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

Percentage Accurate: 73.4% → 82.7%

Time: 28.9s

Alternatives: 27

Speedup: 0.5×

• 57.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 82.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := a \cdot c - y \cdot i\\ \mathbf{if}\;t\_1 + j \cdot t\_2 \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(j, t\_2, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(z - \frac{i \cdot j}{x}\right)\right)\\ \end{array} \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	double t_2 = (a * c) - (y * i);
	double tmp;
	if ((t_1 + (j * t_2)) <= ((double) INFINITY)) {
		tmp = fma(j, t_2, t_1);
	} else {
		tmp = y * (x * (z - ((i * j) / x)));
	}
	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(t * i) - Float64(z * c))))
	t_2 = Float64(Float64(a * c) - Float64(y * i))
	tmp = 0.0
	if (Float64(t_1 + Float64(j * t_2)) <= Inf)
		tmp = fma(j, t_2, t_1);
	else
		tmp = Float64(y * Float64(x * Float64(z - Float64(Float64(i * j) / x))));
	end
	return 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[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$1 + N[(j * t$95$2), $MachinePrecision]), $MachinePrecision], Infinity], N[(j * t$95$2 + t$95$1), $MachinePrecision], N[(y * N[(x * N[(z - N[(N[(i * j), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 90.8%

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

      1. +-commutative 90.8%

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

      2. fma-define 90.8%

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

      3. *-commutative 90.8%

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

      4. *-commutative 90.8%

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

   3. Simplified 90.8%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in y around inf 46.6%

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

      1. +-commutative 46.6%

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

      2. mul-1-neg 46.6%

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

      3. unsub-neg 46.6%

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

      4. *-commutative 46.6%

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

   5. Simplified 46.6%

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

   6. Taylor expanded in x around inf 52.9%

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

      1. associate-*r/ 52.9%

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

      2. mul-1-neg 52.9%

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

      3. *-commutative 52.9%

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

   8. Simplified 52.9%

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

4. Final simplification 84.0%

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

Alternative 2: 82.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 90.8%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in y around inf 46.6%

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

      1. +-commutative 46.6%

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

      2. mul-1-neg 46.6%

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

      3. unsub-neg 46.6%

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

      4. *-commutative 46.6%

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

   5. Simplified 46.6%

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

   6. Taylor expanded in x around inf 52.9%

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

      1. associate-*r/ 52.9%

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

      2. mul-1-neg 52.9%

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

      3. *-commutative 52.9%

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

   8. Simplified 52.9%

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

4. Final simplification 84.0%

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

Alternative 3: 57.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -3.8 \cdot 10^{+246}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -6 \cdot 10^{+96}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;b \leq -6.4 \cdot 10^{+49}:\\ \;\;\;\;t \cdot \left(i \cdot \left(b - a \cdot \frac{x}{i}\right)\right)\\ \mathbf{elif}\;b \leq -0.0066:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-107}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{-174}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{+153}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* j (- (* a c) (* y i))) (* x (* y z))))
        (t_2 (* b (- (* t i) (* z c)))))
   (if (<= b -3.8e+246)
     t_2
     (if (<= b -6e+96)
       (- (* y (- (* x z) (* i j))) (* b (* z c)))
       (if (<= b -6.4e+49)
         (* t (* i (- b (* a (/ x i)))))
         (if (<= b -0.0066)
           t_2
           (if (<= b -2.3e-107)
             t_1
             (if (<= b -8.5e-174)
               (* x (- (* y z) (* t a)))
               (if (<= b 2.2e+153) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((a * c) - (y * i))) + (x * (y * z));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -3.8e+246) {
		tmp = t_2;
	} else if (b <= -6e+96) {
		tmp = (y * ((x * z) - (i * j))) - (b * (z * c));
	} else if (b <= -6.4e+49) {
		tmp = t * (i * (b - (a * (x / i))));
	} else if (b <= -0.0066) {
		tmp = t_2;
	} else if (b <= -2.3e-107) {
		tmp = t_1;
	} else if (b <= -8.5e-174) {
		tmp = x * ((y * z) - (t * a));
	} else if (b <= 2.2e+153) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (j * ((a * c) - (y * i))) + (x * (y * z))
    t_2 = b * ((t * i) - (z * c))
    if (b <= (-3.8d+246)) then
        tmp = t_2
    else if (b <= (-6d+96)) then
        tmp = (y * ((x * z) - (i * j))) - (b * (z * c))
    else if (b <= (-6.4d+49)) then
        tmp = t * (i * (b - (a * (x / i))))
    else if (b <= (-0.0066d0)) then
        tmp = t_2
    else if (b <= (-2.3d-107)) then
        tmp = t_1
    else if (b <= (-8.5d-174)) then
        tmp = x * ((y * z) - (t * a))
    else if (b <= 2.2d+153) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((a * c) - (y * i))) + (x * (y * z));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -3.8e+246) {
		tmp = t_2;
	} else if (b <= -6e+96) {
		tmp = (y * ((x * z) - (i * j))) - (b * (z * c));
	} else if (b <= -6.4e+49) {
		tmp = t * (i * (b - (a * (x / i))));
	} else if (b <= -0.0066) {
		tmp = t_2;
	} else if (b <= -2.3e-107) {
		tmp = t_1;
	} else if (b <= -8.5e-174) {
		tmp = x * ((y * z) - (t * a));
	} else if (b <= 2.2e+153) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((a * c) - (y * i))) + (x * (y * z))
	t_2 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -3.8e+246:
		tmp = t_2
	elif b <= -6e+96:
		tmp = (y * ((x * z) - (i * j))) - (b * (z * c))
	elif b <= -6.4e+49:
		tmp = t * (i * (b - (a * (x / i))))
	elif b <= -0.0066:
		tmp = t_2
	elif b <= -2.3e-107:
		tmp = t_1
	elif b <= -8.5e-174:
		tmp = x * ((y * z) - (t * a))
	elif b <= 2.2e+153:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(x * Float64(y * z)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -3.8e+246)
		tmp = t_2;
	elseif (b <= -6e+96)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) - Float64(b * Float64(z * c)));
	elseif (b <= -6.4e+49)
		tmp = Float64(t * Float64(i * Float64(b - Float64(a * Float64(x / i)))));
	elseif (b <= -0.0066)
		tmp = t_2;
	elseif (b <= -2.3e-107)
		tmp = t_1;
	elseif (b <= -8.5e-174)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (b <= 2.2e+153)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (j * ((a * c) - (y * i))) + (x * (y * z));
	t_2 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -3.8e+246)
		tmp = t_2;
	elseif (b <= -6e+96)
		tmp = (y * ((x * z) - (i * j))) - (b * (z * c));
	elseif (b <= -6.4e+49)
		tmp = t * (i * (b - (a * (x / i))));
	elseif (b <= -0.0066)
		tmp = t_2;
	elseif (b <= -2.3e-107)
		tmp = t_1;
	elseif (b <= -8.5e-174)
		tmp = x * ((y * z) - (t * a));
	elseif (b <= 2.2e+153)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.8e+246], t$95$2, If[LessEqual[b, -6e+96], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -6.4e+49], N[(t * N[(i * N[(b - N[(a * N[(x / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -0.0066], t$95$2, If[LessEqual[b, -2.3e-107], t$95$1, If[LessEqual[b, -8.5e-174], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.2e+153], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -3.79999999999999976e246 or -6.40000000000000028e49 < b < -0.0066 or 2.2e153 < b

   1. Initial program 75.4%

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

   3. Taylor expanded in b around inf 77.3%

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

   if -3.79999999999999976e246 < b < -6.0000000000000001e96

   1. Initial program 80.4%

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

   3. Taylor expanded in a around 0 71.3%

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

   5. Simplified 77.3%

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

   6. Taylor expanded in t around 0 74.4%

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

      1. mul-1-neg 74.4%

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

      2. +-commutative 74.4%

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

      3. cancel-sign-sub-inv 74.4%

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

      4. +-commutative 74.4%

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

      5. +-commutative 74.4%

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

      6. cancel-sign-sub-inv 74.4%

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

      7. *-commutative 74.4%

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

      8. unsub-neg 74.4%

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

      9. *-commutative 74.4%

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

      10. cancel-sign-sub-inv 74.4%

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

      11. +-commutative 74.4%

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

      12. +-commutative 74.4%

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

      13. cancel-sign-sub-inv 74.4%

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

      14. *-commutative 74.4%

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

      15. *-commutative 74.4%

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

   8. Simplified 74.4%

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

   if -6.0000000000000001e96 < b < -6.40000000000000028e49

   1. Initial program 72.6%

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

      1. add-cube-cbrt 72.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(\sqrt[3]{j \cdot \left(c \cdot a - y \cdot i\right)} \cdot \sqrt[3]{j \cdot \left(c \cdot a - y \cdot i\right)}\right) \cdot \sqrt[3]{j \cdot \left(c \cdot a - y \cdot i\right)}} \]

      2. pow3 72.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \color{blue}{{\left(\sqrt[3]{j \cdot \left(c \cdot a - y \cdot i\right)}\right)}^{3}} \]

      3. fma-neg 72.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + {\left(\sqrt[3]{j \cdot \color{blue}{\mathsf{fma}\left(c, a, -y \cdot i\right)}}\right)}^{3} \]

      4. *-commutative 72.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + {\left(\sqrt[3]{j \cdot \mathsf{fma}\left(c, a, -\color{blue}{i \cdot y}\right)}\right)}^{3} \]

      5. distribute-rgt-neg-in 72.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + {\left(\sqrt[3]{j \cdot \mathsf{fma}\left(c, a, \color{blue}{i \cdot \left(-y\right)}\right)}\right)}^{3} \]

   4. Applied egg-rr 72.3%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \color{blue}{{\left(\sqrt[3]{j \cdot \mathsf{fma}\left(c, a, i \cdot \left(-y\right)\right)}\right)}^{3}} \]

   5. Taylor expanded in t around inf 64.6%

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

      1. distribute-lft-out-- 64.6%

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

      2. *-commutative 64.6%

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

   7. Simplified 64.6%

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

   8. Taylor expanded in t around 0 64.6%

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

      1. mul-1-neg 64.6%

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

      2. *-commutative 64.6%

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

      3. distribute-rgt-neg-out 64.6%

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

      4. *-commutative 64.6%

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

   10. Simplified 64.6%

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

   11. Taylor expanded in i around inf 73.1%

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

       1. associate-/l* 72.9%

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

   13. Simplified 72.9%

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

   if -0.0066 < b < -2.30000000000000003e-107 or -8.4999999999999996e-174 < b < 2.2e153

   1. Initial program 72.4%

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

   3. Taylor expanded in y around inf 66.8%

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

      1. *-commutative 66.8%

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

      2. associate-*r* 65.6%

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

      3. *-commutative 65.6%

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

   5. Simplified 65.6%

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

   6. Taylor expanded in b around 0 63.3%

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

   if -2.30000000000000003e-107 < b < -8.4999999999999996e-174

   1. Initial program 82.9%

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

   3. Taylor expanded in x around inf 83.3%

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

      1. cancel-sign-sub-inv 83.3%

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

      2. *-commutative 83.3%

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

      3. *-commutative 83.3%

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

      4. distribute-rgt-neg-out 83.3%

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

      5. sub-neg 83.3%

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

   5. Simplified 83.3%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{+246}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -6 \cdot 10^{+96}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;b \leq -6.4 \cdot 10^{+49}:\\ \;\;\;\;t \cdot \left(i \cdot \left(b - a \cdot \frac{x}{i}\right)\right)\\ \mathbf{elif}\;b \leq -0.0066:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-107}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{-174}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{+153}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 52.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := y \cdot \left(x \cdot \left(z - \frac{i \cdot j}{x}\right)\right)\\ \mathbf{if}\;y \leq -8.2 \cdot 10^{-15}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-108}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-206}:\\ \;\;\;\;a \cdot \left(j \cdot \left(c - t \cdot \frac{x}{j}\right)\right)\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-266}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-279}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+65}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+107}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* y (* x (- z (/ (* i j) x))))))
   (if (<= y -8.2e-15)
     t_2
     (if (<= y -1.05e-108)
       t_1
       (if (<= y -4.2e-206)
         (* a (* j (- c (* t (/ x j)))))
         (if (<= y -1.4e-266)
           t_1
           (if (<= y 1.05e-279)
             (* a (- (* c j) (* x t)))
             (if (<= y 3.9e+65)
               (* c (- (* a j) (* z b)))
               (if (<= y 9.5e+107) (* x (- (* y z) (* t a))) t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = y * (x * (z - ((i * j) / x)));
	double tmp;
	if (y <= -8.2e-15) {
		tmp = t_2;
	} else if (y <= -1.05e-108) {
		tmp = t_1;
	} else if (y <= -4.2e-206) {
		tmp = a * (j * (c - (t * (x / j))));
	} else if (y <= -1.4e-266) {
		tmp = t_1;
	} else if (y <= 1.05e-279) {
		tmp = a * ((c * j) - (x * t));
	} else if (y <= 3.9e+65) {
		tmp = c * ((a * j) - (z * b));
	} else if (y <= 9.5e+107) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = y * (x * (z - ((i * j) / x)))
    if (y <= (-8.2d-15)) then
        tmp = t_2
    else if (y <= (-1.05d-108)) then
        tmp = t_1
    else if (y <= (-4.2d-206)) then
        tmp = a * (j * (c - (t * (x / j))))
    else if (y <= (-1.4d-266)) then
        tmp = t_1
    else if (y <= 1.05d-279) then
        tmp = a * ((c * j) - (x * t))
    else if (y <= 3.9d+65) then
        tmp = c * ((a * j) - (z * b))
    else if (y <= 9.5d+107) then
        tmp = x * ((y * z) - (t * a))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = y * (x * (z - ((i * j) / x)));
	double tmp;
	if (y <= -8.2e-15) {
		tmp = t_2;
	} else if (y <= -1.05e-108) {
		tmp = t_1;
	} else if (y <= -4.2e-206) {
		tmp = a * (j * (c - (t * (x / j))));
	} else if (y <= -1.4e-266) {
		tmp = t_1;
	} else if (y <= 1.05e-279) {
		tmp = a * ((c * j) - (x * t));
	} else if (y <= 3.9e+65) {
		tmp = c * ((a * j) - (z * b));
	} else if (y <= 9.5e+107) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = y * (x * (z - ((i * j) / x)))
	tmp = 0
	if y <= -8.2e-15:
		tmp = t_2
	elif y <= -1.05e-108:
		tmp = t_1
	elif y <= -4.2e-206:
		tmp = a * (j * (c - (t * (x / j))))
	elif y <= -1.4e-266:
		tmp = t_1
	elif y <= 1.05e-279:
		tmp = a * ((c * j) - (x * t))
	elif y <= 3.9e+65:
		tmp = c * ((a * j) - (z * b))
	elif y <= 9.5e+107:
		tmp = x * ((y * z) - (t * a))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(y * Float64(x * Float64(z - Float64(Float64(i * j) / x))))
	tmp = 0.0
	if (y <= -8.2e-15)
		tmp = t_2;
	elseif (y <= -1.05e-108)
		tmp = t_1;
	elseif (y <= -4.2e-206)
		tmp = Float64(a * Float64(j * Float64(c - Float64(t * Float64(x / j)))));
	elseif (y <= -1.4e-266)
		tmp = t_1;
	elseif (y <= 1.05e-279)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (y <= 3.9e+65)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (y <= 9.5e+107)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = y * (x * (z - ((i * j) / x)));
	tmp = 0.0;
	if (y <= -8.2e-15)
		tmp = t_2;
	elseif (y <= -1.05e-108)
		tmp = t_1;
	elseif (y <= -4.2e-206)
		tmp = a * (j * (c - (t * (x / j))));
	elseif (y <= -1.4e-266)
		tmp = t_1;
	elseif (y <= 1.05e-279)
		tmp = a * ((c * j) - (x * t));
	elseif (y <= 3.9e+65)
		tmp = c * ((a * j) - (z * b));
	elseif (y <= 9.5e+107)
		tmp = x * ((y * z) - (t * a));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(x * N[(z - N[(N[(i * j), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.2e-15], t$95$2, If[LessEqual[y, -1.05e-108], t$95$1, If[LessEqual[y, -4.2e-206], N[(a * N[(j * N[(c - N[(t * N[(x / j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.4e-266], t$95$1, If[LessEqual[y, 1.05e-279], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.9e+65], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.5e+107], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -8.20000000000000072e-15 or 9.50000000000000019e107 < y

   1. Initial program 64.0%

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

   3. Taylor expanded in y around inf 66.1%

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

      1. +-commutative 66.1%

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

      2. mul-1-neg 66.1%

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

      3. unsub-neg 66.1%

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

      4. *-commutative 66.1%

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

   5. Simplified 66.1%

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

   6. Taylor expanded in x around inf 67.0%

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

      1. associate-*r/ 67.0%

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

      2. mul-1-neg 67.0%

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

      3. *-commutative 67.0%

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

   8. Simplified 67.0%

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

   if -8.20000000000000072e-15 < y < -1.05e-108 or -4.2000000000000002e-206 < y < -1.4e-266

   1. Initial program 79.0%

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

   3. Taylor expanded in b around inf 64.9%

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

   if -1.05e-108 < y < -4.2000000000000002e-206

   1. Initial program 83.4%

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

   3. Taylor expanded in a around inf 62.6%

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

      1. +-commutative 62.6%

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

      2. mul-1-neg 62.6%

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

      3. unsub-neg 62.6%

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

   5. Simplified 62.6%

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

   6. Taylor expanded in j around inf 67.9%

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

      1. mul-1-neg 67.9%

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

      2. unsub-neg 67.9%

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

      3. associate-/l* 62.8%

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

   8. Simplified 62.8%

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

   if -1.4e-266 < y < 1.05000000000000003e-279

   1. Initial program 79.8%

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

   3. Taylor expanded in a around inf 80.3%

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

      1. +-commutative 80.3%

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

      2. mul-1-neg 80.3%

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

      3. unsub-neg 80.3%

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

   5. Simplified 80.3%

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

   if 1.05000000000000003e-279 < y < 3.8999999999999998e65

   1. Initial program 81.6%

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

   3. Taylor expanded in c around inf 55.5%

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

      1. *-commutative 55.5%

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

   5. Simplified 55.5%

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

   if 3.8999999999999998e65 < y < 9.50000000000000019e107

   1. Initial program 90.8%

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

   3. Taylor expanded in x around inf 82.1%

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

      1. cancel-sign-sub-inv 82.1%

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

      2. *-commutative 82.1%

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

      3. *-commutative 82.1%

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

      4. distribute-rgt-neg-out 82.1%

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

      5. sub-neg 82.1%

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

   5. Simplified 82.1%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-15}:\\ \;\;\;\;y \cdot \left(x \cdot \left(z - \frac{i \cdot j}{x}\right)\right)\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-108}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-206}:\\ \;\;\;\;a \cdot \left(j \cdot \left(c - t \cdot \frac{x}{j}\right)\right)\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-266}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-279}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+65}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+107}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(z - \frac{i \cdot j}{x}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 55.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_2 := b \cdot \left(z \cdot c\right)\\ \mathbf{if}\;i \leq -5.5 \cdot 10^{-20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 1.2 \cdot 10^{-259}:\\ \;\;\;\;\left(y \cdot \left(x \cdot z\right) - t\_2\right) + c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;i \leq 8.6 \cdot 10^{-154}:\\ \;\;\;\;a \cdot \left(j \cdot \left(c - t \cdot \frac{x}{j}\right)\right)\\ \mathbf{elif}\;i \leq 8.8 \cdot 10^{-89}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - t\_2\\ \mathbf{elif}\;i \leq 4 \cdot 10^{-62}:\\ \;\;\;\;a \cdot \left(t \cdot \left(c \cdot \frac{j}{t} - x\right)\right)\\ \mathbf{elif}\;i \leq 7.3:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j)))) (t_2 (* b (* z c))))
   (if (<= i -5.5e-20)
     t_1
     (if (<= i 1.2e-259)
       (+ (- (* y (* x z)) t_2) (* c (* a j)))
       (if (<= i 8.6e-154)
         (* a (* j (- c (* t (/ x j)))))
         (if (<= i 8.8e-89)
           (- (* y (- (* x z) (* i j))) t_2)
           (if (<= i 4e-62)
             (* a (* t (- (* c (/ j t)) x)))
             (if (<= i 7.3)
               (+ (* j (- (* a c) (* y i))) (* x (* y z)))
               t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double t_2 = b * (z * c);
	double tmp;
	if (i <= -5.5e-20) {
		tmp = t_1;
	} else if (i <= 1.2e-259) {
		tmp = ((y * (x * z)) - t_2) + (c * (a * j));
	} else if (i <= 8.6e-154) {
		tmp = a * (j * (c - (t * (x / j))));
	} else if (i <= 8.8e-89) {
		tmp = (y * ((x * z) - (i * j))) - t_2;
	} else if (i <= 4e-62) {
		tmp = a * (t * ((c * (j / t)) - x));
	} else if (i <= 7.3) {
		tmp = (j * ((a * c) - (y * i))) + (x * (y * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i * ((t * b) - (y * j))
    t_2 = b * (z * c)
    if (i <= (-5.5d-20)) then
        tmp = t_1
    else if (i <= 1.2d-259) then
        tmp = ((y * (x * z)) - t_2) + (c * (a * j))
    else if (i <= 8.6d-154) then
        tmp = a * (j * (c - (t * (x / j))))
    else if (i <= 8.8d-89) then
        tmp = (y * ((x * z) - (i * j))) - t_2
    else if (i <= 4d-62) then
        tmp = a * (t * ((c * (j / t)) - x))
    else if (i <= 7.3d0) then
        tmp = (j * ((a * c) - (y * i))) + (x * (y * z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double t_2 = b * (z * c);
	double tmp;
	if (i <= -5.5e-20) {
		tmp = t_1;
	} else if (i <= 1.2e-259) {
		tmp = ((y * (x * z)) - t_2) + (c * (a * j));
	} else if (i <= 8.6e-154) {
		tmp = a * (j * (c - (t * (x / j))));
	} else if (i <= 8.8e-89) {
		tmp = (y * ((x * z) - (i * j))) - t_2;
	} else if (i <= 4e-62) {
		tmp = a * (t * ((c * (j / t)) - x));
	} else if (i <= 7.3) {
		tmp = (j * ((a * c) - (y * i))) + (x * (y * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	t_2 = b * (z * c)
	tmp = 0
	if i <= -5.5e-20:
		tmp = t_1
	elif i <= 1.2e-259:
		tmp = ((y * (x * z)) - t_2) + (c * (a * j))
	elif i <= 8.6e-154:
		tmp = a * (j * (c - (t * (x / j))))
	elif i <= 8.8e-89:
		tmp = (y * ((x * z) - (i * j))) - t_2
	elif i <= 4e-62:
		tmp = a * (t * ((c * (j / t)) - x))
	elif i <= 7.3:
		tmp = (j * ((a * c) - (y * i))) + (x * (y * z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	t_2 = Float64(b * Float64(z * c))
	tmp = 0.0
	if (i <= -5.5e-20)
		tmp = t_1;
	elseif (i <= 1.2e-259)
		tmp = Float64(Float64(Float64(y * Float64(x * z)) - t_2) + Float64(c * Float64(a * j)));
	elseif (i <= 8.6e-154)
		tmp = Float64(a * Float64(j * Float64(c - Float64(t * Float64(x / j)))));
	elseif (i <= 8.8e-89)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) - t_2);
	elseif (i <= 4e-62)
		tmp = Float64(a * Float64(t * Float64(Float64(c * Float64(j / t)) - x)));
	elseif (i <= 7.3)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(x * Float64(y * z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((t * b) - (y * j));
	t_2 = b * (z * c);
	tmp = 0.0;
	if (i <= -5.5e-20)
		tmp = t_1;
	elseif (i <= 1.2e-259)
		tmp = ((y * (x * z)) - t_2) + (c * (a * j));
	elseif (i <= 8.6e-154)
		tmp = a * (j * (c - (t * (x / j))));
	elseif (i <= 8.8e-89)
		tmp = (y * ((x * z) - (i * j))) - t_2;
	elseif (i <= 4e-62)
		tmp = a * (t * ((c * (j / t)) - x));
	elseif (i <= 7.3)
		tmp = (j * ((a * c) - (y * i))) + (x * (y * z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -5.5e-20], t$95$1, If[LessEqual[i, 1.2e-259], N[(N[(N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision] + N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 8.6e-154], N[(a * N[(j * N[(c - N[(t * N[(x / j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 8.8e-89], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[i, 4e-62], N[(a * N[(t * N[(N[(c * N[(j / t), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 7.3], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -5.4999999999999996e-20 or 7.29999999999999982 < i

   1. Initial program 67.6%

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

      1. add-cube-cbrt 67.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(\sqrt[3]{j \cdot \left(c \cdot a - y \cdot i\right)} \cdot \sqrt[3]{j \cdot \left(c \cdot a - y \cdot i\right)}\right) \cdot \sqrt[3]{j \cdot \left(c \cdot a - y \cdot i\right)}} \]

      2. pow3 67.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \color{blue}{{\left(\sqrt[3]{j \cdot \left(c \cdot a - y \cdot i\right)}\right)}^{3}} \]

      3. fma-neg 67.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + {\left(\sqrt[3]{j \cdot \color{blue}{\mathsf{fma}\left(c, a, -y \cdot i\right)}}\right)}^{3} \]

      4. *-commutative 67.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + {\left(\sqrt[3]{j \cdot \mathsf{fma}\left(c, a, -\color{blue}{i \cdot y}\right)}\right)}^{3} \]

      5. distribute-rgt-neg-in 67.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + {\left(\sqrt[3]{j \cdot \mathsf{fma}\left(c, a, \color{blue}{i \cdot \left(-y\right)}\right)}\right)}^{3} \]

   4. Applied egg-rr 67.4%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \color{blue}{{\left(\sqrt[3]{j \cdot \mathsf{fma}\left(c, a, i \cdot \left(-y\right)\right)}\right)}^{3}} \]

   5. Taylor expanded in i around inf 63.9%

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

      1. sub-neg 63.9%

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

      2. mul-1-neg 63.9%

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

      3. remove-double-neg 63.9%

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

      4. +-commutative 63.9%

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

      5. mul-1-neg 63.9%

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

      6. unsub-neg 63.9%

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

   7. Simplified 63.9%

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

   if -5.4999999999999996e-20 < i < 1.2e-259

   1. Initial program 75.7%

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

   3. Taylor expanded in y around inf 63.9%

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

      1. *-commutative 63.9%

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

      2. associate-*r* 70.5%

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

      3. *-commutative 70.5%

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

   5. Simplified 70.5%

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

   6. Taylor expanded in c around inf 61.3%

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

      1. *-commutative 61.3%

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

      2. associate-*r* 69.3%

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

   8. Simplified 69.3%

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

   9. Taylor expanded in c around inf 64.6%

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

   if 1.2e-259 < i < 8.59999999999999983e-154

   1. Initial program 90.0%

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

   3. Taylor expanded in a around inf 75.2%

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

      1. +-commutative 75.2%

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

      2. mul-1-neg 75.2%

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

      3. unsub-neg 75.2%

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

   5. Simplified 75.2%

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

   6. Taylor expanded in j around inf 75.6%

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

      1. mul-1-neg 75.6%

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

      2. unsub-neg 75.6%

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

      3. associate-/l* 80.5%

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

   8. Simplified 80.5%

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

   if 8.59999999999999983e-154 < i < 8.80000000000000048e-89

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0 72.8%

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

   5. Simplified 72.9%

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

   6. Taylor expanded in t around 0 67.6%

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

      1. mul-1-neg 67.6%

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

      2. +-commutative 67.6%

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

      3. cancel-sign-sub-inv 67.6%

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

      4. +-commutative 67.6%

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

      5. +-commutative 67.6%

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

      6. cancel-sign-sub-inv 67.6%

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

      7. *-commutative 67.6%

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

      8. unsub-neg 67.6%

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

      9. *-commutative 67.6%

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

      10. cancel-sign-sub-inv 67.6%

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

      11. +-commutative 67.6%

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

      12. +-commutative 67.6%

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

      13. cancel-sign-sub-inv 67.6%

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

      14. *-commutative 67.6%

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

      15. *-commutative 67.6%

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

   8. Simplified 67.6%

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

   if 8.80000000000000048e-89 < i < 4.0000000000000002e-62

   1. Initial program 66.6%

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

   3. Taylor expanded in a around inf 67.1%

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

      1. +-commutative 67.1%

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

      2. mul-1-neg 67.1%

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

      3. unsub-neg 67.1%

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

   5. Simplified 67.1%

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

   6. Taylor expanded in t around inf 67.0%

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

      1. associate-/l* 67.4%

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

   8. Simplified 67.4%

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

   if 4.0000000000000002e-62 < i < 7.29999999999999982

   1. Initial program 76.2%

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

   3. Taylor expanded in y around inf 88.0%

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

      1. *-commutative 88.0%

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

      2. associate-*r* 77.0%

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

      3. *-commutative 77.0%

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

   5. Simplified 77.0%

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

   6. Taylor expanded in b around 0 88.2%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -5.5 \cdot 10^{-20}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq 1.2 \cdot 10^{-259}:\\ \;\;\;\;\left(y \cdot \left(x \cdot z\right) - b \cdot \left(z \cdot c\right)\right) + c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;i \leq 8.6 \cdot 10^{-154}:\\ \;\;\;\;a \cdot \left(j \cdot \left(c - t \cdot \frac{x}{j}\right)\right)\\ \mathbf{elif}\;i \leq 8.8 \cdot 10^{-89}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;i \leq 4 \cdot 10^{-62}:\\ \;\;\;\;a \cdot \left(t \cdot \left(c \cdot \frac{j}{t} - x\right)\right)\\ \mathbf{elif}\;i \leq 7.3:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_3 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -3.3 \cdot 10^{-15}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-109}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-204}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-261}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-279}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+67}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+107}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t))))
        (t_2 (* b (- (* t i) (* z c))))
        (t_3 (* y (- (* x z) (* i j)))))
   (if (<= y -3.3e-15)
     t_3
     (if (<= y -2.4e-109)
       t_2
       (if (<= y -3.5e-204)
         t_1
         (if (<= y -2.4e-261)
           t_2
           (if (<= y 2.3e-279)
             t_1
             (if (<= y 2.1e+67)
               (* c (- (* a j) (* z b)))
               (if (<= y 9.5e+107) (* x (- (* y z) (* t a))) t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -3.3e-15) {
		tmp = t_3;
	} else if (y <= -2.4e-109) {
		tmp = t_2;
	} else if (y <= -3.5e-204) {
		tmp = t_1;
	} else if (y <= -2.4e-261) {
		tmp = t_2;
	} else if (y <= 2.3e-279) {
		tmp = t_1;
	} else if (y <= 2.1e+67) {
		tmp = c * ((a * j) - (z * b));
	} else if (y <= 9.5e+107) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    t_2 = b * ((t * i) - (z * c))
    t_3 = y * ((x * z) - (i * j))
    if (y <= (-3.3d-15)) then
        tmp = t_3
    else if (y <= (-2.4d-109)) then
        tmp = t_2
    else if (y <= (-3.5d-204)) then
        tmp = t_1
    else if (y <= (-2.4d-261)) then
        tmp = t_2
    else if (y <= 2.3d-279) then
        tmp = t_1
    else if (y <= 2.1d+67) then
        tmp = c * ((a * j) - (z * b))
    else if (y <= 9.5d+107) then
        tmp = x * ((y * z) - (t * a))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -3.3e-15) {
		tmp = t_3;
	} else if (y <= -2.4e-109) {
		tmp = t_2;
	} else if (y <= -3.5e-204) {
		tmp = t_1;
	} else if (y <= -2.4e-261) {
		tmp = t_2;
	} else if (y <= 2.3e-279) {
		tmp = t_1;
	} else if (y <= 2.1e+67) {
		tmp = c * ((a * j) - (z * b));
	} else if (y <= 9.5e+107) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = b * ((t * i) - (z * c))
	t_3 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -3.3e-15:
		tmp = t_3
	elif y <= -2.4e-109:
		tmp = t_2
	elif y <= -3.5e-204:
		tmp = t_1
	elif y <= -2.4e-261:
		tmp = t_2
	elif y <= 2.3e-279:
		tmp = t_1
	elif y <= 2.1e+67:
		tmp = c * ((a * j) - (z * b))
	elif y <= 9.5e+107:
		tmp = x * ((y * z) - (t * a))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_3 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -3.3e-15)
		tmp = t_3;
	elseif (y <= -2.4e-109)
		tmp = t_2;
	elseif (y <= -3.5e-204)
		tmp = t_1;
	elseif (y <= -2.4e-261)
		tmp = t_2;
	elseif (y <= 2.3e-279)
		tmp = t_1;
	elseif (y <= 2.1e+67)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (y <= 9.5e+107)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	t_2 = b * ((t * i) - (z * c));
	t_3 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -3.3e-15)
		tmp = t_3;
	elseif (y <= -2.4e-109)
		tmp = t_2;
	elseif (y <= -3.5e-204)
		tmp = t_1;
	elseif (y <= -2.4e-261)
		tmp = t_2;
	elseif (y <= 2.3e-279)
		tmp = t_1;
	elseif (y <= 2.1e+67)
		tmp = c * ((a * j) - (z * b));
	elseif (y <= 9.5e+107)
		tmp = x * ((y * z) - (t * a));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.3e-15], t$95$3, If[LessEqual[y, -2.4e-109], t$95$2, If[LessEqual[y, -3.5e-204], t$95$1, If[LessEqual[y, -2.4e-261], t$95$2, If[LessEqual[y, 2.3e-279], t$95$1, If[LessEqual[y, 2.1e+67], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.5e+107], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.3e-15 or 9.50000000000000019e107 < y

   1. Initial program 64.0%

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

   3. Taylor expanded in y around inf 66.1%

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

      1. +-commutative 66.1%

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

      2. mul-1-neg 66.1%

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

      3. unsub-neg 66.1%

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

      4. *-commutative 66.1%

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

   5. Simplified 66.1%

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

   if -3.3e-15 < y < -2.39999999999999989e-109 or -3.50000000000000027e-204 < y < -2.40000000000000014e-261

   1. Initial program 79.0%

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

   3. Taylor expanded in b around inf 64.9%

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

   if -2.39999999999999989e-109 < y < -3.50000000000000027e-204 or -2.40000000000000014e-261 < y < 2.29999999999999995e-279

   1. Initial program 81.8%

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

   3. Taylor expanded in a around inf 70.6%

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

      1. +-commutative 70.6%

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

      2. mul-1-neg 70.6%

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

      3. unsub-neg 70.6%

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

   5. Simplified 70.6%

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

   if 2.29999999999999995e-279 < y < 2.1000000000000001e67

   1. Initial program 81.6%

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

   3. Taylor expanded in c around inf 55.5%

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

      1. *-commutative 55.5%

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

   5. Simplified 55.5%

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

   if 2.1000000000000001e67 < y < 9.50000000000000019e107

   1. Initial program 90.8%

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

   3. Taylor expanded in x around inf 82.1%

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

      1. cancel-sign-sub-inv 82.1%

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

      2. *-commutative 82.1%

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

      3. *-commutative 82.1%

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

      4. distribute-rgt-neg-out 82.1%

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

      5. sub-neg 82.1%

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

   5. Simplified 82.1%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-15}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-109}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-204}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-261}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-279}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+67}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+107}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{-18}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-109}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-209}:\\ \;\;\;\;a \cdot \left(j \cdot \left(c - t \cdot \frac{x}{j}\right)\right)\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-268}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-270}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+66}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+107}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* y (- (* x z) (* i j)))))
   (if (<= y -1.2e-18)
     t_2
     (if (<= y -2.1e-109)
       t_1
       (if (<= y -5e-209)
         (* a (* j (- c (* t (/ x j)))))
         (if (<= y -1.02e-268)
           t_1
           (if (<= y 3.6e-270)
             (* a (- (* c j) (* x t)))
             (if (<= y 4.6e+66)
               (* c (- (* a j) (* z b)))
               (if (<= y 8.2e+107) (* x (- (* y z) (* t a))) t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.2e-18) {
		tmp = t_2;
	} else if (y <= -2.1e-109) {
		tmp = t_1;
	} else if (y <= -5e-209) {
		tmp = a * (j * (c - (t * (x / j))));
	} else if (y <= -1.02e-268) {
		tmp = t_1;
	} else if (y <= 3.6e-270) {
		tmp = a * ((c * j) - (x * t));
	} else if (y <= 4.6e+66) {
		tmp = c * ((a * j) - (z * b));
	} else if (y <= 8.2e+107) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = y * ((x * z) - (i * j))
    if (y <= (-1.2d-18)) then
        tmp = t_2
    else if (y <= (-2.1d-109)) then
        tmp = t_1
    else if (y <= (-5d-209)) then
        tmp = a * (j * (c - (t * (x / j))))
    else if (y <= (-1.02d-268)) then
        tmp = t_1
    else if (y <= 3.6d-270) then
        tmp = a * ((c * j) - (x * t))
    else if (y <= 4.6d+66) then
        tmp = c * ((a * j) - (z * b))
    else if (y <= 8.2d+107) then
        tmp = x * ((y * z) - (t * a))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.2e-18) {
		tmp = t_2;
	} else if (y <= -2.1e-109) {
		tmp = t_1;
	} else if (y <= -5e-209) {
		tmp = a * (j * (c - (t * (x / j))));
	} else if (y <= -1.02e-268) {
		tmp = t_1;
	} else if (y <= 3.6e-270) {
		tmp = a * ((c * j) - (x * t));
	} else if (y <= 4.6e+66) {
		tmp = c * ((a * j) - (z * b));
	} else if (y <= 8.2e+107) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -1.2e-18:
		tmp = t_2
	elif y <= -2.1e-109:
		tmp = t_1
	elif y <= -5e-209:
		tmp = a * (j * (c - (t * (x / j))))
	elif y <= -1.02e-268:
		tmp = t_1
	elif y <= 3.6e-270:
		tmp = a * ((c * j) - (x * t))
	elif y <= 4.6e+66:
		tmp = c * ((a * j) - (z * b))
	elif y <= 8.2e+107:
		tmp = x * ((y * z) - (t * a))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -1.2e-18)
		tmp = t_2;
	elseif (y <= -2.1e-109)
		tmp = t_1;
	elseif (y <= -5e-209)
		tmp = Float64(a * Float64(j * Float64(c - Float64(t * Float64(x / j)))));
	elseif (y <= -1.02e-268)
		tmp = t_1;
	elseif (y <= 3.6e-270)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (y <= 4.6e+66)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (y <= 8.2e+107)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -1.2e-18)
		tmp = t_2;
	elseif (y <= -2.1e-109)
		tmp = t_1;
	elseif (y <= -5e-209)
		tmp = a * (j * (c - (t * (x / j))));
	elseif (y <= -1.02e-268)
		tmp = t_1;
	elseif (y <= 3.6e-270)
		tmp = a * ((c * j) - (x * t));
	elseif (y <= 4.6e+66)
		tmp = c * ((a * j) - (z * b));
	elseif (y <= 8.2e+107)
		tmp = x * ((y * z) - (t * a));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.2e-18], t$95$2, If[LessEqual[y, -2.1e-109], t$95$1, If[LessEqual[y, -5e-209], N[(a * N[(j * N[(c - N[(t * N[(x / j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.02e-268], t$95$1, If[LessEqual[y, 3.6e-270], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.6e+66], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.2e+107], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -1.19999999999999997e-18 or 8.1999999999999998e107 < y

   1. Initial program 64.0%

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

   3. Taylor expanded in y around inf 66.1%

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

      1. +-commutative 66.1%

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

      2. mul-1-neg 66.1%

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

      3. unsub-neg 66.1%

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

      4. *-commutative 66.1%

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

   5. Simplified 66.1%

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

   if -1.19999999999999997e-18 < y < -2.09999999999999996e-109 or -5.0000000000000005e-209 < y < -1.0200000000000001e-268

   1. Initial program 79.0%

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

   3. Taylor expanded in b around inf 64.9%

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

   if -2.09999999999999996e-109 < y < -5.0000000000000005e-209

   1. Initial program 83.4%

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

   3. Taylor expanded in a around inf 62.6%

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

      1. +-commutative 62.6%

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

      2. mul-1-neg 62.6%

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

      3. unsub-neg 62.6%

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

   5. Simplified 62.6%

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

   6. Taylor expanded in j around inf 67.9%

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

      1. mul-1-neg 67.9%

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

      2. unsub-neg 67.9%

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

      3. associate-/l* 62.8%

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

   8. Simplified 62.8%

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

   if -1.0200000000000001e-268 < y < 3.5999999999999998e-270

   1. Initial program 79.8%

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

   3. Taylor expanded in a around inf 80.3%

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

      1. +-commutative 80.3%

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

      2. mul-1-neg 80.3%

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

      3. unsub-neg 80.3%

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

   5. Simplified 80.3%

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

   if 3.5999999999999998e-270 < y < 4.6e66

   1. Initial program 81.6%

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

   3. Taylor expanded in c around inf 55.5%

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

      1. *-commutative 55.5%

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

   5. Simplified 55.5%

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

   if 4.6e66 < y < 8.1999999999999998e107

   1. Initial program 90.8%

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

   3. Taylor expanded in x around inf 82.1%

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

      1. cancel-sign-sub-inv 82.1%

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

      2. *-commutative 82.1%

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

      3. *-commutative 82.1%

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

      4. distribute-rgt-neg-out 82.1%

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

      5. sub-neg 82.1%

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

   5. Simplified 82.1%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{-18}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-109}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-209}:\\ \;\;\;\;a \cdot \left(j \cdot \left(c - t \cdot \frac{x}{j}\right)\right)\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-268}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-270}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+66}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+107}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 52.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -9.2 \cdot 10^{-20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 6.5 \cdot 10^{-260}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 1.02 \cdot 10^{-153}:\\ \;\;\;\;a \cdot \left(j \cdot \left(c - t \cdot \frac{x}{j}\right)\right)\\ \mathbf{elif}\;i \leq 6.4 \cdot 10^{-93}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq 9 \cdot 10^{-57}:\\ \;\;\;\;c \cdot \left(a \cdot \left(j - z \cdot \frac{b}{a}\right)\right)\\ \mathbf{elif}\;i \leq 175:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j)))))
   (if (<= i -9.2e-20)
     t_1
     (if (<= i 6.5e-260)
       (* z (- (* x y) (* b c)))
       (if (<= i 1.02e-153)
         (* a (* j (- c (* t (/ x j)))))
         (if (<= i 6.4e-93)
           (* x (- (* y z) (* t a)))
           (if (<= i 9e-57)
             (* c (* a (- j (* z (/ b a)))))
             (if (<= i 175.0) (+ (* x (* y z)) (* a (* 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 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -9.2e-20) {
		tmp = t_1;
	} else if (i <= 6.5e-260) {
		tmp = z * ((x * y) - (b * c));
	} else if (i <= 1.02e-153) {
		tmp = a * (j * (c - (t * (x / j))));
	} else if (i <= 6.4e-93) {
		tmp = x * ((y * z) - (t * a));
	} else if (i <= 9e-57) {
		tmp = c * (a * (j - (z * (b / a))));
	} else if (i <= 175.0) {
		tmp = (x * (y * z)) + (a * (c * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * ((t * b) - (y * j))
    if (i <= (-9.2d-20)) then
        tmp = t_1
    else if (i <= 6.5d-260) then
        tmp = z * ((x * y) - (b * c))
    else if (i <= 1.02d-153) then
        tmp = a * (j * (c - (t * (x / j))))
    else if (i <= 6.4d-93) then
        tmp = x * ((y * z) - (t * a))
    else if (i <= 9d-57) then
        tmp = c * (a * (j - (z * (b / a))))
    else if (i <= 175.0d0) then
        tmp = (x * (y * z)) + (a * (c * j))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -9.2e-20) {
		tmp = t_1;
	} else if (i <= 6.5e-260) {
		tmp = z * ((x * y) - (b * c));
	} else if (i <= 1.02e-153) {
		tmp = a * (j * (c - (t * (x / j))));
	} else if (i <= 6.4e-93) {
		tmp = x * ((y * z) - (t * a));
	} else if (i <= 9e-57) {
		tmp = c * (a * (j - (z * (b / a))));
	} else if (i <= 175.0) {
		tmp = (x * (y * z)) + (a * (c * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -9.2e-20:
		tmp = t_1
	elif i <= 6.5e-260:
		tmp = z * ((x * y) - (b * c))
	elif i <= 1.02e-153:
		tmp = a * (j * (c - (t * (x / j))))
	elif i <= 6.4e-93:
		tmp = x * ((y * z) - (t * a))
	elif i <= 9e-57:
		tmp = c * (a * (j - (z * (b / a))))
	elif i <= 175.0:
		tmp = (x * (y * z)) + (a * (c * j))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -9.2e-20)
		tmp = t_1;
	elseif (i <= 6.5e-260)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (i <= 1.02e-153)
		tmp = Float64(a * Float64(j * Float64(c - Float64(t * Float64(x / j)))));
	elseif (i <= 6.4e-93)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (i <= 9e-57)
		tmp = Float64(c * Float64(a * Float64(j - Float64(z * Float64(b / a)))));
	elseif (i <= 175.0)
		tmp = Float64(Float64(x * Float64(y * z)) + Float64(a * Float64(c * j)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -9.2e-20)
		tmp = t_1;
	elseif (i <= 6.5e-260)
		tmp = z * ((x * y) - (b * c));
	elseif (i <= 1.02e-153)
		tmp = a * (j * (c - (t * (x / j))));
	elseif (i <= 6.4e-93)
		tmp = x * ((y * z) - (t * a));
	elseif (i <= 9e-57)
		tmp = c * (a * (j - (z * (b / a))));
	elseif (i <= 175.0)
		tmp = (x * (y * z)) + (a * (c * j));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -9.2e-20], t$95$1, If[LessEqual[i, 6.5e-260], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.02e-153], N[(a * N[(j * N[(c - N[(t * N[(x / j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 6.4e-93], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 9e-57], N[(c * N[(a * N[(j - N[(z * N[(b / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 175.0], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -9.1999999999999997e-20 or 175 < i

   1. Initial program 68.2%

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

      1. add-cube-cbrt 67.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(\sqrt[3]{j \cdot \left(c \cdot a - y \cdot i\right)} \cdot \sqrt[3]{j \cdot \left(c \cdot a - y \cdot i\right)}\right) \cdot \sqrt[3]{j \cdot \left(c \cdot a - y \cdot i\right)}} \]

      2. pow3 68.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \color{blue}{{\left(\sqrt[3]{j \cdot \left(c \cdot a - y \cdot i\right)}\right)}^{3}} \]

      3. fma-neg 68.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + {\left(\sqrt[3]{j \cdot \color{blue}{\mathsf{fma}\left(c, a, -y \cdot i\right)}}\right)}^{3} \]

      4. *-commutative 68.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + {\left(\sqrt[3]{j \cdot \mathsf{fma}\left(c, a, -\color{blue}{i \cdot y}\right)}\right)}^{3} \]

      5. distribute-rgt-neg-in 68.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + {\left(\sqrt[3]{j \cdot \mathsf{fma}\left(c, a, \color{blue}{i \cdot \left(-y\right)}\right)}\right)}^{3} \]

   4. Applied egg-rr 68.0%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \color{blue}{{\left(\sqrt[3]{j \cdot \mathsf{fma}\left(c, a, i \cdot \left(-y\right)\right)}\right)}^{3}} \]

   5. Taylor expanded in i around inf 64.5%

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

      1. sub-neg 64.5%

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

      2. mul-1-neg 64.5%

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

      3. remove-double-neg 64.5%

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

      4. +-commutative 64.5%

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

      5. mul-1-neg 64.5%

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

      6. unsub-neg 64.5%

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

   7. Simplified 64.5%

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

   if -9.1999999999999997e-20 < i < 6.50000000000000002e-260

   1. Initial program 75.7%

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

   3. Taylor expanded in z around inf 53.2%

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

      1. *-commutative 53.2%

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

   5. Simplified 53.2%

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

   if 6.50000000000000002e-260 < i < 1.02e-153

   1. Initial program 90.0%

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

   3. Taylor expanded in a around inf 75.2%

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

      1. +-commutative 75.2%

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

      2. mul-1-neg 75.2%

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

      3. unsub-neg 75.2%

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

   5. Simplified 75.2%

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

   6. Taylor expanded in j around inf 75.6%

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

      1. mul-1-neg 75.6%

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

      2. unsub-neg 75.6%

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

      3. associate-/l* 80.5%

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

   8. Simplified 80.5%

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

   if 1.02e-153 < i < 6.3999999999999997e-93

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 57.2%

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

      1. cancel-sign-sub-inv 57.2%

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

      2. *-commutative 57.2%

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

      3. *-commutative 57.2%

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

      4. distribute-rgt-neg-out 57.2%

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

      5. sub-neg 57.2%

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

   5. Simplified 57.2%

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

   if 6.3999999999999997e-93 < i < 8.99999999999999945e-57

   1. Initial program 80.0%

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

   3. Taylor expanded in c around inf 53.1%

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

      1. *-commutative 53.1%

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

   5. Simplified 53.1%

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

   6. Taylor expanded in a around inf 62.5%

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

      1. mul-1-neg 62.5%

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

      2. unsub-neg 62.5%

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

      3. *-commutative 62.5%

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

      4. associate-/l* 62.3%

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

   8. Simplified 62.3%

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

   if 8.99999999999999945e-57 < i < 175

   1. Initial program 68.5%

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

   3. Taylor expanded in y around inf 81.0%

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

      1. *-commutative 81.0%

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

      2. associate-*r* 69.3%

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

      3. *-commutative 69.3%

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

   5. Simplified 69.3%

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

   6. Taylor expanded in c around inf 63.5%

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

      1. *-commutative 63.5%

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

      2. associate-*r* 63.8%

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

   8. Simplified 63.8%

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

   9. Taylor expanded in b around 0 81.6%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -9.2 \cdot 10^{-20}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq 6.5 \cdot 10^{-260}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 1.02 \cdot 10^{-153}:\\ \;\;\;\;a \cdot \left(j \cdot \left(c - t \cdot \frac{x}{j}\right)\right)\\ \mathbf{elif}\;i \leq 6.4 \cdot 10^{-93}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq 9 \cdot 10^{-57}:\\ \;\;\;\;c \cdot \left(a \cdot \left(j - z \cdot \frac{b}{a}\right)\right)\\ \mathbf{elif}\;i \leq 175:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 51.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -7 \cdot 10^{-20}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq 9 \cdot 10^{-260}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 1.2 \cdot 10^{-153}:\\ \;\;\;\;a \cdot \left(j \cdot \left(c - t \cdot \frac{x}{j}\right)\right)\\ \mathbf{elif}\;i \leq 3.4 \cdot 10^{-92}:\\ \;\;\;\;t\_1 - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{-58}:\\ \;\;\;\;c \cdot \left(a \cdot \left(j - z \cdot \frac{b}{a}\right)\right)\\ \mathbf{elif}\;i \leq 14200:\\ \;\;\;\;t\_1 + a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))) (t_2 (* i (- (* t b) (* y j)))))
   (if (<= i -7e-20)
     t_2
     (if (<= i 9e-260)
       (* z (- (* x y) (* b c)))
       (if (<= i 1.2e-153)
         (* a (* j (- c (* t (/ x j)))))
         (if (<= i 3.4e-92)
           (- t_1 (* b (* z c)))
           (if (<= i 4.8e-58)
             (* c (* a (- j (* z (/ b a)))))
             (if (<= i 14200.0) (+ t_1 (* a (* c j))) 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);
	double t_2 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -7e-20) {
		tmp = t_2;
	} else if (i <= 9e-260) {
		tmp = z * ((x * y) - (b * c));
	} else if (i <= 1.2e-153) {
		tmp = a * (j * (c - (t * (x / j))));
	} else if (i <= 3.4e-92) {
		tmp = t_1 - (b * (z * c));
	} else if (i <= 4.8e-58) {
		tmp = c * (a * (j - (z * (b / a))));
	} else if (i <= 14200.0) {
		tmp = t_1 + (a * (c * j));
	} 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_2 = i * ((t * b) - (y * j))
    if (i <= (-7d-20)) then
        tmp = t_2
    else if (i <= 9d-260) then
        tmp = z * ((x * y) - (b * c))
    else if (i <= 1.2d-153) then
        tmp = a * (j * (c - (t * (x / j))))
    else if (i <= 3.4d-92) then
        tmp = t_1 - (b * (z * c))
    else if (i <= 4.8d-58) then
        tmp = c * (a * (j - (z * (b / a))))
    else if (i <= 14200.0d0) then
        tmp = t_1 + (a * (c * j))
    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);
	double t_2 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -7e-20) {
		tmp = t_2;
	} else if (i <= 9e-260) {
		tmp = z * ((x * y) - (b * c));
	} else if (i <= 1.2e-153) {
		tmp = a * (j * (c - (t * (x / j))));
	} else if (i <= 3.4e-92) {
		tmp = t_1 - (b * (z * c));
	} else if (i <= 4.8e-58) {
		tmp = c * (a * (j - (z * (b / a))));
	} else if (i <= 14200.0) {
		tmp = t_1 + (a * (c * j));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	t_2 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -7e-20:
		tmp = t_2
	elif i <= 9e-260:
		tmp = z * ((x * y) - (b * c))
	elif i <= 1.2e-153:
		tmp = a * (j * (c - (t * (x / j))))
	elif i <= 3.4e-92:
		tmp = t_1 - (b * (z * c))
	elif i <= 4.8e-58:
		tmp = c * (a * (j - (z * (b / a))))
	elif i <= 14200.0:
		tmp = t_1 + (a * (c * j))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(y * z))
	t_2 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -7e-20)
		tmp = t_2;
	elseif (i <= 9e-260)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (i <= 1.2e-153)
		tmp = Float64(a * Float64(j * Float64(c - Float64(t * Float64(x / j)))));
	elseif (i <= 3.4e-92)
		tmp = Float64(t_1 - Float64(b * Float64(z * c)));
	elseif (i <= 4.8e-58)
		tmp = Float64(c * Float64(a * Float64(j - Float64(z * Float64(b / a)))));
	elseif (i <= 14200.0)
		tmp = Float64(t_1 + Float64(a * Float64(c * j)));
	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_2 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -7e-20)
		tmp = t_2;
	elseif (i <= 9e-260)
		tmp = z * ((x * y) - (b * c));
	elseif (i <= 1.2e-153)
		tmp = a * (j * (c - (t * (x / j))));
	elseif (i <= 3.4e-92)
		tmp = t_1 - (b * (z * c));
	elseif (i <= 4.8e-58)
		tmp = c * (a * (j - (z * (b / a))));
	elseif (i <= 14200.0)
		tmp = t_1 + (a * (c * j));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -7e-20], t$95$2, If[LessEqual[i, 9e-260], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.2e-153], N[(a * N[(j * N[(c - N[(t * N[(x / j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.4e-92], N[(t$95$1 - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4.8e-58], N[(c * N[(a * N[(j - N[(z * N[(b / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 14200.0], N[(t$95$1 + N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -7.00000000000000007e-20 or 14200 < i

   1. Initial program 68.2%

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

      1. add-cube-cbrt 67.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(\sqrt[3]{j \cdot \left(c \cdot a - y \cdot i\right)} \cdot \sqrt[3]{j \cdot \left(c \cdot a - y \cdot i\right)}\right) \cdot \sqrt[3]{j \cdot \left(c \cdot a - y \cdot i\right)}} \]

      2. pow3 68.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \color{blue}{{\left(\sqrt[3]{j \cdot \left(c \cdot a - y \cdot i\right)}\right)}^{3}} \]

      3. fma-neg 68.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + {\left(\sqrt[3]{j \cdot \color{blue}{\mathsf{fma}\left(c, a, -y \cdot i\right)}}\right)}^{3} \]

      4. *-commutative 68.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + {\left(\sqrt[3]{j \cdot \mathsf{fma}\left(c, a, -\color{blue}{i \cdot y}\right)}\right)}^{3} \]

      5. distribute-rgt-neg-in 68.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + {\left(\sqrt[3]{j \cdot \mathsf{fma}\left(c, a, \color{blue}{i \cdot \left(-y\right)}\right)}\right)}^{3} \]

   4. Applied egg-rr 68.0%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \color{blue}{{\left(\sqrt[3]{j \cdot \mathsf{fma}\left(c, a, i \cdot \left(-y\right)\right)}\right)}^{3}} \]

   5. Taylor expanded in i around inf 64.5%

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

      1. sub-neg 64.5%

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

      2. mul-1-neg 64.5%

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

      3. remove-double-neg 64.5%

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

      4. +-commutative 64.5%

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

      5. mul-1-neg 64.5%

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

      6. unsub-neg 64.5%

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

   7. Simplified 64.5%

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

   if -7.00000000000000007e-20 < i < 8.9999999999999995e-260

   1. Initial program 75.7%

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

   3. Taylor expanded in z around inf 53.2%

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

      1. *-commutative 53.2%

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

   5. Simplified 53.2%

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

   if 8.9999999999999995e-260 < i < 1.2000000000000001e-153

   1. Initial program 90.0%

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

   3. Taylor expanded in a around inf 75.2%

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

      1. +-commutative 75.2%

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

      2. mul-1-neg 75.2%

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

      3. unsub-neg 75.2%

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

   5. Simplified 75.2%

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

   6. Taylor expanded in j around inf 75.6%

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

      1. mul-1-neg 75.6%

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

      2. unsub-neg 75.6%

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

      3. associate-/l* 80.5%

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

   8. Simplified 80.5%

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

   if 1.2000000000000001e-153 < i < 3.4000000000000003e-92

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0 71.2%

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

   5. Simplified 71.3%

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

   6. Taylor expanded in i around 0 59.7%

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

   if 3.4000000000000003e-92 < i < 4.8000000000000001e-58

   1. Initial program 77.8%

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

   3. Taylor expanded in c around inf 58.6%

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

      1. *-commutative 58.6%

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

   5. Simplified 58.6%

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

   6. Taylor expanded in a around inf 69.0%

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

      1. mul-1-neg 69.0%

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

      2. unsub-neg 69.0%

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

      3. *-commutative 69.0%

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

      4. associate-/l* 68.8%

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

   8. Simplified 68.8%

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

   if 4.8000000000000001e-58 < i < 14200

   1. Initial program 68.5%

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

   3. Taylor expanded in y around inf 81.0%

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

      1. *-commutative 81.0%

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

      2. associate-*r* 69.3%

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

      3. *-commutative 69.3%

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

   5. Simplified 69.3%

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

   6. Taylor expanded in c around inf 63.5%

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

      1. *-commutative 63.5%

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

      2. associate-*r* 63.8%

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

   8. Simplified 63.8%

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

   9. Taylor expanded in b around 0 81.6%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -7 \cdot 10^{-20}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq 9 \cdot 10^{-260}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 1.2 \cdot 10^{-153}:\\ \;\;\;\;a \cdot \left(j \cdot \left(c - t \cdot \frac{x}{j}\right)\right)\\ \mathbf{elif}\;i \leq 3.4 \cdot 10^{-92}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{-58}:\\ \;\;\;\;c \cdot \left(a \cdot \left(j - z \cdot \frac{b}{a}\right)\right)\\ \mathbf{elif}\;i \leq 14200:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ t_2 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -2.6 \cdot 10^{+87}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -1.6 \cdot 10^{-99}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;c \leq 1.45 \cdot 10^{-195}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{-119}:\\ \;\;\;\;t \cdot \left(x \cdot \left(b \cdot \frac{i}{x} - a\right)\right)\\ \mathbf{elif}\;c \leq 2.65 \cdot 10^{+216}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* j (- (* a c) (* y i))) (* x (* y z))))
        (t_2 (* c (- (* a j) (* z b)))))
   (if (<= c -2.6e+87)
     t_2
     (if (<= c -1.6e-99)
       (* t (- (* b i) (* x a)))
       (if (<= c 1.45e-195)
         t_1
         (if (<= c 2.9e-119)
           (* t (* x (- (* b (/ i x)) a)))
           (if (<= c 2.65e+216) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((a * c) - (y * i))) + (x * (y * z));
	double t_2 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -2.6e+87) {
		tmp = t_2;
	} else if (c <= -1.6e-99) {
		tmp = t * ((b * i) - (x * a));
	} else if (c <= 1.45e-195) {
		tmp = t_1;
	} else if (c <= 2.9e-119) {
		tmp = t * (x * ((b * (i / x)) - a));
	} else if (c <= 2.65e+216) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (j * ((a * c) - (y * i))) + (x * (y * z))
    t_2 = c * ((a * j) - (z * b))
    if (c <= (-2.6d+87)) then
        tmp = t_2
    else if (c <= (-1.6d-99)) then
        tmp = t * ((b * i) - (x * a))
    else if (c <= 1.45d-195) then
        tmp = t_1
    else if (c <= 2.9d-119) then
        tmp = t * (x * ((b * (i / x)) - a))
    else if (c <= 2.65d+216) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((a * c) - (y * i))) + (x * (y * z));
	double t_2 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -2.6e+87) {
		tmp = t_2;
	} else if (c <= -1.6e-99) {
		tmp = t * ((b * i) - (x * a));
	} else if (c <= 1.45e-195) {
		tmp = t_1;
	} else if (c <= 2.9e-119) {
		tmp = t * (x * ((b * (i / x)) - a));
	} else if (c <= 2.65e+216) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((a * c) - (y * i))) + (x * (y * z))
	t_2 = c * ((a * j) - (z * b))
	tmp = 0
	if c <= -2.6e+87:
		tmp = t_2
	elif c <= -1.6e-99:
		tmp = t * ((b * i) - (x * a))
	elif c <= 1.45e-195:
		tmp = t_1
	elif c <= 2.9e-119:
		tmp = t * (x * ((b * (i / x)) - a))
	elif c <= 2.65e+216:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(x * Float64(y * z)))
	t_2 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -2.6e+87)
		tmp = t_2;
	elseif (c <= -1.6e-99)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (c <= 1.45e-195)
		tmp = t_1;
	elseif (c <= 2.9e-119)
		tmp = Float64(t * Float64(x * Float64(Float64(b * Float64(i / x)) - a)));
	elseif (c <= 2.65e+216)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (j * ((a * c) - (y * i))) + (x * (y * z));
	t_2 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -2.6e+87)
		tmp = t_2;
	elseif (c <= -1.6e-99)
		tmp = t * ((b * i) - (x * a));
	elseif (c <= 1.45e-195)
		tmp = t_1;
	elseif (c <= 2.9e-119)
		tmp = t * (x * ((b * (i / x)) - a));
	elseif (c <= 2.65e+216)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.6e+87], t$95$2, If[LessEqual[c, -1.6e-99], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.45e-195], t$95$1, If[LessEqual[c, 2.9e-119], N[(t * N[(x * N[(N[(b * N[(i / x), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.65e+216], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -2.59999999999999998e87 or 2.65000000000000001e216 < c

   1. Initial program 56.2%

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

   3. Taylor expanded in c around inf 69.7%

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

      1. *-commutative 69.7%

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

   5. Simplified 69.7%

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

   if -2.59999999999999998e87 < c < -1.6e-99

   1. Initial program 73.5%

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

      1. add-cube-cbrt 73.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(\sqrt[3]{j \cdot \left(c \cdot a - y \cdot i\right)} \cdot \sqrt[3]{j \cdot \left(c \cdot a - y \cdot i\right)}\right) \cdot \sqrt[3]{j \cdot \left(c \cdot a - y \cdot i\right)}} \]

      2. pow3 73.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \color{blue}{{\left(\sqrt[3]{j \cdot \left(c \cdot a - y \cdot i\right)}\right)}^{3}} \]

      3. fma-neg 73.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + {\left(\sqrt[3]{j \cdot \color{blue}{\mathsf{fma}\left(c, a, -y \cdot i\right)}}\right)}^{3} \]

      4. *-commutative 73.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + {\left(\sqrt[3]{j \cdot \mathsf{fma}\left(c, a, -\color{blue}{i \cdot y}\right)}\right)}^{3} \]

      5. distribute-rgt-neg-in 73.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + {\left(\sqrt[3]{j \cdot \mathsf{fma}\left(c, a, \color{blue}{i \cdot \left(-y\right)}\right)}\right)}^{3} \]

   4. Applied egg-rr 73.6%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \color{blue}{{\left(\sqrt[3]{j \cdot \mathsf{fma}\left(c, a, i \cdot \left(-y\right)\right)}\right)}^{3}} \]

   5. Taylor expanded in t around inf 58.5%

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

      1. distribute-lft-out-- 58.5%

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

      2. *-commutative 58.5%

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

   7. Simplified 58.5%

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

   8. Taylor expanded in t around 0 58.5%

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

      1. mul-1-neg 58.5%

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

      2. *-commutative 58.5%

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

      3. distribute-rgt-neg-out 58.5%

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

      4. *-commutative 58.5%

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

   10. Simplified 58.5%

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

   11. Taylor expanded in t around 0 58.5%

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

   if -1.6e-99 < c < 1.4500000000000001e-195 or 2.9e-119 < c < 2.65000000000000001e216

   1. Initial program 83.6%

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

   3. Taylor expanded in y around inf 77.2%

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

      1. *-commutative 77.2%

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

      2. associate-*r* 77.4%

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

      3. *-commutative 77.4%

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

   5. Simplified 77.4%

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

   6. Taylor expanded in b around 0 62.7%

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

   if 1.4500000000000001e-195 < c < 2.9e-119

   1. Initial program 81.0%

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

      1. add-cube-cbrt 81.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(\sqrt[3]{j \cdot \left(c \cdot a - y \cdot i\right)} \cdot \sqrt[3]{j \cdot \left(c \cdot a - y \cdot i\right)}\right) \cdot \sqrt[3]{j \cdot \left(c \cdot a - y \cdot i\right)}} \]

      2. pow3 81.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \color{blue}{{\left(\sqrt[3]{j \cdot \left(c \cdot a - y \cdot i\right)}\right)}^{3}} \]

      3. fma-neg 81.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + {\left(\sqrt[3]{j \cdot \color{blue}{\mathsf{fma}\left(c, a, -y \cdot i\right)}}\right)}^{3} \]

      4. *-commutative 81.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + {\left(\sqrt[3]{j \cdot \mathsf{fma}\left(c, a, -\color{blue}{i \cdot y}\right)}\right)}^{3} \]

      5. distribute-rgt-neg-in 81.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + {\left(\sqrt[3]{j \cdot \mathsf{fma}\left(c, a, \color{blue}{i \cdot \left(-y\right)}\right)}\right)}^{3} \]

   4. Applied egg-rr 81.0%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \color{blue}{{\left(\sqrt[3]{j \cdot \mathsf{fma}\left(c, a, i \cdot \left(-y\right)\right)}\right)}^{3}} \]

   5. Taylor expanded in t around inf 70.0%

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

      1. distribute-lft-out-- 70.0%

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

      2. *-commutative 70.0%

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

   7. Simplified 70.0%

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

   8. Taylor expanded in t around 0 70.0%

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

      1. mul-1-neg 70.0%

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

      2. *-commutative 70.0%

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

      3. distribute-rgt-neg-out 70.0%

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

      4. *-commutative 70.0%

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

   10. Simplified 70.0%

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

   11. Taylor expanded in x around inf 70.5%

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

       1. mul-1-neg 70.5%

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

       2. unsub-neg 70.5%

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

       3. associate-/l* 70.5%

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

   13. Simplified 70.5%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.6 \cdot 10^{+87}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -1.6 \cdot 10^{-99}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;c \leq 1.45 \cdot 10^{-195}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{-119}:\\ \;\;\;\;t \cdot \left(x \cdot \left(b \cdot \frac{i}{x} - a\right)\right)\\ \mathbf{elif}\;c \leq 2.65 \cdot 10^{+216}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 69.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right) + t\_1\\ t_4 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -8 \cdot 10^{+115}:\\ \;\;\;\;t\_2 - b \cdot \left(z \cdot \left(c - i \cdot \frac{t}{z}\right)\right)\\ \mathbf{elif}\;b \leq -8.8 \cdot 10^{+49}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -5.3 \cdot 10^{-107}:\\ \;\;\;\;t\_1 + \left(y \cdot \left(x \cdot z\right) + t\_4\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-14}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2 + t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i))))
        (t_2 (* y (- (* x z) (* i j))))
        (t_3 (+ (* x (- (* y z) (* t a))) t_1))
        (t_4 (* b (- (* t i) (* z c)))))
   (if (<= b -8e+115)
     (- t_2 (* b (* z (- c (* i (/ t z))))))
     (if (<= b -8.8e+49)
       t_3
       (if (<= b -5.3e-107)
         (+ t_1 (+ (* y (* x z)) t_4))
         (if (<= b 2.4e-14) t_3 (+ t_2 t_4)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = (x * ((y * z) - (t * a))) + t_1;
	double t_4 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -8e+115) {
		tmp = t_2 - (b * (z * (c - (i * (t / z)))));
	} else if (b <= -8.8e+49) {
		tmp = t_3;
	} else if (b <= -5.3e-107) {
		tmp = t_1 + ((y * (x * z)) + t_4);
	} else if (b <= 2.4e-14) {
		tmp = t_3;
	} else {
		tmp = t_2 + t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = y * ((x * z) - (i * j))
    t_3 = (x * ((y * z) - (t * a))) + t_1
    t_4 = b * ((t * i) - (z * c))
    if (b <= (-8d+115)) then
        tmp = t_2 - (b * (z * (c - (i * (t / z)))))
    else if (b <= (-8.8d+49)) then
        tmp = t_3
    else if (b <= (-5.3d-107)) then
        tmp = t_1 + ((y * (x * z)) + t_4)
    else if (b <= 2.4d-14) then
        tmp = t_3
    else
        tmp = t_2 + t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = (x * ((y * z) - (t * a))) + t_1;
	double t_4 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -8e+115) {
		tmp = t_2 - (b * (z * (c - (i * (t / z)))));
	} else if (b <= -8.8e+49) {
		tmp = t_3;
	} else if (b <= -5.3e-107) {
		tmp = t_1 + ((y * (x * z)) + t_4);
	} else if (b <= 2.4e-14) {
		tmp = t_3;
	} else {
		tmp = t_2 + t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = y * ((x * z) - (i * j))
	t_3 = (x * ((y * z) - (t * a))) + t_1
	t_4 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -8e+115:
		tmp = t_2 - (b * (z * (c - (i * (t / z)))))
	elif b <= -8.8e+49:
		tmp = t_3
	elif b <= -5.3e-107:
		tmp = t_1 + ((y * (x * z)) + t_4)
	elif b <= 2.4e-14:
		tmp = t_3
	else:
		tmp = t_2 + t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_3 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_1)
	t_4 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -8e+115)
		tmp = Float64(t_2 - Float64(b * Float64(z * Float64(c - Float64(i * Float64(t / z))))));
	elseif (b <= -8.8e+49)
		tmp = t_3;
	elseif (b <= -5.3e-107)
		tmp = Float64(t_1 + Float64(Float64(y * Float64(x * z)) + t_4));
	elseif (b <= 2.4e-14)
		tmp = t_3;
	else
		tmp = Float64(t_2 + t_4);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = y * ((x * z) - (i * j));
	t_3 = (x * ((y * z) - (t * a))) + t_1;
	t_4 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -8e+115)
		tmp = t_2 - (b * (z * (c - (i * (t / z)))));
	elseif (b <= -8.8e+49)
		tmp = t_3;
	elseif (b <= -5.3e-107)
		tmp = t_1 + ((y * (x * z)) + t_4);
	elseif (b <= 2.4e-14)
		tmp = t_3;
	else
		tmp = t_2 + t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8e+115], N[(t$95$2 - N[(b * N[(z * N[(c - N[(i * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -8.8e+49], t$95$3, If[LessEqual[b, -5.3e-107], N[(t$95$1 + N[(N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.4e-14], t$95$3, N[(t$95$2 + t$95$4), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -8.0000000000000001e115

   1. Initial program 79.7%

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

   3. Taylor expanded in a around 0 80.0%

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

   5. Simplified 85.4%

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

   6. Taylor expanded in z around inf 85.4%

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

      1. associate-*r/ 88.3%

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

   8. Simplified 88.3%

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

   if -8.0000000000000001e115 < b < -8.8000000000000003e49 or -5.3e-107 < b < 2.4e-14

   1. Initial program 73.9%

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

   3. Taylor expanded in b around 0 76.4%

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

   if -8.8000000000000003e49 < b < -5.3e-107

   1. Initial program 75.8%

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

   3. Taylor expanded in y around inf 79.1%

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

      1. *-commutative 79.1%

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

      2. associate-*r* 86.3%

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

      3. *-commutative 86.3%

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

   5. Simplified 86.3%

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

   if 2.4e-14 < b

   1. Initial program 72.5%

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

   3. Taylor expanded in a around 0 65.4%

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

   5. Simplified 72.8%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8 \cdot 10^{+115}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot \left(c - i \cdot \frac{t}{z}\right)\right)\\ \mathbf{elif}\;b \leq -8.8 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq -5.3 \cdot 10^{-107}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + \left(y \cdot \left(x \cdot z\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 69.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{+116} \lor \neg \left(b \leq -1.82 \cdot 10^{+49}\right) \land \left(b \leq -4.7 \cdot 10^{-32} \lor \neg \left(b \leq 2.75 \cdot 10^{-14}\right)\right):\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -1.1e+116)
         (and (not (<= b -1.82e+49))
              (or (<= b -4.7e-32) (not (<= b 2.75e-14)))))
   (+ (* y (- (* x z) (* i j))) (* b (- (* t i) (* z c))))
   (+ (* x (- (* y z) (* t a))) (* j (- (* a c) (* y i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -1.1e+116) || (!(b <= -1.82e+49) && ((b <= -4.7e-32) || !(b <= 2.75e-14)))) {
		tmp = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)));
	} else {
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-1.1d+116)) .or. (.not. (b <= (-1.82d+49))) .and. (b <= (-4.7d-32)) .or. (.not. (b <= 2.75d-14))) then
        tmp = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)))
    else
        tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -1.1e+116) || (!(b <= -1.82e+49) && ((b <= -4.7e-32) || !(b <= 2.75e-14)))) {
		tmp = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)));
	} else {
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -1.1e+116) or (not (b <= -1.82e+49) and ((b <= -4.7e-32) or not (b <= 2.75e-14))):
		tmp = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)))
	else:
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -1.1e+116) || (!(b <= -1.82e+49) && ((b <= -4.7e-32) || !(b <= 2.75e-14))))
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	else
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -1.1e+116) || (~((b <= -1.82e+49)) && ((b <= -4.7e-32) || ~((b <= 2.75e-14)))))
		tmp = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)));
	else
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -1.1e+116], And[N[Not[LessEqual[b, -1.82e+49]], $MachinePrecision], Or[LessEqual[b, -4.7e-32], N[Not[LessEqual[b, 2.75e-14]], $MachinePrecision]]]], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.1e116 or -1.82000000000000013e49 < b < -4.70000000000000019e-32 or 2.74999999999999996e-14 < b

   1. Initial program 74.6%

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

   3. Taylor expanded in a around 0 70.5%

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

   5. Simplified 78.0%

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

   if -1.1e116 < b < -1.82000000000000013e49 or -4.70000000000000019e-32 < b < 2.74999999999999996e-14

   1. Initial program 74.4%

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

   3. Taylor expanded in b around 0 75.8%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{+116} \lor \neg \left(b \leq -1.82 \cdot 10^{+49}\right) \land \left(b \leq -4.7 \cdot 10^{-32} \lor \neg \left(b \leq 2.75 \cdot 10^{-14}\right)\right):\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 63.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.95 \cdot 10^{+117}:\\ \;\;\;\;y \cdot \left(x \cdot \left(z - i \cdot \frac{j}{x}\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{+48} \lor \neg \left(b \leq -0.245\right) \land b \leq 3.7 \cdot 10^{+59}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -1.95e+117)
   (- (* y (* x (- z (* i (/ j x))))) (* b (* z c)))
   (if (or (<= b -1.7e+48) (and (not (<= b -0.245)) (<= b 3.7e+59)))
     (+ (* x (- (* y z) (* t a))) (* j (- (* a c) (* y i))))
     (* b (- (* t i) (* z c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -1.95e+117) {
		tmp = (y * (x * (z - (i * (j / x))))) - (b * (z * c));
	} else if ((b <= -1.7e+48) || (!(b <= -0.245) && (b <= 3.7e+59))) {
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	} else {
		tmp = b * ((t * i) - (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-1.95d+117)) then
        tmp = (y * (x * (z - (i * (j / x))))) - (b * (z * c))
    else if ((b <= (-1.7d+48)) .or. (.not. (b <= (-0.245d0))) .and. (b <= 3.7d+59)) then
        tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)))
    else
        tmp = b * ((t * i) - (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -1.95e+117) {
		tmp = (y * (x * (z - (i * (j / x))))) - (b * (z * c));
	} else if ((b <= -1.7e+48) || (!(b <= -0.245) && (b <= 3.7e+59))) {
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	} else {
		tmp = b * ((t * i) - (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -1.95e+117:
		tmp = (y * (x * (z - (i * (j / x))))) - (b * (z * c))
	elif (b <= -1.7e+48) or (not (b <= -0.245) and (b <= 3.7e+59)):
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)))
	else:
		tmp = b * ((t * i) - (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -1.95e+117)
		tmp = Float64(Float64(y * Float64(x * Float64(z - Float64(i * Float64(j / x))))) - Float64(b * Float64(z * c)));
	elseif ((b <= -1.7e+48) || (!(b <= -0.245) && (b <= 3.7e+59)))
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))));
	else
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -1.95e+117)
		tmp = (y * (x * (z - (i * (j / x))))) - (b * (z * c));
	elseif ((b <= -1.7e+48) || (~((b <= -0.245)) && (b <= 3.7e+59)))
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	else
		tmp = b * ((t * i) - (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -1.95e+117], N[(N[(y * N[(x * N[(z - N[(i * N[(j / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, -1.7e+48], And[N[Not[LessEqual[b, -0.245]], $MachinePrecision], LessEqual[b, 3.7e+59]]], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.94999999999999995e117

   1. Initial program 79.1%

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

   3. Taylor expanded in a around 0 79.4%

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

   5. Simplified 84.9%

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

   6. Taylor expanded in x around inf 84.9%

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

      1. mul-1-neg 84.9%

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

      2. unsub-neg 84.9%

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

      3. associate-/l* 84.9%

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

   8. Simplified 84.9%

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

   9. Taylor expanded in i around 0 71.1%

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

       1. mul-1-neg 71.1%

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

       2. distribute-rgt-neg-in 71.1%

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

       3. distribute-rgt-neg-in 71.1%

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

   11. Simplified 71.1%

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

   if -1.94999999999999995e117 < b < -1.7000000000000002e48 or -0.245 < b < 3.69999999999999997e59

   1. Initial program 75.3%

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

   3. Taylor expanded in b around 0 73.7%

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

   if -1.7000000000000002e48 < b < -0.245 or 3.69999999999999997e59 < b

   1. Initial program 69.8%

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

   3. Taylor expanded in b around inf 70.1%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.95 \cdot 10^{+117}:\\ \;\;\;\;y \cdot \left(x \cdot \left(z - i \cdot \frac{j}{x}\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{+48} \lor \neg \left(b \leq -0.245\right) \land b \leq 3.7 \cdot 10^{+59}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 69.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;b \leq -1.15 \cdot 10^{+116}:\\ \;\;\;\;t\_1 - b \cdot \left(z \cdot \left(c - i \cdot \frac{t}{z}\right)\right)\\ \mathbf{elif}\;b \leq -2 \cdot 10^{+50} \lor \neg \left(b \leq -6.2 \cdot 10^{-32}\right) \land b \leq 2.2 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j)))))
   (if (<= b -1.15e+116)
     (- t_1 (* b (* z (- c (* i (/ t z))))))
     (if (or (<= b -2e+50) (and (not (<= b -6.2e-32)) (<= b 2.2e-14)))
       (+ (* x (- (* y z) (* t a))) (* j (- (* a c) (* y i))))
       (+ t_1 (* b (- (* t i) (* z c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double tmp;
	if (b <= -1.15e+116) {
		tmp = t_1 - (b * (z * (c - (i * (t / z)))));
	} else if ((b <= -2e+50) || (!(b <= -6.2e-32) && (b <= 2.2e-14))) {
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	} else {
		tmp = t_1 + (b * ((t * i) - (z * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((x * z) - (i * j))
    if (b <= (-1.15d+116)) then
        tmp = t_1 - (b * (z * (c - (i * (t / z)))))
    else if ((b <= (-2d+50)) .or. (.not. (b <= (-6.2d-32))) .and. (b <= 2.2d-14)) then
        tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)))
    else
        tmp = t_1 + (b * ((t * i) - (z * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double tmp;
	if (b <= -1.15e+116) {
		tmp = t_1 - (b * (z * (c - (i * (t / z)))));
	} else if ((b <= -2e+50) || (!(b <= -6.2e-32) && (b <= 2.2e-14))) {
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	} else {
		tmp = t_1 + (b * ((t * i) - (z * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	tmp = 0
	if b <= -1.15e+116:
		tmp = t_1 - (b * (z * (c - (i * (t / z)))))
	elif (b <= -2e+50) or (not (b <= -6.2e-32) and (b <= 2.2e-14)):
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)))
	else:
		tmp = t_1 + (b * ((t * i) - (z * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (b <= -1.15e+116)
		tmp = Float64(t_1 - Float64(b * Float64(z * Float64(c - Float64(i * Float64(t / z))))));
	elseif ((b <= -2e+50) || (!(b <= -6.2e-32) && (b <= 2.2e-14)))
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))));
	else
		tmp = Float64(t_1 + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (b <= -1.15e+116)
		tmp = t_1 - (b * (z * (c - (i * (t / z)))));
	elseif ((b <= -2e+50) || (~((b <= -6.2e-32)) && (b <= 2.2e-14)))
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	else
		tmp = t_1 + (b * ((t * i) - (z * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.15e+116], N[(t$95$1 - N[(b * N[(z * N[(c - N[(i * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, -2e+50], And[N[Not[LessEqual[b, -6.2e-32]], $MachinePrecision], LessEqual[b, 2.2e-14]]], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.14999999999999997e116

   1. Initial program 79.7%

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

   3. Taylor expanded in a around 0 80.0%

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

   5. Simplified 85.4%

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

   6. Taylor expanded in z around inf 85.4%

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

      1. associate-*r/ 88.3%

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

   8. Simplified 88.3%

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

   if -1.14999999999999997e116 < b < -2.0000000000000002e50 or -6.20000000000000021e-32 < b < 2.2000000000000001e-14

   1. Initial program 74.4%

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

   3. Taylor expanded in b around 0 75.8%

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

   if -2.0000000000000002e50 < b < -6.20000000000000021e-32 or 2.2000000000000001e-14 < b

   1. Initial program 72.7%

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

   3. Taylor expanded in a around 0 66.9%

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

   5. Simplified 75.2%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{+116}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot \left(c - i \cdot \frac{t}{z}\right)\right)\\ \mathbf{elif}\;b \leq -2 \cdot 10^{+50} \lor \neg \left(b \leq -6.2 \cdot 10^{-32}\right) \land b \leq 2.2 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 30.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j\right)\\ t_2 := c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{if}\;c \leq -2.3 \cdot 10^{+248}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -3.5 \cdot 10^{+215}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -9 \cdot 10^{+87}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -4.2 \cdot 10^{-115}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;c \leq 2 \cdot 10^{-239}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 6.2 \cdot 10^{+86}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* a j))) (t_2 (* c (* z (- b)))))
   (if (<= c -2.3e+248)
     t_2
     (if (<= c -3.5e+215)
       t_1
       (if (<= c -9e+87)
         t_2
         (if (<= c -4.2e-115)
           (* (* x t) (- a))
           (if (<= c 2e-239)
             (* z (* x y))
             (if (<= c 6.2e+86) (* b (* t i)) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (a * j);
	double t_2 = c * (z * -b);
	double tmp;
	if (c <= -2.3e+248) {
		tmp = t_2;
	} else if (c <= -3.5e+215) {
		tmp = t_1;
	} else if (c <= -9e+87) {
		tmp = t_2;
	} else if (c <= -4.2e-115) {
		tmp = (x * t) * -a;
	} else if (c <= 2e-239) {
		tmp = z * (x * y);
	} else if (c <= 6.2e+86) {
		tmp = b * (t * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * (a * j)
    t_2 = c * (z * -b)
    if (c <= (-2.3d+248)) then
        tmp = t_2
    else if (c <= (-3.5d+215)) then
        tmp = t_1
    else if (c <= (-9d+87)) then
        tmp = t_2
    else if (c <= (-4.2d-115)) then
        tmp = (x * t) * -a
    else if (c <= 2d-239) then
        tmp = z * (x * y)
    else if (c <= 6.2d+86) then
        tmp = b * (t * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (a * j);
	double t_2 = c * (z * -b);
	double tmp;
	if (c <= -2.3e+248) {
		tmp = t_2;
	} else if (c <= -3.5e+215) {
		tmp = t_1;
	} else if (c <= -9e+87) {
		tmp = t_2;
	} else if (c <= -4.2e-115) {
		tmp = (x * t) * -a;
	} else if (c <= 2e-239) {
		tmp = z * (x * y);
	} else if (c <= 6.2e+86) {
		tmp = b * (t * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (a * j)
	t_2 = c * (z * -b)
	tmp = 0
	if c <= -2.3e+248:
		tmp = t_2
	elif c <= -3.5e+215:
		tmp = t_1
	elif c <= -9e+87:
		tmp = t_2
	elif c <= -4.2e-115:
		tmp = (x * t) * -a
	elif c <= 2e-239:
		tmp = z * (x * y)
	elif c <= 6.2e+86:
		tmp = b * (t * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(a * j))
	t_2 = Float64(c * Float64(z * Float64(-b)))
	tmp = 0.0
	if (c <= -2.3e+248)
		tmp = t_2;
	elseif (c <= -3.5e+215)
		tmp = t_1;
	elseif (c <= -9e+87)
		tmp = t_2;
	elseif (c <= -4.2e-115)
		tmp = Float64(Float64(x * t) * Float64(-a));
	elseif (c <= 2e-239)
		tmp = Float64(z * Float64(x * y));
	elseif (c <= 6.2e+86)
		tmp = Float64(b * Float64(t * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (a * j);
	t_2 = c * (z * -b);
	tmp = 0.0;
	if (c <= -2.3e+248)
		tmp = t_2;
	elseif (c <= -3.5e+215)
		tmp = t_1;
	elseif (c <= -9e+87)
		tmp = t_2;
	elseif (c <= -4.2e-115)
		tmp = (x * t) * -a;
	elseif (c <= 2e-239)
		tmp = z * (x * y);
	elseif (c <= 6.2e+86)
		tmp = b * (t * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.3e+248], t$95$2, If[LessEqual[c, -3.5e+215], t$95$1, If[LessEqual[c, -9e+87], t$95$2, If[LessEqual[c, -4.2e-115], N[(N[(x * t), $MachinePrecision] * (-a)), $MachinePrecision], If[LessEqual[c, 2e-239], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.2e+86], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -2.3000000000000002e248 or -3.49999999999999977e215 < c < -9.0000000000000005e87

   1. Initial program 58.4%

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

   3. Taylor expanded in c around inf 59.9%

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

      1. *-commutative 59.9%

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

   5. Simplified 59.9%

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

   6. Taylor expanded in j around 0 49.8%

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

      1. mul-1-neg 49.8%

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

      2. distribute-lft-neg-out 49.8%

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

      3. *-commutative 49.8%

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

   8. Simplified 49.8%

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

   if -2.3000000000000002e248 < c < -3.49999999999999977e215 or 6.2000000000000004e86 < c

   1. Initial program 59.6%

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

   3. Taylor expanded in y around inf 63.5%

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

      1. *-commutative 63.5%

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

      2. associate-*r* 67.0%

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

      3. *-commutative 67.0%

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

   5. Simplified 67.0%

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

   6. Taylor expanded in a around inf 45.7%

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

      1. *-commutative 45.7%

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

      2. associate-*l* 47.4%

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

   8. Simplified 47.4%

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

   if -9.0000000000000005e87 < c < -4.20000000000000003e-115

   1. Initial program 74.9%

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

   3. Taylor expanded in a around inf 47.3%

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

      1. +-commutative 47.3%

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

      2. mul-1-neg 47.3%

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

      3. unsub-neg 47.3%

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

   5. Simplified 47.3%

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

   6. Taylor expanded in c around 0 35.7%

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

      1. mul-1-neg 35.7%

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

      2. *-commutative 35.7%

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

      3. distribute-rgt-neg-in 35.7%

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

      4. distribute-rgt-neg-in 35.7%

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

      5. *-commutative 35.7%

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

      6. distribute-lft-neg-out 35.7%

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

   8. Simplified 35.7%

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

   if -4.20000000000000003e-115 < c < 2.0000000000000002e-239

   1. Initial program 87.8%

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

   3. Taylor expanded in y around inf 74.0%

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

      1. *-commutative 74.0%

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

      2. associate-*r* 70.2%

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

      3. *-commutative 70.2%

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

   5. Simplified 70.2%

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

   6. Taylor expanded in c around inf 48.8%

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

      1. *-commutative 48.8%

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

      2. associate-*r* 50.9%

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

   8. Simplified 50.9%

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

   9. Taylor expanded in x around inf 38.6%

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

       1. associate-*r* 38.7%

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

       2. *-commutative 38.7%

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

   11. Simplified 38.7%

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

   if 2.0000000000000002e-239 < c < 6.2000000000000004e86

   1. Initial program 84.3%

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

   3. Taylor expanded in y around inf 78.1%

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

      1. *-commutative 78.1%

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

      2. associate-*r* 76.9%

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

      3. *-commutative 76.9%

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

   5. Simplified 76.9%

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

   6. Taylor expanded in t around inf 33.1%

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

4. Final simplification 40.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.3 \cdot 10^{+248}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;c \leq -3.5 \cdot 10^{+215}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;c \leq -9 \cdot 10^{+87}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;c \leq -4.2 \cdot 10^{-115}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;c \leq 2 \cdot 10^{-239}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 6.2 \cdot 10^{+86}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 52.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_2 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -5.2 \cdot 10^{-20}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{-261}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 1.05 \cdot 10^{-60}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 1.2 \cdot 10^{-45}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 32:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* a j) (* z b)))) (t_2 (* i (- (* t b) (* y j)))))
   (if (<= i -5.2e-20)
     t_2
     (if (<= i 1.3e-261)
       t_1
       (if (<= i 1.05e-60)
         (* a (- (* c j) (* x t)))
         (if (<= i 1.2e-45) (* z (* x y)) (if (<= i 32.0) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (z * b));
	double t_2 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -5.2e-20) {
		tmp = t_2;
	} else if (i <= 1.3e-261) {
		tmp = t_1;
	} else if (i <= 1.05e-60) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= 1.2e-45) {
		tmp = z * (x * y);
	} else if (i <= 32.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * ((a * j) - (z * b))
    t_2 = i * ((t * b) - (y * j))
    if (i <= (-5.2d-20)) then
        tmp = t_2
    else if (i <= 1.3d-261) then
        tmp = t_1
    else if (i <= 1.05d-60) then
        tmp = a * ((c * j) - (x * t))
    else if (i <= 1.2d-45) then
        tmp = z * (x * y)
    else if (i <= 32.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (z * b));
	double t_2 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -5.2e-20) {
		tmp = t_2;
	} else if (i <= 1.3e-261) {
		tmp = t_1;
	} else if (i <= 1.05e-60) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= 1.2e-45) {
		tmp = z * (x * y);
	} else if (i <= 32.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((a * j) - (z * b))
	t_2 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -5.2e-20:
		tmp = t_2
	elif i <= 1.3e-261:
		tmp = t_1
	elif i <= 1.05e-60:
		tmp = a * ((c * j) - (x * t))
	elif i <= 1.2e-45:
		tmp = z * (x * y)
	elif i <= 32.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	t_2 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -5.2e-20)
		tmp = t_2;
	elseif (i <= 1.3e-261)
		tmp = t_1;
	elseif (i <= 1.05e-60)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (i <= 1.2e-45)
		tmp = Float64(z * Float64(x * y));
	elseif (i <= 32.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((a * j) - (z * b));
	t_2 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -5.2e-20)
		tmp = t_2;
	elseif (i <= 1.3e-261)
		tmp = t_1;
	elseif (i <= 1.05e-60)
		tmp = a * ((c * j) - (x * t));
	elseif (i <= 1.2e-45)
		tmp = z * (x * y);
	elseif (i <= 32.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -5.2e-20], t$95$2, If[LessEqual[i, 1.3e-261], t$95$1, If[LessEqual[i, 1.05e-60], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.2e-45], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 32.0], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -5.1999999999999999e-20 or 32 < i

   1. Initial program 68.2%

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

      1. add-cube-cbrt 67.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(\sqrt[3]{j \cdot \left(c \cdot a - y \cdot i\right)} \cdot \sqrt[3]{j \cdot \left(c \cdot a - y \cdot i\right)}\right) \cdot \sqrt[3]{j \cdot \left(c \cdot a - y \cdot i\right)}} \]

      2. pow3 68.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \color{blue}{{\left(\sqrt[3]{j \cdot \left(c \cdot a - y \cdot i\right)}\right)}^{3}} \]

      3. fma-neg 68.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + {\left(\sqrt[3]{j \cdot \color{blue}{\mathsf{fma}\left(c, a, -y \cdot i\right)}}\right)}^{3} \]

      4. *-commutative 68.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + {\left(\sqrt[3]{j \cdot \mathsf{fma}\left(c, a, -\color{blue}{i \cdot y}\right)}\right)}^{3} \]

      5. distribute-rgt-neg-in 68.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + {\left(\sqrt[3]{j \cdot \mathsf{fma}\left(c, a, \color{blue}{i \cdot \left(-y\right)}\right)}\right)}^{3} \]

   4. Applied egg-rr 68.0%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \color{blue}{{\left(\sqrt[3]{j \cdot \mathsf{fma}\left(c, a, i \cdot \left(-y\right)\right)}\right)}^{3}} \]

   5. Taylor expanded in i around inf 64.5%

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

      1. sub-neg 64.5%

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

      2. mul-1-neg 64.5%

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

      3. remove-double-neg 64.5%

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

      4. +-commutative 64.5%

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

      5. mul-1-neg 64.5%

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

      6. unsub-neg 64.5%

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

   7. Simplified 64.5%

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

   if -5.1999999999999999e-20 < i < 1.3000000000000001e-261 or 1.19999999999999995e-45 < i < 32

   1. Initial program 74.1%

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

   3. Taylor expanded in c around inf 52.2%

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

      1. *-commutative 52.2%

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

   5. Simplified 52.2%

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

   if 1.3000000000000001e-261 < i < 1.04999999999999996e-60

   1. Initial program 91.0%

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

   3. Taylor expanded in a around inf 54.4%

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

      1. +-commutative 54.4%

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

      2. mul-1-neg 54.4%

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

      3. unsub-neg 54.4%

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

   5. Simplified 54.4%

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

   if 1.04999999999999996e-60 < i < 1.19999999999999995e-45

   1. Initial program 82.8%

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

   3. Taylor expanded in y around inf 82.8%

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

      1. *-commutative 82.8%

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

      2. associate-*r* 67.3%

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

      3. *-commutative 67.3%

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

   5. Simplified 67.3%

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

   6. Taylor expanded in c around inf 67.3%

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

      1. *-commutative 67.3%

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

      2. associate-*r* 67.3%

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

   8. Simplified 67.3%

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

   9. Taylor expanded in x around inf 80.5%

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

       1. associate-*r* 80.8%

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

       2. *-commutative 80.8%

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

   11. Simplified 80.8%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -5.2 \cdot 10^{-20}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{-261}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 1.05 \cdot 10^{-60}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 1.2 \cdot 10^{-45}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 32:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 28.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -6.6 \cdot 10^{-70}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;j \leq -4.5 \cdot 10^{-281}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;j \leq 1.9 \cdot 10^{-166}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 2 \cdot 10^{+62}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;j \leq 1.9 \cdot 10^{+209}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -6.6e-70)
   (* y (* i (- j)))
   (if (<= j -4.5e-281)
     (* i (* t b))
     (if (<= j 1.9e-166)
       (* y (* x z))
       (if (<= j 2e+62)
         (* (* x t) (- a))
         (if (<= j 1.9e+209) (* c (* z (- b))) (* c (* a j))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -6.6e-70) {
		tmp = y * (i * -j);
	} else if (j <= -4.5e-281) {
		tmp = i * (t * b);
	} else if (j <= 1.9e-166) {
		tmp = y * (x * z);
	} else if (j <= 2e+62) {
		tmp = (x * t) * -a;
	} else if (j <= 1.9e+209) {
		tmp = c * (z * -b);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (j <= (-6.6d-70)) then
        tmp = y * (i * -j)
    else if (j <= (-4.5d-281)) then
        tmp = i * (t * b)
    else if (j <= 1.9d-166) then
        tmp = y * (x * z)
    else if (j <= 2d+62) then
        tmp = (x * t) * -a
    else if (j <= 1.9d+209) then
        tmp = c * (z * -b)
    else
        tmp = c * (a * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -6.6e-70) {
		tmp = y * (i * -j);
	} else if (j <= -4.5e-281) {
		tmp = i * (t * b);
	} else if (j <= 1.9e-166) {
		tmp = y * (x * z);
	} else if (j <= 2e+62) {
		tmp = (x * t) * -a;
	} else if (j <= 1.9e+209) {
		tmp = c * (z * -b);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -6.6e-70:
		tmp = y * (i * -j)
	elif j <= -4.5e-281:
		tmp = i * (t * b)
	elif j <= 1.9e-166:
		tmp = y * (x * z)
	elif j <= 2e+62:
		tmp = (x * t) * -a
	elif j <= 1.9e+209:
		tmp = c * (z * -b)
	else:
		tmp = c * (a * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -6.6e-70)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (j <= -4.5e-281)
		tmp = Float64(i * Float64(t * b));
	elseif (j <= 1.9e-166)
		tmp = Float64(y * Float64(x * z));
	elseif (j <= 2e+62)
		tmp = Float64(Float64(x * t) * Float64(-a));
	elseif (j <= 1.9e+209)
		tmp = Float64(c * Float64(z * Float64(-b)));
	else
		tmp = Float64(c * Float64(a * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -6.6e-70)
		tmp = y * (i * -j);
	elseif (j <= -4.5e-281)
		tmp = i * (t * b);
	elseif (j <= 1.9e-166)
		tmp = y * (x * z);
	elseif (j <= 2e+62)
		tmp = (x * t) * -a;
	elseif (j <= 1.9e+209)
		tmp = c * (z * -b);
	else
		tmp = c * (a * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -6.6e-70], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -4.5e-281], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.9e-166], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2e+62], N[(N[(x * t), $MachinePrecision] * (-a)), $MachinePrecision], If[LessEqual[j, 1.9e+209], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -6.60000000000000033e-70

   1. Initial program 80.0%

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

   3. Taylor expanded in y around inf 45.9%

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

      1. +-commutative 45.9%

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

      2. mul-1-neg 45.9%

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

      3. unsub-neg 45.9%

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

      4. *-commutative 45.9%

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

   5. Simplified 45.9%

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

   6. Taylor expanded in z around 0 36.3%

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

      1. mul-1-neg 36.3%

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

      2. *-commutative 36.3%

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

   8. Simplified 36.3%

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

   if -6.60000000000000033e-70 < j < -4.49999999999999993e-281

   1. Initial program 75.6%

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

   3. Taylor expanded in y around inf 62.3%

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

      1. *-commutative 62.3%

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

      2. associate-*r* 59.5%

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

      3. *-commutative 59.5%

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

   5. Simplified 59.5%

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

   6. Taylor expanded in t around inf 34.7%

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

      1. associate-*r* 32.1%

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

      2. *-commutative 32.1%

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

      3. associate-*r* 37.4%

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

   8. Simplified 37.4%

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

   if -4.49999999999999993e-281 < j < 1.89999999999999991e-166

   1. Initial program 70.5%

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

   3. Taylor expanded in y around inf 46.4%

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

      1. +-commutative 46.4%

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

      2. mul-1-neg 46.4%

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

      3. unsub-neg 46.4%

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

      4. *-commutative 46.4%

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

   5. Simplified 46.4%

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

   6. Taylor expanded in z around inf 41.4%

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

      1. *-commutative 41.4%

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

   8. Simplified 41.4%

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

   if 1.89999999999999991e-166 < j < 2.00000000000000007e62

   1. Initial program 84.3%

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

   3. Taylor expanded in a around inf 49.5%

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

      1. +-commutative 49.5%

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

      2. mul-1-neg 49.5%

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

      3. unsub-neg 49.5%

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

   5. Simplified 49.5%

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

   6. Taylor expanded in c around 0 39.0%

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

      1. mul-1-neg 39.0%

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

      2. *-commutative 39.0%

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

      3. distribute-rgt-neg-in 39.0%

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

      4. distribute-rgt-neg-in 39.0%

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

      5. *-commutative 39.0%

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

      6. distribute-lft-neg-out 39.0%

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

   8. Simplified 39.0%

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

   if 2.00000000000000007e62 < j < 1.89999999999999992e209

   1. Initial program 63.3%

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

   3. Taylor expanded in c around inf 48.3%

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

      1. *-commutative 48.3%

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

   5. Simplified 48.3%

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

   6. Taylor expanded in j around 0 41.2%

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

      1. mul-1-neg 41.2%

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

      2. distribute-lft-neg-out 41.2%

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

      3. *-commutative 41.2%

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

   8. Simplified 41.2%

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

   if 1.89999999999999992e209 < j

   1. Initial program 56.0%

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

   3. Taylor expanded in y around inf 60.3%

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

      1. *-commutative 60.3%

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

      2. associate-*r* 60.5%

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

      3. *-commutative 60.5%

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

   5. Simplified 60.5%

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

   6. Taylor expanded in a around inf 45.1%

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

      1. *-commutative 45.1%

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

      2. associate-*l* 56.4%

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

   8. Simplified 56.4%

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

4. Final simplification 40.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -6.6 \cdot 10^{-70}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;j \leq -4.5 \cdot 10^{-281}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;j \leq 1.9 \cdot 10^{-166}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 2 \cdot 10^{+62}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;j \leq 1.9 \cdot 10^{+209}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 28.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -2 \cdot 10^{-68}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;j \leq -6 \cdot 10^{-282}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;j \leq 3.8 \cdot 10^{-167}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 1.95 \cdot 10^{+63}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;j \leq 1.9 \cdot 10^{+209}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -2e-68)
   (* i (* y (- j)))
   (if (<= j -6e-282)
     (* i (* t b))
     (if (<= j 3.8e-167)
       (* y (* x z))
       (if (<= j 1.95e+63)
         (* (* x t) (- a))
         (if (<= j 1.9e+209) (* c (* z (- b))) (* c (* a j))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -2e-68) {
		tmp = i * (y * -j);
	} else if (j <= -6e-282) {
		tmp = i * (t * b);
	} else if (j <= 3.8e-167) {
		tmp = y * (x * z);
	} else if (j <= 1.95e+63) {
		tmp = (x * t) * -a;
	} else if (j <= 1.9e+209) {
		tmp = c * (z * -b);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (j <= (-2d-68)) then
        tmp = i * (y * -j)
    else if (j <= (-6d-282)) then
        tmp = i * (t * b)
    else if (j <= 3.8d-167) then
        tmp = y * (x * z)
    else if (j <= 1.95d+63) then
        tmp = (x * t) * -a
    else if (j <= 1.9d+209) then
        tmp = c * (z * -b)
    else
        tmp = c * (a * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -2e-68) {
		tmp = i * (y * -j);
	} else if (j <= -6e-282) {
		tmp = i * (t * b);
	} else if (j <= 3.8e-167) {
		tmp = y * (x * z);
	} else if (j <= 1.95e+63) {
		tmp = (x * t) * -a;
	} else if (j <= 1.9e+209) {
		tmp = c * (z * -b);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -2e-68:
		tmp = i * (y * -j)
	elif j <= -6e-282:
		tmp = i * (t * b)
	elif j <= 3.8e-167:
		tmp = y * (x * z)
	elif j <= 1.95e+63:
		tmp = (x * t) * -a
	elif j <= 1.9e+209:
		tmp = c * (z * -b)
	else:
		tmp = c * (a * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -2e-68)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (j <= -6e-282)
		tmp = Float64(i * Float64(t * b));
	elseif (j <= 3.8e-167)
		tmp = Float64(y * Float64(x * z));
	elseif (j <= 1.95e+63)
		tmp = Float64(Float64(x * t) * Float64(-a));
	elseif (j <= 1.9e+209)
		tmp = Float64(c * Float64(z * Float64(-b)));
	else
		tmp = Float64(c * Float64(a * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -2e-68)
		tmp = i * (y * -j);
	elseif (j <= -6e-282)
		tmp = i * (t * b);
	elseif (j <= 3.8e-167)
		tmp = y * (x * z);
	elseif (j <= 1.95e+63)
		tmp = (x * t) * -a;
	elseif (j <= 1.9e+209)
		tmp = c * (z * -b);
	else
		tmp = c * (a * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -2e-68], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -6e-282], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.8e-167], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.95e+63], N[(N[(x * t), $MachinePrecision] * (-a)), $MachinePrecision], If[LessEqual[j, 1.9e+209], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -2.00000000000000013e-68

   1. Initial program 80.0%

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

   3. Taylor expanded in y around inf 45.9%

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

      1. +-commutative 45.9%

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

      2. mul-1-neg 45.9%

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

      3. unsub-neg 45.9%

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

      4. *-commutative 45.9%

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

   5. Simplified 45.9%

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

   6. Taylor expanded in z around 0 39.0%

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

      1. mul-1-neg 39.0%

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

      2. *-commutative 39.0%

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

      3. distribute-rgt-neg-in 39.0%

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

   8. Simplified 39.0%

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

   if -2.00000000000000013e-68 < j < -6.0000000000000001e-282

   1. Initial program 75.6%

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

   3. Taylor expanded in y around inf 62.3%

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

      1. *-commutative 62.3%

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

      2. associate-*r* 59.5%

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

      3. *-commutative 59.5%

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

   5. Simplified 59.5%

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

   6. Taylor expanded in t around inf 34.7%

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

      1. associate-*r* 32.1%

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

      2. *-commutative 32.1%

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

      3. associate-*r* 37.4%

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

   8. Simplified 37.4%

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

   if -6.0000000000000001e-282 < j < 3.79999999999999967e-167

   1. Initial program 70.5%

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

   3. Taylor expanded in y around inf 46.4%

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

      1. +-commutative 46.4%

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

      2. mul-1-neg 46.4%

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

      3. unsub-neg 46.4%

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

      4. *-commutative 46.4%

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

   5. Simplified 46.4%

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

   6. Taylor expanded in z around inf 41.4%

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

      1. *-commutative 41.4%

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

   8. Simplified 41.4%

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

   if 3.79999999999999967e-167 < j < 1.95e63

   1. Initial program 84.3%

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

   3. Taylor expanded in a around inf 49.5%

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

      1. +-commutative 49.5%

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

      2. mul-1-neg 49.5%

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

      3. unsub-neg 49.5%

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

   5. Simplified 49.5%

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

   6. Taylor expanded in c around 0 39.0%

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

      1. mul-1-neg 39.0%

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

      2. *-commutative 39.0%

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

      3. distribute-rgt-neg-in 39.0%

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

      4. distribute-rgt-neg-in 39.0%

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

      5. *-commutative 39.0%

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

      6. distribute-lft-neg-out 39.0%

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

   8. Simplified 39.0%

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

   if 1.95e63 < j < 1.89999999999999992e209

   1. Initial program 63.3%

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

   3. Taylor expanded in c around inf 48.3%

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

      1. *-commutative 48.3%

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

   5. Simplified 48.3%

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

   6. Taylor expanded in j around 0 41.2%

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

      1. mul-1-neg 41.2%

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

      2. distribute-lft-neg-out 41.2%

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

      3. *-commutative 41.2%

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

   8. Simplified 41.2%

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

   if 1.89999999999999992e209 < j

   1. Initial program 56.0%

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

   3. Taylor expanded in y around inf 60.3%

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

      1. *-commutative 60.3%

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

      2. associate-*r* 60.5%

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

      3. *-commutative 60.5%

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

   5. Simplified 60.5%

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

   6. Taylor expanded in a around inf 45.1%

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

      1. *-commutative 45.1%

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

      2. associate-*l* 56.4%

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

   8. Simplified 56.4%

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

4. Final simplification 41.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2 \cdot 10^{-68}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;j \leq -6 \cdot 10^{-282}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;j \leq 3.8 \cdot 10^{-167}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 1.95 \cdot 10^{+63}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;j \leq 1.9 \cdot 10^{+209}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 40.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{if}\;b \leq -6.5 \cdot 10^{+121}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -9.8 \cdot 10^{-175}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{-256}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+144}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))) (t_2 (* c (* z (- b)))))
   (if (<= b -6.5e+121)
     t_2
     (if (<= b -9.8e-175)
       t_1
       (if (<= b -1.6e-256)
         (* i (* y (- j)))
         (if (<= b 2.5e+59) t_1 (if (<= b 8.5e+144) t_2 (* t (* b i)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = c * (z * -b);
	double tmp;
	if (b <= -6.5e+121) {
		tmp = t_2;
	} else if (b <= -9.8e-175) {
		tmp = t_1;
	} else if (b <= -1.6e-256) {
		tmp = i * (y * -j);
	} else if (b <= 2.5e+59) {
		tmp = t_1;
	} else if (b <= 8.5e+144) {
		tmp = t_2;
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    t_2 = c * (z * -b)
    if (b <= (-6.5d+121)) then
        tmp = t_2
    else if (b <= (-9.8d-175)) then
        tmp = t_1
    else if (b <= (-1.6d-256)) then
        tmp = i * (y * -j)
    else if (b <= 2.5d+59) then
        tmp = t_1
    else if (b <= 8.5d+144) then
        tmp = t_2
    else
        tmp = t * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = c * (z * -b);
	double tmp;
	if (b <= -6.5e+121) {
		tmp = t_2;
	} else if (b <= -9.8e-175) {
		tmp = t_1;
	} else if (b <= -1.6e-256) {
		tmp = i * (y * -j);
	} else if (b <= 2.5e+59) {
		tmp = t_1;
	} else if (b <= 8.5e+144) {
		tmp = t_2;
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = c * (z * -b)
	tmp = 0
	if b <= -6.5e+121:
		tmp = t_2
	elif b <= -9.8e-175:
		tmp = t_1
	elif b <= -1.6e-256:
		tmp = i * (y * -j)
	elif b <= 2.5e+59:
		tmp = t_1
	elif b <= 8.5e+144:
		tmp = t_2
	else:
		tmp = t * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_2 = Float64(c * Float64(z * Float64(-b)))
	tmp = 0.0
	if (b <= -6.5e+121)
		tmp = t_2;
	elseif (b <= -9.8e-175)
		tmp = t_1;
	elseif (b <= -1.6e-256)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (b <= 2.5e+59)
		tmp = t_1;
	elseif (b <= 8.5e+144)
		tmp = t_2;
	else
		tmp = Float64(t * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	t_2 = c * (z * -b);
	tmp = 0.0;
	if (b <= -6.5e+121)
		tmp = t_2;
	elseif (b <= -9.8e-175)
		tmp = t_1;
	elseif (b <= -1.6e-256)
		tmp = i * (y * -j);
	elseif (b <= 2.5e+59)
		tmp = t_1;
	elseif (b <= 8.5e+144)
		tmp = t_2;
	else
		tmp = t * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.5e+121], t$95$2, If[LessEqual[b, -9.8e-175], t$95$1, If[LessEqual[b, -1.6e-256], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.5e+59], t$95$1, If[LessEqual[b, 8.5e+144], t$95$2, N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -6.50000000000000019e121 or 2.4999999999999999e59 < b < 8.4999999999999998e144

   1. Initial program 72.9%

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

   3. Taylor expanded in c around inf 51.3%

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

      1. *-commutative 51.3%

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

   5. Simplified 51.3%

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

   6. Taylor expanded in j around 0 49.4%

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

      1. mul-1-neg 49.4%

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

      2. distribute-lft-neg-out 49.4%

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

      3. *-commutative 49.4%

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

   8. Simplified 49.4%

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

   if -6.50000000000000019e121 < b < -9.79999999999999996e-175 or -1.6e-256 < b < 2.4999999999999999e59

   1. Initial program 75.5%

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

   3. Taylor expanded in a around inf 45.4%

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

      1. +-commutative 45.4%

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

      2. mul-1-neg 45.4%

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

      3. unsub-neg 45.4%

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

   5. Simplified 45.4%

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

   if -9.79999999999999996e-175 < b < -1.6e-256

   1. Initial program 73.1%

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

   3. Taylor expanded in y around inf 69.3%

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

      1. +-commutative 69.3%

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

      2. mul-1-neg 69.3%

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

      3. unsub-neg 69.3%

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

      4. *-commutative 69.3%

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

   5. Simplified 69.3%

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

   6. Taylor expanded in z around 0 51.3%

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

      1. mul-1-neg 51.3%

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

      2. *-commutative 51.3%

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

      3. distribute-rgt-neg-in 51.3%

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

   8. Simplified 51.3%

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

   if 8.4999999999999998e144 < b

   1. Initial program 73.6%

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

      1. add-cube-cbrt 73.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(\sqrt[3]{j \cdot \left(c \cdot a - y \cdot i\right)} \cdot \sqrt[3]{j \cdot \left(c \cdot a - y \cdot i\right)}\right) \cdot \sqrt[3]{j \cdot \left(c \cdot a - y \cdot i\right)}} \]

      2. pow3 73.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \color{blue}{{\left(\sqrt[3]{j \cdot \left(c \cdot a - y \cdot i\right)}\right)}^{3}} \]

      3. fma-neg 73.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + {\left(\sqrt[3]{j \cdot \color{blue}{\mathsf{fma}\left(c, a, -y \cdot i\right)}}\right)}^{3} \]

      4. *-commutative 73.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + {\left(\sqrt[3]{j \cdot \mathsf{fma}\left(c, a, -\color{blue}{i \cdot y}\right)}\right)}^{3} \]

      5. distribute-rgt-neg-in 73.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + {\left(\sqrt[3]{j \cdot \mathsf{fma}\left(c, a, \color{blue}{i \cdot \left(-y\right)}\right)}\right)}^{3} \]

   4. Applied egg-rr 73.5%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \color{blue}{{\left(\sqrt[3]{j \cdot \mathsf{fma}\left(c, a, i \cdot \left(-y\right)\right)}\right)}^{3}} \]

   5. Taylor expanded in t around inf 65.4%

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

      1. distribute-lft-out-- 65.4%

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

      2. *-commutative 65.4%

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

   7. Simplified 65.4%

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

   8. Taylor expanded in t around 0 65.4%

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

      1. mul-1-neg 65.4%

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

      2. *-commutative 65.4%

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

      3. distribute-rgt-neg-out 65.4%

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

      4. *-commutative 65.4%

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

   10. Simplified 65.4%

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

   11. Taylor expanded in x around 0 59.8%

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

       1. neg-mul-1 59.8%

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

       2. distribute-rgt-neg-in 59.8%

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

   13. Simplified 59.8%

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

4. Final simplification 48.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.5 \cdot 10^{+121}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;b \leq -9.8 \cdot 10^{-175}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{-256}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+59}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+144}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 51.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -5 \cdot 10^{+31}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+32}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+49}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* a (- (* c j) (* x t)))))
   (if (<= a -5e+31)
     t_2
     (if (<= a 6e-66)
       t_1
       (if (<= a 3.8e+32) (* i (* y (- j))) (if (<= a 5e+49) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -5e+31) {
		tmp = t_2;
	} else if (a <= 6e-66) {
		tmp = t_1;
	} else if (a <= 3.8e+32) {
		tmp = i * (y * -j);
	} else if (a <= 5e+49) {
		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 * ((t * i) - (z * c))
    t_2 = a * ((c * j) - (x * t))
    if (a <= (-5d+31)) then
        tmp = t_2
    else if (a <= 6d-66) then
        tmp = t_1
    else if (a <= 3.8d+32) then
        tmp = i * (y * -j)
    else if (a <= 5d+49) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -5e+31) {
		tmp = t_2;
	} else if (a <= 6e-66) {
		tmp = t_1;
	} else if (a <= 3.8e+32) {
		tmp = i * (y * -j);
	} else if (a <= 5e+49) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -5e+31:
		tmp = t_2
	elif a <= 6e-66:
		tmp = t_1
	elif a <= 3.8e+32:
		tmp = i * (y * -j)
	elif a <= 5e+49:
		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(t * i) - Float64(z * c)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -5e+31)
		tmp = t_2;
	elseif (a <= 6e-66)
		tmp = t_1;
	elseif (a <= 3.8e+32)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (a <= 5e+49)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -5e+31)
		tmp = t_2;
	elseif (a <= 6e-66)
		tmp = t_1;
	elseif (a <= 3.8e+32)
		tmp = i * (y * -j);
	elseif (a <= 5e+49)
		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[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5e+31], t$95$2, If[LessEqual[a, 6e-66], t$95$1, If[LessEqual[a, 3.8e+32], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5e+49], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.00000000000000027e31 or 5.0000000000000004e49 < a

   1. Initial program 69.7%

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

   3. Taylor expanded in a around inf 62.1%

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

      1. +-commutative 62.1%

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

      2. mul-1-neg 62.1%

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

      3. unsub-neg 62.1%

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

   5. Simplified 62.1%

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

   if -5.00000000000000027e31 < a < 6.0000000000000004e-66 or 3.8000000000000003e32 < a < 5.0000000000000004e49

   1. Initial program 79.7%

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

   3. Taylor expanded in b around inf 49.7%

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

   if 6.0000000000000004e-66 < a < 3.8000000000000003e32

   1. Initial program 63.5%

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

   3. Taylor expanded in y around inf 57.0%

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

      1. +-commutative 57.0%

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

      2. mul-1-neg 57.0%

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

      3. unsub-neg 57.0%

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

      4. *-commutative 57.0%

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

   5. Simplified 57.0%

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

   6. Taylor expanded in z around 0 50.7%

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

      1. mul-1-neg 50.7%

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

      2. *-commutative 50.7%

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

      3. distribute-rgt-neg-in 50.7%

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

   8. Simplified 50.7%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{+31}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-66}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+32}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+49}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 51.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -5.6 \cdot 10^{-16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 1.58 \cdot 10^{-248}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1350000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 2.7 \cdot 10^{+128}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (<= j -5.6e-16)
     t_1
     (if (<= j 1.58e-248)
       (* b (- (* t i) (* z c)))
       (if (<= j 1350000.0)
         (* x (- (* y z) (* t a)))
         (if (<= j 2.7e+128) (* c (- (* a j) (* z b))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -5.6e-16) {
		tmp = t_1;
	} else if (j <= 1.58e-248) {
		tmp = b * ((t * i) - (z * c));
	} else if (j <= 1350000.0) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= 2.7e+128) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    if (j <= (-5.6d-16)) then
        tmp = t_1
    else if (j <= 1.58d-248) then
        tmp = b * ((t * i) - (z * c))
    else if (j <= 1350000.0d0) then
        tmp = x * ((y * z) - (t * a))
    else if (j <= 2.7d+128) then
        tmp = c * ((a * j) - (z * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -5.6e-16) {
		tmp = t_1;
	} else if (j <= 1.58e-248) {
		tmp = b * ((t * i) - (z * c));
	} else if (j <= 1350000.0) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= 2.7e+128) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -5.6e-16:
		tmp = t_1
	elif j <= 1.58e-248:
		tmp = b * ((t * i) - (z * c))
	elif j <= 1350000.0:
		tmp = x * ((y * z) - (t * a))
	elif j <= 2.7e+128:
		tmp = c * ((a * j) - (z * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -5.6e-16)
		tmp = t_1;
	elseif (j <= 1.58e-248)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (j <= 1350000.0)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (j <= 2.7e+128)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -5.6e-16)
		tmp = t_1;
	elseif (j <= 1.58e-248)
		tmp = b * ((t * i) - (z * c));
	elseif (j <= 1350000.0)
		tmp = x * ((y * z) - (t * a));
	elseif (j <= 2.7e+128)
		tmp = c * ((a * j) - (z * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -5.6e-16], t$95$1, If[LessEqual[j, 1.58e-248], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1350000.0], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.7e+128], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -5.6000000000000003e-16 or 2.70000000000000001e128 < j

   1. Initial program 72.4%

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

   3. Taylor expanded in j around inf 65.3%

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

      1. *-commutative 65.3%

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

   5. Simplified 65.3%

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

   if -5.6000000000000003e-16 < j < 1.57999999999999992e-248

   1. Initial program 75.2%

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

   3. Taylor expanded in b around inf 53.3%

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

   if 1.57999999999999992e-248 < j < 1.35e6

   1. Initial program 76.6%

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

   3. Taylor expanded in x around inf 53.2%

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

      1. cancel-sign-sub-inv 53.2%

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

      2. *-commutative 53.2%

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

      3. *-commutative 53.2%

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

      4. distribute-rgt-neg-out 53.2%

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

      5. sub-neg 53.2%

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

   5. Simplified 53.2%

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

   if 1.35e6 < j < 2.70000000000000001e128

   1. Initial program 76.8%

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

   3. Taylor expanded in c around inf 58.6%

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

      1. *-commutative 58.6%

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

   5. Simplified 58.6%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -5.6 \cdot 10^{-16}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 1.58 \cdot 10^{-248}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1350000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 2.7 \cdot 10^{+128}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 29.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-284}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-247}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+119}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))))
   (if (<= z -1.65e+35)
     t_1
     (if (<= z -7.5e-284)
       (* b (* t i))
       (if (<= z 2.05e-247)
         (* c (* a j))
         (if (<= z 4.1e+119) (* i (* t 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 = x * (y * z);
	double tmp;
	if (z <= -1.65e+35) {
		tmp = t_1;
	} else if (z <= -7.5e-284) {
		tmp = b * (t * i);
	} else if (z <= 2.05e-247) {
		tmp = c * (a * j);
	} else if (z <= 4.1e+119) {
		tmp = i * (t * 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 = x * (y * z)
    if (z <= (-1.65d+35)) then
        tmp = t_1
    else if (z <= (-7.5d-284)) then
        tmp = b * (t * i)
    else if (z <= 2.05d-247) then
        tmp = c * (a * j)
    else if (z <= 4.1d+119) then
        tmp = i * (t * 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 = x * (y * z);
	double tmp;
	if (z <= -1.65e+35) {
		tmp = t_1;
	} else if (z <= -7.5e-284) {
		tmp = b * (t * i);
	} else if (z <= 2.05e-247) {
		tmp = c * (a * j);
	} else if (z <= 4.1e+119) {
		tmp = i * (t * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	tmp = 0
	if z <= -1.65e+35:
		tmp = t_1
	elif z <= -7.5e-284:
		tmp = b * (t * i)
	elif z <= 2.05e-247:
		tmp = c * (a * j)
	elif z <= 4.1e+119:
		tmp = i * (t * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (z <= -1.65e+35)
		tmp = t_1;
	elseif (z <= -7.5e-284)
		tmp = Float64(b * Float64(t * i));
	elseif (z <= 2.05e-247)
		tmp = Float64(c * Float64(a * j));
	elseif (z <= 4.1e+119)
		tmp = Float64(i * Float64(t * 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 = x * (y * z);
	tmp = 0.0;
	if (z <= -1.65e+35)
		tmp = t_1;
	elseif (z <= -7.5e-284)
		tmp = b * (t * i);
	elseif (z <= 2.05e-247)
		tmp = c * (a * j);
	elseif (z <= 4.1e+119)
		tmp = i * (t * 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[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.65e+35], t$95$1, If[LessEqual[z, -7.5e-284], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.05e-247], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.1e+119], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.6500000000000001e35 or 4.0999999999999997e119 < z

   1. Initial program 62.7%

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

   3. Taylor expanded in y around inf 52.1%

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

      1. +-commutative 52.1%

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

      2. mul-1-neg 52.1%

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

      3. unsub-neg 52.1%

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

      4. *-commutative 52.1%

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

   5. Simplified 52.1%

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

   6. Taylor expanded in z around inf 44.7%

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

   if -1.6500000000000001e35 < z < -7.4999999999999999e-284

   1. Initial program 85.7%

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

   3. Taylor expanded in y around inf 74.8%

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

      1. *-commutative 74.8%

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

      2. associate-*r* 74.8%

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

      3. *-commutative 74.8%

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

   5. Simplified 74.8%

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

   6. Taylor expanded in t around inf 32.6%

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

   if -7.4999999999999999e-284 < z < 2.0499999999999999e-247

   1. Initial program 75.2%

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

   3. Taylor expanded in y around inf 67.2%

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

      1. *-commutative 67.2%

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

      2. associate-*r* 67.2%

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

      3. *-commutative 67.2%

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

   5. Simplified 67.2%

      \[\leadsto \left(\color{blue}{\left(z \cdot x\right) \cdot y} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   6. Taylor expanded in a around inf 42.9%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   7. Step-by-step derivation

      1. *-commutative 42.9%

         \[\leadsto \color{blue}{\left(c \cdot j\right) \cdot a} \]

      2. associate-*l* 51.3%

         \[\leadsto \color{blue}{c \cdot \left(j \cdot a\right)} \]

   8. Simplified 51.3%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a\right)} \]

   if 2.0499999999999999e-247 < z < 4.0999999999999997e119

   1. Initial program 77.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 64.1%

      \[\leadsto \left(\color{blue}{x \cdot \left(y \cdot z\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. *-commutative 64.1%

         \[\leadsto \left(x \cdot \color{blue}{\left(z \cdot y\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. associate-*r* 68.2%

         \[\leadsto \left(\color{blue}{\left(x \cdot z\right) \cdot y} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 68.2%

         \[\leadsto \left(\color{blue}{\left(z \cdot x\right)} \cdot y - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Simplified 68.2%

      \[\leadsto \left(\color{blue}{\left(z \cdot x\right) \cdot y} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   6. Taylor expanded in t around inf 22.7%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 25.1%

         \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot t} \]

      2. *-commutative 25.1%

         \[\leadsto \color{blue}{\left(i \cdot b\right)} \cdot t \]

      3. associate-*r* 25.1%

         \[\leadsto \color{blue}{i \cdot \left(b \cdot t\right)} \]

   8. Simplified 25.1%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot t\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 35.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+35}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-284}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-247}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+119}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 29.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+35}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-284}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-259}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+119}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -8.5e+35)
   (* z (* x y))
   (if (<= z -1.4e-284)
     (* b (* t i))
     (if (<= z 6e-259)
       (* c (* a j))
       (if (<= z 3e+119) (* i (* t b)) (* x (* y z)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -8.5e+35) {
		tmp = z * (x * y);
	} else if (z <= -1.4e-284) {
		tmp = b * (t * i);
	} else if (z <= 6e-259) {
		tmp = c * (a * j);
	} else if (z <= 3e+119) {
		tmp = i * (t * b);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-8.5d+35)) then
        tmp = z * (x * y)
    else if (z <= (-1.4d-284)) then
        tmp = b * (t * i)
    else if (z <= 6d-259) then
        tmp = c * (a * j)
    else if (z <= 3d+119) then
        tmp = i * (t * b)
    else
        tmp = x * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -8.5e+35) {
		tmp = z * (x * y);
	} else if (z <= -1.4e-284) {
		tmp = b * (t * i);
	} else if (z <= 6e-259) {
		tmp = c * (a * j);
	} else if (z <= 3e+119) {
		tmp = i * (t * b);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -8.5e+35:
		tmp = z * (x * y)
	elif z <= -1.4e-284:
		tmp = b * (t * i)
	elif z <= 6e-259:
		tmp = c * (a * j)
	elif z <= 3e+119:
		tmp = i * (t * b)
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -8.5e+35)
		tmp = Float64(z * Float64(x * y));
	elseif (z <= -1.4e-284)
		tmp = Float64(b * Float64(t * i));
	elseif (z <= 6e-259)
		tmp = Float64(c * Float64(a * j));
	elseif (z <= 3e+119)
		tmp = Float64(i * Float64(t * b));
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -8.5e+35)
		tmp = z * (x * y);
	elseif (z <= -1.4e-284)
		tmp = b * (t * i);
	elseif (z <= 6e-259)
		tmp = c * (a * j);
	elseif (z <= 3e+119)
		tmp = i * (t * b);
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -8.5e+35], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.4e-284], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e-259], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e+119], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -8.4999999999999995e35

   1. Initial program 56.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 56.6%

      \[\leadsto \left(\color{blue}{x \cdot \left(y \cdot z\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. *-commutative 56.6%

         \[\leadsto \left(x \cdot \color{blue}{\left(z \cdot y\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. associate-*r* 60.3%

         \[\leadsto \left(\color{blue}{\left(x \cdot z\right) \cdot y} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 60.3%

         \[\leadsto \left(\color{blue}{\left(z \cdot x\right)} \cdot y - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Simplified 60.3%

      \[\leadsto \left(\color{blue}{\left(z \cdot x\right) \cdot y} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   6. Taylor expanded in c around inf 60.5%

      \[\leadsto \left(\left(z \cdot x\right) \cdot y - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \color{blue}{a \cdot \left(c \cdot j\right)} \]
   7. Step-by-step derivation

      1. *-commutative 60.5%

         \[\leadsto \left(\left(z \cdot x\right) \cdot y - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(c \cdot j\right) \cdot a} \]

      2. associate-*r* 62.5%

         \[\leadsto \left(\left(z \cdot x\right) \cdot y - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \color{blue}{c \cdot \left(j \cdot a\right)} \]

   8. Simplified 62.5%

      \[\leadsto \left(\left(z \cdot x\right) \cdot y - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \color{blue}{c \cdot \left(j \cdot a\right)} \]

   9. Taylor expanded in x around inf 45.6%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 47.4%

          \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot z} \]

       2. *-commutative 47.4%

          \[\leadsto \color{blue}{z \cdot \left(x \cdot y\right)} \]

   11. Simplified 47.4%

       \[\leadsto \color{blue}{z \cdot \left(x \cdot y\right)} \]

   if -8.4999999999999995e35 < z < -1.4000000000000001e-284

   1. Initial program 85.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 74.8%

      \[\leadsto \left(\color{blue}{x \cdot \left(y \cdot z\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. *-commutative 74.8%

         \[\leadsto \left(x \cdot \color{blue}{\left(z \cdot y\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. associate-*r* 74.8%

         \[\leadsto \left(\color{blue}{\left(x \cdot z\right) \cdot y} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 74.8%

         \[\leadsto \left(\color{blue}{\left(z \cdot x\right)} \cdot y - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Simplified 74.8%

      \[\leadsto \left(\color{blue}{\left(z \cdot x\right) \cdot y} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   6. Taylor expanded in t around inf 32.6%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]

   if -1.4000000000000001e-284 < z < 6.0000000000000004e-259

   1. Initial program 72.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 64.2%

      \[\leadsto \left(\color{blue}{x \cdot \left(y \cdot z\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. *-commutative 64.2%

         \[\leadsto \left(x \cdot \color{blue}{\left(z \cdot y\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. associate-*r* 64.2%

         \[\leadsto \left(\color{blue}{\left(x \cdot z\right) \cdot y} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 64.2%

         \[\leadsto \left(\color{blue}{\left(z \cdot x\right)} \cdot y - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Simplified 64.2%

      \[\leadsto \left(\color{blue}{\left(z \cdot x\right) \cdot y} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   6. Taylor expanded in a around inf 46.3%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   7. Step-by-step derivation

      1. *-commutative 46.3%

         \[\leadsto \color{blue}{\left(c \cdot j\right) \cdot a} \]

      2. associate-*l* 55.6%

         \[\leadsto \color{blue}{c \cdot \left(j \cdot a\right)} \]

   8. Simplified 55.6%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a\right)} \]

   if 6.0000000000000004e-259 < z < 3.00000000000000001e119

   1. Initial program 77.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 64.6%

      \[\leadsto \left(\color{blue}{x \cdot \left(y \cdot z\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. *-commutative 64.6%

         \[\leadsto \left(x \cdot \color{blue}{\left(z \cdot y\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. associate-*r* 68.6%

         \[\leadsto \left(\color{blue}{\left(x \cdot z\right) \cdot y} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 68.6%

         \[\leadsto \left(\color{blue}{\left(z \cdot x\right)} \cdot y - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Simplified 68.6%

      \[\leadsto \left(\color{blue}{\left(z \cdot x\right) \cdot y} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   6. Taylor expanded in t around inf 22.4%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 24.8%

         \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot t} \]

      2. *-commutative 24.8%

         \[\leadsto \color{blue}{\left(i \cdot b\right)} \cdot t \]

      3. associate-*r* 24.8%

         \[\leadsto \color{blue}{i \cdot \left(b \cdot t\right)} \]

   8. Simplified 24.8%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot t\right)} \]

   if 3.00000000000000001e119 < z

   1. Initial program 70.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 48.3%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 48.3%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 48.3%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 48.3%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 48.3%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   5. Simplified 48.3%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   6. Taylor expanded in z around inf 43.6%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 36.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+35}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-284}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-259}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+119}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 29.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8.5 \cdot 10^{-32}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{-107}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq -6.6 \cdot 10^{-186}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;b \leq 10^{+150}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -8.5e-32)
   (* i (* t b))
   (if (<= b -2.7e-107)
     (* a (* c j))
     (if (<= b -6.6e-186)
       (* (* x t) (- a))
       (if (<= b 1e+150) (* z (* x y)) (* b (* t i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -8.5e-32) {
		tmp = i * (t * b);
	} else if (b <= -2.7e-107) {
		tmp = a * (c * j);
	} else if (b <= -6.6e-186) {
		tmp = (x * t) * -a;
	} else if (b <= 1e+150) {
		tmp = z * (x * y);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-8.5d-32)) then
        tmp = i * (t * b)
    else if (b <= (-2.7d-107)) then
        tmp = a * (c * j)
    else if (b <= (-6.6d-186)) then
        tmp = (x * t) * -a
    else if (b <= 1d+150) then
        tmp = z * (x * y)
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -8.5e-32) {
		tmp = i * (t * b);
	} else if (b <= -2.7e-107) {
		tmp = a * (c * j);
	} else if (b <= -6.6e-186) {
		tmp = (x * t) * -a;
	} else if (b <= 1e+150) {
		tmp = z * (x * y);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -8.5e-32:
		tmp = i * (t * b)
	elif b <= -2.7e-107:
		tmp = a * (c * j)
	elif b <= -6.6e-186:
		tmp = (x * t) * -a
	elif b <= 1e+150:
		tmp = z * (x * y)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -8.5e-32)
		tmp = Float64(i * Float64(t * b));
	elseif (b <= -2.7e-107)
		tmp = Float64(a * Float64(c * j));
	elseif (b <= -6.6e-186)
		tmp = Float64(Float64(x * t) * Float64(-a));
	elseif (b <= 1e+150)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -8.5e-32)
		tmp = i * (t * b);
	elseif (b <= -2.7e-107)
		tmp = a * (c * j);
	elseif (b <= -6.6e-186)
		tmp = (x * t) * -a;
	elseif (b <= 1e+150)
		tmp = z * (x * y);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -8.5e-32], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.7e-107], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -6.6e-186], N[(N[(x * t), $MachinePrecision] * (-a)), $MachinePrecision], If[LessEqual[b, 1e+150], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -8.5000000000000003e-32

   1. Initial program 77.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 70.4%

      \[\leadsto \left(\color{blue}{x \cdot \left(y \cdot z\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. *-commutative 70.4%

         \[\leadsto \left(x \cdot \color{blue}{\left(z \cdot y\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. associate-*r* 74.8%

         \[\leadsto \left(\color{blue}{\left(x \cdot z\right) \cdot y} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 74.8%

         \[\leadsto \left(\color{blue}{\left(z \cdot x\right)} \cdot y - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Simplified 74.8%

      \[\leadsto \left(\color{blue}{\left(z \cdot x\right) \cdot y} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   6. Taylor expanded in t around inf 28.0%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 28.1%

         \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot t} \]

      2. *-commutative 28.1%

         \[\leadsto \color{blue}{\left(i \cdot b\right)} \cdot t \]

      3. associate-*r* 29.5%

         \[\leadsto \color{blue}{i \cdot \left(b \cdot t\right)} \]

   8. Simplified 29.5%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot t\right)} \]

   if -8.5000000000000003e-32 < b < -2.7e-107

   1. Initial program 78.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 55.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 55.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 55.0%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 55.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   5. Simplified 55.0%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   6. Taylor expanded in c around inf 47.9%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   7. Step-by-step derivation

      1. *-commutative 47.9%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   8. Simplified 47.9%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c\right)} \]

   if -2.7e-107 < b < -6.59999999999999998e-186

   1. Initial program 89.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 59.3%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 59.3%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 59.3%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 59.3%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   5. Simplified 59.3%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   6. Taylor expanded in c around 0 48.6%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 48.6%

         \[\leadsto \color{blue}{-a \cdot \left(t \cdot x\right)} \]

      2. *-commutative 48.6%

         \[\leadsto -a \cdot \color{blue}{\left(x \cdot t\right)} \]

      3. distribute-rgt-neg-in 48.6%

         \[\leadsto \color{blue}{a \cdot \left(-x \cdot t\right)} \]

      4. distribute-rgt-neg-in 48.6%

         \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

      5. *-commutative 48.6%

         \[\leadsto a \cdot \color{blue}{\left(\left(-t\right) \cdot x\right)} \]

      6. distribute-lft-neg-out 48.6%

         \[\leadsto a \cdot \color{blue}{\left(-t \cdot x\right)} \]

   8. Simplified 48.6%

      \[\leadsto \color{blue}{a \cdot \left(-t \cdot x\right)} \]

   if -6.59999999999999998e-186 < b < 9.99999999999999981e149

   1. Initial program 70.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 63.2%

      \[\leadsto \left(\color{blue}{x \cdot \left(y \cdot z\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. *-commutative 63.2%

         \[\leadsto \left(x \cdot \color{blue}{\left(z \cdot y\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. associate-*r* 61.7%

         \[\leadsto \left(\color{blue}{\left(x \cdot z\right) \cdot y} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 61.7%

         \[\leadsto \left(\color{blue}{\left(z \cdot x\right)} \cdot y - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Simplified 61.7%

      \[\leadsto \left(\color{blue}{\left(z \cdot x\right) \cdot y} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   6. Taylor expanded in c around inf 49.5%

      \[\leadsto \left(\left(z \cdot x\right) \cdot y - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \color{blue}{a \cdot \left(c \cdot j\right)} \]
   7. Step-by-step derivation

      1. *-commutative 49.5%

         \[\leadsto \left(\left(z \cdot x\right) \cdot y - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(c \cdot j\right) \cdot a} \]

      2. associate-*r* 52.6%

         \[\leadsto \left(\left(z \cdot x\right) \cdot y - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \color{blue}{c \cdot \left(j \cdot a\right)} \]

   8. Simplified 52.6%

      \[\leadsto \left(\left(z \cdot x\right) \cdot y - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \color{blue}{c \cdot \left(j \cdot a\right)} \]

   9. Taylor expanded in x around inf 29.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 31.5%

          \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot z} \]

       2. *-commutative 31.5%

          \[\leadsto \color{blue}{z \cdot \left(x \cdot y\right)} \]

   11. Simplified 31.5%

       \[\leadsto \color{blue}{z \cdot \left(x \cdot y\right)} \]

   if 9.99999999999999981e149 < b

   1. Initial program 72.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 75.2%

      \[\leadsto \left(\color{blue}{x \cdot \left(y \cdot z\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. *-commutative 75.2%

         \[\leadsto \left(x \cdot \color{blue}{\left(z \cdot y\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. associate-*r* 75.1%

         \[\leadsto \left(\color{blue}{\left(x \cdot z\right) \cdot y} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 75.1%

         \[\leadsto \left(\color{blue}{\left(z \cdot x\right)} \cdot y - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Simplified 75.1%

      \[\leadsto \left(\color{blue}{\left(z \cdot x\right) \cdot y} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   6. Taylor expanded in t around inf 63.4%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 37.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.5 \cdot 10^{-32}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{-107}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq -6.6 \cdot 10^{-186}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;b \leq 10^{+150}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 29.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -9.4 \cdot 10^{-20} \lor \neg \left(j \leq 0.0033\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -9.4e-20) (not (<= j 0.0033))) (* a (* c j)) (* b (* t i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -9.4e-20) || !(j <= 0.0033)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((j <= (-9.4d-20)) .or. (.not. (j <= 0.0033d0))) then
        tmp = a * (c * j)
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -9.4e-20) || !(j <= 0.0033)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -9.4e-20) or not (j <= 0.0033):
		tmp = a * (c * j)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -9.4e-20) || !(j <= 0.0033))
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -9.4e-20) || ~((j <= 0.0033)))
		tmp = a * (c * j);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -9.4e-20], N[Not[LessEqual[j, 0.0033]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -9.4000000000000003e-20 or 0.0033 < j

   1. Initial program 73.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 43.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 43.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 43.5%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 43.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   5. Simplified 43.5%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   6. Taylor expanded in c around inf 31.6%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   7. Step-by-step derivation

      1. *-commutative 31.6%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   8. Simplified 31.6%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c\right)} \]

   if -9.4000000000000003e-20 < j < 0.0033

   1. Initial program 75.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 64.3%

      \[\leadsto \left(\color{blue}{x \cdot \left(y \cdot z\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. *-commutative 64.3%

         \[\leadsto \left(x \cdot \color{blue}{\left(z \cdot y\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. associate-*r* 64.2%

         \[\leadsto \left(\color{blue}{\left(x \cdot z\right) \cdot y} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 64.2%

         \[\leadsto \left(\color{blue}{\left(z \cdot x\right)} \cdot y - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Simplified 64.2%

      \[\leadsto \left(\color{blue}{\left(z \cdot x\right) \cdot y} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   6. Taylor expanded in t around inf 30.5%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 31.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -9.4 \cdot 10^{-20} \lor \neg \left(j \leq 0.0033\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 29.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -5 \cdot 10^{-16} \lor \neg \left(j \leq 610000\right):\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -5e-16) (not (<= j 610000.0))) (* c (* a j)) (* b (* t i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -5e-16) || !(j <= 610000.0)) {
		tmp = c * (a * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((j <= (-5d-16)) .or. (.not. (j <= 610000.0d0))) then
        tmp = c * (a * j)
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -5e-16) || !(j <= 610000.0)) {
		tmp = c * (a * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -5e-16) or not (j <= 610000.0):
		tmp = c * (a * j)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -5e-16) || !(j <= 610000.0))
		tmp = Float64(c * Float64(a * j));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -5e-16) || ~((j <= 610000.0)))
		tmp = c * (a * j);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -5e-16], N[Not[LessEqual[j, 610000.0]], $MachinePrecision]], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -5.0000000000000004e-16 or 6.1e5 < j

   1. Initial program 73.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 68.5%

      \[\leadsto \left(\color{blue}{x \cdot \left(y \cdot z\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. *-commutative 68.5%

         \[\leadsto \left(x \cdot \color{blue}{\left(z \cdot y\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. associate-*r* 69.3%

         \[\leadsto \left(\color{blue}{\left(x \cdot z\right) \cdot y} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 69.3%

         \[\leadsto \left(\color{blue}{\left(z \cdot x\right)} \cdot y - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Simplified 69.3%

      \[\leadsto \left(\color{blue}{\left(z \cdot x\right) \cdot y} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   6. Taylor expanded in a around inf 31.8%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   7. Step-by-step derivation

      1. *-commutative 31.8%

         \[\leadsto \color{blue}{\left(c \cdot j\right) \cdot a} \]

      2. associate-*l* 33.3%

         \[\leadsto \color{blue}{c \cdot \left(j \cdot a\right)} \]

   8. Simplified 33.3%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a\right)} \]

   if -5.0000000000000004e-16 < j < 6.1e5

   1. Initial program 75.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 64.6%

      \[\leadsto \left(\color{blue}{x \cdot \left(y \cdot z\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. *-commutative 64.6%

         \[\leadsto \left(x \cdot \color{blue}{\left(z \cdot y\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. associate-*r* 64.5%

         \[\leadsto \left(\color{blue}{\left(x \cdot z\right) \cdot y} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 64.5%

         \[\leadsto \left(\color{blue}{\left(z \cdot x\right)} \cdot y - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Simplified 64.5%

      \[\leadsto \left(\color{blue}{\left(z \cdot x\right) \cdot y} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   6. Taylor expanded in t around inf 30.3%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 31.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -5 \cdot 10^{-16} \lor \neg \left(j \leq 610000\right):\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 21.9% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(c \cdot j\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* c j)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = a * (c * j)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (c * j)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(c * j))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (c * j);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 74.5%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
2. Add Preprocessing

3. Taylor expanded in a around inf 36.3%

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
4. Step-by-step derivation

   1. +-commutative 36.3%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

   2. mul-1-neg 36.3%

      \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

   3. unsub-neg 36.3%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

5. Simplified 36.3%

   \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

6. Taylor expanded in c around inf 20.3%

   \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
7. Step-by-step derivation

   1. *-commutative 20.3%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

8. Simplified 20.3%

   \[\leadsto \color{blue}{a \cdot \left(j \cdot c\right)} \]

9. Final simplification 20.3%

   \[\leadsto a \cdot \left(c \cdot j\right) \]
10. Add Preprocessing

Developer target: 59.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right)\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + t\_1\\ \mathbf{if}\;x < -1.469694296777705 \cdot 10^{-64}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x < 3.2113527362226803 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* c a) (* y i))))
        (t_2
         (+
          (-
           (* x (- (* y z) (* t a)))
           (/
            (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0)))
            (+ (* c z) (* t i))))
          t_1)))
   (if (< x -1.469694296777705e-64)
     t_2
     (if (< x 3.2113527362226803e-147)
       (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) t_1))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (pow((c * z), 2.0) - pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((c * a) - (y * i))
    t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ** 2.0d0) - ((t * i) ** 2.0d0))) / ((c * z) + (t * i)))) + t_1
    if (x < (-1.469694296777705d-64)) then
        tmp = t_2
    else if (x < 3.2113527362226803d-147) then
        tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (Math.pow((c * z), 2.0) - Math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((c * a) - (y * i))
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (math.pow((c * z), 2.0) - math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1
	tmp = 0
	if x < -1.469694296777705e-64:
		tmp = t_2
	elif x < 3.2113527362226803e-147:
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(c * a) - Float64(y * i)))
	t_2 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(Float64(b * Float64((Float64(c * z) ^ 2.0) - (Float64(t * i) ^ 2.0))) / Float64(Float64(c * z) + Float64(t * i)))) + t_1)
	tmp = 0.0
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = Float64(Float64(Float64(Float64(b * i) - Float64(x * a)) * t) - Float64(Float64(z * Float64(c * b)) - t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((c * a) - (y * i));
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ^ 2.0) - ((t * i) ^ 2.0))) / ((c * z) + (t * i)))) + t_1;
	tmp = 0.0;
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[Power[N[(c * z), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(t * i), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * z), $MachinePrecision] + N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[Less[x, -1.469694296777705e-64], t$95$2, If[Less[x, 3.2113527362226803e-147], N[(N[(N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] - N[(N[(z * N[(c * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024078 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :alt
  (if (< x -1.469694296777705e-64) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 3.2113527362226803e-147) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i)))))