmp = b * (z * -c);
	} else if (i <= 1.16e-94) {
		tmp = t * (x * -a);
	} else if (i <= 4.8e+73) {
		tmp = x * (y * z);
	} else if (i <= 3.7e+132) {
		tmp = t_1;
	} else if (i <= 1.1e+161) {
		tmp = i * (a * b);
	} else if (i <= 1.12e+214) {
		tmp = j * (y * -i);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * (t * c)
	tmp = 0
	if i <= -62000000000.0:
		tmp = b * (a * i)
	elif i <= 4e-308:
		tmp = t_1
	elif i <= 7.4e-153:
		tmp = b * (z * -c)
	elif i <= 1.16e-94:
		tmp = t * (x * -a)
	elif i <= 4.8e+73:
		tmp = x * (y * z)
	elif i <= 3.7e+132:
		tmp = t_1
	elif i <= 1.1e+161:
		tmp = i * (a * b)
	elif i <= 1.12e+214:
		tmp = j * (y * -i)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(t * c))
	tmp = 0.0
	if (i <= -62000000000.0)
		tmp = Float64(b * Float64(a * i));
	elseif (i <= 4e-308)
		tmp = t_1;
	elseif (i <= 7.4e-153)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (i <= 1.16e-94)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (i <= 4.8e+73)
		tmp = Float64(x * Float64(y * z));
	elseif (i <= 3.7e+132)
		tmp = t_1;
	elseif (i <= 1.1e+161)
		tmp = Float64(i * Float64(a * b));
	elseif (i <= 1.12e+214)
		tmp = Float64(j * Float64(y * Float64(-i)));
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * (t * c);
	tmp = 0.0;
	if (i <= -62000000000.0)
		tmp = b * (a * i);
	elseif (i <= 4e-308)
		tmp = t_1;
	elseif (i <= 7.4e-153)
		tmp = b * (z * -c);
	elseif (i <= 1.16e-94)
		tmp = t * (x * -a);
	elseif (i <= 4.8e+73)
		tmp = x * (y * z);
	elseif (i <= 3.7e+132)
		tmp = t_1;
	elseif (i <= 1.1e+161)
		tmp = i * (a * b);
	elseif (i <= 1.12e+214)
		tmp = j * (y * -i);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -62000000000.0], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4e-308], t$95$1, If[LessEqual[i, 7.4e-153], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.16e-94], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4.8e+73], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.7e+132], t$95$1, If[LessEqual[i, 1.1e+161], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.12e+214], N[(j * N[(y * (-i)), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if i < -6.2e10

   1. Initial program 71.0%

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

   3. Taylor expanded in b around inf 45.4%

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

      1. *-commutative 45.4%

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

   5. Simplified 45.4%

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

   6. Taylor expanded in a around inf 37.6%

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

   if -6.2e10 < i < 4.00000000000000013e-308 or 4.80000000000000004e73 < i < 3.70000000000000011e132

   1. Initial program 77.9%

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

   3. Taylor expanded in j around inf 47.5%

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

      1. sub-neg 47.5%

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

      2. *-commutative 47.5%

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

      3. *-commutative 47.5%

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

      4. sub-neg 47.5%

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

   5. Simplified 47.5%

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

   6. Taylor expanded in t around inf 42.1%

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

      1. *-commutative 42.1%

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

   8. Simplified 42.1%

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

   if 4.00000000000000013e-308 < i < 7.4000000000000005e-153

   1. Initial program 77.1%

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

   3. Taylor expanded in b around inf 62.6%

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

      1. *-commutative 62.6%

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

   5. Simplified 62.6%

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

   6. Taylor expanded in a around 0 58.7%

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

      1. mul-1-neg 58.7%

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

      2. *-commutative 58.7%

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

      3. *-commutative 58.7%

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

      4. distribute-rgt-neg-in 58.7%

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

      5. *-commutative 58.7%

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

   8. Simplified 58.7%

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

   if 7.4000000000000005e-153 < i < 1.16000000000000001e-94

   1. Initial program 91.8%

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

   3. Taylor expanded in a around inf 43.9%

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

      1. distribute-lft-out-- 43.9%

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

      2. *-commutative 43.9%

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

      3. *-commutative 43.9%

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

   5. Simplified 43.9%

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

   6. Taylor expanded in x around inf 35.5%

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

   7. Taylor expanded in a around 0 35.5%

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

      1. mul-1-neg 35.5%

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

      2. *-commutative 35.5%

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

      3. associate-*r* 51.3%

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

      4. distribute-rgt-neg-in 51.3%

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

   9. Simplified 51.3%

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

   if 1.16000000000000001e-94 < i < 4.80000000000000004e73

   1. Initial program 77.8%

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

   3. Taylor expanded in t around 0 67.1%

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

      1. *-commutative 67.1%

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

      2. associate-*r* 67.3%

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

      3. associate-*r* 70.0%

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

      4. associate-*r* 70.0%

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

      5. distribute-rgt-in 70.0%

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

      6. +-commutative 70.0%

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

      7. mul-1-neg 70.0%

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

      8. unsub-neg 70.0%

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

      9. *-commutative 70.0%

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

      10. *-commutative 70.0%

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

   5. Simplified 70.0%

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

   6. Taylor expanded in x around inf 38.0%

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

      1. *-commutative 38.0%

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

   8. Simplified 38.0%

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

   if 3.70000000000000011e132 < i < 1.1e161

   1. Initial program 83.9%

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

   3. Taylor expanded in b around inf 67.3%

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

      1. *-commutative 67.3%

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

   5. Simplified 67.3%

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

   6. Taylor expanded in a around inf 82.8%

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

      1. associate-*r* 83.1%

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

   8. Simplified 83.1%

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

   if 1.1e161 < i < 1.11999999999999996e214

   1. Initial program 61.4%

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

   3. Taylor expanded in j around inf 55.2%

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

      1. sub-neg 55.2%

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

      2. *-commutative 55.2%

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

      3. *-commutative 55.2%

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

      4. sub-neg 55.2%

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

   5. Simplified 55.2%

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

   6. Taylor expanded in t around 0 70.6%

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

      1. mul-1-neg 70.6%

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

      2. distribute-rgt-neg-in 70.6%

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

   8. Simplified 70.6%

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

   if 1.11999999999999996e214 < i

   1. Initial program 54.6%

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

   3. Taylor expanded in b around inf 55.1%

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

      1. *-commutative 55.1%

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

   5. Simplified 55.1%

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

   6. Taylor expanded in a around inf 69.7%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 47.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -62000000000:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;i \leq 4 \cdot 10^{-308}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;i \leq 7.4 \cdot 10^{-153}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;i \leq 1.16 \cdot 10^{-94}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{+73}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 3.7 \cdot 10^{+132}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;i \leq 1.1 \cdot 10^{+161}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;i \leq 1.12 \cdot 10^{+214}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 29.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c\right)\\ \mathbf{if}\;i \leq -56000000000000:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;i \leq 1.1 \cdot 10^{-305}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 8.5 \cdot 10^{-155}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;i \leq 5.1 \cdot 10^{-95}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;i \leq 2.9 \cdot 10^{+73}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 1.32 \cdot 10^{+132}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 1.8 \cdot 10^{+162}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;i \leq 3.1 \cdot 10^{+215}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (* t c))))
   (if (<= i -56000000000000.0)
     (* b (* a i))
     (if (<= i 1.1e-305)
       t_1
       (if (<= i 8.5e-155)
         (* b (* z (- c)))
         (if (<= i 5.1e-95)
           (* t (* x (- a)))
           (if (<= i 2.9e+73)
             (* x (* y z))
             (if (<= i 1.32e+132)
               t_1
               (if (<= i 1.8e+162)
                 (* i (* a b))
                 (if (<= i 3.1e+215) (* (* y j) (- i)) (* a (* b i))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (t * c);
	double tmp;
	if (i <= -56000000000000.0) {
		tmp = b * (a * i);
	} else if (i <= 1.1e-305) {
		tmp = t_1;
	} else if (i <= 8.5e-155) {
		tmp = b * (z * -c);
	} else if (i <= 5.1e-95) {
		tmp = t * (x * -a);
	} else if (i <= 2.9e+73) {
		tmp = x * (y * z);
	} else if (i <= 1.32e+132) {
		tmp = t_1;
	} else if (i <= 1.8e+162) {
		tmp = i * (a * b);
	} else if (i <= 3.1e+215) {
		tmp = (y * j) * -i;
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (t * c)
    if (i <= (-56000000000000.0d0)) then
        tmp = b * (a * i)
    else if (i <= 1.1d-305) then
        tmp = t_1
    else if (i <= 8.5d-155) then
        tmp = b * (z * -c)
    else if (i <= 5.1d-95) then
        tmp = t * (x * -a)
    else if (i <= 2.9d+73) then
        tmp = x * (y * z)
    else if (i <= 1.32d+132) then
        tmp = t_1
    else if (i <= 1.8d+162) then
        tmp = i * (a * b)
    else if (i <= 3.1d+215) then
        tmp = (y * j) * -i
    else
        tmp = a * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (t * c);
	double tmp;
	if (i <= -56000000000000.0) {
		tmp = b * (a * i);
	} else if (i <= 1.1e-305) {
		tmp = t_1;
	} else if (i <= 8.5e-155) {
		tmp = b * (z * -c);
	} else if (i <= 5.1e-95) {
		tmp = t * (x * -a);
	} else if (i <= 2.9e+73) {
		tmp = x * (y * z);
	} else if (i <= 1.32e+132) {
		tmp = t_1;
	} else if (i <= 1.8e+162) {
		tmp = i * (a * b);
	} else if (i <= 3.1e+215) {
		tmp = (y * j) * -i;
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * (t * c)
	tmp = 0
	if i <= -56000000000000.0:
		tmp = b * (a * i)
	elif i <= 1.1e-305:
		tmp = t_1
	elif i <= 8.5e-155:
		tmp = b * (z * -c)
	elif i <= 5.1e-95:
		tmp = t * (x * -a)
	elif i <= 2.9e+73:
		tmp = x * (y * z)
	elif i <= 1.32e+132:
		tmp = t_1
	elif i <= 1.8e+162:
		tmp = i * (a * b)
	elif i <= 3.1e+215:
		tmp = (y * j) * -i
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(t * c))
	tmp = 0.0
	if (i <= -56000000000000.0)
		tmp = Float64(b * Float64(a * i));
	elseif (i <= 1.1e-305)
		tmp = t_1;
	elseif (i <= 8.5e-155)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (i <= 5.1e-95)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (i <= 2.9e+73)
		tmp = Float64(x * Float64(y * z));
	elseif (i <= 1.32e+132)
		tmp = t_1;
	elseif (i <= 1.8e+162)
		tmp = Float64(i * Float64(a * b));
	elseif (i <= 3.1e+215)
		tmp = Float64(Float64(y * j) * Float64(-i));
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * (t * c);
	tmp = 0.0;
	if (i <= -56000000000000.0)
		tmp = b * (a * i);
	elseif (i <= 1.1e-305)
		tmp = t_1;
	elseif (i <= 8.5e-155)
		tmp = b * (z * -c);
	elseif (i <= 5.1e-95)
		tmp = t * (x * -a);
	elseif (i <= 2.9e+73)
		tmp = x * (y * z);
	elseif (i <= 1.32e+132)
		tmp = t_1;
	elseif (i <= 1.8e+162)
		tmp = i * (a * b);
	elseif (i <= 3.1e+215)
		tmp = (y * j) * -i;
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -56000000000000.0], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.1e-305], t$95$1, If[LessEqual[i, 8.5e-155], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5.1e-95], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.9e+73], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.32e+132], t$95$1, If[LessEqual[i, 1.8e+162], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.1e+215], N[(N[(y * j), $MachinePrecision] * (-i)), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if i < -5.6e13

   1. Initial program 71.0%

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

   3. Taylor expanded in b around inf 45.4%

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

      1. *-commutative 45.4%

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

   5. Simplified 45.4%

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

   6. Taylor expanded in a around inf 37.6%

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

   if -5.6e13 < i < 1.09999999999999998e-305 or 2.9000000000000002e73 < i < 1.3199999999999999e132

   1. Initial program 77.9%

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

   3. Taylor expanded in j around inf 47.5%

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

      1. sub-neg 47.5%

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

      2. *-commutative 47.5%

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

      3. *-commutative 47.5%

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

      4. sub-neg 47.5%

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

   5. Simplified 47.5%

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

   6. Taylor expanded in t around inf 42.1%

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

      1. *-commutative 42.1%

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

   8. Simplified 42.1%

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

   if 1.09999999999999998e-305 < i < 8.4999999999999996e-155

   1. Initial program 77.1%

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

   3. Taylor expanded in b around inf 62.6%

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

      1. *-commutative 62.6%

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

   5. Simplified 62.6%

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

   6. Taylor expanded in a around 0 58.7%

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

      1. mul-1-neg 58.7%

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

      2. *-commutative 58.7%

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

      3. *-commutative 58.7%

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

      4. distribute-rgt-neg-in 58.7%

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

      5. *-commutative 58.7%

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

   8. Simplified 58.7%

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

   if 8.4999999999999996e-155 < i < 5.1e-95

   1. Initial program 91.8%

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

   3. Taylor expanded in a around inf 43.9%

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

      1. distribute-lft-out-- 43.9%

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

      2. *-commutative 43.9%

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

      3. *-commutative 43.9%

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

   5. Simplified 43.9%

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

   6. Taylor expanded in x around inf 35.5%

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

   7. Taylor expanded in a around 0 35.5%

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

      1. mul-1-neg 35.5%

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

      2. *-commutative 35.5%

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

      3. associate-*r* 51.3%

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

      4. distribute-rgt-neg-in 51.3%

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

   9. Simplified 51.3%

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

   if 5.1e-95 < i < 2.9000000000000002e73

   1. Initial program 77.8%

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

   3. Taylor expanded in t around 0 67.1%

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

      1. *-commutative 67.1%

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

      2. associate-*r* 67.3%

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

      3. associate-*r* 70.0%

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

      4. associate-*r* 70.0%

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

      5. distribute-rgt-in 70.0%

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

      6. +-commutative 70.0%

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

      7. mul-1-neg 70.0%

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

      8. unsub-neg 70.0%

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

      9. *-commutative 70.0%

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

      10. *-commutative 70.0%

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

   5. Simplified 70.0%

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

   6. Taylor expanded in x around inf 38.0%

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

      1. *-commutative 38.0%

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

   8. Simplified 38.0%

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

   if 1.3199999999999999e132 < i < 1.79999999999999997e162

   1. Initial program 83.9%

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

   3. Taylor expanded in b around inf 67.3%

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

      1. *-commutative 67.3%

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

   5. Simplified 67.3%

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

   6. Taylor expanded in a around inf 82.8%

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

      1. associate-*r* 83.1%

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

   8. Simplified 83.1%

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

   if 1.79999999999999997e162 < i < 3.0999999999999999e215

   1. Initial program 61.4%

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

   3. Taylor expanded in t around 0 61.5%

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

      1. *-commutative 61.5%

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

      2. associate-*r* 61.4%

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

      3. associate-*r* 54.2%

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

      4. associate-*r* 54.2%

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

      5. distribute-rgt-in 54.2%

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

      6. +-commutative 54.2%

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

      7. mul-1-neg 54.2%

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

      8. unsub-neg 54.2%

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

      9. *-commutative 54.2%

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

      10. *-commutative 54.2%

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

   5. Simplified 54.2%

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

   6. Taylor expanded in j around inf 70.7%

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

      1. mul-1-neg 70.7%

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

      2. *-commutative 70.7%

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

      3. distribute-rgt-neg-in 70.7%

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

      4. *-commutative 70.7%

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

   8. Simplified 70.7%

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

   if 3.0999999999999999e215 < i

   1. Initial program 54.6%

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

   3. Taylor expanded in b around inf 55.1%

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

      1. *-commutative 55.1%

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

   5. Simplified 55.1%

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

   6. Taylor expanded in a around inf 69.7%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 47.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -56000000000000:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;i \leq 1.1 \cdot 10^{-305}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;i \leq 8.5 \cdot 10^{-155}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;i \leq 5.1 \cdot 10^{-95}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;i \leq 2.9 \cdot 10^{+73}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 1.32 \cdot 10^{+132}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;i \leq 1.8 \cdot 10^{+162}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;i \leq 3.1 \cdot 10^{+215}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 57.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_2 := y \cdot \left(x \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -6.5 \cdot 10^{+99}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -8.6 \cdot 10^{-182}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-251}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-284}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-164}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+134}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* a b) (* y j))))
        (t_2 (+ (* y (* x z)) (* b (- (* a i) (* z c)))))
        (t_3 (* t (- (* c j) (* x a)))))
   (if (<= t -6.5e+99)
     t_3
     (if (<= t -8.6e-182)
       t_2
       (if (<= t -4e-251)
         t_1
         (if (<= t 1.75e-284)
           t_2
           (if (<= t 4.4e-164) t_1 (if (<= t 4.4e+134) 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 = i * ((a * b) - (y * j));
	double t_2 = (y * (x * z)) + (b * ((a * i) - (z * c)));
	double t_3 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -6.5e+99) {
		tmp = t_3;
	} else if (t <= -8.6e-182) {
		tmp = t_2;
	} else if (t <= -4e-251) {
		tmp = t_1;
	} else if (t <= 1.75e-284) {
		tmp = t_2;
	} else if (t <= 4.4e-164) {
		tmp = t_1;
	} else if (t <= 4.4e+134) {
		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 = i * ((a * b) - (y * j))
    t_2 = (y * (x * z)) + (b * ((a * i) - (z * c)))
    t_3 = t * ((c * j) - (x * a))
    if (t <= (-6.5d+99)) then
        tmp = t_3
    else if (t <= (-8.6d-182)) then
        tmp = t_2
    else if (t <= (-4d-251)) then
        tmp = t_1
    else if (t <= 1.75d-284) then
        tmp = t_2
    else if (t <= 4.4d-164) then
        tmp = t_1
    else if (t <= 4.4d+134) 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 = i * ((a * b) - (y * j));
	double t_2 = (y * (x * z)) + (b * ((a * i) - (z * c)));
	double t_3 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -6.5e+99) {
		tmp = t_3;
	} else if (t <= -8.6e-182) {
		tmp = t_2;
	} else if (t <= -4e-251) {
		tmp = t_1;
	} else if (t <= 1.75e-284) {
		tmp = t_2;
	} else if (t <= 4.4e-164) {
		tmp = t_1;
	} else if (t <= 4.4e+134) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((a * b) - (y * j))
	t_2 = (y * (x * z)) + (b * ((a * i) - (z * c)))
	t_3 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -6.5e+99:
		tmp = t_3
	elif t <= -8.6e-182:
		tmp = t_2
	elif t <= -4e-251:
		tmp = t_1
	elif t <= 1.75e-284:
		tmp = t_2
	elif t <= 4.4e-164:
		tmp = t_1
	elif t <= 4.4e+134:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	t_2 = Float64(Float64(y * Float64(x * z)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))))
	t_3 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -6.5e+99)
		tmp = t_3;
	elseif (t <= -8.6e-182)
		tmp = t_2;
	elseif (t <= -4e-251)
		tmp = t_1;
	elseif (t <= 1.75e-284)
		tmp = t_2;
	elseif (t <= 4.4e-164)
		tmp = t_1;
	elseif (t <= 4.4e+134)
		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 = i * ((a * b) - (y * j));
	t_2 = (y * (x * z)) + (b * ((a * i) - (z * c)));
	t_3 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -6.5e+99)
		tmp = t_3;
	elseif (t <= -8.6e-182)
		tmp = t_2;
	elseif (t <= -4e-251)
		tmp = t_1;
	elseif (t <= 1.75e-284)
		tmp = t_2;
	elseif (t <= 4.4e-164)
		tmp = t_1;
	elseif (t <= 4.4e+134)
		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[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.5e+99], t$95$3, If[LessEqual[t, -8.6e-182], t$95$2, If[LessEqual[t, -4e-251], t$95$1, If[LessEqual[t, 1.75e-284], t$95$2, If[LessEqual[t, 4.4e-164], t$95$1, If[LessEqual[t, 4.4e+134], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.5000000000000004e99 or 4.4e134 < t

   1. Initial program 62.0%

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

   3. Taylor expanded in t around -inf 70.3%

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

   5. Simplified 70.3%

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

   6. Taylor expanded in t around inf 69.0%

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

   if -6.5000000000000004e99 < t < -8.6e-182 or -4.00000000000000006e-251 < t < 1.74999999999999988e-284 or 4.39999999999999975e-164 < t < 4.4e134

   1. Initial program 82.6%

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

   3. Taylor expanded in t around 0 66.8%

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

      1. *-commutative 66.8%

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

      2. associate-*r* 66.8%

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

      3. associate-*r* 67.4%

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

      4. associate-*r* 67.4%

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

      5. distribute-rgt-in 68.2%

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

      6. +-commutative 68.2%

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

      7. mul-1-neg 68.2%

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

      8. unsub-neg 68.2%

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

      9. *-commutative 68.2%

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

      10. *-commutative 68.2%

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

   5. Simplified 68.2%

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

   6. Taylor expanded in x around inf 63.7%

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

      1. *-commutative 29.0%

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

   8. Simplified 63.7%

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

   if -8.6e-182 < t < -4.00000000000000006e-251 or 1.74999999999999988e-284 < t < 4.39999999999999975e-164

   1. Initial program 67.9%

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

   3. Taylor expanded in i around inf 80.1%

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

      1. distribute-lft-out-- 80.1%

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

      2. *-commutative 80.1%

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

   5. Simplified 80.1%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+99}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -8.6 \cdot 10^{-182}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-251}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-284}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-164}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+134}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -2.5 \cdot 10^{+73}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-14}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-185}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-246}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+104}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j))))
        (t_2 (* b (- (* a i) (* z c))))
        (t_3 (* t (- (* c j) (* x a)))))
   (if (<= t -2.5e+73)
     t_3
     (if (<= t -2.4e-14)
       t_2
       (if (<= t -2.4e-185)
         t_1
         (if (<= t 2.25e-246)
           t_2
           (if (<= t 8.5e-153) t_1 (if (<= t 9e+104) 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 = b * ((a * i) - (z * c));
	double t_3 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -2.5e+73) {
		tmp = t_3;
	} else if (t <= -2.4e-14) {
		tmp = t_2;
	} else if (t <= -2.4e-185) {
		tmp = t_1;
	} else if (t <= 2.25e-246) {
		tmp = t_2;
	} else if (t <= 8.5e-153) {
		tmp = t_1;
	} else if (t <= 9e+104) {
		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 = b * ((a * i) - (z * c))
    t_3 = t * ((c * j) - (x * a))
    if (t <= (-2.5d+73)) then
        tmp = t_3
    else if (t <= (-2.4d-14)) then
        tmp = t_2
    else if (t <= (-2.4d-185)) then
        tmp = t_1
    else if (t <= 2.25d-246) then
        tmp = t_2
    else if (t <= 8.5d-153) then
        tmp = t_1
    else if (t <= 9d+104) 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 = b * ((a * i) - (z * c));
	double t_3 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -2.5e+73) {
		tmp = t_3;
	} else if (t <= -2.4e-14) {
		tmp = t_2;
	} else if (t <= -2.4e-185) {
		tmp = t_1;
	} else if (t <= 2.25e-246) {
		tmp = t_2;
	} else if (t <= 8.5e-153) {
		tmp = t_1;
	} else if (t <= 9e+104) {
		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 = b * ((a * i) - (z * c))
	t_3 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -2.5e+73:
		tmp = t_3
	elif t <= -2.4e-14:
		tmp = t_2
	elif t <= -2.4e-185:
		tmp = t_1
	elif t <= 2.25e-246:
		tmp = t_2
	elif t <= 8.5e-153:
		tmp = t_1
	elif t <= 9e+104:
		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(b * Float64(Float64(a * i) - Float64(z * c)))
	t_3 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -2.5e+73)
		tmp = t_3;
	elseif (t <= -2.4e-14)
		tmp = t_2;
	elseif (t <= -2.4e-185)
		tmp = t_1;
	elseif (t <= 2.25e-246)
		tmp = t_2;
	elseif (t <= 8.5e-153)
		tmp = t_1;
	elseif (t <= 9e+104)
		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 = b * ((a * i) - (z * c));
	t_3 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -2.5e+73)
		tmp = t_3;
	elseif (t <= -2.4e-14)
		tmp = t_2;
	elseif (t <= -2.4e-185)
		tmp = t_1;
	elseif (t <= 2.25e-246)
		tmp = t_2;
	elseif (t <= 8.5e-153)
		tmp = t_1;
	elseif (t <= 9e+104)
		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[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.5e+73], t$95$3, If[LessEqual[t, -2.4e-14], t$95$2, If[LessEqual[t, -2.4e-185], t$95$1, If[LessEqual[t, 2.25e-246], t$95$2, If[LessEqual[t, 8.5e-153], t$95$1, If[LessEqual[t, 9e+104], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.49999999999999988e73 or 8.9999999999999997e104 < t

   1. Initial program 64.0%

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

   3. Taylor expanded in t around -inf 71.5%

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

   5. Simplified 71.4%

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

   6. Taylor expanded in t around inf 66.1%

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

   if -2.49999999999999988e73 < t < -2.4e-14 or -2.4000000000000001e-185 < t < 2.25e-246 or 8.4999999999999996e-153 < t < 8.9999999999999997e104

   1. Initial program 75.4%

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

   3. Taylor expanded in b around inf 59.9%

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

      1. *-commutative 59.9%

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

   5. Simplified 59.9%

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

   if -2.4e-14 < t < -2.4000000000000001e-185 or 2.25e-246 < t < 8.4999999999999996e-153

   1. Initial program 85.1%

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

   3. Taylor expanded in y around inf 54.8%

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

      1. +-commutative 54.8%

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

      2. mul-1-neg 54.8%

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

      3. unsub-neg 54.8%

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

      4. *-commutative 54.8%

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

   5. Simplified 54.8%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+73}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-14}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-185}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-246}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-153}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+104}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -7.2 \cdot 10^{+23}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -6.5 \cdot 10^{-86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 4.1 \cdot 10^{-156}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{+161}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* x (- (* y z) (* t a))) (* b (- (* a i) (* z c)))))
        (t_2 (* c (- (* t j) (* z b)))))
   (if (<= c -7.2e+23)
     t_2
     (if (<= c -6.5e-86)
       t_1
       (if (<= c 4.1e-156)
         (+ (* y (- (* x z) (* i j))) (* a (- (* b i) (* x t))))
         (if (<= c 1.8e+161) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -7.2e+23) {
		tmp = t_2;
	} else if (c <= -6.5e-86) {
		tmp = t_1;
	} else if (c <= 4.1e-156) {
		tmp = (y * ((x * z) - (i * j))) + (a * ((b * i) - (x * t)));
	} else if (c <= 1.8e+161) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))
    t_2 = c * ((t * j) - (z * b))
    if (c <= (-7.2d+23)) then
        tmp = t_2
    else if (c <= (-6.5d-86)) then
        tmp = t_1
    else if (c <= 4.1d-156) then
        tmp = (y * ((x * z) - (i * j))) + (a * ((b * i) - (x * t)))
    else if (c <= 1.8d+161) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -7.2e+23) {
		tmp = t_2;
	} else if (c <= -6.5e-86) {
		tmp = t_1;
	} else if (c <= 4.1e-156) {
		tmp = (y * ((x * z) - (i * j))) + (a * ((b * i) - (x * t)));
	} else if (c <= 1.8e+161) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))
	t_2 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -7.2e+23:
		tmp = t_2
	elif c <= -6.5e-86:
		tmp = t_1
	elif c <= 4.1e-156:
		tmp = (y * ((x * z) - (i * j))) + (a * ((b * i) - (x * t)))
	elif c <= 1.8e+161:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(a * i) - Float64(z * c))))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -7.2e+23)
		tmp = t_2;
	elseif (c <= -6.5e-86)
		tmp = t_1;
	elseif (c <= 4.1e-156)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(a * Float64(Float64(b * i) - Float64(x * t))));
	elseif (c <= 1.8e+161)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	t_2 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -7.2e+23)
		tmp = t_2;
	elseif (c <= -6.5e-86)
		tmp = t_1;
	elseif (c <= 4.1e-156)
		tmp = (y * ((x * z) - (i * j))) + (a * ((b * i) - (x * t)));
	elseif (c <= 1.8e+161)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -7.2e+23], t$95$2, If[LessEqual[c, -6.5e-86], t$95$1, If[LessEqual[c, 4.1e-156], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.8e+161], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -7.1999999999999997e23 or 1.79999999999999992e161 < c

   1. Initial program 54.9%

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

   3. Taylor expanded in c around inf 70.6%

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

      1. *-commutative 70.6%

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

      2. *-commutative 70.6%

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

   5. Simplified 70.6%

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

   if -7.1999999999999997e23 < c < -6.50000000000000028e-86 or 4.1000000000000002e-156 < c < 1.79999999999999992e161

   1. Initial program 83.3%

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

   3. Taylor expanded in j around 0 63.8%

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

      1. *-commutative 63.8%

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

   5. Simplified 63.8%

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

   if -6.50000000000000028e-86 < c < 4.1000000000000002e-156

   1. Initial program 80.4%

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

   3. Taylor expanded in t around -inf 80.4%

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

   5. Simplified 84.6%

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

   6. Taylor expanded in c around 0 78.4%

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

      1. sub-neg 78.4%

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

      2. +-commutative 78.4%

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

      3. associate-+l+ 78.4%

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

      4. sub-neg 78.4%

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

      5. *-commutative 78.4%

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

      6. sub-neg 78.4%

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

      7. associate-*r* 78.4%

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

      8. *-commutative 78.4%

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

      9. associate-*r* 78.4%

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

      10. *-commutative 78.4%

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

      11. distribute-rgt-neg-in 78.4%

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

      12. distribute-lft-in 78.4%

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

      13. neg-mul-1 78.4%

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

      14. sub-neg 78.4%

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

   8. Simplified 78.4%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -7.2 \cdot 10^{+23}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -6.5 \cdot 10^{-86}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq 4.1 \cdot 10^{-156}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{+161}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_3 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -3.7 \cdot 10^{+68}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -1.95 \cdot 10^{-237}:\\ \;\;\;\;t_2 + t_1\\ \mathbf{elif}\;c \leq 2.1 \cdot 10^{-154}:\\ \;\;\;\;t_2 + a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 6.5 \cdot 10^{+160}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c))))
        (t_2 (* y (- (* x z) (* i j))))
        (t_3 (* c (- (* t j) (* z b)))))
   (if (<= c -3.7e+68)
     t_3
     (if (<= c -1.95e-237)
       (+ t_2 t_1)
       (if (<= c 2.1e-154)
         (+ t_2 (* a (- (* b i) (* x t))))
         (if (<= c 6.5e+160) (+ (* x (- (* y z) (* t a))) t_1) t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -3.7e+68) {
		tmp = t_3;
	} else if (c <= -1.95e-237) {
		tmp = t_2 + t_1;
	} else if (c <= 2.1e-154) {
		tmp = t_2 + (a * ((b * i) - (x * t)));
	} else if (c <= 6.5e+160) {
		tmp = (x * ((y * z) - (t * a))) + t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = y * ((x * z) - (i * j))
    t_3 = c * ((t * j) - (z * b))
    if (c <= (-3.7d+68)) then
        tmp = t_3
    else if (c <= (-1.95d-237)) then
        tmp = t_2 + t_1
    else if (c <= 2.1d-154) then
        tmp = t_2 + (a * ((b * i) - (x * t)))
    else if (c <= 6.5d+160) then
        tmp = (x * ((y * z) - (t * a))) + t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -3.7e+68) {
		tmp = t_3;
	} else if (c <= -1.95e-237) {
		tmp = t_2 + t_1;
	} else if (c <= 2.1e-154) {
		tmp = t_2 + (a * ((b * i) - (x * t)));
	} else if (c <= 6.5e+160) {
		tmp = (x * ((y * z) - (t * a))) + t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = y * ((x * z) - (i * j))
	t_3 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -3.7e+68:
		tmp = t_3
	elif c <= -1.95e-237:
		tmp = t_2 + t_1
	elif c <= 2.1e-154:
		tmp = t_2 + (a * ((b * i) - (x * t)))
	elif c <= 6.5e+160:
		tmp = (x * ((y * z) - (t * a))) + t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_3 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -3.7e+68)
		tmp = t_3;
	elseif (c <= -1.95e-237)
		tmp = Float64(t_2 + t_1);
	elseif (c <= 2.1e-154)
		tmp = Float64(t_2 + Float64(a * Float64(Float64(b * i) - Float64(x * t))));
	elseif (c <= 6.5e+160)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_1);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = y * ((x * z) - (i * j));
	t_3 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -3.7e+68)
		tmp = t_3;
	elseif (c <= -1.95e-237)
		tmp = t_2 + t_1;
	elseif (c <= 2.1e-154)
		tmp = t_2 + (a * ((b * i) - (x * t)));
	elseif (c <= 6.5e+160)
		tmp = (x * ((y * z) - (t * a))) + t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.7e+68], t$95$3, If[LessEqual[c, -1.95e-237], N[(t$95$2 + t$95$1), $MachinePrecision], If[LessEqual[c, 2.1e-154], N[(t$95$2 + N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.5e+160], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], t$95$3]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -3.69999999999999998e68 or 6.4999999999999995e160 < c

   1. Initial program 55.4%

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

   3. Taylor expanded in c around inf 73.0%

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

      1. *-commutative 73.0%

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

      2. *-commutative 73.0%

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

   5. Simplified 73.0%

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

   if -3.69999999999999998e68 < c < -1.9499999999999999e-237

   1. Initial program 76.6%

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

   3. Taylor expanded in t around 0 67.7%

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

      1. *-commutative 67.7%

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

      2. associate-*r* 72.1%

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

      3. associate-*r* 70.7%

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

      4. associate-*r* 70.7%

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

      5. distribute-rgt-in 72.2%

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

      6. +-commutative 72.2%

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

      7. mul-1-neg 72.2%

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

      8. unsub-neg 72.2%

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

      9. *-commutative 72.2%

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

      10. *-commutative 72.2%

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

   5. Simplified 72.2%

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

   if -1.9499999999999999e-237 < c < 2.09999999999999984e-154

   1. Initial program 84.3%

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

   3. Taylor expanded in t around -inf 79.6%

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

   5. Simplified 79.7%

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

   6. Taylor expanded in c around 0 79.9%

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

      1. sub-neg 79.9%

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

      2. +-commutative 79.9%

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

      3. associate-+l+ 79.9%

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

      4. sub-neg 79.9%

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

      5. *-commutative 79.9%

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

      6. sub-neg 79.9%

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

      7. associate-*r* 79.9%

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

      8. *-commutative 79.9%

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

      9. associate-*r* 79.9%

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

      10. *-commutative 79.9%

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

      11. distribute-rgt-neg-in 79.9%

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

      12. distribute-lft-in 79.9%

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

      13. neg-mul-1 79.9%

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

      14. sub-neg 79.9%

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

   8. Simplified 79.9%

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

   if 2.09999999999999984e-154 < c < 6.4999999999999995e160

   1. Initial program 80.8%

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

   3. Taylor expanded in j around 0 62.8%

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

      1. *-commutative 62.8%

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

   5. Simplified 62.8%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.7 \cdot 10^{+68}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -1.95 \cdot 10^{-237}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq 2.1 \cdot 10^{-154}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 6.5 \cdot 10^{+160}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 29.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b\right)\\ \mathbf{if}\;b \leq -6 \cdot 10^{+170}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2.85 \cdot 10^{+76}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{+51}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{-48}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq 170000:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{+246}:\\ \;\;\;\;z \cdot \left(-b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* a b))))
   (if (<= b -6e+170)
     t_1
     (if (<= b -2.85e+76)
       (* x (* y z))
       (if (<= b -1.75e+51)
         (* b (* a i))
         (if (<= b -6.2e-48)
           (* y (* x z))
           (if (<= b 170000.0)
             (* j (* t c))
             (if (<= b 1.2e+246) (* z (- (* b c))) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (a * b);
	double tmp;
	if (b <= -6e+170) {
		tmp = t_1;
	} else if (b <= -2.85e+76) {
		tmp = x * (y * z);
	} else if (b <= -1.75e+51) {
		tmp = b * (a * i);
	} else if (b <= -6.2e-48) {
		tmp = y * (x * z);
	} else if (b <= 170000.0) {
		tmp = j * (t * c);
	} else if (b <= 1.2e+246) {
		tmp = z * -(b * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * (a * b)
    if (b <= (-6d+170)) then
        tmp = t_1
    else if (b <= (-2.85d+76)) then
        tmp = x * (y * z)
    else if (b <= (-1.75d+51)) then
        tmp = b * (a * i)
    else if (b <= (-6.2d-48)) then
        tmp = y * (x * z)
    else if (b <= 170000.0d0) then
        tmp = j * (t * c)
    else if (b <= 1.2d+246) then
        tmp = z * -(b * c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (a * b);
	double tmp;
	if (b <= -6e+170) {
		tmp = t_1;
	} else if (b <= -2.85e+76) {
		tmp = x * (y * z);
	} else if (b <= -1.75e+51) {
		tmp = b * (a * i);
	} else if (b <= -6.2e-48) {
		tmp = y * (x * z);
	} else if (b <= 170000.0) {
		tmp = j * (t * c);
	} else if (b <= 1.2e+246) {
		tmp = z * -(b * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (a * b)
	tmp = 0
	if b <= -6e+170:
		tmp = t_1
	elif b <= -2.85e+76:
		tmp = x * (y * z)
	elif b <= -1.75e+51:
		tmp = b * (a * i)
	elif b <= -6.2e-48:
		tmp = y * (x * z)
	elif b <= 170000.0:
		tmp = j * (t * c)
	elif b <= 1.2e+246:
		tmp = z * -(b * c)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(a * b))
	tmp = 0.0
	if (b <= -6e+170)
		tmp = t_1;
	elseif (b <= -2.85e+76)
		tmp = Float64(x * Float64(y * z));
	elseif (b <= -1.75e+51)
		tmp = Float64(b * Float64(a * i));
	elseif (b <= -6.2e-48)
		tmp = Float64(y * Float64(x * z));
	elseif (b <= 170000.0)
		tmp = Float64(j * Float64(t * c));
	elseif (b <= 1.2e+246)
		tmp = Float64(z * Float64(-Float64(b * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * (a * b);
	tmp = 0.0;
	if (b <= -6e+170)
		tmp = t_1;
	elseif (b <= -2.85e+76)
		tmp = x * (y * z);
	elseif (b <= -1.75e+51)
		tmp = b * (a * i);
	elseif (b <= -6.2e-48)
		tmp = y * (x * z);
	elseif (b <= 170000.0)
		tmp = j * (t * c);
	elseif (b <= 1.2e+246)
		tmp = z * -(b * c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6e+170], t$95$1, If[LessEqual[b, -2.85e+76], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.75e+51], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -6.2e-48], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 170000.0], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.2e+246], N[(z * (-N[(b * c), $MachinePrecision])), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -5.99999999999999994e170 or 1.2e246 < b

   1. Initial program 73.9%

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

   3. Taylor expanded in b around inf 76.3%

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

      1. *-commutative 76.3%

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

   5. Simplified 76.3%

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

   6. Taylor expanded in a around inf 48.9%

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

      1. associate-*r* 63.0%

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

   8. Simplified 63.0%

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

   if -5.99999999999999994e170 < b < -2.85000000000000002e76

   1. Initial program 72.7%

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

   3. Taylor expanded in t around 0 63.7%

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

      1. *-commutative 63.7%

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

      2. associate-*r* 68.2%

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

      3. associate-*r* 63.9%

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

      4. associate-*r* 63.9%

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

      5. distribute-rgt-in 68.5%

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

      6. +-commutative 68.5%

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

      7. mul-1-neg 68.5%

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

      8. unsub-neg 68.5%

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

      9. *-commutative 68.5%

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

      10. *-commutative 68.5%

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

   5. Simplified 68.5%

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

   6. Taylor expanded in x around inf 51.1%

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

      1. *-commutative 51.1%

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

   8. Simplified 51.1%

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

   if -2.85000000000000002e76 < b < -1.75e51

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf 58.5%

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

      1. *-commutative 58.5%

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

   5. Simplified 58.5%

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

   6. Taylor expanded in a around inf 57.8%

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

   if -1.75e51 < b < -6.20000000000000033e-48

   1. Initial program 80.4%

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

   3. Taylor expanded in y around inf 51.9%

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

      1. +-commutative 51.9%

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

      2. mul-1-neg 51.9%

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

      3. unsub-neg 51.9%

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

      4. *-commutative 51.9%

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

   5. Simplified 51.9%

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

   6. Taylor expanded in x around inf 41.7%

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

      1. *-commutative 41.7%

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

   8. Simplified 41.7%

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

   if -6.20000000000000033e-48 < b < 1.7e5

   1. Initial program 72.9%

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

   3. Taylor expanded in j around inf 51.4%

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

      1. sub-neg 51.4%

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

      2. *-commutative 51.4%

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

      3. *-commutative 51.4%

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

      4. sub-neg 51.4%

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

   5. Simplified 51.4%

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

   6. Taylor expanded in t around inf 33.2%

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

      1. *-commutative 33.2%

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

   8. Simplified 33.2%

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

   if 1.7e5 < b < 1.2e246

   1. Initial program 69.3%

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

   3. Taylor expanded in z around inf 56.1%

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

      1. *-commutative 56.1%

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

   5. Simplified 56.1%

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

   6. Taylor expanded in x around 0 43.5%

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

      1. mul-1-neg 43.5%

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

      2. distribute-rgt-neg-in 43.5%

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

   8. Simplified 43.5%

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

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{+170}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq -2.85 \cdot 10^{+76}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{+51}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{-48}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq 170000:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{+246}:\\ \;\;\;\;z \cdot \left(-b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 29.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c\right)\\ \mathbf{if}\;i \leq -600000000:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;i \leq 5 \cdot 10^{-303}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 3 \cdot 10^{-155}:\\ \;\;\;\;z \cdot \left(-b \cdot c\right)\\ \mathbf{elif}\;i \leq 2.95 \cdot 10^{-95}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;i \leq 3.4 \cdot 10^{+73}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 1.32 \cdot 10^{+132}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (* t c))))
   (if (<= i -600000000.0)
     (* b (* a i))
     (if (<= i 5e-303)
       t_1
       (if (<= i 3e-155)
         (* z (- (* b c)))
         (if (<= i 2.95e-95)
           (* t (* x (- a)))
           (if (<= i 3.4e+73)
             (* x (* y z))
             (if (<= i 1.32e+132) t_1 (* a (* b i))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (t * c);
	double tmp;
	if (i <= -600000000.0) {
		tmp = b * (a * i);
	} else if (i <= 5e-303) {
		tmp = t_1;
	} else if (i <= 3e-155) {
		tmp = z * -(b * c);
	} else if (i <= 2.95e-95) {
		tmp = t * (x * -a);
	} else if (i <= 3.4e+73) {
		tmp = x * (y * z);
	} else if (i <= 1.32e+132) {
		tmp = t_1;
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (t * c)
    if (i <= (-600000000.0d0)) then
        tmp = b * (a * i)
    else if (i <= 5d-303) then
        tmp = t_1
    else if (i <= 3d-155) then
        tmp = z * -(b * c)
    else if (i <= 2.95d-95) then
        tmp = t * (x * -a)
    else if (i <= 3.4d+73) then
        tmp = x * (y * z)
    else if (i <= 1.32d+132) then
        tmp = t_1
    else
        tmp = a * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (t * c);
	double tmp;
	if (i <= -600000000.0) {
		tmp = b * (a * i);
	} else if (i <= 5e-303) {
		tmp = t_1;
	} else if (i <= 3e-155) {
		tmp = z * -(b * c);
	} else if (i <= 2.95e-95) {
		tmp = t * (x * -a);
	} else if (i <= 3.4e+73) {
		tmp = x * (y * z);
	} else if (i <= 1.32e+132) {
		tmp = t_1;
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * (t * c)
	tmp = 0
	if i <= -600000000.0:
		tmp = b * (a * i)
	elif i <= 5e-303:
		tmp = t_1
	elif i <= 3e-155:
		tmp = z * -(b * c)
	elif i <= 2.95e-95:
		tmp = t * (x * -a)
	elif i <= 3.4e+73:
		tmp = x * (y * z)
	elif i <= 1.32e+132:
		tmp = t_1
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(t * c))
	tmp = 0.0
	if (i <= -600000000.0)
		tmp = Float64(b * Float64(a * i));
	elseif (i <= 5e-303)
		tmp = t_1;
	elseif (i <= 3e-155)
		tmp = Float64(z * Float64(-Float64(b * c)));
	elseif (i <= 2.95e-95)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (i <= 3.4e+73)
		tmp = Float64(x * Float64(y * z));
	elseif (i <= 1.32e+132)
		tmp = t_1;
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * (t * c);
	tmp = 0.0;
	if (i <= -600000000.0)
		tmp = b * (a * i);
	elseif (i <= 5e-303)
		tmp = t_1;
	elseif (i <= 3e-155)
		tmp = z * -(b * c);
	elseif (i <= 2.95e-95)
		tmp = t * (x * -a);
	elseif (i <= 3.4e+73)
		tmp = x * (y * z);
	elseif (i <= 1.32e+132)
		tmp = t_1;
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -600000000.0], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5e-303], t$95$1, If[LessEqual[i, 3e-155], N[(z * (-N[(b * c), $MachinePrecision])), $MachinePrecision], If[LessEqual[i, 2.95e-95], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.4e+73], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.32e+132], t$95$1, N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -6e8

   1. Initial program 71.0%

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

   3. Taylor expanded in b around inf 45.4%

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

      1. *-commutative 45.4%

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

   5. Simplified 45.4%

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

   6. Taylor expanded in a around inf 37.6%

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

   if -6e8 < i < 4.9999999999999998e-303 or 3.4000000000000002e73 < i < 1.3199999999999999e132

   1. Initial program 77.9%

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

   3. Taylor expanded in j around inf 47.5%

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

      1. sub-neg 47.5%

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

      2. *-commutative 47.5%

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

      3. *-commutative 47.5%

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

      4. sub-neg 47.5%

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

   5. Simplified 47.5%

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

   6. Taylor expanded in t around inf 42.1%

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

      1. *-commutative 42.1%

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

   8. Simplified 42.1%

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

   if 4.9999999999999998e-303 < i < 2.99999999999999984e-155

   1. Initial program 77.1%

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

   3. Taylor expanded in z around inf 66.9%

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

      1. *-commutative 66.9%

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

   5. Simplified 66.9%

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

   6. Taylor expanded in x around 0 55.2%

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

      1. mul-1-neg 55.2%

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

      2. distribute-rgt-neg-in 55.2%

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

   8. Simplified 55.2%

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

   if 2.99999999999999984e-155 < i < 2.9499999999999999e-95

   1. Initial program 91.8%

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

   3. Taylor expanded in a around inf 43.9%

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

      1. distribute-lft-out-- 43.9%

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

      2. *-commutative 43.9%

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

      3. *-commutative 43.9%

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

   5. Simplified 43.9%

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

   6. Taylor expanded in x around inf 35.5%

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

   7. Taylor expanded in a around 0 35.5%

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

      1. mul-1-neg 35.5%

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

      2. *-commutative 35.5%

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

      3. associate-*r* 51.3%

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

      4. distribute-rgt-neg-in 51.3%

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

   9. Simplified 51.3%

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

   if 2.9499999999999999e-95 < i < 3.4000000000000002e73

   1. Initial program 77.8%

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

   3. Taylor expanded in t around 0 67.1%

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

      1. *-commutative 67.1%

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

      2. associate-*r* 67.3%

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

      3. associate-*r* 70.0%

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

      4. associate-*r* 70.0%

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

      5. distribute-rgt-in 70.0%

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

      6. +-commutative 70.0%

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

      7. mul-1-neg 70.0%

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

      8. unsub-neg 70.0%

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

      9. *-commutative 70.0%

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

      10. *-commutative 70.0%

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

   5. Simplified 70.0%

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

   6. Taylor expanded in x around inf 38.0%

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

      1. *-commutative 38.0%

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

   8. Simplified 38.0%

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

   if 1.3199999999999999e132 < i

   1. Initial program 60.5%

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

   3. Taylor expanded in b around inf 47.9%

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

      1. *-commutative 47.9%

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

   5. Simplified 47.9%

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

   6. Taylor expanded in a around inf 56.3%

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

4. Final simplification 44.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -600000000:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;i \leq 5 \cdot 10^{-303}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;i \leq 3 \cdot 10^{-155}:\\ \;\;\;\;z \cdot \left(-b \cdot c\right)\\ \mathbf{elif}\;i \leq 2.95 \cdot 10^{-95}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;i \leq 3.4 \cdot 10^{+73}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 1.32 \cdot 10^{+132}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 29.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c\right)\\ \mathbf{if}\;t \leq -1.25 \cdot 10^{+101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-185}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+106}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+153} \lor \neg \left(t \leq 6.5 \cdot 10^{+171}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (* t c))))
   (if (<= t -1.25e+101)
     t_1
     (if (<= t -1.5e-185)
       (* y (* x z))
       (if (<= t 2.6e+106)
         (* i (* a b))
         (if (or (<= t 4.6e+153) (not (<= t 6.5e+171)))
           t_1
           (* a (* t (- x)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (t * c);
	double tmp;
	if (t <= -1.25e+101) {
		tmp = t_1;
	} else if (t <= -1.5e-185) {
		tmp = y * (x * z);
	} else if (t <= 2.6e+106) {
		tmp = i * (a * b);
	} else if ((t <= 4.6e+153) || !(t <= 6.5e+171)) {
		tmp = t_1;
	} else {
		tmp = a * (t * -x);
	}
	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 * (t * c)
    if (t <= (-1.25d+101)) then
        tmp = t_1
    else if (t <= (-1.5d-185)) then
        tmp = y * (x * z)
    else if (t <= 2.6d+106) then
        tmp = i * (a * b)
    else if ((t <= 4.6d+153) .or. (.not. (t <= 6.5d+171))) then
        tmp = t_1
    else
        tmp = a * (t * -x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (t * c);
	double tmp;
	if (t <= -1.25e+101) {
		tmp = t_1;
	} else if (t <= -1.5e-185) {
		tmp = y * (x * z);
	} else if (t <= 2.6e+106) {
		tmp = i * (a * b);
	} else if ((t <= 4.6e+153) || !(t <= 6.5e+171)) {
		tmp = t_1;
	} else {
		tmp = a * (t * -x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * (t * c)
	tmp = 0
	if t <= -1.25e+101:
		tmp = t_1
	elif t <= -1.5e-185:
		tmp = y * (x * z)
	elif t <= 2.6e+106:
		tmp = i * (a * b)
	elif (t <= 4.6e+153) or not (t <= 6.5e+171):
		tmp = t_1
	else:
		tmp = a * (t * -x)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(t * c))
	tmp = 0.0
	if (t <= -1.25e+101)
		tmp = t_1;
	elseif (t <= -1.5e-185)
		tmp = Float64(y * Float64(x * z));
	elseif (t <= 2.6e+106)
		tmp = Float64(i * Float64(a * b));
	elseif ((t <= 4.6e+153) || !(t <= 6.5e+171))
		tmp = t_1;
	else
		tmp = Float64(a * Float64(t * Float64(-x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * (t * c);
	tmp = 0.0;
	if (t <= -1.25e+101)
		tmp = t_1;
	elseif (t <= -1.5e-185)
		tmp = y * (x * z);
	elseif (t <= 2.6e+106)
		tmp = i * (a * b);
	elseif ((t <= 4.6e+153) || ~((t <= 6.5e+171)))
		tmp = t_1;
	else
		tmp = a * (t * -x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.25e+101], t$95$1, If[LessEqual[t, -1.5e-185], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.6e+106], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 4.6e+153], N[Not[LessEqual[t, 6.5e+171]], $MachinePrecision]], t$95$1, N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.24999999999999997e101 or 2.6000000000000002e106 < t < 4.6000000000000003e153 or 6.5e171 < t

   1. Initial program 60.1%

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

   3. Taylor expanded in j around inf 59.5%

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

      1. sub-neg 59.5%

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

      2. *-commutative 59.5%

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

      3. *-commutative 59.5%

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

      4. sub-neg 59.5%

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

   5. Simplified 59.5%

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

   6. Taylor expanded in t around inf 54.6%

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

      1. *-commutative 54.6%

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

   8. Simplified 54.6%

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

   if -1.24999999999999997e101 < t < -1.50000000000000015e-185

   1. Initial program 88.8%

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

   3. Taylor expanded in y around inf 43.6%

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

      1. +-commutative 43.6%

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

      2. mul-1-neg 43.6%

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

      3. unsub-neg 43.6%

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

      4. *-commutative 43.6%

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

   5. Simplified 43.6%

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

   6. Taylor expanded in x around inf 34.0%

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

      1. *-commutative 34.0%

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

   8. Simplified 34.0%

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

   if -1.50000000000000015e-185 < t < 2.6000000000000002e106

   1. Initial program 73.2%

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

   3. Taylor expanded in b around inf 53.7%

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

      1. *-commutative 53.7%

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

   5. Simplified 53.7%

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

   6. Taylor expanded in a around inf 34.2%

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

      1. associate-*r* 39.8%

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

   8. Simplified 39.8%

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

   if 4.6000000000000003e153 < t < 6.5e171

   1. Initial program 85.7%

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

   3. Taylor expanded in a around inf 85.7%

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

      1. distribute-lft-out-- 85.7%

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

      2. *-commutative 85.7%

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

      3. *-commutative 85.7%

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

   5. Simplified 85.7%

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

   6. Taylor expanded in x around inf 86.3%

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

   7. Taylor expanded in a around 0 86.3%

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

      1. mul-1-neg 86.3%

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

      2. *-commutative 86.3%

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

      3. distribute-rgt-neg-in 86.3%

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

   9. Simplified 86.3%

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

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+101}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-185}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+106}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+153} \lor \neg \left(t \leq 6.5 \cdot 10^{+171}\right):\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 50.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+83} \lor \neg \left(t \leq -4.1 \cdot 10^{-41} \lor \neg \left(t \leq -7 \cdot 10^{-116}\right) \land t \leq 3.3 \cdot 10^{+106}\right):\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -4.6e+83)
         (not (or (<= t -4.1e-41) (and (not (<= t -7e-116)) (<= t 3.3e+106)))))
   (* t (- (* c j) (* x a)))
   (* b (- (* a 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 ((t <= -4.6e+83) || !((t <= -4.1e-41) || (!(t <= -7e-116) && (t <= 3.3e+106)))) {
		tmp = t * ((c * j) - (x * a));
	} else {
		tmp = b * ((a * 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 ((t <= (-4.6d+83)) .or. (.not. (t <= (-4.1d-41)) .or. (.not. (t <= (-7d-116))) .and. (t <= 3.3d+106))) then
        tmp = t * ((c * j) - (x * a))
    else
        tmp = b * ((a * 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 ((t <= -4.6e+83) || !((t <= -4.1e-41) || (!(t <= -7e-116) && (t <= 3.3e+106)))) {
		tmp = t * ((c * j) - (x * a));
	} else {
		tmp = b * ((a * i) - (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -4.6e+83) or not ((t <= -4.1e-41) or (not (t <= -7e-116) and (t <= 3.3e+106))):
		tmp = t * ((c * j) - (x * a))
	else:
		tmp = b * ((a * i) - (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -4.6e+83) || !((t <= -4.1e-41) || (!(t <= -7e-116) && (t <= 3.3e+106))))
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	else
		tmp = Float64(b * Float64(Float64(a * 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 ((t <= -4.6e+83) || ~(((t <= -4.1e-41) || (~((t <= -7e-116)) && (t <= 3.3e+106)))))
		tmp = t * ((c * j) - (x * a));
	else
		tmp = b * ((a * i) - (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -4.6e+83], N[Not[Or[LessEqual[t, -4.1e-41], And[N[Not[LessEqual[t, -7e-116]], $MachinePrecision], LessEqual[t, 3.3e+106]]]], $MachinePrecision]], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.5999999999999999e83 or -4.10000000000000014e-41 < t < -6.99999999999999968e-116 or 3.30000000000000008e106 < t

   1. Initial program 69.7%

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

   3. Taylor expanded in t around -inf 74.0%

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

   5. Simplified 72.3%

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

   6. Taylor expanded in t around inf 64.6%

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

   if -4.5999999999999999e83 < t < -4.10000000000000014e-41 or -6.99999999999999968e-116 < t < 3.30000000000000008e106

   1. Initial program 77.0%

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

   3. Taylor expanded in b around inf 52.4%

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

      1. *-commutative 52.4%

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

   5. Simplified 52.4%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+83} \lor \neg \left(t \leq -4.1 \cdot 10^{-41} \lor \neg \left(t \leq -7 \cdot 10^{-116}\right) \land t \leq 3.3 \cdot 10^{+106}\right):\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 50.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.62 \cdot 10^{-12}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-218}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-259}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;b \leq 230000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))) (t_2 (* b (- (* a i) (* z c)))))
   (if (<= b -1.62e-12)
     t_2
     (if (<= b -2e-218)
       t_1
       (if (<= b -8e-259) (* a (* t (- x))) (if (<= b 230000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.62e-12) {
		tmp = t_2;
	} else if (b <= -2e-218) {
		tmp = t_1;
	} else if (b <= -8e-259) {
		tmp = a * (t * -x);
	} else if (b <= 230000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = b * ((a * i) - (z * c))
    if (b <= (-1.62d-12)) then
        tmp = t_2
    else if (b <= (-2d-218)) then
        tmp = t_1
    else if (b <= (-8d-259)) then
        tmp = a * (t * -x)
    else if (b <= 230000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.62e-12) {
		tmp = t_2;
	} else if (b <= -2e-218) {
		tmp = t_1;
	} else if (b <= -8e-259) {
		tmp = a * (t * -x);
	} else if (b <= 230000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -1.62e-12:
		tmp = t_2
	elif b <= -2e-218:
		tmp = t_1
	elif b <= -8e-259:
		tmp = a * (t * -x)
	elif b <= 230000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -1.62e-12)
		tmp = t_2;
	elseif (b <= -2e-218)
		tmp = t_1;
	elseif (b <= -8e-259)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (b <= 230000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -1.62e-12)
		tmp = t_2;
	elseif (b <= -2e-218)
		tmp = t_1;
	elseif (b <= -8e-259)
		tmp = a * (t * -x);
	elseif (b <= 230000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.62e-12], t$95$2, If[LessEqual[b, -2e-218], t$95$1, If[LessEqual[b, -8e-259], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 230000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.62e-12 or 2.3e5 < b

   1. Initial program 75.4%

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

   3. Taylor expanded in b around inf 60.0%

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

      1. *-commutative 60.0%

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

   5. Simplified 60.0%

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

   if -1.62e-12 < b < -2.0000000000000001e-218 or -8.0000000000000006e-259 < b < 2.3e5

   1. Initial program 71.3%

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

   3. Taylor expanded in j around inf 55.2%

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

      1. sub-neg 55.2%

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

      2. *-commutative 55.2%

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

      3. *-commutative 55.2%

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

      4. sub-neg 55.2%

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

   5. Simplified 55.2%

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

   if -2.0000000000000001e-218 < b < -8.0000000000000006e-259

   1. Initial program 73.5%

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

   3. Taylor expanded in a around inf 49.6%

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

      1. distribute-lft-out-- 49.6%

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

      2. *-commutative 49.6%

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

      3. *-commutative 49.6%

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

   5. Simplified 49.6%

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

   6. Taylor expanded in x around inf 49.7%

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

   7. Taylor expanded in a around 0 49.7%

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

      1. mul-1-neg 49.7%

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

      2. *-commutative 49.7%

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

      3. distribute-rgt-neg-in 49.7%

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

   9. Simplified 49.7%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.62 \cdot 10^{-12}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-218}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-259}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;b \leq 230000:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 51.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -8.5 \cdot 10^{+80}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-116}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+104}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))) (t_2 (* t (- (* c j) (* x a)))))
   (if (<= t -8.5e+80)
     t_2
     (if (<= t -1.8e-25)
       t_1
       (if (<= t -2.4e-116)
         (* x (- (* y z) (* t a)))
         (if (<= t 4.5e+104) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -8.5e+80) {
		tmp = t_2;
	} else if (t <= -1.8e-25) {
		tmp = t_1;
	} else if (t <= -2.4e-116) {
		tmp = x * ((y * z) - (t * a));
	} else if (t <= 4.5e+104) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = t * ((c * j) - (x * a))
    if (t <= (-8.5d+80)) then
        tmp = t_2
    else if (t <= (-1.8d-25)) then
        tmp = t_1
    else if (t <= (-2.4d-116)) then
        tmp = x * ((y * z) - (t * a))
    else if (t <= 4.5d+104) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -8.5e+80) {
		tmp = t_2;
	} else if (t <= -1.8e-25) {
		tmp = t_1;
	} else if (t <= -2.4e-116) {
		tmp = x * ((y * z) - (t * a));
	} else if (t <= 4.5e+104) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -8.5e+80:
		tmp = t_2
	elif t <= -1.8e-25:
		tmp = t_1
	elif t <= -2.4e-116:
		tmp = x * ((y * z) - (t * a))
	elif t <= 4.5e+104:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -8.5e+80)
		tmp = t_2;
	elseif (t <= -1.8e-25)
		tmp = t_1;
	elseif (t <= -2.4e-116)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (t <= 4.5e+104)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -8.5e+80)
		tmp = t_2;
	elseif (t <= -1.8e-25)
		tmp = t_1;
	elseif (t <= -2.4e-116)
		tmp = x * ((y * z) - (t * a));
	elseif (t <= 4.5e+104)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.5e+80], t$95$2, If[LessEqual[t, -1.8e-25], t$95$1, If[LessEqual[t, -2.4e-116], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e+104], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.50000000000000007e80 or 4.4999999999999998e104 < t

   1. Initial program 64.0%

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

   3. Taylor expanded in t around -inf 71.5%

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

   5. Simplified 71.4%

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

   6. Taylor expanded in t around inf 66.1%

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

   if -8.50000000000000007e80 < t < -1.8e-25 or -2.39999999999999993e-116 < t < 4.4999999999999998e104

   1. Initial program 76.1%

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

   3. Taylor expanded in b around inf 52.7%

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

      1. *-commutative 52.7%

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

   5. Simplified 52.7%

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

   if -1.8e-25 < t < -2.39999999999999993e-116

   1. Initial program 96.0%

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

   3. Taylor expanded in t around -inf 88.3%

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

   5. Simplified 80.8%

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

   6. Taylor expanded in x around inf 55.4%

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

      1. +-commutative 55.4%

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

      2. mul-1-neg 55.4%

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

      3. unsub-neg 55.4%

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

      4. *-commutative 55.4%

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

      5. *-commutative 55.4%

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

   8. Simplified 55.4%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+80}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-25}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-116}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+104}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 52.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -2.6 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-246}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-149}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+106}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a)))))
   (if (<= t -2.6e+67)
     t_1
     (if (<= t 2.8e-246)
       (* z (- (* x y) (* b c)))
       (if (<= t 4.5e-149)
         (* y (- (* x z) (* i j)))
         (if (<= t 6e+106) (* b (- (* a i) (* z c))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -2.6e+67) {
		tmp = t_1;
	} else if (t <= 2.8e-246) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 4.5e-149) {
		tmp = y * ((x * z) - (i * j));
	} else if (t <= 6e+106) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((c * j) - (x * a))
    if (t <= (-2.6d+67)) then
        tmp = t_1
    else if (t <= 2.8d-246) then
        tmp = z * ((x * y) - (b * c))
    else if (t <= 4.5d-149) then
        tmp = y * ((x * z) - (i * j))
    else if (t <= 6d+106) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -2.6e+67) {
		tmp = t_1;
	} else if (t <= 2.8e-246) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 4.5e-149) {
		tmp = y * ((x * z) - (i * j));
	} else if (t <= 6e+106) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -2.6e+67:
		tmp = t_1
	elif t <= 2.8e-246:
		tmp = z * ((x * y) - (b * c))
	elif t <= 4.5e-149:
		tmp = y * ((x * z) - (i * j))
	elif t <= 6e+106:
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -2.6e+67)
		tmp = t_1;
	elseif (t <= 2.8e-246)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (t <= 4.5e-149)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (t <= 6e+106)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -2.6e+67)
		tmp = t_1;
	elseif (t <= 2.8e-246)
		tmp = z * ((x * y) - (b * c));
	elseif (t <= 4.5e-149)
		tmp = y * ((x * z) - (i * j));
	elseif (t <= 6e+106)
		tmp = b * ((a * i) - (z * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.6e+67], t$95$1, If[LessEqual[t, 2.8e-246], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e-149], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e+106], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.6e67 or 6.0000000000000001e106 < t

   1. Initial program 64.8%

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

   3. Taylor expanded in t around -inf 72.1%

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

   5. Simplified 72.0%

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

   6. Taylor expanded in t around inf 66.8%

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

   if -2.6e67 < t < 2.7999999999999999e-246

   1. Initial program 78.6%

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

   3. Taylor expanded in z around inf 52.5%

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

      1. *-commutative 52.5%

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

   5. Simplified 52.5%

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

   if 2.7999999999999999e-246 < t < 4.4999999999999998e-149

   1. Initial program 82.0%

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

   3. Taylor expanded in y around inf 64.7%

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

      1. +-commutative 64.7%

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

      2. mul-1-neg 64.7%

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

      3. unsub-neg 64.7%

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

      4. *-commutative 64.7%

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

   5. Simplified 64.7%

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

   if 4.4999999999999998e-149 < t < 6.0000000000000001e106

   1. Initial program 78.7%

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

   3. Taylor expanded in b around inf 59.7%

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

      1. *-commutative 59.7%

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

   5. Simplified 59.7%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+67}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-246}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-149}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+106}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 52.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -4.5 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-285}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-44}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+107}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a)))))
   (if (<= t -4.5e+68)
     t_1
     (if (<= t 6e-285)
       (* z (- (* x y) (* b c)))
       (if (<= t 2.6e-44)
         (* i (- (* a b) (* y j)))
         (if (<= t 3.2e+107) (* b (- (* a i) (* z c))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -4.5e+68) {
		tmp = t_1;
	} else if (t <= 6e-285) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 2.6e-44) {
		tmp = i * ((a * b) - (y * j));
	} else if (t <= 3.2e+107) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((c * j) - (x * a))
    if (t <= (-4.5d+68)) then
        tmp = t_1
    else if (t <= 6d-285) then
        tmp = z * ((x * y) - (b * c))
    else if (t <= 2.6d-44) then
        tmp = i * ((a * b) - (y * j))
    else if (t <= 3.2d+107) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -4.5e+68) {
		tmp = t_1;
	} else if (t <= 6e-285) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 2.6e-44) {
		tmp = i * ((a * b) - (y * j));
	} else if (t <= 3.2e+107) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -4.5e+68:
		tmp = t_1
	elif t <= 6e-285:
		tmp = z * ((x * y) - (b * c))
	elif t <= 2.6e-44:
		tmp = i * ((a * b) - (y * j))
	elif t <= 3.2e+107:
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -4.5e+68)
		tmp = t_1;
	elseif (t <= 6e-285)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (t <= 2.6e-44)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (t <= 3.2e+107)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -4.5e+68)
		tmp = t_1;
	elseif (t <= 6e-285)
		tmp = z * ((x * y) - (b * c));
	elseif (t <= 2.6e-44)
		tmp = i * ((a * b) - (y * j));
	elseif (t <= 3.2e+107)
		tmp = b * ((a * i) - (z * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.5e+68], t$95$1, If[LessEqual[t, 6e-285], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.6e-44], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.2e+107], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.5000000000000003e68 or 3.20000000000000029e107 < t

   1. Initial program 64.8%

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

   3. Taylor expanded in t around -inf 72.1%

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

   5. Simplified 72.0%

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

   6. Taylor expanded in t around inf 66.8%

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

   if -4.5000000000000003e68 < t < 6.00000000000000007e-285

   1. Initial program 79.6%

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

   3. Taylor expanded in z around inf 53.1%

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

      1. *-commutative 53.1%

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

   5. Simplified 53.1%

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

   if 6.00000000000000007e-285 < t < 2.5999999999999998e-44

   1. Initial program 79.9%

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

   3. Taylor expanded in i around inf 63.5%

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

      1. distribute-lft-out-- 63.5%

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

      2. *-commutative 63.5%

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

   5. Simplified 63.5%

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

   if 2.5999999999999998e-44 < t < 3.20000000000000029e107

   1. Initial program 76.3%

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

   3. Taylor expanded in b around inf 66.3%

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

      1. *-commutative 66.3%

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

   5. Simplified 66.3%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+68}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-285}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-44}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+107}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 41.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+177}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-229}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{+81}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+113}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -3.4e+177)
   (* x (* y z))
   (if (<= y 1.3e-229)
     (* b (- (* a i) (* z c)))
     (if (<= y 3.05e+81)
       (* c (- (* t j) (* z b)))
       (if (<= y 3.4e+113) (* z (* x y)) (* j (* y (- i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -3.4e+177) {
		tmp = x * (y * z);
	} else if (y <= 1.3e-229) {
		tmp = b * ((a * i) - (z * c));
	} else if (y <= 3.05e+81) {
		tmp = c * ((t * j) - (z * b));
	} else if (y <= 3.4e+113) {
		tmp = z * (x * y);
	} else {
		tmp = j * (y * -i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-3.4d+177)) then
        tmp = x * (y * z)
    else if (y <= 1.3d-229) then
        tmp = b * ((a * i) - (z * c))
    else if (y <= 3.05d+81) then
        tmp = c * ((t * j) - (z * b))
    else if (y <= 3.4d+113) then
        tmp = z * (x * y)
    else
        tmp = j * (y * -i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -3.4e+177) {
		tmp = x * (y * z);
	} else if (y <= 1.3e-229) {
		tmp = b * ((a * i) - (z * c));
	} else if (y <= 3.05e+81) {
		tmp = c * ((t * j) - (z * b));
	} else if (y <= 3.4e+113) {
		tmp = z * (x * y);
	} else {
		tmp = j * (y * -i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -3.4e+177:
		tmp = x * (y * z)
	elif y <= 1.3e-229:
		tmp = b * ((a * i) - (z * c))
	elif y <= 3.05e+81:
		tmp = c * ((t * j) - (z * b))
	elif y <= 3.4e+113:
		tmp = z * (x * y)
	else:
		tmp = j * (y * -i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -3.4e+177)
		tmp = Float64(x * Float64(y * z));
	elseif (y <= 1.3e-229)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (y <= 3.05e+81)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (y <= 3.4e+113)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = Float64(j * Float64(y * Float64(-i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -3.4e+177)
		tmp = x * (y * z);
	elseif (y <= 1.3e-229)
		tmp = b * ((a * i) - (z * c));
	elseif (y <= 3.05e+81)
		tmp = c * ((t * j) - (z * b));
	elseif (y <= 3.4e+113)
		tmp = z * (x * y);
	else
		tmp = j * (y * -i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -3.4e+177], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e-229], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.05e+81], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e+113], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(j * N[(y * (-i)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.3999999999999998e177

   1. Initial program 55.0%

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

   3. Taylor expanded in t around 0 66.8%

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

      1. *-commutative 66.8%

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

      2. associate-*r* 66.8%

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

      3. associate-*r* 69.8%

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

      4. associate-*r* 69.8%

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

      5. distribute-rgt-in 69.8%

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

      6. +-commutative 69.8%

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

      7. mul-1-neg 69.8%

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

      8. unsub-neg 69.8%

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

      9. *-commutative 69.8%

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

      10. *-commutative 69.8%

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

   5. Simplified 69.8%

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

   6. Taylor expanded in x around inf 67.4%

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

      1. *-commutative 67.4%

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

   8. Simplified 67.4%

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

   if -3.3999999999999998e177 < y < 1.3000000000000001e-229

   1. Initial program 74.1%

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

   3. Taylor expanded in b around inf 50.7%

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

      1. *-commutative 50.7%

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

   5. Simplified 50.7%

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

   if 1.3000000000000001e-229 < y < 3.05000000000000019e81

   1. Initial program 78.8%

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

   3. Taylor expanded in c around inf 56.5%

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

      1. *-commutative 56.5%

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

      2. *-commutative 56.5%

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

   5. Simplified 56.5%

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

   if 3.05000000000000019e81 < y < 3.40000000000000019e113

   1. Initial program 84.3%

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

   3. Taylor expanded in z around inf 63.4%

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

      1. *-commutative 63.4%

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

   5. Simplified 63.4%

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

   6. Taylor expanded in x around inf 60.8%

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

   if 3.40000000000000019e113 < y

   1. Initial program 78.7%

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

   3. Taylor expanded in j around inf 61.4%

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

      1. sub-neg 61.4%

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

      2. *-commutative 61.4%

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

      3. *-commutative 61.4%

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

      4. sub-neg 61.4%

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

   5. Simplified 61.4%

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

   6. Taylor expanded in t around 0 47.4%

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

      1. mul-1-neg 47.4%

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

      2. distribute-rgt-neg-in 47.4%

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

   8. Simplified 47.4%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+177}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-229}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{+81}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+113}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 29.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i\right)\\ t_2 := j \cdot \left(t \cdot c\right)\\ \mathbf{if}\;t \leq -4.6 \cdot 10^{+89}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-220}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+106}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* b i))) (t_2 (* j (* t c))))
   (if (<= t -4.6e+89)
     t_2
     (if (<= t -5.5e-40)
       t_1
       (if (<= t 2.7e-220) (* x (* y z)) (if (<= t 1.2e+106) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (b * i);
	double t_2 = j * (t * c);
	double tmp;
	if (t <= -4.6e+89) {
		tmp = t_2;
	} else if (t <= -5.5e-40) {
		tmp = t_1;
	} else if (t <= 2.7e-220) {
		tmp = x * (y * z);
	} else if (t <= 1.2e+106) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (b * i)
    t_2 = j * (t * c)
    if (t <= (-4.6d+89)) then
        tmp = t_2
    else if (t <= (-5.5d-40)) then
        tmp = t_1
    else if (t <= 2.7d-220) then
        tmp = x * (y * z)
    else if (t <= 1.2d+106) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (b * i);
	double t_2 = j * (t * c);
	double tmp;
	if (t <= -4.6e+89) {
		tmp = t_2;
	} else if (t <= -5.5e-40) {
		tmp = t_1;
	} else if (t <= 2.7e-220) {
		tmp = x * (y * z);
	} else if (t <= 1.2e+106) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (b * i)
	t_2 = j * (t * c)
	tmp = 0
	if t <= -4.6e+89:
		tmp = t_2
	elif t <= -5.5e-40:
		tmp = t_1
	elif t <= 2.7e-220:
		tmp = x * (y * z)
	elif t <= 1.2e+106:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(b * i))
	t_2 = Float64(j * Float64(t * c))
	tmp = 0.0
	if (t <= -4.6e+89)
		tmp = t_2;
	elseif (t <= -5.5e-40)
		tmp = t_1;
	elseif (t <= 2.7e-220)
		tmp = Float64(x * Float64(y * z));
	elseif (t <= 1.2e+106)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (b * i);
	t_2 = j * (t * c);
	tmp = 0.0;
	if (t <= -4.6e+89)
		tmp = t_2;
	elseif (t <= -5.5e-40)
		tmp = t_1;
	elseif (t <= 2.7e-220)
		tmp = x * (y * z);
	elseif (t <= 1.2e+106)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.6e+89], t$95$2, If[LessEqual[t, -5.5e-40], t$95$1, If[LessEqual[t, 2.7e-220], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e+106], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.5999999999999998e89 or 1.2e106 < t

   1. Initial program 63.8%

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

   3. Taylor expanded in j around inf 54.8%

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

      1. sub-neg 54.8%

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

      2. *-commutative 54.8%

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

      3. *-commutative 54.8%

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

      4. sub-neg 54.8%

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

   5. Simplified 54.8%

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

   6. Taylor expanded in t around inf 50.4%

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

      1. *-commutative 50.4%

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

   8. Simplified 50.4%

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

   if -4.5999999999999998e89 < t < -5.50000000000000002e-40 or 2.7e-220 < t < 1.2e106

   1. Initial program 80.3%

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

   3. Taylor expanded in b around inf 52.2%

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

      1. *-commutative 52.2%

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

   5. Simplified 52.2%

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

   6. Taylor expanded in a around inf 38.7%

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

   if -5.50000000000000002e-40 < t < 2.7e-220

   1. Initial program 77.8%

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

   3. Taylor expanded in t around 0 63.5%

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

      1. *-commutative 63.5%

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

      2. associate-*r* 62.4%

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

      3. associate-*r* 63.6%

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

      4. associate-*r* 63.6%

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

      5. distribute-rgt-in 65.0%

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

      6. +-commutative 65.0%

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

      7. mul-1-neg 65.0%

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

      8. unsub-neg 65.0%

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

      9. *-commutative 65.0%

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

      10. *-commutative 65.0%

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

   5. Simplified 65.0%

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

   6. Taylor expanded in x around inf 33.9%

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

      1. *-commutative 33.9%

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

   8. Simplified 33.9%

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

4. Final simplification 41.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+89}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-40}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-220}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+106}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 39.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+179}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-55}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+81}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -5.4e+179)
   (* x (* y z))
   (if (<= y 1.85e-55)
     (* b (- (* a i) (* z c)))
     (if (<= y 9.2e+81) (* j (* t c)) (* j (* y (- i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -5.4e+179) {
		tmp = x * (y * z);
	} else if (y <= 1.85e-55) {
		tmp = b * ((a * i) - (z * c));
	} else if (y <= 9.2e+81) {
		tmp = j * (t * c);
	} else {
		tmp = j * (y * -i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-5.4d+179)) then
        tmp = x * (y * z)
    else if (y <= 1.85d-55) then
        tmp = b * ((a * i) - (z * c))
    else if (y <= 9.2d+81) then
        tmp = j * (t * c)
    else
        tmp = j * (y * -i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -5.4e+179) {
		tmp = x * (y * z);
	} else if (y <= 1.85e-55) {
		tmp = b * ((a * i) - (z * c));
	} else if (y <= 9.2e+81) {
		tmp = j * (t * c);
	} else {
		tmp = j * (y * -i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -5.4e+179:
		tmp = x * (y * z)
	elif y <= 1.85e-55:
		tmp = b * ((a * i) - (z * c))
	elif y <= 9.2e+81:
		tmp = j * (t * c)
	else:
		tmp = j * (y * -i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -5.4e+179)
		tmp = Float64(x * Float64(y * z));
	elseif (y <= 1.85e-55)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (y <= 9.2e+81)
		tmp = Float64(j * Float64(t * c));
	else
		tmp = Float64(j * Float64(y * Float64(-i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -5.4e+179)
		tmp = x * (y * z);
	elseif (y <= 1.85e-55)
		tmp = b * ((a * i) - (z * c));
	elseif (y <= 9.2e+81)
		tmp = j * (t * c);
	else
		tmp = j * (y * -i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -5.4e+179], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.85e-55], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.2e+81], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], N[(j * N[(y * (-i)), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.39999999999999964e179

   1. Initial program 55.0%

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

   3. Taylor expanded in t around 0 66.8%

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

      1. *-commutative 66.8%

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

      2. associate-*r* 66.8%

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

      3. associate-*r* 69.8%

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

      4. associate-*r* 69.8%

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

      5. distribute-rgt-in 69.8%

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

      6. +-commutative 69.8%

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

      7. mul-1-neg 69.8%

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

      8. unsub-neg 69.8%

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

      9. *-commutative 69.8%

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

      10. *-commutative 69.8%

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

   5. Simplified 69.8%

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

   6. Taylor expanded in x around inf 67.4%

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

      1. *-commutative 67.4%

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

   8. Simplified 67.4%

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

   if -5.39999999999999964e179 < y < 1.84999999999999993e-55

   1. Initial program 75.5%

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

   3. Taylor expanded in b around inf 49.0%

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

      1. *-commutative 49.0%

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

   5. Simplified 49.0%

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

   if 1.84999999999999993e-55 < y < 9.1999999999999995e81

   1. Initial program 76.3%

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

   3. Taylor expanded in j around inf 67.6%

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

      1. sub-neg 67.6%

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

      2. *-commutative 67.6%

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

      3. *-commutative 67.6%

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

      4. sub-neg 67.6%

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

   5. Simplified 67.6%

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

   6. Taylor expanded in t around inf 58.3%

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

      1. *-commutative 58.3%

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

   8. Simplified 58.3%

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

   if 9.1999999999999995e81 < y

   1. Initial program 80.4%

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

   3. Taylor expanded in j around inf 53.4%

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

      1. sub-neg 53.4%

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

      2. *-commutative 53.4%

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

      3. *-commutative 53.4%

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

      4. sub-neg 53.4%

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

   5. Simplified 53.4%

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

   6. Taylor expanded in t around 0 43.6%

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

      1. mul-1-neg 43.6%

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

      2. distribute-rgt-neg-in 43.6%

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

   8. Simplified 43.6%

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

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+179}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-55}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+81}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 29.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c\right)\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{+101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-185}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+104}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (* t c))))
   (if (<= t -1.15e+101)
     t_1
     (if (<= t -2.4e-185)
       (* y (* x z))
       (if (<= t 5e+104) (* a (* b i)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (t * c);
	double tmp;
	if (t <= -1.15e+101) {
		tmp = t_1;
	} else if (t <= -2.4e-185) {
		tmp = y * (x * z);
	} else if (t <= 5e+104) {
		tmp = a * (b * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (t * c)
    if (t <= (-1.15d+101)) then
        tmp = t_1
    else if (t <= (-2.4d-185)) then
        tmp = y * (x * z)
    else if (t <= 5d+104) then
        tmp = a * (b * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (t * c);
	double tmp;
	if (t <= -1.15e+101) {
		tmp = t_1;
	} else if (t <= -2.4e-185) {
		tmp = y * (x * z);
	} else if (t <= 5e+104) {
		tmp = a * (b * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * (t * c)
	tmp = 0
	if t <= -1.15e+101:
		tmp = t_1
	elif t <= -2.4e-185:
		tmp = y * (x * z)
	elif t <= 5e+104:
		tmp = a * (b * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(t * c))
	tmp = 0.0
	if (t <= -1.15e+101)
		tmp = t_1;
	elseif (t <= -2.4e-185)
		tmp = Float64(y * Float64(x * z));
	elseif (t <= 5e+104)
		tmp = Float64(a * Float64(b * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * (t * c);
	tmp = 0.0;
	if (t <= -1.15e+101)
		tmp = t_1;
	elseif (t <= -2.4e-185)
		tmp = y * (x * z);
	elseif (t <= 5e+104)
		tmp = a * (b * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.15e+101], t$95$1, If[LessEqual[t, -2.4e-185], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5e+104], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.1500000000000001e101 or 4.9999999999999997e104 < t

   1. Initial program 62.2%

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

   3. Taylor expanded in j around inf 56.0%

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

      1. sub-neg 56.0%

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

      2. *-commutative 56.0%

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

      3. *-commutative 56.0%

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

      4. sub-neg 56.0%

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

   5. Simplified 56.0%

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

   6. Taylor expanded in t around inf 51.5%

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

      1. *-commutative 51.5%

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

   8. Simplified 51.5%

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

   if -1.1500000000000001e101 < t < -2.4000000000000001e-185

   1. Initial program 88.8%

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

   3. Taylor expanded in y around inf 43.6%

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

      1. +-commutative 43.6%

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

      2. mul-1-neg 43.6%

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

      3. unsub-neg 43.6%

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

      4. *-commutative 43.6%

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

   5. Simplified 43.6%

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

   6. Taylor expanded in x around inf 34.0%

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

      1. *-commutative 34.0%

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

   8. Simplified 34.0%

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

   if -2.4000000000000001e-185 < t < 4.9999999999999997e104

   1. Initial program 73.2%

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

   3. Taylor expanded in b around inf 53.7%

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

      1. *-commutative 53.7%

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

   5. Simplified 53.7%

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

   6. Taylor expanded in a around inf 34.2%

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

4. Final simplification 40.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+101}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-185}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+104}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 29.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c\right)\\ \mathbf{if}\;t \leq -1.3 \cdot 10^{+101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-185}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+107}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (* t c))))
   (if (<= t -1.3e+101)
     t_1
     (if (<= t -1.05e-185)
       (* y (* x z))
       (if (<= t 7e+107) (* i (* a 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 = j * (t * c);
	double tmp;
	if (t <= -1.3e+101) {
		tmp = t_1;
	} else if (t <= -1.05e-185) {
		tmp = y * (x * z);
	} else if (t <= 7e+107) {
		tmp = i * (a * 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 = j * (t * c)
    if (t <= (-1.3d+101)) then
        tmp = t_1
    else if (t <= (-1.05d-185)) then
        tmp = y * (x * z)
    else if (t <= 7d+107) then
        tmp = i * (a * 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 = j * (t * c);
	double tmp;
	if (t <= -1.3e+101) {
		tmp = t_1;
	} else if (t <= -1.05e-185) {
		tmp = y * (x * z);
	} else if (t <= 7e+107) {
		tmp = i * (a * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * (t * c)
	tmp = 0
	if t <= -1.3e+101:
		tmp = t_1
	elif t <= -1.05e-185:
		tmp = y * (x * z)
	elif t <= 7e+107:
		tmp = i * (a * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(t * c))
	tmp = 0.0
	if (t <= -1.3e+101)
		tmp = t_1;
	elseif (t <= -1.05e-185)
		tmp = Float64(y * Float64(x * z));
	elseif (t <= 7e+107)
		tmp = Float64(i * Float64(a * 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 = j * (t * c);
	tmp = 0.0;
	if (t <= -1.3e+101)
		tmp = t_1;
	elseif (t <= -1.05e-185)
		tmp = y * (x * z);
	elseif (t <= 7e+107)
		tmp = i * (a * 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[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.3e+101], t$95$1, If[LessEqual[t, -1.05e-185], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e+107], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.3e101 or 6.9999999999999995e107 < t

   1. Initial program 62.2%

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

   3. Taylor expanded in j around inf 56.0%

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

      1. sub-neg 56.0%

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

      2. *-commutative 56.0%

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

      3. *-commutative 56.0%

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

      4. sub-neg 56.0%

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

   5. Simplified 56.0%

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

   6. Taylor expanded in t around inf 51.5%

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

      1. *-commutative 51.5%

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

   8. Simplified 51.5%

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

   if -1.3e101 < t < -1.05e-185

   1. Initial program 88.8%

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

   3. Taylor expanded in y around inf 43.6%

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

      1. +-commutative 43.6%

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

      2. mul-1-neg 43.6%

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

      3. unsub-neg 43.6%

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

      4. *-commutative 43.6%

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

   5. Simplified 43.6%

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

   6. Taylor expanded in x around inf 34.0%

      \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-commutative 34.0%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} \]

   8. Simplified 34.0%

      \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} \]

   if -1.05e-185 < t < 6.9999999999999995e107

   1. Initial program 73.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 53.7%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 53.7%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   5. Simplified 53.7%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   6. Taylor expanded in a around inf 34.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 39.8%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot i} \]

   8. Simplified 39.8%

      \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot i} \]
3. Recombined 3 regimes into one program.

4. Final simplification 42.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+101}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-185}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+107}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 30.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -85000:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;i \leq 1.35 \cdot 10^{+132}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -85000.0)
   (* b (* a i))
   (if (<= i 1.35e+132) (* j (* t c)) (* a (* b i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -85000.0) {
		tmp = b * (a * i);
	} else if (i <= 1.35e+132) {
		tmp = j * (t * c);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (i <= (-85000.0d0)) then
        tmp = b * (a * i)
    else if (i <= 1.35d+132) then
        tmp = j * (t * c)
    else
        tmp = a * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -85000.0) {
		tmp = b * (a * i);
	} else if (i <= 1.35e+132) {
		tmp = j * (t * c);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -85000.0:
		tmp = b * (a * i)
	elif i <= 1.35e+132:
		tmp = j * (t * c)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -85000.0)
		tmp = Float64(b * Float64(a * i));
	elseif (i <= 1.35e+132)
		tmp = Float64(j * Float64(t * c));
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -85000.0)
		tmp = b * (a * i);
	elseif (i <= 1.35e+132)
		tmp = j * (t * c);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -85000.0], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.35e+132], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if i < -85000

   1. Initial program 71.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 45.4%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 45.4%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   5. Simplified 45.4%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   6. Taylor expanded in a around inf 37.6%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]

   if -85000 < i < 1.35e132

   1. Initial program 78.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 38.1%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]
   4. Step-by-step derivation

      1. sub-neg 38.1%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t + \left(-i \cdot y\right)\right)} \]

      2. *-commutative 38.1%

         \[\leadsto j \cdot \left(\color{blue}{t \cdot c} + \left(-i \cdot y\right)\right) \]

      3. *-commutative 38.1%

         \[\leadsto j \cdot \left(t \cdot c + \left(-\color{blue}{y \cdot i}\right)\right) \]

      4. sub-neg 38.1%

         \[\leadsto j \cdot \color{blue}{\left(t \cdot c - y \cdot i\right)} \]

   5. Simplified 38.1%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot c - y \cdot i\right)} \]

   6. Taylor expanded in t around inf 32.1%

      \[\leadsto j \cdot \color{blue}{\left(c \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 32.1%

         \[\leadsto j \cdot \color{blue}{\left(t \cdot c\right)} \]

   8. Simplified 32.1%

      \[\leadsto j \cdot \color{blue}{\left(t \cdot c\right)} \]

   if 1.35e132 < i

   1. Initial program 60.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 47.9%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 47.9%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   5. Simplified 47.9%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   6. Taylor expanded in a around inf 56.3%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 37.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -85000:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;i \leq 1.35 \cdot 10^{+132}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 21.5% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(b \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* b i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (b * i);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = a * (b * i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (b * i);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (b * i)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(b * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (b * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 73.7%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
2. Add Preprocessing

3. Taylor expanded in b around inf 41.2%

   \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
4. Step-by-step derivation

   1. *-commutative 41.2%

      \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

5. Simplified 41.2%

   \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

6. Taylor expanded in a around inf 24.4%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

7. Final simplification 24.4%

   \[\leadsto a \cdot \left(b \cdot i\right) \]
8. Add Preprocessing

Developer target: 68.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ t_2 := x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{if}\;t < -8.120978919195912 \cdot 10^{-33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t < -4.712553818218485 \cdot 10^{-169}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t < -7.633533346031584 \cdot 10^{-308}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t < 1.0535888557455487 \cdot 10^{-139}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
          (/
           (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0)))
           (+ (* c t) (* i y)))))
        (t_2
         (-
          (* x (- (* z y) (* a t)))
          (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))
   (if (< t -8.120978919195912e-33)
     t_2
     (if (< t -4.712553818218485e-169)
       t_1
       (if (< t -7.633533346031584e-308)
         t_2
         (if (< t 1.0535888557455487e-139) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (pow((c * t), 2.0) - pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ** 2.0d0) - ((i * y) ** 2.0d0))) / ((c * t) + (i * y)))
    t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
    if (t < (-8.120978919195912d-33)) then
        tmp = t_2
    else if (t < (-4.712553818218485d-169)) then
        tmp = t_1
    else if (t < (-7.633533346031584d-308)) then
        tmp = t_2
    else if (t < 1.0535888557455487d-139) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (Math.pow((c * t), 2.0) - Math.pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (math.pow((c * t), 2.0) - math.pow((i * y), 2.0))) / ((c * t) + (i * y)))
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
	tmp = 0
	if t < -8.120978919195912e-33:
		tmp = t_2
	elif t < -4.712553818218485e-169:
		tmp = t_1
	elif t < -7.633533346031584e-308:
		tmp = t_2
	elif t < 1.0535888557455487e-139:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(Float64(j * Float64((Float64(c * t) ^ 2.0) - (Float64(i * y) ^ 2.0))) / Float64(Float64(c * t) + Float64(i * y))))
	t_2 = Float64(Float64(x * Float64(Float64(z * y) - Float64(a * t))) - Float64(Float64(b * Float64(Float64(z * c) - Float64(a * i))) - Float64(Float64(Float64(c * t) - Float64(y * i)) * j)))
	tmp = 0.0
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ^ 2.0) - ((i * y) ^ 2.0))) / ((c * t) + (i * y)));
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	tmp = 0.0;
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[Power[N[(c * t), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(i * y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * t), $MachinePrecision] + N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(c * t), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -8.120978919195912e-33], t$95$2, If[Less[t, -4.712553818218485e-169], t$95$1, If[Less[t, -7.633533346031584e-308], t$95$2, If[Less[t, 1.0535888557455487e-139], t$95$1, t$95$2]]]]]]

Reproduce

herbie shell --seed 2024026 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< t -8.120978919195912e-33) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -4.712553818218485e-169) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (if (< t -7.633533346031584e-308) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 1.0535888557455487e-139) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))