Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.5% → 81.7%

Time: 34.3s

Alternatives: 25

Speedup: 0.5×

• 58.4% 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: 73.5% 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: 81.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := t \cdot c - y \cdot i\\ \mathbf{if}\;t_1 + j \cdot t_2 \leq \infty:\\ \;\;\;\;t_1 + \frac{j}{\frac{1}{t_2}}\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \end{array} \]

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)))))
        (t_2 (- (* t c) (* y i))))
   (if (<= (+ t_1 (* j t_2)) INFINITY)
     (+ t_1 (/ j (/ 1.0 t_2)))
     (* c (- (* t j) (* z b))))))

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 = (t * c) - (y * i);
	double tmp;
	if ((t_1 + (j * t_2)) <= ((double) INFINITY)) {
		tmp = t_1 + (j / (1.0 / t_2));
	} else {
		tmp = c * ((t * j) - (z * b));
	}
	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)));
	double t_2 = (t * c) - (y * i);
	double tmp;
	if ((t_1 + (j * t_2)) <= Double.POSITIVE_INFINITY) {
		tmp = t_1 + (j / (1.0 / t_2));
	} else {
		tmp = c * ((t * j) - (z * b));
	}
	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 = (t * c) - (y * i)
	tmp = 0
	if (t_1 + (j * t_2)) <= math.inf:
		tmp = t_1 + (j / (1.0 / t_2))
	else:
		tmp = c * ((t * j) - (z * b))
	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(Float64(t * c) - Float64(y * i))
	tmp = 0.0
	if (Float64(t_1 + Float64(j * t_2)) <= Inf)
		tmp = Float64(t_1 + Float64(j / Float64(1.0 / t_2)));
	else
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	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 = (t * c) - (y * i);
	tmp = 0.0;
	if ((t_1 + (j * t_2)) <= Inf)
		tmp = t_1 + (j / (1.0 / t_2));
	else
		tmp = c * ((t * j) - (z * b));
	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[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$1 + N[(j * t$95$2), $MachinePrecision]), $MachinePrecision], Infinity], N[(t$95$1 + N[(j / N[(1.0 / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $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 90.5%

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

      1. *-commutative 90.5%

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

      2. *-commutative 90.5%

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

      3. flip-- 67.7%

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

      4. clear-num 67.7%

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

      5. un-div-inv 67.7%

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

      6. clear-num 67.7%

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

      7. flip-- 90.5%

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

      8. *-commutative 90.5%

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

      9. *-commutative 90.5%

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

   3. Applied egg-rr 90.5%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in c around inf 53.2%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \leq \infty:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right) + \frac{j}{\frac{1}{t \cdot c - y \cdot i}}\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 2: 81.7% accurate, 0.5× speedup

Math

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

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 (* c (- (* t j) (* z b))))))

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 = c * ((t * j) - (z * b));
	}
	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 = c * ((t * j) - (z * b));
	}
	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 = c * ((t * j) - (z * b))
	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(c * Float64(Float64(t * j) - Float64(z * b)));
	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 = c * ((t * j) - (z * b));
	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[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $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 90.5%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in c around inf 53.2%

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

4. Final simplification 82.5%

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

Alternative 3: 70.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(x \cdot t\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_3 := \left(t_2 + z \cdot \left(x \cdot y - b \cdot c\right)\right) - t_1\\ \mathbf{if}\;j \leq -4.8 \cdot 10^{+150}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -3.3 \cdot 10^{-51}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{-90}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z\right) - t_1\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 6.2 \cdot 10^{+144}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* x t)))
        (t_2 (* j (- (* t c) (* y i))))
        (t_3 (- (+ t_2 (* z (- (* x y) (* b c)))) t_1)))
   (if (<= j -4.8e+150)
     t_2
     (if (<= j -3.3e-51)
       t_3
       (if (<= j 2.6e-90)
         (+ (- (* x (* y z)) t_1) (* b (- (* a i) (* z c))))
         (if (<= j 6.2e+144) 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 = a * (x * t);
	double t_2 = j * ((t * c) - (y * i));
	double t_3 = (t_2 + (z * ((x * y) - (b * c)))) - t_1;
	double tmp;
	if (j <= -4.8e+150) {
		tmp = t_2;
	} else if (j <= -3.3e-51) {
		tmp = t_3;
	} else if (j <= 2.6e-90) {
		tmp = ((x * (y * z)) - t_1) + (b * ((a * i) - (z * c)));
	} else if (j <= 6.2e+144) {
		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 = a * (x * t)
    t_2 = j * ((t * c) - (y * i))
    t_3 = (t_2 + (z * ((x * y) - (b * c)))) - t_1
    if (j <= (-4.8d+150)) then
        tmp = t_2
    else if (j <= (-3.3d-51)) then
        tmp = t_3
    else if (j <= 2.6d-90) then
        tmp = ((x * (y * z)) - t_1) + (b * ((a * i) - (z * c)))
    else if (j <= 6.2d+144) 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 = a * (x * t);
	double t_2 = j * ((t * c) - (y * i));
	double t_3 = (t_2 + (z * ((x * y) - (b * c)))) - t_1;
	double tmp;
	if (j <= -4.8e+150) {
		tmp = t_2;
	} else if (j <= -3.3e-51) {
		tmp = t_3;
	} else if (j <= 2.6e-90) {
		tmp = ((x * (y * z)) - t_1) + (b * ((a * i) - (z * c)));
	} else if (j <= 6.2e+144) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (x * t)
	t_2 = j * ((t * c) - (y * i))
	t_3 = (t_2 + (z * ((x * y) - (b * c)))) - t_1
	tmp = 0
	if j <= -4.8e+150:
		tmp = t_2
	elif j <= -3.3e-51:
		tmp = t_3
	elif j <= 2.6e-90:
		tmp = ((x * (y * z)) - t_1) + (b * ((a * i) - (z * c)))
	elif j <= 6.2e+144:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(x * t))
	t_2 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_3 = Float64(Float64(t_2 + Float64(z * Float64(Float64(x * y) - Float64(b * c)))) - t_1)
	tmp = 0.0
	if (j <= -4.8e+150)
		tmp = t_2;
	elseif (j <= -3.3e-51)
		tmp = t_3;
	elseif (j <= 2.6e-90)
		tmp = Float64(Float64(Float64(x * Float64(y * z)) - t_1) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (j <= 6.2e+144)
		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 = a * (x * t);
	t_2 = j * ((t * c) - (y * i));
	t_3 = (t_2 + (z * ((x * y) - (b * c)))) - t_1;
	tmp = 0.0;
	if (j <= -4.8e+150)
		tmp = t_2;
	elseif (j <= -3.3e-51)
		tmp = t_3;
	elseif (j <= 2.6e-90)
		tmp = ((x * (y * z)) - t_1) + (b * ((a * i) - (z * c)));
	elseif (j <= 6.2e+144)
		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[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t$95$2 + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, If[LessEqual[j, -4.8e+150], t$95$2, If[LessEqual[j, -3.3e-51], t$95$3, If[LessEqual[j, 2.6e-90], N[(N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6.2e+144], t$95$3, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -4.80000000000000005e150 or 6.2000000000000003e144 < j

   1. Initial program 67.1%

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

   2. Taylor expanded in j around inf 82.3%

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

   if -4.80000000000000005e150 < j < -3.29999999999999973e-51 or 2.6e-90 < j < 6.2000000000000003e144

   1. Initial program 74.9%

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

      1. *-commutative 74.9%

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

      2. *-commutative 74.9%

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

      3. flip-- 57.7%

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

      4. clear-num 57.7%

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

      5. un-div-inv 57.7%

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

      6. clear-num 57.8%

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

      7. flip-- 74.9%

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

      8. *-commutative 74.9%

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

      9. *-commutative 74.9%

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

   3. Applied egg-rr 74.9%

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

   4. Taylor expanded in c around inf 71.9%

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

   5. Taylor expanded in z around 0 73.7%

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

   if -3.29999999999999973e-51 < j < 2.6e-90

   1. Initial program 70.3%

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

      1. sub-neg 70.3%

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

      2. distribute-lft-in 70.3%

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

      3. associate-*r* 72.4%

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

      4. distribute-rgt-neg-in 72.4%

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

      5. associate-*r* 73.3%

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

   3. Applied egg-rr 73.3%

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

   4. Taylor expanded in j around 0 75.5%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4.8 \cdot 10^{+150}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -3.3 \cdot 10^{-51}:\\ \;\;\;\;\left(j \cdot \left(t \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{-90}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z\right) - a \cdot \left(x \cdot t\right)\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 6.2 \cdot 10^{+144}:\\ \;\;\;\;\left(j \cdot \left(t \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 4: 69.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot c - y \cdot i\\ t_2 := j \cdot t_1\\ t_3 := a \cdot \left(x \cdot t\right)\\ \mathbf{if}\;j \leq -3 \cdot 10^{-49}:\\ \;\;\;\;\frac{j}{\frac{1}{t_1}} + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 1.4 \cdot 10^{-91}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z\right) - t_3\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 3.25 \cdot 10^{+136}:\\ \;\;\;\;\left(t_2 + z \cdot \left(x \cdot y - b \cdot c\right)\right) - t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* t c) (* y i))) (t_2 (* j t_1)) (t_3 (* a (* x t))))
   (if (<= j -3e-49)
     (+ (/ j (/ 1.0 t_1)) (- (* x (- (* y z) (* t a))) (* b (* z c))))
     (if (<= j 1.4e-91)
       (+ (- (* x (* y z)) t_3) (* b (- (* a i) (* z c))))
       (if (<= j 3.25e+136) (- (+ t_2 (* z (- (* x y) (* b c)))) 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 = (t * c) - (y * i);
	double t_2 = j * t_1;
	double t_3 = a * (x * t);
	double tmp;
	if (j <= -3e-49) {
		tmp = (j / (1.0 / t_1)) + ((x * ((y * z) - (t * a))) - (b * (z * c)));
	} else if (j <= 1.4e-91) {
		tmp = ((x * (y * z)) - t_3) + (b * ((a * i) - (z * c)));
	} else if (j <= 3.25e+136) {
		tmp = (t_2 + (z * ((x * y) - (b * c)))) - 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 = (t * c) - (y * i)
    t_2 = j * t_1
    t_3 = a * (x * t)
    if (j <= (-3d-49)) then
        tmp = (j / (1.0d0 / t_1)) + ((x * ((y * z) - (t * a))) - (b * (z * c)))
    else if (j <= 1.4d-91) then
        tmp = ((x * (y * z)) - t_3) + (b * ((a * i) - (z * c)))
    else if (j <= 3.25d+136) then
        tmp = (t_2 + (z * ((x * y) - (b * c)))) - 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 = (t * c) - (y * i);
	double t_2 = j * t_1;
	double t_3 = a * (x * t);
	double tmp;
	if (j <= -3e-49) {
		tmp = (j / (1.0 / t_1)) + ((x * ((y * z) - (t * a))) - (b * (z * c)));
	} else if (j <= 1.4e-91) {
		tmp = ((x * (y * z)) - t_3) + (b * ((a * i) - (z * c)));
	} else if (j <= 3.25e+136) {
		tmp = (t_2 + (z * ((x * y) - (b * c)))) - t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (t * c) - (y * i)
	t_2 = j * t_1
	t_3 = a * (x * t)
	tmp = 0
	if j <= -3e-49:
		tmp = (j / (1.0 / t_1)) + ((x * ((y * z) - (t * a))) - (b * (z * c)))
	elif j <= 1.4e-91:
		tmp = ((x * (y * z)) - t_3) + (b * ((a * i) - (z * c)))
	elif j <= 3.25e+136:
		tmp = (t_2 + (z * ((x * y) - (b * c)))) - t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(t * c) - Float64(y * i))
	t_2 = Float64(j * t_1)
	t_3 = Float64(a * Float64(x * t))
	tmp = 0.0
	if (j <= -3e-49)
		tmp = Float64(Float64(j / Float64(1.0 / t_1)) + Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(z * c))));
	elseif (j <= 1.4e-91)
		tmp = Float64(Float64(Float64(x * Float64(y * z)) - t_3) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (j <= 3.25e+136)
		tmp = Float64(Float64(t_2 + Float64(z * Float64(Float64(x * y) - Float64(b * c)))) - 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 = (t * c) - (y * i);
	t_2 = j * t_1;
	t_3 = a * (x * t);
	tmp = 0.0;
	if (j <= -3e-49)
		tmp = (j / (1.0 / t_1)) + ((x * ((y * z) - (t * a))) - (b * (z * c)));
	elseif (j <= 1.4e-91)
		tmp = ((x * (y * z)) - t_3) + (b * ((a * i) - (z * c)));
	elseif (j <= 3.25e+136)
		tmp = (t_2 + (z * ((x * y) - (b * c)))) - 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[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3e-49], N[(N[(j / N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.4e-91], N[(N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.25e+136], N[(N[(t$95$2 + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -3e-49

   1. Initial program 75.3%

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

      1. *-commutative 75.3%

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

      2. *-commutative 75.3%

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

      3. flip-- 53.7%

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

      4. clear-num 53.7%

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

      5. un-div-inv 53.7%

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

      6. clear-num 53.7%

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

      7. flip-- 75.3%

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

      8. *-commutative 75.3%

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

      9. *-commutative 75.3%

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

   3. Applied egg-rr 75.3%

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

   4. Taylor expanded in c around inf 74.2%

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

   if -3e-49 < j < 1.4e-91

   1. Initial program 69.6%

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

      1. sub-neg 69.6%

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

      2. distribute-lft-in 69.6%

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

      3. associate-*r* 71.6%

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

      4. distribute-rgt-neg-in 71.6%

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

      5. associate-*r* 72.6%

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

   3. Applied egg-rr 72.6%

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

   4. Taylor expanded in j around 0 74.8%

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

   if 1.4e-91 < j < 3.2499999999999999e136

   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. Step-by-step derivation

      1. *-commutative 73.5%

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

      2. *-commutative 73.5%

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

      3. flip-- 57.7%

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

      4. clear-num 57.7%

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

      5. un-div-inv 57.7%

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

      6. clear-num 57.7%

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

      7. flip-- 73.5%

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

      8. *-commutative 73.5%

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

      9. *-commutative 73.5%

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

   3. Applied egg-rr 73.5%

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

   4. Taylor expanded in c around inf 68.3%

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

   5. Taylor expanded in z around 0 70.1%

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

   if 3.2499999999999999e136 < j

   1. Initial program 60.7%

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

   2. Taylor expanded in j around inf 89.3%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3 \cdot 10^{-49}:\\ \;\;\;\;\frac{j}{\frac{1}{t \cdot c - y \cdot i}} + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 1.4 \cdot 10^{-91}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z\right) - a \cdot \left(x \cdot t\right)\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 3.25 \cdot 10^{+136}:\\ \;\;\;\;\left(j \cdot \left(t \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 5: 67.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot c - y \cdot i\\ \mathbf{if}\;j \leq -8 \cdot 10^{-12}:\\ \;\;\;\;\frac{j}{\frac{1}{t_1}} + \left(x \cdot \left(y \cdot z\right) - b \cdot \left(z \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 1.48 \cdot 10^{-241}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{+74}:\\ \;\;\;\;\left(c \cdot \left(t \cdot j\right) - a \cdot \left(x \cdot t\right)\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* t c) (* y i))))
   (if (<= j -8e-12)
     (+ (/ j (/ 1.0 t_1)) (- (* x (* y z)) (* b (* z c))))
     (if (<= j 1.48e-241)
       (- (* x (- (* y z) (* t a))) (* b (- (* z c) (* a i))))
       (if (<= j 1.7e+74)
         (+ (- (* c (* t j)) (* a (* x t))) (* b (- (* a i) (* z c))))
         (* j t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (t * c) - (y * i);
	double tmp;
	if (j <= -8e-12) {
		tmp = (j / (1.0 / t_1)) + ((x * (y * z)) - (b * (z * c)));
	} else if (j <= 1.48e-241) {
		tmp = (x * ((y * z) - (t * a))) - (b * ((z * c) - (a * i)));
	} else if (j <= 1.7e+74) {
		tmp = ((c * (t * j)) - (a * (x * t))) + (b * ((a * i) - (z * c)));
	} else {
		tmp = j * 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) - (y * i)
    if (j <= (-8d-12)) then
        tmp = (j / (1.0d0 / t_1)) + ((x * (y * z)) - (b * (z * c)))
    else if (j <= 1.48d-241) then
        tmp = (x * ((y * z) - (t * a))) - (b * ((z * c) - (a * i)))
    else if (j <= 1.7d+74) then
        tmp = ((c * (t * j)) - (a * (x * t))) + (b * ((a * i) - (z * c)))
    else
        tmp = j * 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) - (y * i);
	double tmp;
	if (j <= -8e-12) {
		tmp = (j / (1.0 / t_1)) + ((x * (y * z)) - (b * (z * c)));
	} else if (j <= 1.48e-241) {
		tmp = (x * ((y * z) - (t * a))) - (b * ((z * c) - (a * i)));
	} else if (j <= 1.7e+74) {
		tmp = ((c * (t * j)) - (a * (x * t))) + (b * ((a * i) - (z * c)));
	} else {
		tmp = j * t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (t * c) - (y * i)
	tmp = 0
	if j <= -8e-12:
		tmp = (j / (1.0 / t_1)) + ((x * (y * z)) - (b * (z * c)))
	elif j <= 1.48e-241:
		tmp = (x * ((y * z) - (t * a))) - (b * ((z * c) - (a * i)))
	elif j <= 1.7e+74:
		tmp = ((c * (t * j)) - (a * (x * t))) + (b * ((a * i) - (z * c)))
	else:
		tmp = j * t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(t * c) - Float64(y * i))
	tmp = 0.0
	if (j <= -8e-12)
		tmp = Float64(Float64(j / Float64(1.0 / t_1)) + Float64(Float64(x * Float64(y * z)) - Float64(b * Float64(z * c))));
	elseif (j <= 1.48e-241)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(z * c) - Float64(a * i))));
	elseif (j <= 1.7e+74)
		tmp = Float64(Float64(Float64(c * Float64(t * j)) - Float64(a * Float64(x * t))) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	else
		tmp = Float64(j * t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (t * c) - (y * i);
	tmp = 0.0;
	if (j <= -8e-12)
		tmp = (j / (1.0 / t_1)) + ((x * (y * z)) - (b * (z * c)));
	elseif (j <= 1.48e-241)
		tmp = (x * ((y * z) - (t * a))) - (b * ((z * c) - (a * i)));
	elseif (j <= 1.7e+74)
		tmp = ((c * (t * j)) - (a * (x * t))) + (b * ((a * i) - (z * c)));
	else
		tmp = j * t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -8e-12], N[(N[(j / N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.48e-241], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.7e+74], N[(N[(N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -7.99999999999999984e-12

   1. Initial program 75.7%

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

      1. *-commutative 75.7%

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

      2. *-commutative 75.7%

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

      3. flip-- 54.7%

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

      4. clear-num 54.7%

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

      5. un-div-inv 54.7%

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

      6. clear-num 54.8%

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

      7. flip-- 75.7%

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

      8. *-commutative 75.7%

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

      9. *-commutative 75.7%

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

   3. Applied egg-rr 75.7%

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

   4. Taylor expanded in c around inf 73.0%

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

   5. Taylor expanded in y around inf 71.8%

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

   if -7.99999999999999984e-12 < j < 1.47999999999999999e-241

   1. Initial program 75.6%

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

   2. Taylor expanded in j around 0 78.0%

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

      1. *-commutative 78.0%

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

      2. *-commutative 78.0%

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

   4. Simplified 78.0%

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

   if 1.47999999999999999e-241 < j < 1.7e74

   1. Initial program 63.5%

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

   2. Taylor expanded in y around 0 66.2%

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

   if 1.7e74 < j

   1. Initial program 66.2%

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

   2. Taylor expanded in j around inf 75.6%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -8 \cdot 10^{-12}:\\ \;\;\;\;\frac{j}{\frac{1}{t \cdot c - y \cdot i}} + \left(x \cdot \left(y \cdot z\right) - b \cdot \left(z \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 1.48 \cdot 10^{-241}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{+74}:\\ \;\;\;\;\left(c \cdot \left(t \cdot j\right) - a \cdot \left(x \cdot t\right)\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 6: 66.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot c - y \cdot i\\ t_2 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;j \leq -1.7 \cdot 10^{-49}:\\ \;\;\;\;\frac{j}{\frac{1}{t_1}} + \left(t_2 - b \cdot \left(z \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{+32}:\\ \;\;\;\;\left(t_2 - a \cdot \left(x \cdot t\right)\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* t c) (* y i))) (t_2 (* x (* y z))))
   (if (<= j -1.7e-49)
     (+ (/ j (/ 1.0 t_1)) (- t_2 (* b (* z c))))
     (if (<= j 2.5e+32)
       (+ (- t_2 (* a (* x t))) (* b (- (* a i) (* z c))))
       (* j t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (t * c) - (y * i);
	double t_2 = x * (y * z);
	double tmp;
	if (j <= -1.7e-49) {
		tmp = (j / (1.0 / t_1)) + (t_2 - (b * (z * c)));
	} else if (j <= 2.5e+32) {
		tmp = (t_2 - (a * (x * t))) + (b * ((a * i) - (z * c)));
	} else {
		tmp = j * t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t * c) - (y * i)
    t_2 = x * (y * z)
    if (j <= (-1.7d-49)) then
        tmp = (j / (1.0d0 / t_1)) + (t_2 - (b * (z * c)))
    else if (j <= 2.5d+32) then
        tmp = (t_2 - (a * (x * t))) + (b * ((a * i) - (z * c)))
    else
        tmp = j * 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) - (y * i);
	double t_2 = x * (y * z);
	double tmp;
	if (j <= -1.7e-49) {
		tmp = (j / (1.0 / t_1)) + (t_2 - (b * (z * c)));
	} else if (j <= 2.5e+32) {
		tmp = (t_2 - (a * (x * t))) + (b * ((a * i) - (z * c)));
	} else {
		tmp = j * t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (t * c) - (y * i)
	t_2 = x * (y * z)
	tmp = 0
	if j <= -1.7e-49:
		tmp = (j / (1.0 / t_1)) + (t_2 - (b * (z * c)))
	elif j <= 2.5e+32:
		tmp = (t_2 - (a * (x * t))) + (b * ((a * i) - (z * c)))
	else:
		tmp = j * t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(t * c) - Float64(y * i))
	t_2 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (j <= -1.7e-49)
		tmp = Float64(Float64(j / Float64(1.0 / t_1)) + Float64(t_2 - Float64(b * Float64(z * c))));
	elseif (j <= 2.5e+32)
		tmp = Float64(Float64(t_2 - Float64(a * Float64(x * t))) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	else
		tmp = Float64(j * t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (t * c) - (y * i);
	t_2 = x * (y * z);
	tmp = 0.0;
	if (j <= -1.7e-49)
		tmp = (j / (1.0 / t_1)) + (t_2 - (b * (z * c)));
	elseif (j <= 2.5e+32)
		tmp = (t_2 - (a * (x * t))) + (b * ((a * i) - (z * c)));
	else
		tmp = j * t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.7e-49], N[(N[(j / N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.5e+32], N[(N[(t$95$2 - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.70000000000000002e-49

   1. Initial program 75.3%

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

      1. *-commutative 75.3%

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

      2. *-commutative 75.3%

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

      3. flip-- 53.7%

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

      4. clear-num 53.7%

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

      5. un-div-inv 53.7%

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

      6. clear-num 53.7%

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

      7. flip-- 75.3%

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

      8. *-commutative 75.3%

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

      9. *-commutative 75.3%

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

   3. Applied egg-rr 75.3%

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

   4. Taylor expanded in c around inf 74.2%

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

   5. Taylor expanded in y around inf 70.6%

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

   if -1.70000000000000002e-49 < j < 2.4999999999999999e32

   1. Initial program 70.2%

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

      1. sub-neg 70.2%

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

      2. distribute-lft-in 70.2%

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

      3. associate-*r* 70.4%

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

      4. distribute-rgt-neg-in 70.4%

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

      5. associate-*r* 72.6%

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

   3. Applied egg-rr 72.6%

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

   4. Taylor expanded in j around 0 73.1%

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

   if 2.4999999999999999e32 < j

   1. Initial program 67.5%

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

   2. Taylor expanded in j around inf 71.7%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.7 \cdot 10^{-49}:\\ \;\;\;\;\frac{j}{\frac{1}{t \cdot c - y \cdot i}} + \left(x \cdot \left(y \cdot z\right) - b \cdot \left(z \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{+32}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z\right) - a \cdot \left(x \cdot t\right)\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 7: 67.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot c - y \cdot i\\ \mathbf{if}\;j \leq -1.04 \cdot 10^{-11}:\\ \;\;\;\;\frac{j}{\frac{1}{t_1}} + \left(x \cdot \left(y \cdot z\right) - b \cdot \left(z \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 7 \cdot 10^{+31}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* t c) (* y i))))
   (if (<= j -1.04e-11)
     (+ (/ j (/ 1.0 t_1)) (- (* x (* y z)) (* b (* z c))))
     (if (<= j 7e+31)
       (+ (* x (- (* y z) (* t a))) (* b (- (* a i) (* z c))))
       (* j t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (t * c) - (y * i);
	double tmp;
	if (j <= -1.04e-11) {
		tmp = (j / (1.0 / t_1)) + ((x * (y * z)) - (b * (z * c)));
	} else if (j <= 7e+31) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	} else {
		tmp = j * 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) - (y * i)
    if (j <= (-1.04d-11)) then
        tmp = (j / (1.0d0 / t_1)) + ((x * (y * z)) - (b * (z * c)))
    else if (j <= 7d+31) then
        tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))
    else
        tmp = j * 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) - (y * i);
	double tmp;
	if (j <= -1.04e-11) {
		tmp = (j / (1.0 / t_1)) + ((x * (y * z)) - (b * (z * c)));
	} else if (j <= 7e+31) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	} else {
		tmp = j * t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (t * c) - (y * i)
	tmp = 0
	if j <= -1.04e-11:
		tmp = (j / (1.0 / t_1)) + ((x * (y * z)) - (b * (z * c)))
	elif j <= 7e+31:
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))
	else:
		tmp = j * t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(t * c) - Float64(y * i))
	tmp = 0.0
	if (j <= -1.04e-11)
		tmp = Float64(Float64(j / Float64(1.0 / t_1)) + Float64(Float64(x * Float64(y * z)) - Float64(b * Float64(z * c))));
	elseif (j <= 7e+31)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	else
		tmp = Float64(j * t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (t * c) - (y * i);
	tmp = 0.0;
	if (j <= -1.04e-11)
		tmp = (j / (1.0 / t_1)) + ((x * (y * z)) - (b * (z * c)));
	elseif (j <= 7e+31)
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	else
		tmp = j * t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.04e-11], N[(N[(j / N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7e+31], 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 * t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.03999999999999993e-11

   1. Initial program 75.7%

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

      1. *-commutative 75.7%

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

      2. *-commutative 75.7%

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

      3. flip-- 54.7%

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

      4. clear-num 54.7%

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

      5. un-div-inv 54.7%

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

      6. clear-num 54.8%

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

      7. flip-- 75.7%

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

      8. *-commutative 75.7%

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

      9. *-commutative 75.7%

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

   3. Applied egg-rr 75.7%

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

   4. Taylor expanded in c around inf 73.0%

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

   5. Taylor expanded in y around inf 71.8%

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

   if -1.03999999999999993e-11 < j < 7e31

   1. Initial program 70.3%

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

   2. Taylor expanded in j around 0 71.2%

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

      1. *-commutative 71.2%

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

      2. *-commutative 71.2%

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

   4. Simplified 71.2%

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

   if 7e31 < j

   1. Initial program 67.5%

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

   2. Taylor expanded in j around inf 71.7%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.04 \cdot 10^{-11}:\\ \;\;\;\;\frac{j}{\frac{1}{t \cdot c - y \cdot i}} + \left(x \cdot \left(y \cdot z\right) - b \cdot \left(z \cdot c\right)\right)\\ \mathbf{elif}\;j \leq 7 \cdot 10^{+31}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 8: 66.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.45 \cdot 10^{+37} \lor \neg \left(j \leq 2.8 \cdot 10^{+32}\right):\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -1.45e+37) (not (<= j 2.8e+32)))
   (* j (- (* t c) (* y i)))
   (+ (* x (- (* y z) (* t 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 ((j <= -1.45e+37) || !(j <= 2.8e+32)) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = (x * ((y * z) - (t * a))) + (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 ((j <= (-1.45d+37)) .or. (.not. (j <= 2.8d+32))) then
        tmp = j * ((t * c) - (y * i))
    else
        tmp = (x * ((y * z) - (t * a))) + (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 ((j <= -1.45e+37) || !(j <= 2.8e+32)) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -1.45e+37) or not (j <= 2.8e+32):
		tmp = j * ((t * c) - (y * i))
	else:
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -1.45e+37) || !(j <= 2.8e+32))
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	else
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + 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 ((j <= -1.45e+37) || ~((j <= 2.8e+32)))
		tmp = j * ((t * c) - (y * i));
	else
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -1.45e+37], N[Not[LessEqual[j, 2.8e+32]], $MachinePrecision]], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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]]

Derivation

1. Split input into 2 regimes

2. if j < -1.44999999999999989e37 or 2.8e32 < j

   1. Initial program 70.5%

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

   2. Taylor expanded in j around inf 71.6%

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

   if -1.44999999999999989e37 < j < 2.8e32

   1. Initial program 71.5%

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

   2. Taylor expanded in j around 0 71.1%

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

      1. *-commutative 71.1%

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

      2. *-commutative 71.1%

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

   4. Simplified 71.1%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.45 \cdot 10^{+37} \lor \neg \left(j \leq 2.8 \cdot 10^{+32}\right):\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 9: 44.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -9.5 \cdot 10^{-20}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -1.2 \cdot 10^{-58}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq -1.7 \cdot 10^{-88}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -7.2 \cdot 10^{-248}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 4.4 \cdot 10^{-170}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{elif}\;c \leq 6.8 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))) (t_2 (* c (- (* t j) (* z b)))))
   (if (<= c -9.5e-20)
     t_2
     (if (<= c -1.2e-58)
       (* x (* y z))
       (if (<= c -1.7e-88)
         t_2
         (if (<= c -7.2e-248)
           t_1
           (if (<= c 4.4e-170)
             (* (* t a) (- x))
             (if (<= c 6.8e+57) 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 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -9.5e-20) {
		tmp = t_2;
	} else if (c <= -1.2e-58) {
		tmp = x * (y * z);
	} else if (c <= -1.7e-88) {
		tmp = t_2;
	} else if (c <= -7.2e-248) {
		tmp = t_1;
	} else if (c <= 4.4e-170) {
		tmp = (t * a) * -x;
	} else if (c <= 6.8e+57) {
		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 = c * ((t * j) - (z * b))
    if (c <= (-9.5d-20)) then
        tmp = t_2
    else if (c <= (-1.2d-58)) then
        tmp = x * (y * z)
    else if (c <= (-1.7d-88)) then
        tmp = t_2
    else if (c <= (-7.2d-248)) then
        tmp = t_1
    else if (c <= 4.4d-170) then
        tmp = (t * a) * -x
    else if (c <= 6.8d+57) 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 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -9.5e-20) {
		tmp = t_2;
	} else if (c <= -1.2e-58) {
		tmp = x * (y * z);
	} else if (c <= -1.7e-88) {
		tmp = t_2;
	} else if (c <= -7.2e-248) {
		tmp = t_1;
	} else if (c <= 4.4e-170) {
		tmp = (t * a) * -x;
	} else if (c <= 6.8e+57) {
		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 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -9.5e-20:
		tmp = t_2
	elif c <= -1.2e-58:
		tmp = x * (y * z)
	elif c <= -1.7e-88:
		tmp = t_2
	elif c <= -7.2e-248:
		tmp = t_1
	elif c <= 4.4e-170:
		tmp = (t * a) * -x
	elif c <= 6.8e+57:
		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(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -9.5e-20)
		tmp = t_2;
	elseif (c <= -1.2e-58)
		tmp = Float64(x * Float64(y * z));
	elseif (c <= -1.7e-88)
		tmp = t_2;
	elseif (c <= -7.2e-248)
		tmp = t_1;
	elseif (c <= 4.4e-170)
		tmp = Float64(Float64(t * a) * Float64(-x));
	elseif (c <= 6.8e+57)
		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 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -9.5e-20)
		tmp = t_2;
	elseif (c <= -1.2e-58)
		tmp = x * (y * z);
	elseif (c <= -1.7e-88)
		tmp = t_2;
	elseif (c <= -7.2e-248)
		tmp = t_1;
	elseif (c <= 4.4e-170)
		tmp = (t * a) * -x;
	elseif (c <= 6.8e+57)
		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[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -9.5e-20], t$95$2, If[LessEqual[c, -1.2e-58], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.7e-88], t$95$2, If[LessEqual[c, -7.2e-248], t$95$1, If[LessEqual[c, 4.4e-170], N[(N[(t * a), $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[c, 6.8e+57], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -9.5e-20 or -1.2e-58 < c < -1.69999999999999987e-88 or 6.79999999999999984e57 < c

   1. Initial program 63.1%

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

   2. Taylor expanded in c around inf 65.2%

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

   if -9.5e-20 < c < -1.2e-58

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 85.8%

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

      1. +-commutative 85.8%

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

      2. mul-1-neg 85.8%

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

      3. unsub-neg 85.8%

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

      4. *-commutative 85.8%

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

   4. Applied egg-rr 85.8%

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

   5. Taylor expanded in x around inf 86.1%

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

   if -1.69999999999999987e-88 < c < -7.19999999999999969e-248 or 4.40000000000000029e-170 < c < 6.79999999999999984e57

   1. Initial program 82.2%

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

   2. Taylor expanded in b around inf 47.6%

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

      1. *-commutative 47.6%

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

   4. Simplified 47.6%

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

   if -7.19999999999999969e-248 < c < 4.40000000000000029e-170

   1. Initial program 72.1%

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

   2. Taylor expanded in y around 0 54.3%

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

   3. Taylor expanded in x around inf 39.9%

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

      1. associate-*r* 39.9%

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

      2. neg-mul-1 39.9%

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

      3. *-commutative 39.9%

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

      4. *-commutative 39.9%

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

      5. associate-*l* 44.0%

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

   5. Simplified 44.0%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -9.5 \cdot 10^{-20}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -1.2 \cdot 10^{-58}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq -1.7 \cdot 10^{-88}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -7.2 \cdot 10^{-248}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq 4.4 \cdot 10^{-170}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{elif}\;c \leq 6.8 \cdot 10^{+57}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 10: 52.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -6.2 \cdot 10^{-18}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -4.2 \cdot 10^{-61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.35 \cdot 10^{-123}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq -4.8 \cdot 10^{-225}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -1.16 \cdot 10^{-296}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{-19}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (* b (- (* a i) (* z c))))
        (t_3 (* j (- (* t c) (* y i)))))
   (if (<= j -6.2e-18)
     t_3
     (if (<= j -4.2e-61)
       t_1
       (if (<= j -1.35e-123)
         (* c (- (* t j) (* z b)))
         (if (<= j -4.8e-225)
           t_2
           (if (<= j -1.16e-296) t_1 (if (<= j 1.7e-19) t_2 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -6.2e-18) {
		tmp = t_3;
	} else if (j <= -4.2e-61) {
		tmp = t_1;
	} else if (j <= -1.35e-123) {
		tmp = c * ((t * j) - (z * b));
	} else if (j <= -4.8e-225) {
		tmp = t_2;
	} else if (j <= -1.16e-296) {
		tmp = t_1;
	} else if (j <= 1.7e-19) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = b * ((a * i) - (z * c))
    t_3 = j * ((t * c) - (y * i))
    if (j <= (-6.2d-18)) then
        tmp = t_3
    else if (j <= (-4.2d-61)) then
        tmp = t_1
    else if (j <= (-1.35d-123)) then
        tmp = c * ((t * j) - (z * b))
    else if (j <= (-4.8d-225)) then
        tmp = t_2
    else if (j <= (-1.16d-296)) then
        tmp = t_1
    else if (j <= 1.7d-19) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -6.2e-18) {
		tmp = t_3;
	} else if (j <= -4.2e-61) {
		tmp = t_1;
	} else if (j <= -1.35e-123) {
		tmp = c * ((t * j) - (z * b));
	} else if (j <= -4.8e-225) {
		tmp = t_2;
	} else if (j <= -1.16e-296) {
		tmp = t_1;
	} else if (j <= 1.7e-19) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = b * ((a * i) - (z * c))
	t_3 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -6.2e-18:
		tmp = t_3
	elif j <= -4.2e-61:
		tmp = t_1
	elif j <= -1.35e-123:
		tmp = c * ((t * j) - (z * b))
	elif j <= -4.8e-225:
		tmp = t_2
	elif j <= -1.16e-296:
		tmp = t_1
	elif j <= 1.7e-19:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_3 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -6.2e-18)
		tmp = t_3;
	elseif (j <= -4.2e-61)
		tmp = t_1;
	elseif (j <= -1.35e-123)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (j <= -4.8e-225)
		tmp = t_2;
	elseif (j <= -1.16e-296)
		tmp = t_1;
	elseif (j <= 1.7e-19)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = b * ((a * i) - (z * c));
	t_3 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -6.2e-18)
		tmp = t_3;
	elseif (j <= -4.2e-61)
		tmp = t_1;
	elseif (j <= -1.35e-123)
		tmp = c * ((t * j) - (z * b));
	elseif (j <= -4.8e-225)
		tmp = t_2;
	elseif (j <= -1.16e-296)
		tmp = t_1;
	elseif (j <= 1.7e-19)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $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[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -6.2e-18], t$95$3, If[LessEqual[j, -4.2e-61], t$95$1, If[LessEqual[j, -1.35e-123], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -4.8e-225], t$95$2, If[LessEqual[j, -1.16e-296], t$95$1, If[LessEqual[j, 1.7e-19], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -6.20000000000000014e-18 or 1.7000000000000001e-19 < j

   1. Initial program 72.8%

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

   2. Taylor expanded in j around inf 66.5%

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

   if -6.20000000000000014e-18 < j < -4.1999999999999998e-61 or -4.79999999999999992e-225 < j < -1.15999999999999996e-296

   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. Taylor expanded in x around inf 74.7%

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

      1. *-commutative 74.7%

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

   4. Simplified 74.7%

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

   if -4.1999999999999998e-61 < j < -1.35e-123

   1. Initial program 63.4%

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

   2. Taylor expanded in c around inf 69.7%

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

   if -1.35e-123 < j < -4.79999999999999992e-225 or -1.15999999999999996e-296 < j < 1.7000000000000001e-19

   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. Taylor expanded in b around inf 51.3%

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

      1. *-commutative 51.3%

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

   4. Simplified 51.3%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -6.2 \cdot 10^{-18}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -4.2 \cdot 10^{-61}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq -1.35 \cdot 10^{-123}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq -4.8 \cdot 10^{-225}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -1.16 \cdot 10^{-296}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{-19}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 11: 52.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -58000000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -5.8 \cdot 10^{-236}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq -6.8 \cdot 10^{-298}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 6.5 \cdot 10^{-87}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 7 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))) (t_2 (* j (- (* t c) (* y i)))))
   (if (<= j -58000000000000.0)
     t_2
     (if (<= j -5.8e-236)
       (* z (- (* x y) (* b c)))
       (if (<= j -6.8e-298)
         t_1
         (if (<= j 6.5e-87)
           (* b (- (* a i) (* z c)))
           (if (<= j 7e+31) 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) - (x * t));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -58000000000000.0) {
		tmp = t_2;
	} else if (j <= -5.8e-236) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= -6.8e-298) {
		tmp = t_1;
	} else if (j <= 6.5e-87) {
		tmp = b * ((a * i) - (z * c));
	} else if (j <= 7e+31) {
		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) - (x * t))
    t_2 = j * ((t * c) - (y * i))
    if (j <= (-58000000000000.0d0)) then
        tmp = t_2
    else if (j <= (-5.8d-236)) then
        tmp = z * ((x * y) - (b * c))
    else if (j <= (-6.8d-298)) then
        tmp = t_1
    else if (j <= 6.5d-87) then
        tmp = b * ((a * i) - (z * c))
    else if (j <= 7d+31) 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) - (x * t));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -58000000000000.0) {
		tmp = t_2;
	} else if (j <= -5.8e-236) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= -6.8e-298) {
		tmp = t_1;
	} else if (j <= 6.5e-87) {
		tmp = b * ((a * i) - (z * c));
	} else if (j <= 7e+31) {
		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) - (x * t))
	t_2 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -58000000000000.0:
		tmp = t_2
	elif j <= -5.8e-236:
		tmp = z * ((x * y) - (b * c))
	elif j <= -6.8e-298:
		tmp = t_1
	elif j <= 6.5e-87:
		tmp = b * ((a * i) - (z * c))
	elif j <= 7e+31:
		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(Float64(b * i) - Float64(x * t)))
	t_2 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -58000000000000.0)
		tmp = t_2;
	elseif (j <= -5.8e-236)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (j <= -6.8e-298)
		tmp = t_1;
	elseif (j <= 6.5e-87)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (j <= 7e+31)
		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) - (x * t));
	t_2 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -58000000000000.0)
		tmp = t_2;
	elseif (j <= -5.8e-236)
		tmp = z * ((x * y) - (b * c));
	elseif (j <= -6.8e-298)
		tmp = t_1;
	elseif (j <= 6.5e-87)
		tmp = b * ((a * i) - (z * c));
	elseif (j <= 7e+31)
		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[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -58000000000000.0], t$95$2, If[LessEqual[j, -5.8e-236], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -6.8e-298], t$95$1, If[LessEqual[j, 6.5e-87], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7e+31], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -5.8e13 or 7e31 < j

   1. Initial program 71.5%

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

   2. Taylor expanded in j around inf 71.0%

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

   if -5.8e13 < j < -5.8e-236

   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. Taylor expanded in z around inf 56.1%

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

      1. *-commutative 56.1%

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

      2. *-commutative 56.1%

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

   4. Simplified 56.1%

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

   if -5.8e-236 < j < -6.8e-298 or 6.5000000000000003e-87 < j < 7e31

   1. Initial program 73.6%

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

   2. Taylor expanded in a around -inf 59.6%

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

      1. associate-*r* 59.6%

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

      2. neg-mul-1 59.6%

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

      3. *-commutative 59.6%

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

   4. Simplified 59.6%

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

   if -6.8e-298 < j < 6.5000000000000003e-87

   1. Initial program 60.8%

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

   2. Taylor expanded in b around inf 55.5%

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

      1. *-commutative 55.5%

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

   4. Simplified 55.5%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -58000000000000:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -5.8 \cdot 10^{-236}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq -6.8 \cdot 10^{-298}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;j \leq 6.5 \cdot 10^{-87}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 7 \cdot 10^{+31}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 12: 60.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.35 \cdot 10^{+35} \lor \neg \left(j \leq 8.5 \cdot 10^{+31}\right):\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - c \cdot \left(z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -1.35e+35) (not (<= j 8.5e+31)))
   (* j (- (* t c) (* y i)))
   (- (* x (- (* y z) (* t a))) (* c (* z b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -1.35e+35) || !(j <= 8.5e+31)) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = (x * ((y * z) - (t * a))) - (c * (z * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((j <= (-1.35d+35)) .or. (.not. (j <= 8.5d+31))) then
        tmp = j * ((t * c) - (y * i))
    else
        tmp = (x * ((y * z) - (t * a))) - (c * (z * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -1.35e+35) || !(j <= 8.5e+31)) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = (x * ((y * z) - (t * a))) - (c * (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -1.35e+35) or not (j <= 8.5e+31):
		tmp = j * ((t * c) - (y * i))
	else:
		tmp = (x * ((y * z) - (t * a))) - (c * (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -1.35e+35) || !(j <= 8.5e+31))
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	else
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(c * Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -1.35e+35) || ~((j <= 8.5e+31)))
		tmp = j * ((t * c) - (y * i));
	else
		tmp = (x * ((y * z) - (t * a))) - (c * (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -1.35e+35], N[Not[LessEqual[j, 8.5e+31]], $MachinePrecision]], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -1.35000000000000001e35 or 8.49999999999999947e31 < j

   1. Initial program 70.5%

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

   2. Taylor expanded in j around inf 71.6%

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

   if -1.35000000000000001e35 < j < 8.49999999999999947e31

   1. Initial program 71.5%

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

      1. *-commutative 71.5%

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

      2. *-commutative 71.5%

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

      3. flip-- 50.7%

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

      4. clear-num 50.7%

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

      5. un-div-inv 50.7%

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

      6. clear-num 50.7%

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

      7. flip-- 71.6%

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

      8. *-commutative 71.6%

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

      9. *-commutative 71.6%

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

   3. Applied egg-rr 71.6%

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

   4. Taylor expanded in c around inf 61.0%

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

   5. Taylor expanded in j around 0 58.5%

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

      1. associate-*r* 60.4%

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

      2. *-commutative 60.4%

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

      3. associate-*r* 60.3%

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

      4. *-commutative 60.3%

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

      5. *-commutative 60.3%

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

   7. Simplified 60.3%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.35 \cdot 10^{+35} \lor \neg \left(j \leq 8.5 \cdot 10^{+31}\right):\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - c \cdot \left(z \cdot b\right)\\ \end{array} \]

Alternative 13: 59.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -160000 \lor \neg \left(j \leq 2.2 \cdot 10^{+32}\right):\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -160000.0) (not (<= j 2.2e+32)))
   (* j (- (* t c) (* y i)))
   (- (* b (- (* a i) (* z c))) (* x (* t a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -160000.0) || !(j <= 2.2e+32)) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = (b * ((a * i) - (z * c))) - (x * (t * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((j <= (-160000.0d0)) .or. (.not. (j <= 2.2d+32))) then
        tmp = j * ((t * c) - (y * i))
    else
        tmp = (b * ((a * i) - (z * c))) - (x * (t * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -160000.0) || !(j <= 2.2e+32)) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = (b * ((a * i) - (z * c))) - (x * (t * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -160000.0) or not (j <= 2.2e+32):
		tmp = j * ((t * c) - (y * i))
	else:
		tmp = (b * ((a * i) - (z * c))) - (x * (t * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -160000.0) || !(j <= 2.2e+32))
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	else
		tmp = Float64(Float64(b * Float64(Float64(a * i) - Float64(z * c))) - Float64(x * Float64(t * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -160000.0) || ~((j <= 2.2e+32)))
		tmp = j * ((t * c) - (y * i));
	else
		tmp = (b * ((a * i) - (z * c))) - (x * (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -160000.0], N[Not[LessEqual[j, 2.2e+32]], $MachinePrecision]], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -1.6e5 or 2.20000000000000001e32 < j

   1. Initial program 71.5%

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

   2. Taylor expanded in j around inf 71.0%

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

   if -1.6e5 < j < 2.20000000000000001e32

   1. Initial program 70.7%

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

   2. Taylor expanded in y around 0 66.5%

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

   3. Taylor expanded in j around 0 65.1%

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

      1. associate-*r* 65.1%

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

      2. neg-mul-1 65.1%

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

      3. *-commutative 65.1%

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

      4. *-commutative 65.1%

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

      5. associate-*l* 62.6%

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

      6. *-commutative 62.6%

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

      7. *-commutative 62.6%

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

      8. *-commutative 62.6%

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

   5. Simplified 62.6%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -160000 \lor \neg \left(j \leq 2.2 \cdot 10^{+32}\right):\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a\right)\\ \end{array} \]

Alternative 14: 60.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -4.8 \cdot 10^{+14} \lor \neg \left(j \leq 2.25 \cdot 10^{+32}\right):\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - a \cdot \left(x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -4.8e+14) (not (<= j 2.25e+32)))
   (* j (- (* t c) (* y i)))
   (- (* b (- (* a i) (* z c))) (* a (* x t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -4.8e+14) || !(j <= 2.25e+32)) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = (b * ((a * i) - (z * c))) - (a * (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((j <= (-4.8d+14)) .or. (.not. (j <= 2.25d+32))) then
        tmp = j * ((t * c) - (y * i))
    else
        tmp = (b * ((a * i) - (z * c))) - (a * (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -4.8e+14) || !(j <= 2.25e+32)) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = (b * ((a * i) - (z * c))) - (a * (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -4.8e+14) or not (j <= 2.25e+32):
		tmp = j * ((t * c) - (y * i))
	else:
		tmp = (b * ((a * i) - (z * c))) - (a * (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -4.8e+14) || !(j <= 2.25e+32))
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	else
		tmp = Float64(Float64(b * Float64(Float64(a * i) - Float64(z * c))) - Float64(a * Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -4.8e+14) || ~((j <= 2.25e+32)))
		tmp = j * ((t * c) - (y * i));
	else
		tmp = (b * ((a * i) - (z * c))) - (a * (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -4.8e+14], N[Not[LessEqual[j, 2.25e+32]], $MachinePrecision]], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -4.8e14 or 2.2500000000000002e32 < j

   1. Initial program 71.5%

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

   2. Taylor expanded in j around inf 71.0%

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

   if -4.8e14 < j < 2.2500000000000002e32

   1. Initial program 70.7%

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

   2. Taylor expanded in y around 0 66.5%

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

   3. Taylor expanded in j around 0 65.1%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4.8 \cdot 10^{+14} \lor \neg \left(j \leq 2.25 \cdot 10^{+32}\right):\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - a \cdot \left(x \cdot t\right)\\ \end{array} \]

Alternative 15: 52.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -23:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.76 \cdot 10^{-236}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq -5.1 \cdot 10^{-297}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 4.8 \cdot 10^{-20}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))))
   (if (<= j -23.0)
     t_1
     (if (<= j -1.76e-236)
       (* z (- (* x y) (* b c)))
       (if (<= j -5.1e-297)
         (* x (- (* y z) (* t a)))
         (if (<= j 4.8e-20) (* 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 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -23.0) {
		tmp = t_1;
	} else if (j <= -1.76e-236) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= -5.1e-297) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= 4.8e-20) {
		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 = j * ((t * c) - (y * i))
    if (j <= (-23.0d0)) then
        tmp = t_1
    else if (j <= (-1.76d-236)) then
        tmp = z * ((x * y) - (b * c))
    else if (j <= (-5.1d-297)) then
        tmp = x * ((y * z) - (t * a))
    else if (j <= 4.8d-20) 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 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -23.0) {
		tmp = t_1;
	} else if (j <= -1.76e-236) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= -5.1e-297) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= 4.8e-20) {
		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 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -23.0:
		tmp = t_1
	elif j <= -1.76e-236:
		tmp = z * ((x * y) - (b * c))
	elif j <= -5.1e-297:
		tmp = x * ((y * z) - (t * a))
	elif j <= 4.8e-20:
		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(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -23.0)
		tmp = t_1;
	elseif (j <= -1.76e-236)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (j <= -5.1e-297)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (j <= 4.8e-20)
		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 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -23.0)
		tmp = t_1;
	elseif (j <= -1.76e-236)
		tmp = z * ((x * y) - (b * c));
	elseif (j <= -5.1e-297)
		tmp = x * ((y * z) - (t * a));
	elseif (j <= 4.8e-20)
		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[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -23.0], t$95$1, If[LessEqual[j, -1.76e-236], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -5.1e-297], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.8e-20], 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 j < -23 or 4.79999999999999986e-20 < j

   1. Initial program 72.2%

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

   2. Taylor expanded in j around inf 67.2%

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

   if -23 < j < -1.75999999999999998e-236

   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. Taylor expanded in z around inf 56.1%

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

      1. *-commutative 56.1%

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

      2. *-commutative 56.1%

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

   4. Simplified 56.1%

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

   if -1.75999999999999998e-236 < j < -5.10000000000000008e-297

   1. Initial program 77.4%

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

   2. Taylor expanded in x around inf 77.7%

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

      1. *-commutative 77.7%

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

   4. Simplified 77.7%

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

   if -5.10000000000000008e-297 < j < 4.79999999999999986e-20

   1. Initial program 62.5%

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

   2. Taylor expanded in b around inf 50.2%

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

      1. *-commutative 50.2%

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

   4. Simplified 50.2%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -23:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -1.76 \cdot 10^{-236}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq -5.1 \cdot 10^{-297}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 4.8 \cdot 10^{-20}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 16: 41.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -2.1 \cdot 10^{+25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-251}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+20}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= b -2.1e+25)
     t_1
     (if (<= b 6.5e-251)
       (* (* t a) (- x))
       (if (<= b 4.5e+20) (* i (* y (- j))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -2.1e+25) {
		tmp = t_1;
	} else if (b <= 6.5e-251) {
		tmp = (t * a) * -x;
	} else if (b <= 4.5e+20) {
		tmp = i * (y * -j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    if (b <= (-2.1d+25)) then
        tmp = t_1
    else if (b <= 6.5d-251) then
        tmp = (t * a) * -x
    else if (b <= 4.5d+20) then
        tmp = i * (y * -j)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -2.1e+25) {
		tmp = t_1;
	} else if (b <= 6.5e-251) {
		tmp = (t * a) * -x;
	} else if (b <= 4.5e+20) {
		tmp = i * (y * -j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -2.1e+25:
		tmp = t_1
	elif b <= 6.5e-251:
		tmp = (t * a) * -x
	elif b <= 4.5e+20:
		tmp = i * (y * -j)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -2.1e+25)
		tmp = t_1;
	elseif (b <= 6.5e-251)
		tmp = Float64(Float64(t * a) * Float64(-x));
	elseif (b <= 4.5e+20)
		tmp = Float64(i * Float64(y * Float64(-j)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -2.1e+25)
		tmp = t_1;
	elseif (b <= 6.5e-251)
		tmp = (t * a) * -x;
	elseif (b <= 4.5e+20)
		tmp = i * (y * -j);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.1e+25], t$95$1, If[LessEqual[b, 6.5e-251], N[(N[(t * a), $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[b, 4.5e+20], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.0999999999999999e25 or 4.5e20 < b

   1. Initial program 71.4%

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

   2. Taylor expanded in b around inf 62.4%

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

      1. *-commutative 62.4%

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

   4. Simplified 62.4%

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

   if -2.0999999999999999e25 < b < 6.5000000000000002e-251

   1. Initial program 71.5%

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

   2. Taylor expanded in y around 0 51.8%

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

   3. Taylor expanded in x around inf 37.3%

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

      1. associate-*r* 37.3%

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

      2. neg-mul-1 37.3%

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

      3. *-commutative 37.3%

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

      4. *-commutative 37.3%

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

      5. associate-*l* 38.5%

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

   5. Simplified 38.5%

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

   if 6.5000000000000002e-251 < b < 4.5e20

   1. Initial program 69.5%

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

      1. *-commutative 69.5%

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

      2. *-commutative 69.5%

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

      3. flip-- 41.2%

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

      4. clear-num 41.2%

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

      5. un-div-inv 41.2%

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

      6. clear-num 41.2%

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

      7. flip-- 69.6%

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

      8. *-commutative 69.6%

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

      9. *-commutative 69.6%

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

   3. Applied egg-rr 69.6%

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

   4. Taylor expanded in c around inf 68.9%

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

   5. Taylor expanded in i around inf 38.2%

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

      1. associate-*r* 38.2%

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

      2. neg-mul-1 38.2%

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

      3. *-commutative 38.2%

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

   7. Simplified 38.2%

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

4. Final simplification 50.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.1 \cdot 10^{+25}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-251}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+20}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 17: 51.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -2.9 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -1.7 \cdot 10^{-240}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;i \leq 1.92 \cdot 10^{-72}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* a b) (* y j)))))
   (if (<= i -2.9e-7)
     t_1
     (if (<= i -1.7e-240)
       (* t (- (* c j) (* x a)))
       (if (<= i 1.92e-72) (* c (- (* t j) (* z b))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -2.9e-7) {
		tmp = t_1;
	} else if (i <= -1.7e-240) {
		tmp = t * ((c * j) - (x * a));
	} else if (i <= 1.92e-72) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * ((a * b) - (y * j))
    if (i <= (-2.9d-7)) then
        tmp = t_1
    else if (i <= (-1.7d-240)) then
        tmp = t * ((c * j) - (x * a))
    else if (i <= 1.92d-72) then
        tmp = c * ((t * j) - (z * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -2.9e-7) {
		tmp = t_1;
	} else if (i <= -1.7e-240) {
		tmp = t * ((c * j) - (x * a));
	} else if (i <= 1.92e-72) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((a * b) - (y * j))
	tmp = 0
	if i <= -2.9e-7:
		tmp = t_1
	elif i <= -1.7e-240:
		tmp = t * ((c * j) - (x * a))
	elif i <= 1.92e-72:
		tmp = c * ((t * j) - (z * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -2.9e-7)
		tmp = t_1;
	elseif (i <= -1.7e-240)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (i <= 1.92e-72)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((a * b) - (y * j));
	tmp = 0.0;
	if (i <= -2.9e-7)
		tmp = t_1;
	elseif (i <= -1.7e-240)
		tmp = t * ((c * j) - (x * a));
	elseif (i <= 1.92e-72)
		tmp = c * ((t * j) - (z * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.9e-7], t$95$1, If[LessEqual[i, -1.7e-240], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.92e-72], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if i < -2.8999999999999998e-7 or 1.92000000000000004e-72 < i

   1. Initial program 64.5%

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

   2. Taylor expanded in i around -inf 60.6%

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

      1. associate-*r* 60.6%

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

      2. mul-1-neg 60.6%

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

      3. *-commutative 60.6%

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

   4. Simplified 60.6%

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

   if -2.8999999999999998e-7 < i < -1.69999999999999995e-240

   1. Initial program 84.6%

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

   2. Taylor expanded in t around inf 57.0%

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

   if -1.69999999999999995e-240 < i < 1.92000000000000004e-72

   1. Initial program 74.5%

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

   2. Taylor expanded in c around inf 64.9%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.9 \cdot 10^{-7}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -1.7 \cdot 10^{-240}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;i \leq 1.92 \cdot 10^{-72}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \]

Alternative 18: 52.1% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -7.5 \cdot 10^{-48} \lor \neg \left(j \leq 3 \cdot 10^{-19}\right):\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -7.5e-48) (not (<= j 3e-19)))
   (* j (- (* t c) (* y i)))
   (* 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 ((j <= -7.5e-48) || !(j <= 3e-19)) {
		tmp = j * ((t * c) - (y * i));
	} 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 ((j <= (-7.5d-48)) .or. (.not. (j <= 3d-19))) then
        tmp = j * ((t * c) - (y * i))
    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 ((j <= -7.5e-48) || !(j <= 3e-19)) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = b * ((a * i) - (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -7.5e-48) or not (j <= 3e-19):
		tmp = j * ((t * c) - (y * i))
	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 ((j <= -7.5e-48) || !(j <= 3e-19))
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	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 ((j <= -7.5e-48) || ~((j <= 3e-19)))
		tmp = j * ((t * c) - (y * i));
	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[j, -7.5e-48], N[Not[LessEqual[j, 3e-19]], $MachinePrecision]], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $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 j < -7.50000000000000042e-48 or 2.99999999999999993e-19 < j

   1. Initial program 72.6%

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

   2. Taylor expanded in j around inf 65.2%

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

   if -7.50000000000000042e-48 < j < 2.99999999999999993e-19

   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. Taylor expanded in b around inf 50.4%

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

      1. *-commutative 50.4%

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

   4. Simplified 50.4%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -7.5 \cdot 10^{-48} \lor \neg \left(j \leq 3 \cdot 10^{-19}\right):\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 19: 29.7% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(-z \cdot b\right)\\ \mathbf{if}\;c \leq -1 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.6 \cdot 10^{-114}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 3.6 \cdot 10^{+72}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* z b)))))
   (if (<= c -1e-19)
     t_1
     (if (<= c -1.6e-114)
       (* z (* x y))
       (if (<= c 3.6e+72) (* 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 = c * -(z * b);
	double tmp;
	if (c <= -1e-19) {
		tmp = t_1;
	} else if (c <= -1.6e-114) {
		tmp = z * (x * y);
	} else if (c <= 3.6e+72) {
		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 = c * -(z * b)
    if (c <= (-1d-19)) then
        tmp = t_1
    else if (c <= (-1.6d-114)) then
        tmp = z * (x * y)
    else if (c <= 3.6d+72) 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 = c * -(z * b);
	double tmp;
	if (c <= -1e-19) {
		tmp = t_1;
	} else if (c <= -1.6e-114) {
		tmp = z * (x * y);
	} else if (c <= 3.6e+72) {
		tmp = i * (a * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * -(z * b)
	tmp = 0
	if c <= -1e-19:
		tmp = t_1
	elif c <= -1.6e-114:
		tmp = z * (x * y)
	elif c <= 3.6e+72:
		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(c * Float64(-Float64(z * b)))
	tmp = 0.0
	if (c <= -1e-19)
		tmp = t_1;
	elseif (c <= -1.6e-114)
		tmp = Float64(z * Float64(x * y));
	elseif (c <= 3.6e+72)
		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 = c * -(z * b);
	tmp = 0.0;
	if (c <= -1e-19)
		tmp = t_1;
	elseif (c <= -1.6e-114)
		tmp = z * (x * y);
	elseif (c <= 3.6e+72)
		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[(c * (-N[(z * b), $MachinePrecision])), $MachinePrecision]}, If[LessEqual[c, -1e-19], t$95$1, If[LessEqual[c, -1.6e-114], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.6e+72], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -9.9999999999999998e-20 or 3.60000000000000035e72 < c

   1. Initial program 62.6%

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

   2. Taylor expanded in z around inf 45.4%

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

      1. *-commutative 45.4%

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

      2. *-commutative 45.4%

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

   4. Simplified 45.4%

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

   5. Taylor expanded in y around 0 37.7%

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

      1. *-commutative 37.7%

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

      2. mul-1-neg 37.7%

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

      3. distribute-rgt-neg-in 37.7%

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

   7. Simplified 37.7%

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

   8. Taylor expanded in z around 0 33.5%

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

      1. mul-1-neg 33.5%

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

      2. associate-*r* 37.7%

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

      3. *-commutative 37.7%

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

      4. associate-*r* 37.1%

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

      5. *-commutative 37.1%

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

      6. distribute-lft-neg-out 37.1%

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

      7. *-commutative 37.1%

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

      8. distribute-lft-neg-in 37.1%

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

      9. *-commutative 37.1%

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

   10. Simplified 37.1%

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

   if -9.9999999999999998e-20 < c < -1.6000000000000001e-114

   1. Initial program 89.5%

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

   2. Taylor expanded in z around inf 48.8%

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

      1. *-commutative 48.8%

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

      2. *-commutative 48.8%

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

   4. Simplified 48.8%

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

   5. Taylor expanded in y around inf 48.9%

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

   if -1.6000000000000001e-114 < c < 3.60000000000000035e72

   1. Initial program 77.6%

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

   2. Taylor expanded in b around inf 39.1%

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

      1. *-commutative 39.1%

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

   4. Simplified 39.1%

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

   5. Taylor expanded in i around inf 31.3%

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

   6. Taylor expanded in b around 0 30.5%

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

      1. associate-*r* 31.5%

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

      2. *-commutative 31.5%

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

   8. Simplified 31.5%

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

4. Final simplification 35.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1 \cdot 10^{-19}:\\ \;\;\;\;c \cdot \left(-z \cdot b\right)\\ \mathbf{elif}\;c \leq -1.6 \cdot 10^{-114}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 3.6 \cdot 10^{+72}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(-z \cdot b\right)\\ \end{array} \]

Alternative 20: 29.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+27}:\\ \;\;\;\;c \cdot \left(-z \cdot b\right)\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{-251}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+102}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -7.5e+27)
   (* c (- (* z b)))
   (if (<= b 6.8e-251)
     (* (* t a) (- x))
     (if (<= b 2.5e+102) (* i (* y (- j))) (* 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 (b <= -7.5e+27) {
		tmp = c * -(z * b);
	} else if (b <= 6.8e-251) {
		tmp = (t * a) * -x;
	} else if (b <= 2.5e+102) {
		tmp = i * (y * -j);
	} 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 (b <= (-7.5d+27)) then
        tmp = c * -(z * b)
    else if (b <= 6.8d-251) then
        tmp = (t * a) * -x
    else if (b <= 2.5d+102) then
        tmp = i * (y * -j)
    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 (b <= -7.5e+27) {
		tmp = c * -(z * b);
	} else if (b <= 6.8e-251) {
		tmp = (t * a) * -x;
	} else if (b <= 2.5e+102) {
		tmp = i * (y * -j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -7.5e+27:
		tmp = c * -(z * b)
	elif b <= 6.8e-251:
		tmp = (t * a) * -x
	elif b <= 2.5e+102:
		tmp = i * (y * -j)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -7.5e+27)
		tmp = Float64(c * Float64(-Float64(z * b)));
	elseif (b <= 6.8e-251)
		tmp = Float64(Float64(t * a) * Float64(-x));
	elseif (b <= 2.5e+102)
		tmp = Float64(i * Float64(y * Float64(-j)));
	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 (b <= -7.5e+27)
		tmp = c * -(z * b);
	elseif (b <= 6.8e-251)
		tmp = (t * a) * -x;
	elseif (b <= 2.5e+102)
		tmp = i * (y * -j);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -7.5e+27], N[(c * (-N[(z * b), $MachinePrecision])), $MachinePrecision], If[LessEqual[b, 6.8e-251], N[(N[(t * a), $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[b, 2.5e+102], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -7.5000000000000002e27

   1. Initial program 71.4%

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

   2. Taylor expanded in z around inf 47.7%

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

      1. *-commutative 47.7%

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

      2. *-commutative 47.7%

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

   4. Simplified 47.7%

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

   5. Taylor expanded in y around 0 36.6%

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

      1. *-commutative 36.6%

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

      2. mul-1-neg 36.6%

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

      3. distribute-rgt-neg-in 36.6%

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

   7. Simplified 36.6%

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

   8. Taylor expanded in z around 0 38.0%

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

      1. mul-1-neg 38.0%

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

      2. associate-*r* 36.6%

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

      3. *-commutative 36.6%

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

      4. associate-*r* 41.9%

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

      5. *-commutative 41.9%

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

      6. distribute-lft-neg-out 41.9%

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

      7. *-commutative 41.9%

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

      8. distribute-lft-neg-in 41.9%

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

      9. *-commutative 41.9%

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

   10. Simplified 41.9%

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

   if -7.5000000000000002e27 < b < 6.80000000000000034e-251

   1. Initial program 70.8%

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

   2. Taylor expanded in y around 0 51.2%

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

   3. Taylor expanded in x around inf 36.9%

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

      1. associate-*r* 36.9%

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

      2. neg-mul-1 36.9%

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

      3. *-commutative 36.9%

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

      4. *-commutative 36.9%

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

      5. associate-*l* 38.0%

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

   5. Simplified 38.0%

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

   if 6.80000000000000034e-251 < b < 2.5e102

   1. Initial program 65.5%

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

      1. *-commutative 65.5%

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

      2. *-commutative 65.5%

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

      3. flip-- 41.5%

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

      4. clear-num 41.5%

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

      5. un-div-inv 41.5%

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

      6. clear-num 41.5%

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

      7. flip-- 65.5%

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

      8. *-commutative 65.5%

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

      9. *-commutative 65.5%

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

   3. Applied egg-rr 65.5%

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

   4. Taylor expanded in c around inf 62.2%

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

   5. Taylor expanded in i around inf 34.9%

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

      1. associate-*r* 34.9%

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

      2. neg-mul-1 34.9%

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

      3. *-commutative 34.9%

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

   7. Simplified 34.9%

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

   if 2.5e102 < b

   1. Initial program 80.2%

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

   2. Taylor expanded in b around inf 66.5%

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

      1. *-commutative 66.5%

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

   4. Simplified 66.5%

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

   5. Taylor expanded in i around inf 44.4%

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

   6. Taylor expanded in b around 0 44.5%

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

4. Final simplification 39.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+27}:\\ \;\;\;\;c \cdot \left(-z \cdot b\right)\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{-251}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+102}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 21: 29.2% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.8 \cdot 10^{+27}:\\ \;\;\;\;c \cdot \left(-z \cdot b\right)\\ \mathbf{elif}\;b \leq 3600000000000:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -4.8e+27)
   (* c (- (* z b)))
   (if (<= b 3600000000000.0) (* (* t a) (- x)) (* 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 (b <= -4.8e+27) {
		tmp = c * -(z * b);
	} else if (b <= 3600000000000.0) {
		tmp = (t * a) * -x;
	} 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 (b <= (-4.8d+27)) then
        tmp = c * -(z * b)
    else if (b <= 3600000000000.0d0) then
        tmp = (t * a) * -x
    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 (b <= -4.8e+27) {
		tmp = c * -(z * b);
	} else if (b <= 3600000000000.0) {
		tmp = (t * a) * -x;
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -4.8e+27:
		tmp = c * -(z * b)
	elif b <= 3600000000000.0:
		tmp = (t * a) * -x
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -4.8e+27)
		tmp = Float64(c * Float64(-Float64(z * b)));
	elseif (b <= 3600000000000.0)
		tmp = Float64(Float64(t * a) * Float64(-x));
	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 (b <= -4.8e+27)
		tmp = c * -(z * b);
	elseif (b <= 3600000000000.0)
		tmp = (t * a) * -x;
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -4.8e+27], N[(c * (-N[(z * b), $MachinePrecision])), $MachinePrecision], If[LessEqual[b, 3600000000000.0], N[(N[(t * a), $MachinePrecision] * (-x)), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.79999999999999995e27

   1. Initial program 71.4%

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

   2. Taylor expanded in z around inf 47.7%

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

      1. *-commutative 47.7%

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

      2. *-commutative 47.7%

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

   4. Simplified 47.7%

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

   5. Taylor expanded in y around 0 36.6%

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

      1. *-commutative 36.6%

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

      2. mul-1-neg 36.6%

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

      3. distribute-rgt-neg-in 36.6%

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

   7. Simplified 36.6%

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

   8. Taylor expanded in z around 0 38.0%

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

      1. mul-1-neg 38.0%

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

      2. associate-*r* 36.6%

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

      3. *-commutative 36.6%

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

      4. associate-*r* 41.9%

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

      5. *-commutative 41.9%

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

      6. distribute-lft-neg-out 41.9%

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

      7. *-commutative 41.9%

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

      8. distribute-lft-neg-in 41.9%

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

      9. *-commutative 41.9%

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

   10. Simplified 41.9%

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

   if -4.79999999999999995e27 < b < 3.6e12

   1. Initial program 69.6%

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

   2. Taylor expanded in y around 0 46.9%

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

   3. Taylor expanded in x around inf 31.0%

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

      1. associate-*r* 31.0%

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

      2. neg-mul-1 31.0%

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

      3. *-commutative 31.0%

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

      4. *-commutative 31.0%

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

      5. associate-*l* 32.8%

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

   5. Simplified 32.8%

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

   if 3.6e12 < b

   1. Initial program 74.0%

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

   2. Taylor expanded in b around inf 59.1%

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

      1. *-commutative 59.1%

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

   4. Simplified 59.1%

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

   5. Taylor expanded in i around inf 35.2%

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

   6. Taylor expanded in b around 0 36.9%

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

4. Final simplification 36.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.8 \cdot 10^{+27}:\\ \;\;\;\;c \cdot \left(-z \cdot b\right)\\ \mathbf{elif}\;b \leq 3600000000000:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 22: 30.4% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+39} \lor \neg \left(z \leq 19\right):\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= z -5.6e+39) (not (<= z 19.0))) (* y (* x z)) (* 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 ((z <= -5.6e+39) || !(z <= 19.0)) {
		tmp = y * (x * z);
	} 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 ((z <= (-5.6d+39)) .or. (.not. (z <= 19.0d0))) then
        tmp = y * (x * z)
    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 ((z <= -5.6e+39) || !(z <= 19.0)) {
		tmp = y * (x * z);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (z <= -5.6e+39) or not (z <= 19.0):
		tmp = y * (x * z)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((z <= -5.6e+39) || !(z <= 19.0))
		tmp = Float64(y * Float64(x * z));
	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 ((z <= -5.6e+39) || ~((z <= 19.0)))
		tmp = y * (x * z);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[z, -5.6e+39], N[Not[LessEqual[z, 19.0]], $MachinePrecision]], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.60000000000000003e39 or 19 < z

   1. Initial program 56.9%

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

   2. Taylor expanded in y around inf 40.7%

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

   3. Taylor expanded in i around 0 31.4%

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

   if -5.60000000000000003e39 < z < 19

   1. Initial program 81.1%

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

   2. Taylor expanded in b around inf 35.7%

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

      1. *-commutative 35.7%

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

   4. Simplified 35.7%

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

   5. Taylor expanded in i around inf 26.8%

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

   6. Taylor expanded in b around 0 28.7%

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

4. Final simplification 29.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+39} \lor \neg \left(z \leq 19\right):\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 23: 30.4% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+33}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;z \leq 0.0029:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -5.2e+33)
   (* (* z c) (- b))
   (if (<= z 0.0029) (* a (* b i)) (* y (* x z)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -5.2e+33) {
		tmp = (z * c) * -b;
	} else if (z <= 0.0029) {
		tmp = a * (b * i);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-5.2d+33)) then
        tmp = (z * c) * -b
    else if (z <= 0.0029d0) then
        tmp = a * (b * i)
    else
        tmp = y * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -5.2e+33) {
		tmp = (z * c) * -b;
	} else if (z <= 0.0029) {
		tmp = a * (b * i);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -5.2e+33:
		tmp = (z * c) * -b
	elif z <= 0.0029:
		tmp = a * (b * i)
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -5.2e+33)
		tmp = Float64(Float64(z * c) * Float64(-b));
	elseif (z <= 0.0029)
		tmp = Float64(a * Float64(b * i));
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -5.2e+33)
		tmp = (z * c) * -b;
	elseif (z <= 0.0029)
		tmp = a * (b * i);
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -5.2e+33], N[(N[(z * c), $MachinePrecision] * (-b)), $MachinePrecision], If[LessEqual[z, 0.0029], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.1999999999999995e33

   1. Initial program 61.3%

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

   2. Taylor expanded in b around inf 48.6%

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

      1. *-commutative 48.6%

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

   4. Simplified 48.6%

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

   5. Taylor expanded in i around 0 43.0%

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

      1. mul-1-neg 43.0%

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

      2. *-commutative 43.0%

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

      3. distribute-rgt-neg-out 43.0%

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

   7. Simplified 43.0%

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

   if -5.1999999999999995e33 < z < 0.0029

   1. Initial program 81.0%

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

   2. Taylor expanded in b around inf 35.3%

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

      1. *-commutative 35.3%

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

   4. Simplified 35.3%

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

   5. Taylor expanded in i around inf 26.9%

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

   6. Taylor expanded in b around 0 28.9%

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

   if 0.0029 < z

   1. Initial program 53.7%

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

   2. Taylor expanded in y around inf 52.4%

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

   3. Taylor expanded in i around 0 41.8%

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

4. Final simplification 34.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+33}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;z \leq 0.0029:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 24: 26.1% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 68:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z 68.0) (* a (* b i)) (* x (* y z))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= 68.0) {
		tmp = a * (b * i);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= 68.0d0) then
        tmp = a * (b * i)
    else
        tmp = x * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= 68.0) {
		tmp = a * (b * i);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= 68.0:
		tmp = a * (b * i)
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= 68.0)
		tmp = Float64(a * Float64(b * i));
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= 68.0)
		tmp = a * (b * i);
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, 68.0], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 68

   1. Initial program 75.9%

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

   2. Taylor expanded in b around inf 38.7%

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

      1. *-commutative 38.7%

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

   4. Simplified 38.7%

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

   5. Taylor expanded in i around inf 23.2%

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

   6. Taylor expanded in b around 0 24.2%

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

   if 68 < z

   1. Initial program 53.7%

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

   2. Taylor expanded in y around inf 52.4%

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

      1. +-commutative 52.4%

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

      2. mul-1-neg 52.4%

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

      3. unsub-neg 52.4%

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

      4. *-commutative 52.4%

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

   4. Applied egg-rr 52.4%

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

   5. Taylor expanded in x around inf 36.8%

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

4. Final simplification 26.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 68:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 25: 22.4% 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 71.1%

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

2. Taylor expanded in b around inf 37.3%

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

   1. *-commutative 37.3%

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

4. Simplified 37.3%

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

5. Taylor expanded in i around inf 20.9%

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

6. Taylor expanded in b around 0 21.6%

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

7. Final simplification 21.6%

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

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 2023297 
(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)))))