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

Percentage Accurate: 73.3% → 81.6%

Time: 25.0s

Alternatives: 26

Speedup: 0.5×

• 58.2% 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: 73.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 81.6% accurate, 0.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 90.1%

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

   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. Step-by-step derivation

      1. +-commutative 0.0%

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

      2. fma-define 9.5%

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

      3. *-commutative 9.5%

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

      4. sub-neg 9.5%

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

      5. *-commutative 9.5%

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

      6. sub-neg 9.5%

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

      7. *-commutative 9.5%

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

      8. *-commutative 9.5%

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

   3. Simplified 9.5%

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

   5. Taylor expanded in c around inf 45.5%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)}\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 45.5%

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

      2. *-commutative 45.5%

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

      3. associate-*l* 54.8%

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

      4. *-commutative 54.8%

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

      5. distribute-rgt-neg-in 54.8%

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

      6. distribute-rgt-neg-in 54.8%

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

   7. Simplified 54.8%

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

4. Final simplification 84.3%

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

Alternative 2: 81.3% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (+ (* b (- (* t i) (* z c))) (* x (- (* y z) (* t a))))
          (* j (- (* a c) (* y i))))))
   (if (<= t_1 INFINITY)
     t_1
     (- (* c (- (* a j) (* i (/ (* y j) c)))) (* z (* b 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 = ((b * ((t * i) - (z * c))) + (x * ((y * z) - (t * a)))) + (j * ((a * c) - (y * i)));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = (c * ((a * j) - (i * ((y * j) / c)))) - (z * (b * c));
	}
	return tmp;
}

Java

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

Python

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

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) + Float64(x * Float64(Float64(y * z) - Float64(t * a)))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(c * Float64(Float64(a * j) - Float64(i * Float64(Float64(y * j) / c)))) - Float64(z * Float64(b * c)));
	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))) + (x * ((y * z) - (t * a)))) + (j * ((a * c) - (y * i)));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = (c * ((a * j) - (i * ((y * j) / c)))) - (z * (b * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $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[(N[(c * N[(N[(a * j), $MachinePrecision] - N[(i * N[(N[(y * j), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[(b * c), $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 90.1%

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

   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. Step-by-step derivation

      1. +-commutative 0.0%

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

      2. fma-define 9.5%

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

      3. *-commutative 9.5%

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

      4. sub-neg 9.5%

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

      5. *-commutative 9.5%

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

      6. sub-neg 9.5%

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

      7. *-commutative 9.5%

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

      8. *-commutative 9.5%

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

   3. Simplified 9.5%

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

   5. Taylor expanded in x around -inf 23.8%

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

      1. mul-1-neg 23.8%

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

      2. distribute-rgt-neg-in 23.8%

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

      3. +-commutative 23.8%

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

      4. mul-1-neg 23.8%

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

      5. unsub-neg 23.8%

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

      6. associate-/l* 28.6%

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

   7. Simplified 28.6%

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

   8. Taylor expanded in x around 0 35.9%

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

      1. +-commutative 35.9%

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

      2. *-commutative 35.9%

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

      3. sub-neg 35.9%

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

      4. sub-neg 35.9%

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

      5. mul-1-neg 35.9%

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

      6. unsub-neg 35.9%

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

   10. Simplified 35.9%

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

   11. Taylor expanded in c around inf 40.8%

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

       1. associate-*r* 47.7%

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

       2. *-commutative 47.7%

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

   13. Simplified 47.7%

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

   14. Taylor expanded in c around inf 52.4%

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

       1. +-commutative 52.4%

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

       2. mul-1-neg 52.4%

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

       3. unsub-neg 52.4%

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

       4. *-commutative 52.4%

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

       5. associate-/l* 54.8%

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

   16. Simplified 54.8%

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

4. Final simplification 84.3%

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

Alternative 3: 50.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_3 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;t \leq -1.05 \cdot 10^{+142}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{+98}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{+63}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-69}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-168}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-291}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-250}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-69}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+161}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i))))
        (t_2 (* t (- (* b i) (* x a))))
        (t_3 (* z (- (* x y) (* b c)))))
   (if (<= t -1.05e+142)
     t_2
     (if (<= t -4.8e+98)
       (* y (- (* x z) (* i j)))
       (if (<= t -3.8e+63)
         t_2
         (if (<= t -3.2e+24)
           t_1
           (if (<= t -2.7e-69)
             t_3
             (if (<= t -3.8e-168)
               (- (* a (* c j)) (* b (* z c)))
               (if (<= t -4.4e-291)
                 t_3
                 (if (<= t 4.4e-250)
                   t_1
                   (if (<= t 1.8e-69)
                     (- (* (* z c) (- b)) (* i (* y j)))
                     (if (<= t 1.8e+161)
                       (* b (- (* t i) (* z c)))
                       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));
	double t_2 = t * ((b * i) - (x * a));
	double t_3 = z * ((x * y) - (b * c));
	double tmp;
	if (t <= -1.05e+142) {
		tmp = t_2;
	} else if (t <= -4.8e+98) {
		tmp = y * ((x * z) - (i * j));
	} else if (t <= -3.8e+63) {
		tmp = t_2;
	} else if (t <= -3.2e+24) {
		tmp = t_1;
	} else if (t <= -2.7e-69) {
		tmp = t_3;
	} else if (t <= -3.8e-168) {
		tmp = (a * (c * j)) - (b * (z * c));
	} else if (t <= -4.4e-291) {
		tmp = t_3;
	} else if (t <= 4.4e-250) {
		tmp = t_1;
	} else if (t <= 1.8e-69) {
		tmp = ((z * c) * -b) - (i * (y * j));
	} else if (t <= 1.8e+161) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = t * ((b * i) - (x * a))
    t_3 = z * ((x * y) - (b * c))
    if (t <= (-1.05d+142)) then
        tmp = t_2
    else if (t <= (-4.8d+98)) then
        tmp = y * ((x * z) - (i * j))
    else if (t <= (-3.8d+63)) then
        tmp = t_2
    else if (t <= (-3.2d+24)) then
        tmp = t_1
    else if (t <= (-2.7d-69)) then
        tmp = t_3
    else if (t <= (-3.8d-168)) then
        tmp = (a * (c * j)) - (b * (z * c))
    else if (t <= (-4.4d-291)) then
        tmp = t_3
    else if (t <= 4.4d-250) then
        tmp = t_1
    else if (t <= 1.8d-69) then
        tmp = ((z * c) * -b) - (i * (y * j))
    else if (t <= 1.8d+161) then
        tmp = b * ((t * i) - (z * c))
    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));
	double t_2 = t * ((b * i) - (x * a));
	double t_3 = z * ((x * y) - (b * c));
	double tmp;
	if (t <= -1.05e+142) {
		tmp = t_2;
	} else if (t <= -4.8e+98) {
		tmp = y * ((x * z) - (i * j));
	} else if (t <= -3.8e+63) {
		tmp = t_2;
	} else if (t <= -3.2e+24) {
		tmp = t_1;
	} else if (t <= -2.7e-69) {
		tmp = t_3;
	} else if (t <= -3.8e-168) {
		tmp = (a * (c * j)) - (b * (z * c));
	} else if (t <= -4.4e-291) {
		tmp = t_3;
	} else if (t <= 4.4e-250) {
		tmp = t_1;
	} else if (t <= 1.8e-69) {
		tmp = ((z * c) * -b) - (i * (y * j));
	} else if (t <= 1.8e+161) {
		tmp = b * ((t * i) - (z * c));
	} 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))
	t_2 = t * ((b * i) - (x * a))
	t_3 = z * ((x * y) - (b * c))
	tmp = 0
	if t <= -1.05e+142:
		tmp = t_2
	elif t <= -4.8e+98:
		tmp = y * ((x * z) - (i * j))
	elif t <= -3.8e+63:
		tmp = t_2
	elif t <= -3.2e+24:
		tmp = t_1
	elif t <= -2.7e-69:
		tmp = t_3
	elif t <= -3.8e-168:
		tmp = (a * (c * j)) - (b * (z * c))
	elif t <= -4.4e-291:
		tmp = t_3
	elif t <= 4.4e-250:
		tmp = t_1
	elif t <= 1.8e-69:
		tmp = ((z * c) * -b) - (i * (y * j))
	elif t <= 1.8e+161:
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = t_2
	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(t * Float64(Float64(b * i) - Float64(x * a)))
	t_3 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (t <= -1.05e+142)
		tmp = t_2;
	elseif (t <= -4.8e+98)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (t <= -3.8e+63)
		tmp = t_2;
	elseif (t <= -3.2e+24)
		tmp = t_1;
	elseif (t <= -2.7e-69)
		tmp = t_3;
	elseif (t <= -3.8e-168)
		tmp = Float64(Float64(a * Float64(c * j)) - Float64(b * Float64(z * c)));
	elseif (t <= -4.4e-291)
		tmp = t_3;
	elseif (t <= 4.4e-250)
		tmp = t_1;
	elseif (t <= 1.8e-69)
		tmp = Float64(Float64(Float64(z * c) * Float64(-b)) - Float64(i * Float64(y * j)));
	elseif (t <= 1.8e+161)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	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));
	t_2 = t * ((b * i) - (x * a));
	t_3 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (t <= -1.05e+142)
		tmp = t_2;
	elseif (t <= -4.8e+98)
		tmp = y * ((x * z) - (i * j));
	elseif (t <= -3.8e+63)
		tmp = t_2;
	elseif (t <= -3.2e+24)
		tmp = t_1;
	elseif (t <= -2.7e-69)
		tmp = t_3;
	elseif (t <= -3.8e-168)
		tmp = (a * (c * j)) - (b * (z * c));
	elseif (t <= -4.4e-291)
		tmp = t_3;
	elseif (t <= 4.4e-250)
		tmp = t_1;
	elseif (t <= 1.8e-69)
		tmp = ((z * c) * -b) - (i * (y * j));
	elseif (t <= 1.8e+161)
		tmp = b * ((t * i) - (z * c));
	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[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.05e+142], t$95$2, If[LessEqual[t, -4.8e+98], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.8e+63], t$95$2, If[LessEqual[t, -3.2e+24], t$95$1, If[LessEqual[t, -2.7e-69], t$95$3, If[LessEqual[t, -3.8e-168], N[(N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.4e-291], t$95$3, If[LessEqual[t, 4.4e-250], t$95$1, If[LessEqual[t, 1.8e-69], N[(N[(N[(z * c), $MachinePrecision] * (-b)), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.8e+161], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -1.05e142 or -4.7999999999999997e98 < t < -3.8000000000000001e63 or 1.79999999999999992e161 < t

   1. Initial program 71.1%

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

   3. Taylor expanded in t around inf 81.7%

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

      1. distribute-lft-out-- 81.7%

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

      2. *-commutative 81.7%

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

   5. Simplified 81.7%

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

   if -1.05e142 < t < -4.7999999999999997e98

   1. Initial program 75.0%

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

   3. Taylor expanded in y around inf 87.8%

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

      1. +-commutative 87.8%

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

      2. mul-1-neg 87.8%

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

      3. unsub-neg 87.8%

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

      4. *-commutative 87.8%

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

      5. *-commutative 87.8%

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

   5. Simplified 87.8%

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

   if -3.8000000000000001e63 < t < -3.1999999999999997e24 or -4.40000000000000005e-291 < t < 4.4e-250

   1. Initial program 76.7%

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

      1. +-commutative 76.7%

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

      2. fma-define 76.7%

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

      3. *-commutative 76.7%

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

      4. sub-neg 76.7%

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

      5. *-commutative 76.7%

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

      6. sub-neg 76.7%

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

      7. *-commutative 76.7%

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

      8. *-commutative 76.7%

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

   3. Simplified 76.7%

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

   5. Taylor expanded in x around -inf 80.5%

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

      1. mul-1-neg 80.5%

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

      2. distribute-rgt-neg-in 80.5%

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

      3. +-commutative 80.5%

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

      4. mul-1-neg 80.5%

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

      5. unsub-neg 80.5%

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

      6. associate-/l* 76.9%

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

   7. Simplified 76.9%

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

   8. Taylor expanded in j around inf 78.8%

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

      1. *-commutative 78.8%

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

      2. sub-neg 78.8%

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

      3. sub-neg 78.8%

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

   10. Simplified 78.8%

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

   if -3.1999999999999997e24 < t < -2.6999999999999997e-69 or -3.8e-168 < t < -4.40000000000000005e-291

   1. Initial program 79.9%

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

   3. Taylor expanded in z around inf 66.1%

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

      1. *-commutative 66.1%

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

      2. *-commutative 66.1%

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

   5. Simplified 66.1%

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

   if -2.6999999999999997e-69 < t < -3.8e-168

   1. Initial program 84.9%

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

      1. +-commutative 84.9%

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

      2. fma-define 84.9%

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

      3. *-commutative 84.9%

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

      4. sub-neg 84.9%

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

      5. *-commutative 84.9%

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

      6. sub-neg 84.9%

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

      7. *-commutative 84.9%

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

      8. *-commutative 84.9%

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

   3. Simplified 84.9%

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

   5. Taylor expanded in x around -inf 76.1%

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

      1. mul-1-neg 76.1%

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

      2. distribute-rgt-neg-in 76.1%

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

      3. +-commutative 76.1%

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

      4. mul-1-neg 76.1%

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

      5. unsub-neg 76.1%

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

      6. associate-/l* 71.3%

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

   7. Simplified 71.3%

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

   8. Taylor expanded in x around 0 85.2%

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

      1. +-commutative 85.2%

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

      2. *-commutative 85.2%

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

      3. sub-neg 85.2%

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

      4. sub-neg 85.2%

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

      5. mul-1-neg 85.2%

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

      6. unsub-neg 85.2%

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

   10. Simplified 85.2%

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

   11. Taylor expanded in i around 0 71.9%

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

   if 4.4e-250 < t < 1.80000000000000009e-69

   1. Initial program 75.0%

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

      1. +-commutative 75.0%

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

      2. fma-define 77.1%

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

      3. *-commutative 77.1%

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

      4. sub-neg 77.1%

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

      5. *-commutative 77.1%

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

      6. sub-neg 77.1%

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

      7. *-commutative 77.1%

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

      8. *-commutative 77.1%

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

   3. Simplified 77.1%

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

   5. Taylor expanded in x around -inf 73.1%

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

      1. mul-1-neg 73.1%

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

      2. distribute-rgt-neg-in 73.1%

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

      3. +-commutative 73.1%

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

      4. mul-1-neg 73.1%

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

      5. unsub-neg 73.1%

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

      6. associate-/l* 73.1%

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

   7. Simplified 73.1%

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

   8. Taylor expanded in x around 0 59.0%

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

      1. +-commutative 59.0%

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

      2. *-commutative 59.0%

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

      3. sub-neg 59.0%

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

      4. sub-neg 59.0%

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

      5. mul-1-neg 59.0%

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

      6. unsub-neg 59.0%

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

   10. Simplified 59.0%

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

   11. Taylor expanded in c around inf 61.2%

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

       1. associate-*r* 65.2%

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

       2. *-commutative 65.2%

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

   13. Simplified 65.2%

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

   14. Taylor expanded in a around 0 56.7%

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

       1. associate-*r* 56.7%

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

       2. neg-mul-1 56.7%

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

       3. *-commutative 56.7%

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

   16. Simplified 56.7%

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

   if 1.80000000000000009e-69 < t < 1.79999999999999992e161

   1. Initial program 70.7%

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

   3. Taylor expanded in b around inf 64.8%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+142}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{+98}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{+63}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{+24}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-69}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-168}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-291}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-250}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-69}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+161}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 54.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ t_3 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -7.2 \cdot 10^{+141}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -2 \cdot 10^{+98}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq -2.85 \cdot 10^{+64}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{+23}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-73}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{-168}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-251}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-69}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+161}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c))))
        (t_2 (+ (* j (- (* a c) (* y i))) (* x (* y z))))
        (t_3 (* t (- (* b i) (* x a)))))
   (if (<= t -7.2e+141)
     t_3
     (if (<= t -2e+98)
       (* y (- (* x z) (* i j)))
       (if (<= t -2.85e+64)
         t_3
         (if (<= t -4.5e+23)
           t_2
           (if (<= t -3e-73)
             t_1
             (if (<= t -3.7e-168)
               (- (* a (* c j)) (* b (* z c)))
               (if (<= t -3.3e-251)
                 t_1
                 (if (<= t 5.2e-69)
                   t_2
                   (if (<= t 1.55e+161)
                     (* b (- (* t i) (* z c)))
                     t_3)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double t_2 = (j * ((a * c) - (y * i))) + (x * (y * z));
	double t_3 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -7.2e+141) {
		tmp = t_3;
	} else if (t <= -2e+98) {
		tmp = y * ((x * z) - (i * j));
	} else if (t <= -2.85e+64) {
		tmp = t_3;
	} else if (t <= -4.5e+23) {
		tmp = t_2;
	} else if (t <= -3e-73) {
		tmp = t_1;
	} else if (t <= -3.7e-168) {
		tmp = (a * (c * j)) - (b * (z * c));
	} else if (t <= -3.3e-251) {
		tmp = t_1;
	} else if (t <= 5.2e-69) {
		tmp = t_2;
	} else if (t <= 1.55e+161) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = z * ((x * y) - (b * c))
    t_2 = (j * ((a * c) - (y * i))) + (x * (y * z))
    t_3 = t * ((b * i) - (x * a))
    if (t <= (-7.2d+141)) then
        tmp = t_3
    else if (t <= (-2d+98)) then
        tmp = y * ((x * z) - (i * j))
    else if (t <= (-2.85d+64)) then
        tmp = t_3
    else if (t <= (-4.5d+23)) then
        tmp = t_2
    else if (t <= (-3d-73)) then
        tmp = t_1
    else if (t <= (-3.7d-168)) then
        tmp = (a * (c * j)) - (b * (z * c))
    else if (t <= (-3.3d-251)) then
        tmp = t_1
    else if (t <= 5.2d-69) then
        tmp = t_2
    else if (t <= 1.55d+161) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double t_2 = (j * ((a * c) - (y * i))) + (x * (y * z));
	double t_3 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -7.2e+141) {
		tmp = t_3;
	} else if (t <= -2e+98) {
		tmp = y * ((x * z) - (i * j));
	} else if (t <= -2.85e+64) {
		tmp = t_3;
	} else if (t <= -4.5e+23) {
		tmp = t_2;
	} else if (t <= -3e-73) {
		tmp = t_1;
	} else if (t <= -3.7e-168) {
		tmp = (a * (c * j)) - (b * (z * c));
	} else if (t <= -3.3e-251) {
		tmp = t_1;
	} else if (t <= 5.2e-69) {
		tmp = t_2;
	} else if (t <= 1.55e+161) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * ((x * y) - (b * c))
	t_2 = (j * ((a * c) - (y * i))) + (x * (y * z))
	t_3 = t * ((b * i) - (x * a))
	tmp = 0
	if t <= -7.2e+141:
		tmp = t_3
	elif t <= -2e+98:
		tmp = y * ((x * z) - (i * j))
	elif t <= -2.85e+64:
		tmp = t_3
	elif t <= -4.5e+23:
		tmp = t_2
	elif t <= -3e-73:
		tmp = t_1
	elif t <= -3.7e-168:
		tmp = (a * (c * j)) - (b * (z * c))
	elif t <= -3.3e-251:
		tmp = t_1
	elif t <= 5.2e-69:
		tmp = t_2
	elif t <= 1.55e+161:
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	t_2 = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(x * Float64(y * z)))
	t_3 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	tmp = 0.0
	if (t <= -7.2e+141)
		tmp = t_3;
	elseif (t <= -2e+98)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (t <= -2.85e+64)
		tmp = t_3;
	elseif (t <= -4.5e+23)
		tmp = t_2;
	elseif (t <= -3e-73)
		tmp = t_1;
	elseif (t <= -3.7e-168)
		tmp = Float64(Float64(a * Float64(c * j)) - Float64(b * Float64(z * c)));
	elseif (t <= -3.3e-251)
		tmp = t_1;
	elseif (t <= 5.2e-69)
		tmp = t_2;
	elseif (t <= 1.55e+161)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * ((x * y) - (b * c));
	t_2 = (j * ((a * c) - (y * i))) + (x * (y * z));
	t_3 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -7.2e+141)
		tmp = t_3;
	elseif (t <= -2e+98)
		tmp = y * ((x * z) - (i * j));
	elseif (t <= -2.85e+64)
		tmp = t_3;
	elseif (t <= -4.5e+23)
		tmp = t_2;
	elseif (t <= -3e-73)
		tmp = t_1;
	elseif (t <= -3.7e-168)
		tmp = (a * (c * j)) - (b * (z * c));
	elseif (t <= -3.3e-251)
		tmp = t_1;
	elseif (t <= 5.2e-69)
		tmp = t_2;
	elseif (t <= 1.55e+161)
		tmp = b * ((t * i) - (z * c));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = 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$3 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.2e+141], t$95$3, If[LessEqual[t, -2e+98], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.85e+64], t$95$3, If[LessEqual[t, -4.5e+23], t$95$2, If[LessEqual[t, -3e-73], t$95$1, If[LessEqual[t, -3.7e-168], N[(N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.3e-251], t$95$1, If[LessEqual[t, 5.2e-69], t$95$2, If[LessEqual[t, 1.55e+161], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -7.2000000000000003e141 or -2e98 < t < -2.85000000000000008e64 or 1.55000000000000003e161 < t

   1. Initial program 71.1%

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

   3. Taylor expanded in t around inf 81.7%

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

      1. distribute-lft-out-- 81.7%

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

      2. *-commutative 81.7%

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

   5. Simplified 81.7%

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

   if -7.2000000000000003e141 < t < -2e98

   1. Initial program 75.0%

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

   3. Taylor expanded in y around inf 87.8%

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

      1. +-commutative 87.8%

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

      2. mul-1-neg 87.8%

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

      3. unsub-neg 87.8%

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

      4. *-commutative 87.8%

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

      5. *-commutative 87.8%

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

   5. Simplified 87.8%

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

   if -2.85000000000000008e64 < t < -4.49999999999999979e23 or -3.3e-251 < t < 5.2000000000000004e-69

   1. Initial program 77.7%

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

   3. Taylor expanded in b around 0 70.5%

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

   4. Taylor expanded in t around 0 67.5%

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

   if -4.49999999999999979e23 < t < -3e-73 or -3.69999999999999997e-168 < t < -3.3e-251

   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 z around inf 65.1%

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

      1. *-commutative 65.1%

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

      2. *-commutative 65.1%

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

   5. Simplified 65.1%

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

   if -3e-73 < t < -3.69999999999999997e-168

   1. Initial program 84.9%

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

      1. +-commutative 84.9%

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

      2. fma-define 84.9%

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

      3. *-commutative 84.9%

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

      4. sub-neg 84.9%

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

      5. *-commutative 84.9%

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

      6. sub-neg 84.9%

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

      7. *-commutative 84.9%

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

      8. *-commutative 84.9%

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

   3. Simplified 84.9%

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

   5. Taylor expanded in x around -inf 76.1%

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

      1. mul-1-neg 76.1%

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

      2. distribute-rgt-neg-in 76.1%

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

      3. +-commutative 76.1%

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

      4. mul-1-neg 76.1%

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

      5. unsub-neg 76.1%

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

      6. associate-/l* 71.3%

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

   7. Simplified 71.3%

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

   8. Taylor expanded in x around 0 85.2%

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

      1. +-commutative 85.2%

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

      2. *-commutative 85.2%

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

      3. sub-neg 85.2%

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

      4. sub-neg 85.2%

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

      5. mul-1-neg 85.2%

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

      6. unsub-neg 85.2%

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

   10. Simplified 85.2%

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

   11. Taylor expanded in i around 0 71.9%

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

   if 5.2000000000000004e-69 < t < 1.55000000000000003e161

   1. Initial program 70.7%

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

   3. Taylor expanded in b around inf 64.8%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+141}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -2 \cdot 10^{+98}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq -2.85 \cdot 10^{+64}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{+23}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-73}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{-168}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-251}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-69}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+161}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_3 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;t \leq -8.8 \cdot 10^{+141}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{+98}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{+62}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -8.6 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{-72}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-168}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-275}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+153}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i))))
        (t_2 (* t (- (* b i) (* x a))))
        (t_3 (* z (- (* x y) (* b c)))))
   (if (<= t -8.8e+141)
     t_2
     (if (<= t -4.8e+98)
       (* y (- (* x z) (* i j)))
       (if (<= t -1.75e+62)
         t_2
         (if (<= t -8.6e+23)
           t_1
           (if (<= t -2.15e-72)
             t_3
             (if (<= t -3.8e-168)
               (- (* a (* c j)) (* b (* z c)))
               (if (<= t -3e-275)
                 t_3
                 (if (<= t 1.2e-69)
                   t_1
                   (if (<= t 1.3e+153) (* b (- (* t i) (* z c))) 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));
	double t_2 = t * ((b * i) - (x * a));
	double t_3 = z * ((x * y) - (b * c));
	double tmp;
	if (t <= -8.8e+141) {
		tmp = t_2;
	} else if (t <= -4.8e+98) {
		tmp = y * ((x * z) - (i * j));
	} else if (t <= -1.75e+62) {
		tmp = t_2;
	} else if (t <= -8.6e+23) {
		tmp = t_1;
	} else if (t <= -2.15e-72) {
		tmp = t_3;
	} else if (t <= -3.8e-168) {
		tmp = (a * (c * j)) - (b * (z * c));
	} else if (t <= -3e-275) {
		tmp = t_3;
	} else if (t <= 1.2e-69) {
		tmp = t_1;
	} else if (t <= 1.3e+153) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = t * ((b * i) - (x * a))
    t_3 = z * ((x * y) - (b * c))
    if (t <= (-8.8d+141)) then
        tmp = t_2
    else if (t <= (-4.8d+98)) then
        tmp = y * ((x * z) - (i * j))
    else if (t <= (-1.75d+62)) then
        tmp = t_2
    else if (t <= (-8.6d+23)) then
        tmp = t_1
    else if (t <= (-2.15d-72)) then
        tmp = t_3
    else if (t <= (-3.8d-168)) then
        tmp = (a * (c * j)) - (b * (z * c))
    else if (t <= (-3d-275)) then
        tmp = t_3
    else if (t <= 1.2d-69) then
        tmp = t_1
    else if (t <= 1.3d+153) then
        tmp = b * ((t * i) - (z * c))
    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));
	double t_2 = t * ((b * i) - (x * a));
	double t_3 = z * ((x * y) - (b * c));
	double tmp;
	if (t <= -8.8e+141) {
		tmp = t_2;
	} else if (t <= -4.8e+98) {
		tmp = y * ((x * z) - (i * j));
	} else if (t <= -1.75e+62) {
		tmp = t_2;
	} else if (t <= -8.6e+23) {
		tmp = t_1;
	} else if (t <= -2.15e-72) {
		tmp = t_3;
	} else if (t <= -3.8e-168) {
		tmp = (a * (c * j)) - (b * (z * c));
	} else if (t <= -3e-275) {
		tmp = t_3;
	} else if (t <= 1.2e-69) {
		tmp = t_1;
	} else if (t <= 1.3e+153) {
		tmp = b * ((t * i) - (z * c));
	} 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))
	t_2 = t * ((b * i) - (x * a))
	t_3 = z * ((x * y) - (b * c))
	tmp = 0
	if t <= -8.8e+141:
		tmp = t_2
	elif t <= -4.8e+98:
		tmp = y * ((x * z) - (i * j))
	elif t <= -1.75e+62:
		tmp = t_2
	elif t <= -8.6e+23:
		tmp = t_1
	elif t <= -2.15e-72:
		tmp = t_3
	elif t <= -3.8e-168:
		tmp = (a * (c * j)) - (b * (z * c))
	elif t <= -3e-275:
		tmp = t_3
	elif t <= 1.2e-69:
		tmp = t_1
	elif t <= 1.3e+153:
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = t_2
	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(t * Float64(Float64(b * i) - Float64(x * a)))
	t_3 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (t <= -8.8e+141)
		tmp = t_2;
	elseif (t <= -4.8e+98)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (t <= -1.75e+62)
		tmp = t_2;
	elseif (t <= -8.6e+23)
		tmp = t_1;
	elseif (t <= -2.15e-72)
		tmp = t_3;
	elseif (t <= -3.8e-168)
		tmp = Float64(Float64(a * Float64(c * j)) - Float64(b * Float64(z * c)));
	elseif (t <= -3e-275)
		tmp = t_3;
	elseif (t <= 1.2e-69)
		tmp = t_1;
	elseif (t <= 1.3e+153)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	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));
	t_2 = t * ((b * i) - (x * a));
	t_3 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (t <= -8.8e+141)
		tmp = t_2;
	elseif (t <= -4.8e+98)
		tmp = y * ((x * z) - (i * j));
	elseif (t <= -1.75e+62)
		tmp = t_2;
	elseif (t <= -8.6e+23)
		tmp = t_1;
	elseif (t <= -2.15e-72)
		tmp = t_3;
	elseif (t <= -3.8e-168)
		tmp = (a * (c * j)) - (b * (z * c));
	elseif (t <= -3e-275)
		tmp = t_3;
	elseif (t <= 1.2e-69)
		tmp = t_1;
	elseif (t <= 1.3e+153)
		tmp = b * ((t * i) - (z * c));
	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[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.8e+141], t$95$2, If[LessEqual[t, -4.8e+98], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.75e+62], t$95$2, If[LessEqual[t, -8.6e+23], t$95$1, If[LessEqual[t, -2.15e-72], t$95$3, If[LessEqual[t, -3.8e-168], N[(N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3e-275], t$95$3, If[LessEqual[t, 1.2e-69], t$95$1, If[LessEqual[t, 1.3e+153], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -8.8e141 or -4.7999999999999997e98 < t < -1.74999999999999992e62 or 1.2999999999999999e153 < t

   1. Initial program 71.1%

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

   3. Taylor expanded in t around inf 81.7%

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

      1. distribute-lft-out-- 81.7%

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

      2. *-commutative 81.7%

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

   5. Simplified 81.7%

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

   if -8.8e141 < t < -4.7999999999999997e98

   1. Initial program 75.0%

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

   3. Taylor expanded in y around inf 87.8%

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

      1. +-commutative 87.8%

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

      2. mul-1-neg 87.8%

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

      3. unsub-neg 87.8%

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

      4. *-commutative 87.8%

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

      5. *-commutative 87.8%

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

   5. Simplified 87.8%

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

   if -1.74999999999999992e62 < t < -8.5999999999999997e23 or -3e-275 < t < 1.2000000000000001e-69

   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. Step-by-step derivation

      1. +-commutative 75.6%

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

      2. fma-define 77.0%

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

      3. *-commutative 77.0%

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

      4. sub-neg 77.0%

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

      5. *-commutative 77.0%

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

      6. sub-neg 77.0%

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

      7. *-commutative 77.0%

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

      8. *-commutative 77.0%

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

   3. Simplified 77.0%

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

   5. Taylor expanded in x around -inf 75.8%

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

      1. mul-1-neg 75.8%

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

      2. distribute-rgt-neg-in 75.8%

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

      3. +-commutative 75.8%

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

      4. mul-1-neg 75.8%

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

      5. unsub-neg 75.8%

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

      6. associate-/l* 74.4%

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

   7. Simplified 74.4%

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

   8. Taylor expanded in j around inf 57.8%

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

      1. *-commutative 57.8%

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

      2. sub-neg 57.8%

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

      3. sub-neg 57.8%

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

   10. Simplified 57.8%

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

   if -8.5999999999999997e23 < t < -2.1499999999999999e-72 or -3.8e-168 < t < -3e-275

   1. Initial program 79.9%

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

   3. Taylor expanded in z around inf 66.1%

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

      1. *-commutative 66.1%

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

      2. *-commutative 66.1%

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

   5. Simplified 66.1%

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

   if -2.1499999999999999e-72 < t < -3.8e-168

   1. Initial program 84.9%

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

      1. +-commutative 84.9%

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

      2. fma-define 84.9%

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

      3. *-commutative 84.9%

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

      4. sub-neg 84.9%

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

      5. *-commutative 84.9%

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

      6. sub-neg 84.9%

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

      7. *-commutative 84.9%

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

      8. *-commutative 84.9%

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

   3. Simplified 84.9%

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

   5. Taylor expanded in x around -inf 76.1%

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

      1. mul-1-neg 76.1%

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

      2. distribute-rgt-neg-in 76.1%

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

      3. +-commutative 76.1%

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

      4. mul-1-neg 76.1%

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

      5. unsub-neg 76.1%

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

      6. associate-/l* 71.3%

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

   7. Simplified 71.3%

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

   8. Taylor expanded in x around 0 85.2%

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

      1. +-commutative 85.2%

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

      2. *-commutative 85.2%

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

      3. sub-neg 85.2%

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

      4. sub-neg 85.2%

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

      5. mul-1-neg 85.2%

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

      6. unsub-neg 85.2%

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

   10. Simplified 85.2%

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

   11. Taylor expanded in i around 0 71.9%

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

   if 1.2000000000000001e-69 < t < 1.2999999999999999e153

   1. Initial program 70.7%

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

   3. Taylor expanded in b around inf 64.8%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{+141}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{+98}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{+62}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -8.6 \cdot 10^{+23}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{-72}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-168}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-275}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-69}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+153}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 29.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ t_2 := z \cdot \left(b \cdot \left(-c\right)\right)\\ t_3 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;y \leq -5.9 \cdot 10^{+82}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-127}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-303}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;y \leq 6.7 \cdot 10^{-251}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-96}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-10}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+46}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+158}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))) (t_2 (* z (* b (- c)))) (t_3 (* x (* y z))))
   (if (<= y -5.9e+82)
     t_3
     (if (<= y -2.4e-127)
       t_1
       (if (<= y 7e-303)
         (* i (* t b))
         (if (<= y 6.7e-251)
           t_1
           (if (<= y 2.3e-96)
             t_2
             (if (<= y 1.12e-10)
               (* b (* t i))
               (if (<= y 1.15e+46)
                 t_2
                 (if (<= y 8.2e+158) t_3 (* (* y j) (- 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);
	double t_2 = z * (b * -c);
	double t_3 = x * (y * z);
	double tmp;
	if (y <= -5.9e+82) {
		tmp = t_3;
	} else if (y <= -2.4e-127) {
		tmp = t_1;
	} else if (y <= 7e-303) {
		tmp = i * (t * b);
	} else if (y <= 6.7e-251) {
		tmp = t_1;
	} else if (y <= 2.3e-96) {
		tmp = t_2;
	} else if (y <= 1.12e-10) {
		tmp = b * (t * i);
	} else if (y <= 1.15e+46) {
		tmp = t_2;
	} else if (y <= 8.2e+158) {
		tmp = t_3;
	} else {
		tmp = (y * j) * -i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a * (c * j)
    t_2 = z * (b * -c)
    t_3 = x * (y * z)
    if (y <= (-5.9d+82)) then
        tmp = t_3
    else if (y <= (-2.4d-127)) then
        tmp = t_1
    else if (y <= 7d-303) then
        tmp = i * (t * b)
    else if (y <= 6.7d-251) then
        tmp = t_1
    else if (y <= 2.3d-96) then
        tmp = t_2
    else if (y <= 1.12d-10) then
        tmp = b * (t * i)
    else if (y <= 1.15d+46) then
        tmp = t_2
    else if (y <= 8.2d+158) then
        tmp = t_3
    else
        tmp = (y * j) * -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);
	double t_2 = z * (b * -c);
	double t_3 = x * (y * z);
	double tmp;
	if (y <= -5.9e+82) {
		tmp = t_3;
	} else if (y <= -2.4e-127) {
		tmp = t_1;
	} else if (y <= 7e-303) {
		tmp = i * (t * b);
	} else if (y <= 6.7e-251) {
		tmp = t_1;
	} else if (y <= 2.3e-96) {
		tmp = t_2;
	} else if (y <= 1.12e-10) {
		tmp = b * (t * i);
	} else if (y <= 1.15e+46) {
		tmp = t_2;
	} else if (y <= 8.2e+158) {
		tmp = t_3;
	} else {
		tmp = (y * j) * -i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	t_2 = z * (b * -c)
	t_3 = x * (y * z)
	tmp = 0
	if y <= -5.9e+82:
		tmp = t_3
	elif y <= -2.4e-127:
		tmp = t_1
	elif y <= 7e-303:
		tmp = i * (t * b)
	elif y <= 6.7e-251:
		tmp = t_1
	elif y <= 2.3e-96:
		tmp = t_2
	elif y <= 1.12e-10:
		tmp = b * (t * i)
	elif y <= 1.15e+46:
		tmp = t_2
	elif y <= 8.2e+158:
		tmp = t_3
	else:
		tmp = (y * j) * -i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	t_2 = Float64(z * Float64(b * Float64(-c)))
	t_3 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (y <= -5.9e+82)
		tmp = t_3;
	elseif (y <= -2.4e-127)
		tmp = t_1;
	elseif (y <= 7e-303)
		tmp = Float64(i * Float64(t * b));
	elseif (y <= 6.7e-251)
		tmp = t_1;
	elseif (y <= 2.3e-96)
		tmp = t_2;
	elseif (y <= 1.12e-10)
		tmp = Float64(b * Float64(t * i));
	elseif (y <= 1.15e+46)
		tmp = t_2;
	elseif (y <= 8.2e+158)
		tmp = t_3;
	else
		tmp = Float64(Float64(y * j) * Float64(-i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (c * j);
	t_2 = z * (b * -c);
	t_3 = x * (y * z);
	tmp = 0.0;
	if (y <= -5.9e+82)
		tmp = t_3;
	elseif (y <= -2.4e-127)
		tmp = t_1;
	elseif (y <= 7e-303)
		tmp = i * (t * b);
	elseif (y <= 6.7e-251)
		tmp = t_1;
	elseif (y <= 2.3e-96)
		tmp = t_2;
	elseif (y <= 1.12e-10)
		tmp = b * (t * i);
	elseif (y <= 1.15e+46)
		tmp = t_2;
	elseif (y <= 8.2e+158)
		tmp = t_3;
	else
		tmp = (y * j) * -i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.9e+82], t$95$3, If[LessEqual[y, -2.4e-127], t$95$1, If[LessEqual[y, 7e-303], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.7e-251], t$95$1, If[LessEqual[y, 2.3e-96], t$95$2, If[LessEqual[y, 1.12e-10], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e+46], t$95$2, If[LessEqual[y, 8.2e+158], t$95$3, N[(N[(y * j), $MachinePrecision] * (-i)), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -5.8999999999999997e82 or 1.15e46 < y < 8.20000000000000008e158

   1. Initial program 68.7%

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

   3. Taylor expanded in z around inf 59.4%

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

      1. *-commutative 59.4%

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

      2. *-commutative 59.4%

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

   5. Simplified 59.4%

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

   6. Taylor expanded in y around 0 51.0%

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

   7. Taylor expanded in b around 0 45.4%

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

   if -5.8999999999999997e82 < y < -2.39999999999999982e-127 or 7e-303 < y < 6.69999999999999977e-251

   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 a around inf 57.8%

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

      1. +-commutative 57.8%

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

      2. mul-1-neg 57.8%

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

      3. unsub-neg 57.8%

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

      4. *-commutative 57.8%

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

   5. Simplified 57.8%

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

   6. Taylor expanded in j around inf 44.6%

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

   if -2.39999999999999982e-127 < y < 7e-303

   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. Step-by-step derivation

      1. +-commutative 79.8%

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

      2. fma-define 84.8%

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

      3. *-commutative 84.8%

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

      4. sub-neg 84.8%

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

      5. *-commutative 84.8%

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

      6. sub-neg 84.8%

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

      7. *-commutative 84.8%

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

      8. *-commutative 84.8%

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

   3. Simplified 84.8%

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

   5. Taylor expanded in x around -inf 85.1%

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

      1. mul-1-neg 85.1%

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

      2. distribute-rgt-neg-in 85.1%

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

      3. +-commutative 85.1%

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

      4. mul-1-neg 85.1%

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

      5. unsub-neg 85.1%

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

      6. associate-/l* 82.7%

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

   7. Simplified 82.7%

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

   8. Taylor expanded in i around inf 60.1%

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

      1. +-commutative 60.1%

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

      2. mul-1-neg 60.1%

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

      3. unsub-neg 60.1%

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

      4. *-commutative 60.1%

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

   10. Simplified 60.1%

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

   11. Taylor expanded in b around inf 57.7%

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

   if 6.69999999999999977e-251 < y < 2.3e-96 or 1.12e-10 < y < 1.15e46

   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 z around inf 51.5%

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

      1. *-commutative 51.5%

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

      2. *-commutative 51.5%

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

   5. Simplified 51.5%

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

   6. Taylor expanded in y around 0 40.4%

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

      1. neg-mul-1 40.4%

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

      2. distribute-rgt-neg-in 40.4%

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

   8. Simplified 40.4%

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

   if 2.3e-96 < y < 1.12e-10

   1. Initial program 78.1%

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

      1. +-commutative 78.1%

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

      2. fma-define 78.1%

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

      3. *-commutative 78.1%

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

      4. sub-neg 78.1%

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

      5. *-commutative 78.1%

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

      6. sub-neg 78.1%

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

      7. *-commutative 78.1%

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

      8. *-commutative 78.1%

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

   3. Simplified 78.1%

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

   5. Taylor expanded in x around -inf 78.6%

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

      1. mul-1-neg 78.6%

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

      2. distribute-rgt-neg-in 78.6%

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

      3. +-commutative 78.6%

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

      4. mul-1-neg 78.6%

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

      5. unsub-neg 78.6%

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

      6. associate-/l* 74.3%

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

   7. Simplified 74.3%

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

   8. Taylor expanded in x around 0 72.5%

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

      1. +-commutative 72.5%

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

      2. *-commutative 72.5%

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

      3. sub-neg 72.5%

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

      4. sub-neg 72.5%

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

      5. mul-1-neg 72.5%

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

      6. unsub-neg 72.5%

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

   10. Simplified 72.5%

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

   11. Taylor expanded in t around inf 40.7%

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

   if 8.20000000000000008e158 < y

   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. Step-by-step derivation

      1. +-commutative 74.9%

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

      2. fma-define 74.9%

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

      3. *-commutative 74.9%

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

      4. sub-neg 74.9%

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

      5. *-commutative 74.9%

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

      6. sub-neg 74.9%

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

      7. *-commutative 74.9%

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

      8. *-commutative 74.9%

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

   3. Simplified 74.9%

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

   5. Taylor expanded in x around -inf 71.6%

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

      1. mul-1-neg 71.6%

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

      2. distribute-rgt-neg-in 71.6%

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

      3. +-commutative 71.6%

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

      4. mul-1-neg 71.6%

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

      5. unsub-neg 71.6%

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

      6. associate-/l* 68.1%

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

   7. Simplified 68.1%

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

   8. Taylor expanded in i around inf 69.2%

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

      1. +-commutative 69.2%

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

      2. mul-1-neg 69.2%

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

      3. unsub-neg 69.2%

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

      4. *-commutative 69.2%

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

   10. Simplified 69.2%

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

   11. Taylor expanded in b around 0 65.6%

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

       1. neg-mul-1 65.6%

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

       2. distribute-lft-neg-in 65.6%

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

   13. Simplified 65.6%

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

4. Final simplification 48.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{+82}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-127}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-303}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;y \leq 6.7 \cdot 10^{-251}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-96}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-10}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+46}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+158}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{+119}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.56 \cdot 10^{-135}:\\ \;\;\;\;\left(x \cdot a\right) \cdot \left(j \cdot \frac{c}{x} - t\right)\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-255}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-157}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-50}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* j (- (* a c) (* y i))) (* z (* b c)))))
   (if (<= z -1.15e+119)
     (* z (- (* x y) (* b c)))
     (if (<= z -2.2e-60)
       t_1
       (if (<= z -2.56e-135)
         (* (* x a) (- (* j (/ c x)) t))
         (if (<= z 2.45e-255)
           (* i (- (* t b) (* y j)))
           (if (<= z 5e-157)
             (- (* x (- (* y z) (* t a))) (* i (* y j)))
             (if (<= z 6.5e-50) (* t (- (* b i) (* x a))) 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))) - (z * (b * c));
	double tmp;
	if (z <= -1.15e+119) {
		tmp = z * ((x * y) - (b * c));
	} else if (z <= -2.2e-60) {
		tmp = t_1;
	} else if (z <= -2.56e-135) {
		tmp = (x * a) * ((j * (c / x)) - t);
	} else if (z <= 2.45e-255) {
		tmp = i * ((t * b) - (y * j));
	} else if (z <= 5e-157) {
		tmp = (x * ((y * z) - (t * a))) - (i * (y * j));
	} else if (z <= 6.5e-50) {
		tmp = t * ((b * i) - (x * a));
	} 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))) - (z * (b * c))
    if (z <= (-1.15d+119)) then
        tmp = z * ((x * y) - (b * c))
    else if (z <= (-2.2d-60)) then
        tmp = t_1
    else if (z <= (-2.56d-135)) then
        tmp = (x * a) * ((j * (c / x)) - t)
    else if (z <= 2.45d-255) then
        tmp = i * ((t * b) - (y * j))
    else if (z <= 5d-157) then
        tmp = (x * ((y * z) - (t * a))) - (i * (y * j))
    else if (z <= 6.5d-50) then
        tmp = t * ((b * i) - (x * a))
    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))) - (z * (b * c));
	double tmp;
	if (z <= -1.15e+119) {
		tmp = z * ((x * y) - (b * c));
	} else if (z <= -2.2e-60) {
		tmp = t_1;
	} else if (z <= -2.56e-135) {
		tmp = (x * a) * ((j * (c / x)) - t);
	} else if (z <= 2.45e-255) {
		tmp = i * ((t * b) - (y * j));
	} else if (z <= 5e-157) {
		tmp = (x * ((y * z) - (t * a))) - (i * (y * j));
	} else if (z <= 6.5e-50) {
		tmp = t * ((b * i) - (x * a));
	} 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))) - (z * (b * c))
	tmp = 0
	if z <= -1.15e+119:
		tmp = z * ((x * y) - (b * c))
	elif z <= -2.2e-60:
		tmp = t_1
	elif z <= -2.56e-135:
		tmp = (x * a) * ((j * (c / x)) - t)
	elif z <= 2.45e-255:
		tmp = i * ((t * b) - (y * j))
	elif z <= 5e-157:
		tmp = (x * ((y * z) - (t * a))) - (i * (y * j))
	elif z <= 6.5e-50:
		tmp = t * ((b * i) - (x * a))
	else:
		tmp = t_1
	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(z * Float64(b * c)))
	tmp = 0.0
	if (z <= -1.15e+119)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (z <= -2.2e-60)
		tmp = t_1;
	elseif (z <= -2.56e-135)
		tmp = Float64(Float64(x * a) * Float64(Float64(j * Float64(c / x)) - t));
	elseif (z <= 2.45e-255)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (z <= 5e-157)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(i * Float64(y * j)));
	elseif (z <= 6.5e-50)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	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))) - (z * (b * c));
	tmp = 0.0;
	if (z <= -1.15e+119)
		tmp = z * ((x * y) - (b * c));
	elseif (z <= -2.2e-60)
		tmp = t_1;
	elseif (z <= -2.56e-135)
		tmp = (x * a) * ((j * (c / x)) - t);
	elseif (z <= 2.45e-255)
		tmp = i * ((t * b) - (y * j));
	elseif (z <= 5e-157)
		tmp = (x * ((y * z) - (t * a))) - (i * (y * j));
	elseif (z <= 6.5e-50)
		tmp = t * ((b * i) - (x * a));
	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[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.15e+119], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.2e-60], t$95$1, If[LessEqual[z, -2.56e-135], N[(N[(x * a), $MachinePrecision] * N[(N[(j * N[(c / x), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.45e-255], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e-157], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e-50], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.15e119

   1. Initial program 67.9%

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

   3. Taylor expanded in z around inf 75.1%

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

      1. *-commutative 75.1%

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

      2. *-commutative 75.1%

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

   5. Simplified 75.1%

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

   if -1.15e119 < z < -2.1999999999999999e-60 or 6.49999999999999987e-50 < z

   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. Step-by-step derivation

      1. +-commutative 72.9%

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

      2. fma-define 72.9%

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

      3. *-commutative 72.9%

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

      4. sub-neg 72.9%

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

      5. *-commutative 72.9%

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

      6. sub-neg 72.9%

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

      7. *-commutative 72.9%

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

      8. *-commutative 72.9%

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

   3. Simplified 72.9%

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

   5. Taylor expanded in x around -inf 69.7%

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

      1. mul-1-neg 69.7%

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

      2. distribute-rgt-neg-in 69.7%

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

      3. +-commutative 69.7%

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

      4. mul-1-neg 69.7%

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

      5. unsub-neg 69.7%

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

      6. associate-/l* 68.9%

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

   7. Simplified 68.9%

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

   8. Taylor expanded in x around 0 68.5%

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

      1. +-commutative 68.5%

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

      2. *-commutative 68.5%

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

      3. sub-neg 68.5%

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

      4. sub-neg 68.5%

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

      5. mul-1-neg 68.5%

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

      6. unsub-neg 68.5%

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

   10. Simplified 68.5%

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

   11. Taylor expanded in c around inf 63.8%

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

       1. associate-*r* 68.9%

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

       2. *-commutative 68.9%

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

   13. Simplified 68.9%

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

   if -2.1999999999999999e-60 < z < -2.55999999999999994e-135

   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 68.0%

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

      1. +-commutative 68.0%

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

      2. mul-1-neg 68.0%

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

      3. unsub-neg 68.0%

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

      4. *-commutative 68.0%

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

   5. Simplified 68.0%

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

   6. Taylor expanded in x around inf 60.5%

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

      1. associate-/l* 60.5%

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

   8. Simplified 60.5%

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

   9. Taylor expanded in a around 0 60.5%

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

       1. associate-*r* 68.0%

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

       2. *-commutative 68.0%

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

       3. associate-/l* 68.0%

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

   11. Simplified 68.0%

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

   if -2.55999999999999994e-135 < z < 2.4499999999999998e-255

   1. Initial program 83.9%

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

      1. +-commutative 83.9%

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

      2. fma-define 88.4%

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

      3. *-commutative 88.4%

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

      4. sub-neg 88.4%

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

      5. *-commutative 88.4%

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

      6. sub-neg 88.4%

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

      7. *-commutative 88.4%

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

      8. *-commutative 88.4%

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

   3. Simplified 88.4%

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

   5. Taylor expanded in x around -inf 90.6%

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

      1. mul-1-neg 90.6%

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

      2. distribute-rgt-neg-in 90.6%

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

      3. +-commutative 90.6%

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

      4. mul-1-neg 90.6%

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

      5. unsub-neg 90.6%

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

      6. associate-/l* 90.6%

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

   7. Simplified 90.6%

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

   8. Taylor expanded in i around inf 65.7%

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

      1. +-commutative 65.7%

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

      2. mul-1-neg 65.7%

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

      3. unsub-neg 65.7%

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

      4. *-commutative 65.7%

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

   10. Simplified 65.7%

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

   if 2.4499999999999998e-255 < z < 5.0000000000000002e-157

   1. Initial program 70.8%

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

   3. Taylor expanded in b around 0 76.0%

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

   4. Taylor expanded in c around 0 80.3%

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

      1. +-commutative 80.3%

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

      2. sub-neg 80.3%

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

      3. *-commutative 80.3%

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

      4. *-commutative 80.3%

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

      5. sub-neg 80.3%

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

      6. mul-1-neg 80.3%

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

      7. unsub-neg 80.3%

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

      8. *-commutative 80.3%

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

   6. Simplified 80.3%

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

   if 5.0000000000000002e-157 < z < 6.49999999999999987e-50

   1. Initial program 81.4%

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

   3. Taylor expanded in t around inf 74.6%

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

      1. distribute-lft-out-- 74.6%

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

      2. *-commutative 74.6%

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

   5. Simplified 74.6%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x - i \cdot b\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+119}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-60}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;z \leq -2.56 \cdot 10^{-135}:\\ \;\;\;\;\left(x \cdot a\right) \cdot \left(j \cdot \frac{c}{x} - t\right)\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-255}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-157}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-50}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - z \cdot \left(b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_3 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;y \leq -5.4 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -0.00012:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-141}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-303}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-226}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-16}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j))))
        (t_2 (* a (- (* c j) (* x t))))
        (t_3 (* b (- (* t i) (* z c)))))
   (if (<= y -5.4e+60)
     t_1
     (if (<= y -0.00012)
       t_2
       (if (<= y -6.5e-34)
         t_1
         (if (<= y -6.8e-141)
           t_2
           (if (<= y 4.5e-303)
             t_3
             (if (<= y 5.8e-226)
               (* c (- (* a j) (* z b)))
               (if (<= y 4.2e-16) t_3 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 = y * ((x * z) - (i * j));
	double t_2 = a * ((c * j) - (x * t));
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if (y <= -5.4e+60) {
		tmp = t_1;
	} else if (y <= -0.00012) {
		tmp = t_2;
	} else if (y <= -6.5e-34) {
		tmp = t_1;
	} else if (y <= -6.8e-141) {
		tmp = t_2;
	} else if (y <= 4.5e-303) {
		tmp = t_3;
	} else if (y <= 5.8e-226) {
		tmp = c * ((a * j) - (z * b));
	} else if (y <= 4.2e-16) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = y * ((x * z) - (i * j))
    t_2 = a * ((c * j) - (x * t))
    t_3 = b * ((t * i) - (z * c))
    if (y <= (-5.4d+60)) then
        tmp = t_1
    else if (y <= (-0.00012d0)) then
        tmp = t_2
    else if (y <= (-6.5d-34)) then
        tmp = t_1
    else if (y <= (-6.8d-141)) then
        tmp = t_2
    else if (y <= 4.5d-303) then
        tmp = t_3
    else if (y <= 5.8d-226) then
        tmp = c * ((a * j) - (z * b))
    else if (y <= 4.2d-16) then
        tmp = t_3
    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 = y * ((x * z) - (i * j));
	double t_2 = a * ((c * j) - (x * t));
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if (y <= -5.4e+60) {
		tmp = t_1;
	} else if (y <= -0.00012) {
		tmp = t_2;
	} else if (y <= -6.5e-34) {
		tmp = t_1;
	} else if (y <= -6.8e-141) {
		tmp = t_2;
	} else if (y <= 4.5e-303) {
		tmp = t_3;
	} else if (y <= 5.8e-226) {
		tmp = c * ((a * j) - (z * b));
	} else if (y <= 4.2e-16) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	t_2 = a * ((c * j) - (x * t))
	t_3 = b * ((t * i) - (z * c))
	tmp = 0
	if y <= -5.4e+60:
		tmp = t_1
	elif y <= -0.00012:
		tmp = t_2
	elif y <= -6.5e-34:
		tmp = t_1
	elif y <= -6.8e-141:
		tmp = t_2
	elif y <= 4.5e-303:
		tmp = t_3
	elif y <= 5.8e-226:
		tmp = c * ((a * j) - (z * b))
	elif y <= 4.2e-16:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_3 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (y <= -5.4e+60)
		tmp = t_1;
	elseif (y <= -0.00012)
		tmp = t_2;
	elseif (y <= -6.5e-34)
		tmp = t_1;
	elseif (y <= -6.8e-141)
		tmp = t_2;
	elseif (y <= 4.5e-303)
		tmp = t_3;
	elseif (y <= 5.8e-226)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (y <= 4.2e-16)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((x * z) - (i * j));
	t_2 = a * ((c * j) - (x * t));
	t_3 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (y <= -5.4e+60)
		tmp = t_1;
	elseif (y <= -0.00012)
		tmp = t_2;
	elseif (y <= -6.5e-34)
		tmp = t_1;
	elseif (y <= -6.8e-141)
		tmp = t_2;
	elseif (y <= 4.5e-303)
		tmp = t_3;
	elseif (y <= 5.8e-226)
		tmp = c * ((a * j) - (z * b));
	elseif (y <= 4.2e-16)
		tmp = t_3;
	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[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.4e+60], t$95$1, If[LessEqual[y, -0.00012], t$95$2, If[LessEqual[y, -6.5e-34], t$95$1, If[LessEqual[y, -6.8e-141], t$95$2, If[LessEqual[y, 4.5e-303], t$95$3, If[LessEqual[y, 5.8e-226], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e-16], t$95$3, t$95$1]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.3999999999999999e60 or -1.20000000000000003e-4 < y < -6.49999999999999985e-34 or 4.2000000000000002e-16 < y

   1. Initial program 74.8%

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

   3. Taylor expanded in y around inf 66.4%

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

      1. +-commutative 66.4%

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

      2. mul-1-neg 66.4%

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

      3. unsub-neg 66.4%

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

      4. *-commutative 66.4%

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

      5. *-commutative 66.4%

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

   5. Simplified 66.4%

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

   if -5.3999999999999999e60 < y < -1.20000000000000003e-4 or -6.49999999999999985e-34 < y < -6.7999999999999997e-141

   1. Initial program 70.0%

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

   3. Taylor expanded in a around inf 62.2%

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

      1. +-commutative 62.2%

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

      2. mul-1-neg 62.2%

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

      3. unsub-neg 62.2%

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

      4. *-commutative 62.2%

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

   5. Simplified 62.2%

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

   if -6.7999999999999997e-141 < y < 4.5000000000000001e-303 or 5.80000000000000003e-226 < y < 4.2000000000000002e-16

   1. Initial program 79.5%

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

   3. Taylor expanded in b around inf 60.6%

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

   if 4.5000000000000001e-303 < y < 5.80000000000000003e-226

   1. Initial program 67.0%

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

   3. Taylor expanded in c around inf 83.7%

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

      1. *-commutative 83.7%

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

   5. Simplified 83.7%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+60}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -0.00012:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-34}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-141}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-303}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-226}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-16}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 51.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -0.0116:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-137}:\\ \;\;\;\;a \cdot \left(x \cdot \left(c \cdot \frac{j}{x} - t\right)\right)\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{-303}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-225}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-12}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j)))) (t_2 (* b (- (* t i) (* z c)))))
   (if (<= y -4.5e+60)
     t_1
     (if (<= y -0.0116)
       (* a (- (* c j) (* x t)))
       (if (<= y -7e-34)
         t_1
         (if (<= y -4.2e-137)
           (* a (* x (- (* c (/ j x)) t)))
           (if (<= y 2.55e-303)
             t_2
             (if (<= y 1.7e-225)
               (* c (- (* a j) (* z b)))
               (if (<= y 4.8e-12) t_2 t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (y <= -4.5e+60) {
		tmp = t_1;
	} else if (y <= -0.0116) {
		tmp = a * ((c * j) - (x * t));
	} else if (y <= -7e-34) {
		tmp = t_1;
	} else if (y <= -4.2e-137) {
		tmp = a * (x * ((c * (j / x)) - t));
	} else if (y <= 2.55e-303) {
		tmp = t_2;
	} else if (y <= 1.7e-225) {
		tmp = c * ((a * j) - (z * b));
	} else if (y <= 4.8e-12) {
		tmp = t_2;
	} 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 = y * ((x * z) - (i * j))
    t_2 = b * ((t * i) - (z * c))
    if (y <= (-4.5d+60)) then
        tmp = t_1
    else if (y <= (-0.0116d0)) then
        tmp = a * ((c * j) - (x * t))
    else if (y <= (-7d-34)) then
        tmp = t_1
    else if (y <= (-4.2d-137)) then
        tmp = a * (x * ((c * (j / x)) - t))
    else if (y <= 2.55d-303) then
        tmp = t_2
    else if (y <= 1.7d-225) then
        tmp = c * ((a * j) - (z * b))
    else if (y <= 4.8d-12) then
        tmp = t_2
    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 = y * ((x * z) - (i * j));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (y <= -4.5e+60) {
		tmp = t_1;
	} else if (y <= -0.0116) {
		tmp = a * ((c * j) - (x * t));
	} else if (y <= -7e-34) {
		tmp = t_1;
	} else if (y <= -4.2e-137) {
		tmp = a * (x * ((c * (j / x)) - t));
	} else if (y <= 2.55e-303) {
		tmp = t_2;
	} else if (y <= 1.7e-225) {
		tmp = c * ((a * j) - (z * b));
	} else if (y <= 4.8e-12) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	t_2 = b * ((t * i) - (z * c))
	tmp = 0
	if y <= -4.5e+60:
		tmp = t_1
	elif y <= -0.0116:
		tmp = a * ((c * j) - (x * t))
	elif y <= -7e-34:
		tmp = t_1
	elif y <= -4.2e-137:
		tmp = a * (x * ((c * (j / x)) - t))
	elif y <= 2.55e-303:
		tmp = t_2
	elif y <= 1.7e-225:
		tmp = c * ((a * j) - (z * b))
	elif y <= 4.8e-12:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (y <= -4.5e+60)
		tmp = t_1;
	elseif (y <= -0.0116)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (y <= -7e-34)
		tmp = t_1;
	elseif (y <= -4.2e-137)
		tmp = Float64(a * Float64(x * Float64(Float64(c * Float64(j / x)) - t)));
	elseif (y <= 2.55e-303)
		tmp = t_2;
	elseif (y <= 1.7e-225)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (y <= 4.8e-12)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((x * z) - (i * j));
	t_2 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (y <= -4.5e+60)
		tmp = t_1;
	elseif (y <= -0.0116)
		tmp = a * ((c * j) - (x * t));
	elseif (y <= -7e-34)
		tmp = t_1;
	elseif (y <= -4.2e-137)
		tmp = a * (x * ((c * (j / x)) - t));
	elseif (y <= 2.55e-303)
		tmp = t_2;
	elseif (y <= 1.7e-225)
		tmp = c * ((a * j) - (z * b));
	elseif (y <= 4.8e-12)
		tmp = t_2;
	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[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.5e+60], t$95$1, If[LessEqual[y, -0.0116], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7e-34], t$95$1, If[LessEqual[y, -4.2e-137], N[(a * N[(x * N[(N[(c * N[(j / x), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.55e-303], t$95$2, If[LessEqual[y, 1.7e-225], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.8e-12], t$95$2, t$95$1]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -4.50000000000000013e60 or -0.0116 < y < -7e-34 or 4.79999999999999974e-12 < y

   1. Initial program 74.8%

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

   3. Taylor expanded in y around inf 66.4%

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

      1. +-commutative 66.4%

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

      2. mul-1-neg 66.4%

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

      3. unsub-neg 66.4%

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

      4. *-commutative 66.4%

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

      5. *-commutative 66.4%

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

   5. Simplified 66.4%

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

   if -4.50000000000000013e60 < y < -0.0116

   1. Initial program 83.2%

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

   3. Taylor expanded in a around inf 75.9%

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

      1. +-commutative 75.9%

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

      2. mul-1-neg 75.9%

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

      3. unsub-neg 75.9%

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

      4. *-commutative 75.9%

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

   5. Simplified 75.9%

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

   if -7e-34 < y < -4.19999999999999983e-137

   1. Initial program 63.4%

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

   3. Taylor expanded in a around inf 55.3%

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

      1. +-commutative 55.3%

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

      2. mul-1-neg 55.3%

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

      3. unsub-neg 55.3%

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

      4. *-commutative 55.3%

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

   5. Simplified 55.3%

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

   6. Taylor expanded in x around inf 59.9%

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

      1. associate-/l* 56.1%

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

   8. Simplified 56.1%

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

   if -4.19999999999999983e-137 < y < 2.55e-303 or 1.7e-225 < y < 4.79999999999999974e-12

   1. Initial program 79.5%

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

   3. Taylor expanded in b around inf 60.6%

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

   if 2.55e-303 < y < 1.7e-225

   1. Initial program 67.0%

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

   3. Taylor expanded in c around inf 83.7%

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

      1. *-commutative 83.7%

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

   5. Simplified 83.7%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+60}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -0.0116:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-34}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-137}:\\ \;\;\;\;a \cdot \left(x \cdot \left(c \cdot \frac{j}{x} - t\right)\right)\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{-303}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-225}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-12}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{+60}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -2.35 \cdot 10^{-11}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-34}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-110}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-303}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{-225}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-15}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* a j) (* z b)))) (t_2 (* y (- (* x z) (* i j)))))
   (if (<= y -5.2e+60)
     t_2
     (if (<= y -2.35e-11)
       (* a (- (* c j) (* x t)))
       (if (<= y -5e-34)
         t_2
         (if (<= y -2e-110)
           t_1
           (if (<= y 1.9e-303)
             (* t (- (* b i) (* x a)))
             (if (<= y 5.3e-225)
               t_1
               (if (<= y 6.8e-15) (* b (- (* t i) (* z c))) 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 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -5.2e+60) {
		tmp = t_2;
	} else if (y <= -2.35e-11) {
		tmp = a * ((c * j) - (x * t));
	} else if (y <= -5e-34) {
		tmp = t_2;
	} else if (y <= -2e-110) {
		tmp = t_1;
	} else if (y <= 1.9e-303) {
		tmp = t * ((b * i) - (x * a));
	} else if (y <= 5.3e-225) {
		tmp = t_1;
	} else if (y <= 6.8e-15) {
		tmp = b * ((t * i) - (z * c));
	} 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 = y * ((x * z) - (i * j))
    if (y <= (-5.2d+60)) then
        tmp = t_2
    else if (y <= (-2.35d-11)) then
        tmp = a * ((c * j) - (x * t))
    else if (y <= (-5d-34)) then
        tmp = t_2
    else if (y <= (-2d-110)) then
        tmp = t_1
    else if (y <= 1.9d-303) then
        tmp = t * ((b * i) - (x * a))
    else if (y <= 5.3d-225) then
        tmp = t_1
    else if (y <= 6.8d-15) then
        tmp = b * ((t * i) - (z * c))
    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 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -5.2e+60) {
		tmp = t_2;
	} else if (y <= -2.35e-11) {
		tmp = a * ((c * j) - (x * t));
	} else if (y <= -5e-34) {
		tmp = t_2;
	} else if (y <= -2e-110) {
		tmp = t_1;
	} else if (y <= 1.9e-303) {
		tmp = t * ((b * i) - (x * a));
	} else if (y <= 5.3e-225) {
		tmp = t_1;
	} else if (y <= 6.8e-15) {
		tmp = b * ((t * i) - (z * c));
	} 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 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -5.2e+60:
		tmp = t_2
	elif y <= -2.35e-11:
		tmp = a * ((c * j) - (x * t))
	elif y <= -5e-34:
		tmp = t_2
	elif y <= -2e-110:
		tmp = t_1
	elif y <= 1.9e-303:
		tmp = t * ((b * i) - (x * a))
	elif y <= 5.3e-225:
		tmp = t_1
	elif y <= 6.8e-15:
		tmp = b * ((t * i) - (z * c))
	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(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -5.2e+60)
		tmp = t_2;
	elseif (y <= -2.35e-11)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (y <= -5e-34)
		tmp = t_2;
	elseif (y <= -2e-110)
		tmp = t_1;
	elseif (y <= 1.9e-303)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (y <= 5.3e-225)
		tmp = t_1;
	elseif (y <= 6.8e-15)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	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 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -5.2e+60)
		tmp = t_2;
	elseif (y <= -2.35e-11)
		tmp = a * ((c * j) - (x * t));
	elseif (y <= -5e-34)
		tmp = t_2;
	elseif (y <= -2e-110)
		tmp = t_1;
	elseif (y <= 1.9e-303)
		tmp = t * ((b * i) - (x * a));
	elseif (y <= 5.3e-225)
		tmp = t_1;
	elseif (y <= 6.8e-15)
		tmp = b * ((t * i) - (z * c));
	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[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.2e+60], t$95$2, If[LessEqual[y, -2.35e-11], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5e-34], t$95$2, If[LessEqual[y, -2e-110], t$95$1, If[LessEqual[y, 1.9e-303], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.3e-225], t$95$1, If[LessEqual[y, 6.8e-15], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -5.20000000000000016e60 or -2.34999999999999996e-11 < y < -5.0000000000000003e-34 or 6.8000000000000001e-15 < y

   1. Initial program 74.8%

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

   3. Taylor expanded in y around inf 66.4%

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

      1. +-commutative 66.4%

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

      2. mul-1-neg 66.4%

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

      3. unsub-neg 66.4%

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

      4. *-commutative 66.4%

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

      5. *-commutative 66.4%

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

   5. Simplified 66.4%

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

   if -5.20000000000000016e60 < y < -2.34999999999999996e-11

   1. Initial program 83.2%

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

   3. Taylor expanded in a around inf 75.9%

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

      1. +-commutative 75.9%

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

      2. mul-1-neg 75.9%

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

      3. unsub-neg 75.9%

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

      4. *-commutative 75.9%

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

   5. Simplified 75.9%

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

   if -5.0000000000000003e-34 < y < -2.0000000000000001e-110 or 1.90000000000000005e-303 < y < 5.30000000000000005e-225

   1. Initial program 63.2%

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

   3. Taylor expanded in c around inf 70.5%

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

      1. *-commutative 70.5%

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

   5. Simplified 70.5%

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

   if -2.0000000000000001e-110 < y < 1.90000000000000005e-303

   1. Initial program 80.3%

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

   3. Taylor expanded in t around inf 69.5%

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

      1. distribute-lft-out-- 69.5%

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

      2. *-commutative 69.5%

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

   5. Simplified 69.5%

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

   if 5.30000000000000005e-225 < y < 6.8000000000000001e-15

   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 53.1%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+60}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -2.35 \cdot 10^{-11}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-34}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-110}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-303}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{-225}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-15}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 66.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(b \cdot c\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right) - t\_1\\ t_3 := b \cdot \left(t \cdot i - z \cdot c\right) + a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;y \leq -8.2 \cdot 10^{+152}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{+113}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -1000000000000:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - t\_1\\ \mathbf{elif}\;y \leq -7.3 \cdot 10^{-34}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - j \cdot \left(y \cdot i\right)\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-11}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* b c)))
        (t_2 (- (* y (- (* x z) (* i j))) t_1))
        (t_3 (+ (* b (- (* t i) (* z c))) (* a (- (* c j) (* x t))))))
   (if (<= y -8.2e+152)
     t_2
     (if (<= y -1.2e+113)
       t_3
       (if (<= y -1000000000000.0)
         (- (* j (- (* a c) (* y i))) t_1)
         (if (<= y -7.3e-34)
           (- (* x (- (* y z) (* t a))) (* j (* y i)))
           (if (<= y 5.5e-11) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (b * c);
	double t_2 = (y * ((x * z) - (i * j))) - t_1;
	double t_3 = (b * ((t * i) - (z * c))) + (a * ((c * j) - (x * t)));
	double tmp;
	if (y <= -8.2e+152) {
		tmp = t_2;
	} else if (y <= -1.2e+113) {
		tmp = t_3;
	} else if (y <= -1000000000000.0) {
		tmp = (j * ((a * c) - (y * i))) - t_1;
	} else if (y <= -7.3e-34) {
		tmp = (x * ((y * z) - (t * a))) - (j * (y * i));
	} else if (y <= 5.5e-11) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = z * (b * c)
    t_2 = (y * ((x * z) - (i * j))) - t_1
    t_3 = (b * ((t * i) - (z * c))) + (a * ((c * j) - (x * t)))
    if (y <= (-8.2d+152)) then
        tmp = t_2
    else if (y <= (-1.2d+113)) then
        tmp = t_3
    else if (y <= (-1000000000000.0d0)) then
        tmp = (j * ((a * c) - (y * i))) - t_1
    else if (y <= (-7.3d-34)) then
        tmp = (x * ((y * z) - (t * a))) - (j * (y * i))
    else if (y <= 5.5d-11) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (b * c);
	double t_2 = (y * ((x * z) - (i * j))) - t_1;
	double t_3 = (b * ((t * i) - (z * c))) + (a * ((c * j) - (x * t)));
	double tmp;
	if (y <= -8.2e+152) {
		tmp = t_2;
	} else if (y <= -1.2e+113) {
		tmp = t_3;
	} else if (y <= -1000000000000.0) {
		tmp = (j * ((a * c) - (y * i))) - t_1;
	} else if (y <= -7.3e-34) {
		tmp = (x * ((y * z) - (t * a))) - (j * (y * i));
	} else if (y <= 5.5e-11) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (b * c)
	t_2 = (y * ((x * z) - (i * j))) - t_1
	t_3 = (b * ((t * i) - (z * c))) + (a * ((c * j) - (x * t)))
	tmp = 0
	if y <= -8.2e+152:
		tmp = t_2
	elif y <= -1.2e+113:
		tmp = t_3
	elif y <= -1000000000000.0:
		tmp = (j * ((a * c) - (y * i))) - t_1
	elif y <= -7.3e-34:
		tmp = (x * ((y * z) - (t * a))) - (j * (y * i))
	elif y <= 5.5e-11:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(b * c))
	t_2 = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) - t_1)
	t_3 = Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) + Float64(a * Float64(Float64(c * j) - Float64(x * t))))
	tmp = 0.0
	if (y <= -8.2e+152)
		tmp = t_2;
	elseif (y <= -1.2e+113)
		tmp = t_3;
	elseif (y <= -1000000000000.0)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) - t_1);
	elseif (y <= -7.3e-34)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(j * Float64(y * i)));
	elseif (y <= 5.5e-11)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * (b * c);
	t_2 = (y * ((x * z) - (i * j))) - t_1;
	t_3 = (b * ((t * i) - (z * c))) + (a * ((c * j) - (x * t)));
	tmp = 0.0;
	if (y <= -8.2e+152)
		tmp = t_2;
	elseif (y <= -1.2e+113)
		tmp = t_3;
	elseif (y <= -1000000000000.0)
		tmp = (j * ((a * c) - (y * i))) - t_1;
	elseif (y <= -7.3e-34)
		tmp = (x * ((y * z) - (t * a))) - (j * (y * i));
	elseif (y <= 5.5e-11)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.2e+152], t$95$2, If[LessEqual[y, -1.2e+113], t$95$3, If[LessEqual[y, -1000000000000.0], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[y, -7.3e-34], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.5e-11], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -8.1999999999999996e152 or 5.49999999999999975e-11 < y

   1. Initial program 71.1%

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

   3. Taylor expanded in a around 0 64.3%

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

   5. Simplified 71.7%

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

   6. Taylor expanded in t around 0 76.5%

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

      1. neg-mul-1 76.5%

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

      2. +-commutative 76.5%

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

      3. *-commutative 76.5%

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

      4. *-commutative 76.5%

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

      5. sub-neg 76.5%

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

      6. sub-neg 76.5%

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

      7. unsub-neg 76.5%

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

      8. associate-*r* 79.8%

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

      9. *-commutative 79.8%

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

   8. Simplified 79.8%

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

   if -8.1999999999999996e152 < y < -1.19999999999999992e113 or -7.29999999999999996e-34 < y < 5.49999999999999975e-11

   1. Initial program 74.0%

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

   3. Taylor expanded in y around 0 70.7%

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

      1. cancel-sign-sub-inv 70.7%

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

      2. *-commutative 70.7%

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

      3. associate-*r* 70.7%

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

      4. *-commutative 70.7%

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

      5. distribute-rgt-in 72.1%

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

      6. +-commutative 72.1%

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

      7. mul-1-neg 72.1%

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

      8. unsub-neg 72.1%

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

      9. *-commutative 72.1%

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

      10. distribute-lft-neg-in 72.1%

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

      11. sub-neg 72.1%

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

      12. distribute-rgt-neg-out 72.1%

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

      13. distribute-lft-out 69.3%

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

      14. +-commutative 69.3%

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

      15. distribute-rgt-neg-out 69.3%

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

      16. distribute-rgt-neg-in 69.3%

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

      17. mul-1-neg 69.3%

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

   5. Simplified 72.1%

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

   if -1.19999999999999992e113 < y < -1e12

   1. Initial program 93.7%

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

      1. +-commutative 93.7%

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

      2. fma-define 93.7%

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

      3. *-commutative 93.7%

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

      4. sub-neg 93.7%

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

      5. *-commutative 93.7%

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

      6. sub-neg 93.7%

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

      7. *-commutative 93.7%

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

      8. *-commutative 93.7%

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

   3. Simplified 93.7%

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

   5. Taylor expanded in x around -inf 93.7%

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

      1. mul-1-neg 93.7%

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

      2. distribute-rgt-neg-in 93.7%

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

      3. +-commutative 93.7%

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

      4. mul-1-neg 93.7%

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

      5. unsub-neg 93.7%

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

      6. associate-/l* 87.4%

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

   7. Simplified 87.4%

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

   8. Taylor expanded in x around 0 87.6%

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

      1. +-commutative 87.6%

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

      2. *-commutative 87.6%

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

      3. sub-neg 87.6%

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

      4. sub-neg 87.6%

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

      5. mul-1-neg 87.6%

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

      6. unsub-neg 87.6%

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

   10. Simplified 87.6%

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

   11. Taylor expanded in c around inf 81.5%

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

       1. associate-*r* 81.5%

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

       2. *-commutative 81.5%

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

   13. Simplified 81.5%

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

   if -1e12 < y < -7.29999999999999996e-34

   1. Initial program 92.6%

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

   3. Taylor expanded in b around 0 99.8%

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

   4. Taylor expanded in a around 0 86.0%

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

      1. neg-mul-1 86.0%

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

      2. distribute-rgt-neg-in 86.0%

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

   6. Simplified 86.0%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+152}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{+113}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) + a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq -1000000000000:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;y \leq -7.3 \cdot 10^{-34}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - j \cdot \left(y \cdot i\right)\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-11}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) + a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - z \cdot \left(b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 63.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;i \leq -3.7 \cdot 10^{+257}:\\ \;\;\;\;t\_2 - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;i \leq -3.25 \cdot 10^{-34}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + t\_1\\ \mathbf{elif}\;i \leq -6.5 \cdot 10^{-262}:\\ \;\;\;\;t\_1 + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq 1.06 \cdot 10^{-82}:\\ \;\;\;\;t\_1 + a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 4.3 \cdot 10^{+108}:\\ \;\;\;\;t\_2 + t\_1\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* j (- (* a c) (* y i)))))
   (if (<= i -3.7e+257)
     (- t_2 (* z (* b c)))
     (if (<= i -3.25e-34)
       (+ (* y (- (* x z) (* i j))) t_1)
       (if (<= i -6.5e-262)
         (+ t_1 (* x (- (* y z) (* t a))))
         (if (<= i 1.06e-82)
           (+ t_1 (* a (- (* c j) (* x t))))
           (if (<= i 4.3e+108) (+ t_2 t_1) (* i (- (* t b) (* y j))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (i <= -3.7e+257) {
		tmp = t_2 - (z * (b * c));
	} else if (i <= -3.25e-34) {
		tmp = (y * ((x * z) - (i * j))) + t_1;
	} else if (i <= -6.5e-262) {
		tmp = t_1 + (x * ((y * z) - (t * a)));
	} else if (i <= 1.06e-82) {
		tmp = t_1 + (a * ((c * j) - (x * t)));
	} else if (i <= 4.3e+108) {
		tmp = t_2 + t_1;
	} else {
		tmp = i * ((t * b) - (y * 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = j * ((a * c) - (y * i))
    if (i <= (-3.7d+257)) then
        tmp = t_2 - (z * (b * c))
    else if (i <= (-3.25d-34)) then
        tmp = (y * ((x * z) - (i * j))) + t_1
    else if (i <= (-6.5d-262)) then
        tmp = t_1 + (x * ((y * z) - (t * a)))
    else if (i <= 1.06d-82) then
        tmp = t_1 + (a * ((c * j) - (x * t)))
    else if (i <= 4.3d+108) then
        tmp = t_2 + t_1
    else
        tmp = i * ((t * b) - (y * 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 t_1 = b * ((t * i) - (z * c));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (i <= -3.7e+257) {
		tmp = t_2 - (z * (b * c));
	} else if (i <= -3.25e-34) {
		tmp = (y * ((x * z) - (i * j))) + t_1;
	} else if (i <= -6.5e-262) {
		tmp = t_1 + (x * ((y * z) - (t * a)));
	} else if (i <= 1.06e-82) {
		tmp = t_1 + (a * ((c * j) - (x * t)));
	} else if (i <= 4.3e+108) {
		tmp = t_2 + t_1;
	} else {
		tmp = i * ((t * b) - (y * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = j * ((a * c) - (y * i))
	tmp = 0
	if i <= -3.7e+257:
		tmp = t_2 - (z * (b * c))
	elif i <= -3.25e-34:
		tmp = (y * ((x * z) - (i * j))) + t_1
	elif i <= -6.5e-262:
		tmp = t_1 + (x * ((y * z) - (t * a)))
	elif i <= 1.06e-82:
		tmp = t_1 + (a * ((c * j) - (x * t)))
	elif i <= 4.3e+108:
		tmp = t_2 + t_1
	else:
		tmp = i * ((t * b) - (y * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (i <= -3.7e+257)
		tmp = Float64(t_2 - Float64(z * Float64(b * c)));
	elseif (i <= -3.25e-34)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + t_1);
	elseif (i <= -6.5e-262)
		tmp = Float64(t_1 + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	elseif (i <= 1.06e-82)
		tmp = Float64(t_1 + Float64(a * Float64(Float64(c * j) - Float64(x * t))));
	elseif (i <= 4.3e+108)
		tmp = Float64(t_2 + t_1);
	else
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (i <= -3.7e+257)
		tmp = t_2 - (z * (b * c));
	elseif (i <= -3.25e-34)
		tmp = (y * ((x * z) - (i * j))) + t_1;
	elseif (i <= -6.5e-262)
		tmp = t_1 + (x * ((y * z) - (t * a)));
	elseif (i <= 1.06e-82)
		tmp = t_1 + (a * ((c * j) - (x * t)));
	elseif (i <= 4.3e+108)
		tmp = t_2 + t_1;
	else
		tmp = i * ((t * b) - (y * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -3.7e+257], N[(t$95$2 - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -3.25e-34], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[i, -6.5e-262], N[(t$95$1 + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.06e-82], N[(t$95$1 + N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4.3e+108], N[(t$95$2 + t$95$1), $MachinePrecision], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -3.69999999999999991e257

   1. Initial program 51.3%

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

      1. +-commutative 51.3%

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

      2. fma-define 51.3%

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

      3. *-commutative 51.3%

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

      4. sub-neg 51.3%

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

      5. *-commutative 51.3%

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

      6. sub-neg 51.3%

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

      7. *-commutative 51.3%

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

      8. *-commutative 51.3%

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

   3. Simplified 51.3%

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

   5. Taylor expanded in x around -inf 51.3%

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

      1. mul-1-neg 51.3%

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

      2. distribute-rgt-neg-in 51.3%

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

      3. +-commutative 51.3%

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

      4. mul-1-neg 51.3%

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

      5. unsub-neg 51.3%

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

      6. associate-/l* 51.3%

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

   7. Simplified 51.3%

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

   8. Taylor expanded in x around 0 51.3%

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

      1. +-commutative 51.3%

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

      2. *-commutative 51.3%

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

      3. sub-neg 51.3%

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

      4. sub-neg 51.3%

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

      5. mul-1-neg 51.3%

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

      6. unsub-neg 51.3%

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

   10. Simplified 51.3%

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

   11. Taylor expanded in c around inf 76.3%

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

       1. associate-*r* 99.8%

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

       2. *-commutative 99.8%

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

   13. Simplified 99.8%

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

   if -3.69999999999999991e257 < i < -3.24999999999999993e-34

   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 a around 0 75.4%

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

   5. Simplified 78.4%

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

   if -3.24999999999999993e-34 < i < -6.5000000000000003e-262

   1. Initial program 80.7%

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

   3. Taylor expanded in j around 0 80.4%

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

   if -6.5000000000000003e-262 < i < 1.06e-82

   1. Initial program 84.8%

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

   3. Taylor expanded in y around 0 75.3%

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

      1. cancel-sign-sub-inv 75.3%

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

      2. *-commutative 75.3%

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

      3. associate-*r* 75.3%

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

      4. *-commutative 75.3%

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

      5. distribute-rgt-in 75.3%

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

      6. +-commutative 75.3%

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

      7. mul-1-neg 75.3%

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

      8. unsub-neg 75.3%

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

      9. *-commutative 75.3%

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

      10. distribute-lft-neg-in 75.3%

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

      11. sub-neg 75.3%

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

      12. distribute-rgt-neg-out 75.3%

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

      13. distribute-lft-out 75.3%

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

      14. +-commutative 75.3%

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

      15. distribute-rgt-neg-out 75.3%

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

      16. distribute-rgt-neg-in 75.3%

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

      17. mul-1-neg 75.3%

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

   5. Simplified 75.3%

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

   if 1.06e-82 < i < 4.29999999999999996e108

   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 x around 0 74.6%

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

   if 4.29999999999999996e108 < i

   1. Initial program 54.2%

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

      1. +-commutative 54.2%

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

      2. fma-define 54.2%

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

      3. *-commutative 54.2%

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

      4. sub-neg 54.2%

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

      5. *-commutative 54.2%

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

      6. sub-neg 54.2%

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

      7. *-commutative 54.2%

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

      8. *-commutative 54.2%

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

   3. Simplified 54.2%

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

   5. Taylor expanded in x around -inf 57.5%

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

      1. mul-1-neg 57.5%

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

      2. distribute-rgt-neg-in 57.5%

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

      3. +-commutative 57.5%

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

      4. mul-1-neg 57.5%

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

      5. unsub-neg 57.5%

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

      6. associate-/l* 54.4%

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

   7. Simplified 54.4%

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

   8. Taylor expanded in i around inf 78.4%

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

      1. +-commutative 78.4%

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

      2. mul-1-neg 78.4%

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

      3. unsub-neg 78.4%

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

      4. *-commutative 78.4%

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

   10. Simplified 78.4%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.7 \cdot 10^{+257}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;i \leq -3.25 \cdot 10^{-34}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq -6.5 \cdot 10^{-262}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq 1.06 \cdot 10^{-82}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) + a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 4.3 \cdot 10^{+108}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 65.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;a \leq -3.8 \cdot 10^{+25}:\\ \;\;\;\;t\_2 + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-78}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{+108}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_1 + a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* j (- (* a c) (* y i)))))
   (if (<= a -3.8e+25)
     (+ t_2 (* x (- (* y z) (* t a))))
     (if (<= a -4.6e-59)
       t_1
       (if (<= a -8e-78)
         t_2
         (if (<= a 4.3e+108)
           (+ (* y (- (* x z) (* i j))) t_1)
           (+ t_1 (* a (- (* c j) (* x t))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (a <= -3.8e+25) {
		tmp = t_2 + (x * ((y * z) - (t * a)));
	} else if (a <= -4.6e-59) {
		tmp = t_1;
	} else if (a <= -8e-78) {
		tmp = t_2;
	} else if (a <= 4.3e+108) {
		tmp = (y * ((x * z) - (i * j))) + t_1;
	} else {
		tmp = t_1 + (a * ((c * j) - (x * t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = j * ((a * c) - (y * i))
    if (a <= (-3.8d+25)) then
        tmp = t_2 + (x * ((y * z) - (t * a)))
    else if (a <= (-4.6d-59)) then
        tmp = t_1
    else if (a <= (-8d-78)) then
        tmp = t_2
    else if (a <= 4.3d+108) then
        tmp = (y * ((x * z) - (i * j))) + t_1
    else
        tmp = t_1 + (a * ((c * j) - (x * t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (a <= -3.8e+25) {
		tmp = t_2 + (x * ((y * z) - (t * a)));
	} else if (a <= -4.6e-59) {
		tmp = t_1;
	} else if (a <= -8e-78) {
		tmp = t_2;
	} else if (a <= 4.3e+108) {
		tmp = (y * ((x * z) - (i * j))) + t_1;
	} else {
		tmp = t_1 + (a * ((c * j) - (x * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = j * ((a * c) - (y * i))
	tmp = 0
	if a <= -3.8e+25:
		tmp = t_2 + (x * ((y * z) - (t * a)))
	elif a <= -4.6e-59:
		tmp = t_1
	elif a <= -8e-78:
		tmp = t_2
	elif a <= 4.3e+108:
		tmp = (y * ((x * z) - (i * j))) + t_1
	else:
		tmp = t_1 + (a * ((c * j) - (x * t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (a <= -3.8e+25)
		tmp = Float64(t_2 + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	elseif (a <= -4.6e-59)
		tmp = t_1;
	elseif (a <= -8e-78)
		tmp = t_2;
	elseif (a <= 4.3e+108)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + t_1);
	else
		tmp = Float64(t_1 + Float64(a * Float64(Float64(c * j) - Float64(x * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (a <= -3.8e+25)
		tmp = t_2 + (x * ((y * z) - (t * a)));
	elseif (a <= -4.6e-59)
		tmp = t_1;
	elseif (a <= -8e-78)
		tmp = t_2;
	elseif (a <= 4.3e+108)
		tmp = (y * ((x * z) - (i * j))) + t_1;
	else
		tmp = t_1 + (a * ((c * j) - (x * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.8e+25], N[(t$95$2 + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.6e-59], t$95$1, If[LessEqual[a, -8e-78], t$95$2, If[LessEqual[a, 4.3e+108], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(t$95$1 + N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -3.8e25

   1. Initial program 74.0%

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

   3. Taylor expanded in b around 0 73.8%

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

   if -3.8e25 < a < -4.59999999999999959e-59

   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 b around inf 84.9%

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

   if -4.59999999999999959e-59 < a < -7.99999999999999999e-78

   1. Initial program 50.0%

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

      1. +-commutative 50.0%

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

      2. fma-define 50.0%

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

      3. *-commutative 50.0%

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

      4. sub-neg 50.0%

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

      5. *-commutative 50.0%

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

      6. sub-neg 50.0%

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

      7. *-commutative 50.0%

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

      8. *-commutative 50.0%

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

   3. Simplified 50.0%

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

   5. Taylor expanded in x around -inf 25.0%

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

      1. mul-1-neg 25.0%

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

      2. distribute-rgt-neg-in 25.0%

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

      3. +-commutative 25.0%

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

      4. mul-1-neg 25.0%

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

      5. unsub-neg 25.0%

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

      6. associate-/l* 25.0%

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

   7. Simplified 25.0%

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

   8. Taylor expanded in j around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. sub-neg 100.0%

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

   10. Simplified 100.0%

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

   if -7.99999999999999999e-78 < a < 4.29999999999999996e108

   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 0 75.4%

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

   5. Simplified 74.0%

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

   if 4.29999999999999996e108 < a

   1. Initial program 60.9%

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

   3. Taylor expanded in y around 0 77.9%

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

      1. cancel-sign-sub-inv 77.9%

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

      2. *-commutative 77.9%

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

      3. associate-*r* 77.9%

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

      4. *-commutative 77.9%

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

      5. distribute-rgt-in 80.4%

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

      6. +-commutative 80.4%

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

      7. mul-1-neg 80.4%

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

      8. unsub-neg 80.4%

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

      9. *-commutative 80.4%

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

      10. distribute-lft-neg-in 80.4%

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

      11. sub-neg 80.4%

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

      12. distribute-rgt-neg-out 80.4%

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

      13. distribute-lft-out 77.9%

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

      14. +-commutative 77.9%

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

      15. distribute-rgt-neg-out 77.9%

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

      16. distribute-rgt-neg-in 77.9%

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

      17. mul-1-neg 77.9%

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

   5. Simplified 80.4%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{+25}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-59}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-78}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{+108}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) + a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 29.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ t_2 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;y \leq -1.65 \cdot 10^{+83}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-114}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-304}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-247}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+46}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+158}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))) (t_2 (* x (* y z))))
   (if (<= y -1.65e+83)
     t_2
     (if (<= y -6.5e-114)
       t_1
       (if (<= y 1.75e-304)
         (* i (* t b))
         (if (<= y 1.55e-247)
           t_1
           (if (<= y 2.25e+46)
             (* (* z c) (- b))
             (if (<= y 3.5e+158) t_2 (* (* y j) (- 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);
	double t_2 = x * (y * z);
	double tmp;
	if (y <= -1.65e+83) {
		tmp = t_2;
	} else if (y <= -6.5e-114) {
		tmp = t_1;
	} else if (y <= 1.75e-304) {
		tmp = i * (t * b);
	} else if (y <= 1.55e-247) {
		tmp = t_1;
	} else if (y <= 2.25e+46) {
		tmp = (z * c) * -b;
	} else if (y <= 3.5e+158) {
		tmp = t_2;
	} else {
		tmp = (y * j) * -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)
    t_2 = x * (y * z)
    if (y <= (-1.65d+83)) then
        tmp = t_2
    else if (y <= (-6.5d-114)) then
        tmp = t_1
    else if (y <= 1.75d-304) then
        tmp = i * (t * b)
    else if (y <= 1.55d-247) then
        tmp = t_1
    else if (y <= 2.25d+46) then
        tmp = (z * c) * -b
    else if (y <= 3.5d+158) then
        tmp = t_2
    else
        tmp = (y * j) * -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);
	double t_2 = x * (y * z);
	double tmp;
	if (y <= -1.65e+83) {
		tmp = t_2;
	} else if (y <= -6.5e-114) {
		tmp = t_1;
	} else if (y <= 1.75e-304) {
		tmp = i * (t * b);
	} else if (y <= 1.55e-247) {
		tmp = t_1;
	} else if (y <= 2.25e+46) {
		tmp = (z * c) * -b;
	} else if (y <= 3.5e+158) {
		tmp = t_2;
	} else {
		tmp = (y * j) * -i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	t_2 = x * (y * z)
	tmp = 0
	if y <= -1.65e+83:
		tmp = t_2
	elif y <= -6.5e-114:
		tmp = t_1
	elif y <= 1.75e-304:
		tmp = i * (t * b)
	elif y <= 1.55e-247:
		tmp = t_1
	elif y <= 2.25e+46:
		tmp = (z * c) * -b
	elif y <= 3.5e+158:
		tmp = t_2
	else:
		tmp = (y * j) * -i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	t_2 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (y <= -1.65e+83)
		tmp = t_2;
	elseif (y <= -6.5e-114)
		tmp = t_1;
	elseif (y <= 1.75e-304)
		tmp = Float64(i * Float64(t * b));
	elseif (y <= 1.55e-247)
		tmp = t_1;
	elseif (y <= 2.25e+46)
		tmp = Float64(Float64(z * c) * Float64(-b));
	elseif (y <= 3.5e+158)
		tmp = t_2;
	else
		tmp = Float64(Float64(y * j) * Float64(-i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (c * j);
	t_2 = x * (y * z);
	tmp = 0.0;
	if (y <= -1.65e+83)
		tmp = t_2;
	elseif (y <= -6.5e-114)
		tmp = t_1;
	elseif (y <= 1.75e-304)
		tmp = i * (t * b);
	elseif (y <= 1.55e-247)
		tmp = t_1;
	elseif (y <= 2.25e+46)
		tmp = (z * c) * -b;
	elseif (y <= 3.5e+158)
		tmp = t_2;
	else
		tmp = (y * j) * -i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.65e+83], t$95$2, If[LessEqual[y, -6.5e-114], t$95$1, If[LessEqual[y, 1.75e-304], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.55e-247], t$95$1, If[LessEqual[y, 2.25e+46], N[(N[(z * c), $MachinePrecision] * (-b)), $MachinePrecision], If[LessEqual[y, 3.5e+158], t$95$2, N[(N[(y * j), $MachinePrecision] * (-i)), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.64999999999999992e83 or 2.25000000000000005e46 < y < 3.5000000000000001e158

   1. Initial program 68.7%

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

   3. Taylor expanded in z around inf 59.4%

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

      1. *-commutative 59.4%

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

      2. *-commutative 59.4%

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

   5. Simplified 59.4%

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

   6. Taylor expanded in y around 0 51.0%

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

   7. Taylor expanded in b around 0 45.4%

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

   if -1.64999999999999992e83 < y < -6.4999999999999998e-114 or 1.75e-304 < y < 1.55000000000000008e-247

   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 a around inf 57.8%

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

      1. +-commutative 57.8%

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

      2. mul-1-neg 57.8%

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

      3. unsub-neg 57.8%

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

      4. *-commutative 57.8%

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

   5. Simplified 57.8%

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

   6. Taylor expanded in j around inf 44.6%

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

   if -6.4999999999999998e-114 < y < 1.75e-304

   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. Step-by-step derivation

      1. +-commutative 79.8%

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

      2. fma-define 84.8%

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

      3. *-commutative 84.8%

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

      4. sub-neg 84.8%

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

      5. *-commutative 84.8%

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

      6. sub-neg 84.8%

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

      7. *-commutative 84.8%

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

      8. *-commutative 84.8%

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

   3. Simplified 84.8%

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

   5. Taylor expanded in x around -inf 85.1%

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

      1. mul-1-neg 85.1%

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

      2. distribute-rgt-neg-in 85.1%

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

      3. +-commutative 85.1%

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

      4. mul-1-neg 85.1%

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

      5. unsub-neg 85.1%

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

      6. associate-/l* 82.7%

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

   7. Simplified 82.7%

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

   8. Taylor expanded in i around inf 60.1%

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

      1. +-commutative 60.1%

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

      2. mul-1-neg 60.1%

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

      3. unsub-neg 60.1%

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

      4. *-commutative 60.1%

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

   10. Simplified 60.1%

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

   11. Taylor expanded in b around inf 57.7%

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

   if 1.55000000000000008e-247 < y < 2.25000000000000005e46

   1. Initial program 78.4%

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

      1. +-commutative 78.4%

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

      2. fma-define 78.4%

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

      3. *-commutative 78.4%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. sub-neg 78.4%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}\right) \]

      5. *-commutative 78.4%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z + \left(-\color{blue}{i \cdot t}\right)\right)\right) \]

      6. sub-neg 78.4%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - i \cdot t\right)}\right) \]

      7. *-commutative 78.4%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) \]

      8. *-commutative 78.4%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) \]

   3. Simplified 78.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf 73.0%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \left(y \cdot z - a \cdot t\right) + \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x}\right)\right)}\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 73.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-x \cdot \left(-1 \cdot \left(y \cdot z - a \cdot t\right) + \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x}\right)}\right) \]

      2. distribute-rgt-neg-in 73.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{x \cdot \left(-\left(-1 \cdot \left(y \cdot z - a \cdot t\right) + \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x}\right)\right)}\right) \]

      3. +-commutative 73.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\color{blue}{\left(\frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + -1 \cdot \left(y \cdot z - a \cdot t\right)\right)}\right)\right) \]

      4. mul-1-neg 73.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\left(\frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + \color{blue}{\left(-\left(y \cdot z - a \cdot t\right)\right)}\right)\right)\right) \]

      5. unsub-neg 73.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\color{blue}{\left(\frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} - \left(y \cdot z - a \cdot t\right)\right)}\right)\right) \]

      6. associate-/l* 71.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\left(\color{blue}{b \cdot \frac{c \cdot z - i \cdot t}{x}} - \left(y \cdot z - a \cdot t\right)\right)\right)\right) \]

   7. Simplified 71.6%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{x \cdot \left(-\left(b \cdot \frac{c \cdot z - i \cdot t}{x} - \left(y \cdot z - a \cdot t\right)\right)\right)}\right) \]

   8. Taylor expanded in x around 0 66.6%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right) + j \cdot \left(a \cdot c - i \cdot y\right)} \]
   9. Step-by-step derivation

      1. +-commutative 66.6%

         \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + -1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right)} \]

      2. *-commutative 66.6%

         \[\leadsto j \cdot \left(\color{blue}{c \cdot a} - i \cdot y\right) + -1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      3. sub-neg 66.6%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot a + \left(-i \cdot y\right)\right)} + -1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      4. sub-neg 66.6%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot a - i \cdot y\right)} + -1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      5. mul-1-neg 66.6%

         \[\leadsto j \cdot \left(c \cdot a - i \cdot y\right) + \color{blue}{\left(-b \cdot \left(c \cdot z - i \cdot t\right)\right)} \]

      6. unsub-neg 66.6%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   10. Simplified 66.6%

       \[\leadsto \color{blue}{j \cdot \left(c \cdot a - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   11. Taylor expanded in z around inf 29.7%

       \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} \]
   12. Step-by-step derivation

       1. neg-mul-1 29.7%

          \[\leadsto \color{blue}{-b \cdot \left(c \cdot z\right)} \]

       2. distribute-rgt-neg-in 29.7%

          \[\leadsto \color{blue}{b \cdot \left(-c \cdot z\right)} \]

       3. distribute-rgt-neg-in 29.7%

          \[\leadsto b \cdot \color{blue}{\left(c \cdot \left(-z\right)\right)} \]

   13. Simplified 29.7%

       \[\leadsto \color{blue}{b \cdot \left(c \cdot \left(-z\right)\right)} \]

   if 3.5000000000000001e158 < y

   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. Step-by-step derivation

      1. +-commutative 74.9%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-define 74.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 74.9%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. sub-neg 74.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}\right) \]

      5. *-commutative 74.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z + \left(-\color{blue}{i \cdot t}\right)\right)\right) \]

      6. sub-neg 74.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - i \cdot t\right)}\right) \]

      7. *-commutative 74.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) \]

      8. *-commutative 74.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) \]

   3. Simplified 74.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf 71.6%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \left(y \cdot z - a \cdot t\right) + \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x}\right)\right)}\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 71.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-x \cdot \left(-1 \cdot \left(y \cdot z - a \cdot t\right) + \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x}\right)}\right) \]

      2. distribute-rgt-neg-in 71.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{x \cdot \left(-\left(-1 \cdot \left(y \cdot z - a \cdot t\right) + \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x}\right)\right)}\right) \]

      3. +-commutative 71.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\color{blue}{\left(\frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + -1 \cdot \left(y \cdot z - a \cdot t\right)\right)}\right)\right) \]

      4. mul-1-neg 71.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\left(\frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + \color{blue}{\left(-\left(y \cdot z - a \cdot t\right)\right)}\right)\right)\right) \]

      5. unsub-neg 71.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\color{blue}{\left(\frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} - \left(y \cdot z - a \cdot t\right)\right)}\right)\right) \]

      6. associate-/l* 68.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\left(\color{blue}{b \cdot \frac{c \cdot z - i \cdot t}{x}} - \left(y \cdot z - a \cdot t\right)\right)\right)\right) \]

   7. Simplified 68.1%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{x \cdot \left(-\left(b \cdot \frac{c \cdot z - i \cdot t}{x} - \left(y \cdot z - a \cdot t\right)\right)\right)}\right) \]

   8. Taylor expanded in i around inf 69.2%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]
   9. Step-by-step derivation

      1. +-commutative 69.2%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      2. mul-1-neg 69.2%

         \[\leadsto i \cdot \left(b \cdot t + \color{blue}{\left(-j \cdot y\right)}\right) \]

      3. unsub-neg 69.2%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t - j \cdot y\right)} \]

      4. *-commutative 69.2%

         \[\leadsto i \cdot \left(b \cdot t - \color{blue}{y \cdot j}\right) \]

   10. Simplified 69.2%

       \[\leadsto \color{blue}{i \cdot \left(b \cdot t - y \cdot j\right)} \]

   11. Taylor expanded in b around 0 65.6%

       \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y\right)\right)} \]
   12. Step-by-step derivation

       1. neg-mul-1 65.6%

          \[\leadsto i \cdot \color{blue}{\left(-j \cdot y\right)} \]

       2. distribute-lft-neg-in 65.6%

          \[\leadsto i \cdot \color{blue}{\left(\left(-j\right) \cdot y\right)} \]

   13. Simplified 65.6%

       \[\leadsto i \cdot \color{blue}{\left(\left(-j\right) \cdot y\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+83}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-114}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-304}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-247}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+46}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+158}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 39.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{if}\;b \leq -5 \cdot 10^{-39}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{-69}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+68}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+180}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{+280}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))) (t_2 (* z (* b (- c)))))
   (if (<= b -5e-39)
     t_2
     (if (<= b 1.7e-82)
       t_1
       (if (<= b 2.25e-69)
         t_2
         (if (<= b 2.5e+68)
           t_1
           (if (<= b 3.7e+180)
             (* b (* t i))
             (if (<= b 1.35e+280) (* (* z c) (- b)) (* i (* t b))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = z * (b * -c);
	double tmp;
	if (b <= -5e-39) {
		tmp = t_2;
	} else if (b <= 1.7e-82) {
		tmp = t_1;
	} else if (b <= 2.25e-69) {
		tmp = t_2;
	} else if (b <= 2.5e+68) {
		tmp = t_1;
	} else if (b <= 3.7e+180) {
		tmp = b * (t * i);
	} else if (b <= 1.35e+280) {
		tmp = (z * c) * -b;
	} else {
		tmp = i * (t * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    t_2 = z * (b * -c)
    if (b <= (-5d-39)) then
        tmp = t_2
    else if (b <= 1.7d-82) then
        tmp = t_1
    else if (b <= 2.25d-69) then
        tmp = t_2
    else if (b <= 2.5d+68) then
        tmp = t_1
    else if (b <= 3.7d+180) then
        tmp = b * (t * i)
    else if (b <= 1.35d+280) then
        tmp = (z * c) * -b
    else
        tmp = i * (t * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = z * (b * -c);
	double tmp;
	if (b <= -5e-39) {
		tmp = t_2;
	} else if (b <= 1.7e-82) {
		tmp = t_1;
	} else if (b <= 2.25e-69) {
		tmp = t_2;
	} else if (b <= 2.5e+68) {
		tmp = t_1;
	} else if (b <= 3.7e+180) {
		tmp = b * (t * i);
	} else if (b <= 1.35e+280) {
		tmp = (z * c) * -b;
	} else {
		tmp = i * (t * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = z * (b * -c)
	tmp = 0
	if b <= -5e-39:
		tmp = t_2
	elif b <= 1.7e-82:
		tmp = t_1
	elif b <= 2.25e-69:
		tmp = t_2
	elif b <= 2.5e+68:
		tmp = t_1
	elif b <= 3.7e+180:
		tmp = b * (t * i)
	elif b <= 1.35e+280:
		tmp = (z * c) * -b
	else:
		tmp = i * (t * b)
	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(z * Float64(b * Float64(-c)))
	tmp = 0.0
	if (b <= -5e-39)
		tmp = t_2;
	elseif (b <= 1.7e-82)
		tmp = t_1;
	elseif (b <= 2.25e-69)
		tmp = t_2;
	elseif (b <= 2.5e+68)
		tmp = t_1;
	elseif (b <= 3.7e+180)
		tmp = Float64(b * Float64(t * i));
	elseif (b <= 1.35e+280)
		tmp = Float64(Float64(z * c) * Float64(-b));
	else
		tmp = Float64(i * Float64(t * b));
	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 = z * (b * -c);
	tmp = 0.0;
	if (b <= -5e-39)
		tmp = t_2;
	elseif (b <= 1.7e-82)
		tmp = t_1;
	elseif (b <= 2.25e-69)
		tmp = t_2;
	elseif (b <= 2.5e+68)
		tmp = t_1;
	elseif (b <= 3.7e+180)
		tmp = b * (t * i);
	elseif (b <= 1.35e+280)
		tmp = (z * c) * -b;
	else
		tmp = i * (t * b);
	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[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5e-39], t$95$2, If[LessEqual[b, 1.7e-82], t$95$1, If[LessEqual[b, 2.25e-69], t$95$2, If[LessEqual[b, 2.5e+68], t$95$1, If[LessEqual[b, 3.7e+180], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.35e+280], N[(N[(z * c), $MachinePrecision] * (-b)), $MachinePrecision], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -4.9999999999999998e-39 or 1.69999999999999988e-82 < b < 2.25000000000000005e-69

   1. Initial program 71.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 54.3%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 54.3%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

      2. *-commutative 54.3%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) \]

   5. Simplified 54.3%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   6. Taylor expanded in y around 0 45.7%

      \[\leadsto z \cdot \color{blue}{\left(-1 \cdot \left(b \cdot c\right)\right)} \]
   7. Step-by-step derivation

      1. neg-mul-1 45.7%

         \[\leadsto z \cdot \color{blue}{\left(-b \cdot c\right)} \]

      2. distribute-rgt-neg-in 45.7%

         \[\leadsto z \cdot \color{blue}{\left(b \cdot \left(-c\right)\right)} \]

   8. Simplified 45.7%

      \[\leadsto z \cdot \color{blue}{\left(b \cdot \left(-c\right)\right)} \]

   if -4.9999999999999998e-39 < b < 1.69999999999999988e-82 or 2.25000000000000005e-69 < b < 2.5000000000000002e68

   1. Initial program 77.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 48.3%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 48.3%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 48.3%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 48.3%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 48.3%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 48.3%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   if 2.5000000000000002e68 < b < 3.7000000000000002e180

   1. Initial program 82.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 82.5%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-define 82.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 82.5%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. sub-neg 82.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}\right) \]

      5. *-commutative 82.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z + \left(-\color{blue}{i \cdot t}\right)\right)\right) \]

      6. sub-neg 82.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - i \cdot t\right)}\right) \]

      7. *-commutative 82.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) \]

      8. *-commutative 82.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) \]

   3. Simplified 82.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf 82.5%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \left(y \cdot z - a \cdot t\right) + \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x}\right)\right)}\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 82.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-x \cdot \left(-1 \cdot \left(y \cdot z - a \cdot t\right) + \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x}\right)}\right) \]

      2. distribute-rgt-neg-in 82.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{x \cdot \left(-\left(-1 \cdot \left(y \cdot z - a \cdot t\right) + \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x}\right)\right)}\right) \]

      3. +-commutative 82.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\color{blue}{\left(\frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + -1 \cdot \left(y \cdot z - a \cdot t\right)\right)}\right)\right) \]

      4. mul-1-neg 82.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\left(\frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + \color{blue}{\left(-\left(y \cdot z - a \cdot t\right)\right)}\right)\right)\right) \]

      5. unsub-neg 82.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\color{blue}{\left(\frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} - \left(y \cdot z - a \cdot t\right)\right)}\right)\right) \]

      6. associate-/l* 82.4%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\left(\color{blue}{b \cdot \frac{c \cdot z - i \cdot t}{x}} - \left(y \cdot z - a \cdot t\right)\right)\right)\right) \]

   7. Simplified 82.4%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{x \cdot \left(-\left(b \cdot \frac{c \cdot z - i \cdot t}{x} - \left(y \cdot z - a \cdot t\right)\right)\right)}\right) \]

   8. Taylor expanded in x around 0 77.0%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right) + j \cdot \left(a \cdot c - i \cdot y\right)} \]
   9. Step-by-step derivation

      1. +-commutative 77.0%

         \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + -1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right)} \]

      2. *-commutative 77.0%

         \[\leadsto j \cdot \left(\color{blue}{c \cdot a} - i \cdot y\right) + -1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      3. sub-neg 77.0%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot a + \left(-i \cdot y\right)\right)} + -1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      4. sub-neg 77.0%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot a - i \cdot y\right)} + -1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      5. mul-1-neg 77.0%

         \[\leadsto j \cdot \left(c \cdot a - i \cdot y\right) + \color{blue}{\left(-b \cdot \left(c \cdot z - i \cdot t\right)\right)} \]

      6. unsub-neg 77.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   10. Simplified 77.0%

       \[\leadsto \color{blue}{j \cdot \left(c \cdot a - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   11. Taylor expanded in t around inf 51.8%

       \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]

   if 3.7000000000000002e180 < b < 1.35000000000000008e280

   1. Initial program 70.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 70.7%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-define 74.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 74.9%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. sub-neg 74.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}\right) \]

      5. *-commutative 74.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z + \left(-\color{blue}{i \cdot t}\right)\right)\right) \]

      6. sub-neg 74.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - i \cdot t\right)}\right) \]

      7. *-commutative 74.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) \]

      8. *-commutative 74.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) \]

   3. Simplified 74.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf 75.3%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \left(y \cdot z - a \cdot t\right) + \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x}\right)\right)}\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 75.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-x \cdot \left(-1 \cdot \left(y \cdot z - a \cdot t\right) + \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x}\right)}\right) \]

      2. distribute-rgt-neg-in 75.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{x \cdot \left(-\left(-1 \cdot \left(y \cdot z - a \cdot t\right) + \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x}\right)\right)}\right) \]

      3. +-commutative 75.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\color{blue}{\left(\frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + -1 \cdot \left(y \cdot z - a \cdot t\right)\right)}\right)\right) \]

      4. mul-1-neg 75.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\left(\frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + \color{blue}{\left(-\left(y \cdot z - a \cdot t\right)\right)}\right)\right)\right) \]

      5. unsub-neg 75.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\color{blue}{\left(\frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} - \left(y \cdot z - a \cdot t\right)\right)}\right)\right) \]

      6. associate-/l* 79.4%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\left(\color{blue}{b \cdot \frac{c \cdot z - i \cdot t}{x}} - \left(y \cdot z - a \cdot t\right)\right)\right)\right) \]

   7. Simplified 79.4%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{x \cdot \left(-\left(b \cdot \frac{c \cdot z - i \cdot t}{x} - \left(y \cdot z - a \cdot t\right)\right)\right)}\right) \]

   8. Taylor expanded in x around 0 62.7%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right) + j \cdot \left(a \cdot c - i \cdot y\right)} \]
   9. Step-by-step derivation

      1. +-commutative 62.7%

         \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + -1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right)} \]

      2. *-commutative 62.7%

         \[\leadsto j \cdot \left(\color{blue}{c \cdot a} - i \cdot y\right) + -1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      3. sub-neg 62.7%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot a + \left(-i \cdot y\right)\right)} + -1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      4. sub-neg 62.7%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot a - i \cdot y\right)} + -1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      5. mul-1-neg 62.7%

         \[\leadsto j \cdot \left(c \cdot a - i \cdot y\right) + \color{blue}{\left(-b \cdot \left(c \cdot z - i \cdot t\right)\right)} \]

      6. unsub-neg 62.7%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   10. Simplified 62.7%

       \[\leadsto \color{blue}{j \cdot \left(c \cdot a - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   11. Taylor expanded in z around inf 53.5%

       \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} \]
   12. Step-by-step derivation

       1. neg-mul-1 53.5%

          \[\leadsto \color{blue}{-b \cdot \left(c \cdot z\right)} \]

       2. distribute-rgt-neg-in 53.5%

          \[\leadsto \color{blue}{b \cdot \left(-c \cdot z\right)} \]

       3. distribute-rgt-neg-in 53.5%

          \[\leadsto b \cdot \color{blue}{\left(c \cdot \left(-z\right)\right)} \]

   13. Simplified 53.5%

       \[\leadsto \color{blue}{b \cdot \left(c \cdot \left(-z\right)\right)} \]

   if 1.35000000000000008e280 < b

   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. Step-by-step derivation

      1. +-commutative 79.7%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-define 99.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 99.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. sub-neg 99.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}\right) \]

      5. *-commutative 99.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z + \left(-\color{blue}{i \cdot t}\right)\right)\right) \]

      6. sub-neg 99.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - i \cdot t\right)}\right) \]

      7. *-commutative 99.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) \]

      8. *-commutative 99.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf 99.7%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \left(y \cdot z - a \cdot t\right) + \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x}\right)\right)}\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 99.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-x \cdot \left(-1 \cdot \left(y \cdot z - a \cdot t\right) + \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x}\right)}\right) \]

      2. distribute-rgt-neg-in 99.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{x \cdot \left(-\left(-1 \cdot \left(y \cdot z - a \cdot t\right) + \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x}\right)\right)}\right) \]

      3. +-commutative 99.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\color{blue}{\left(\frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + -1 \cdot \left(y \cdot z - a \cdot t\right)\right)}\right)\right) \]

      4. mul-1-neg 99.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\left(\frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + \color{blue}{\left(-\left(y \cdot z - a \cdot t\right)\right)}\right)\right)\right) \]

      5. unsub-neg 99.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\color{blue}{\left(\frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} - \left(y \cdot z - a \cdot t\right)\right)}\right)\right) \]

      6. associate-/l* 99.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\left(\color{blue}{b \cdot \frac{c \cdot z - i \cdot t}{x}} - \left(y \cdot z - a \cdot t\right)\right)\right)\right) \]

   7. Simplified 99.7%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{x \cdot \left(-\left(b \cdot \frac{c \cdot z - i \cdot t}{x} - \left(y \cdot z - a \cdot t\right)\right)\right)}\right) \]

   8. Taylor expanded in i around inf 100.0%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]
   9. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      2. mul-1-neg 100.0%

         \[\leadsto i \cdot \left(b \cdot t + \color{blue}{\left(-j \cdot y\right)}\right) \]

      3. unsub-neg 100.0%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t - j \cdot y\right)} \]

      4. *-commutative 100.0%

         \[\leadsto i \cdot \left(b \cdot t - \color{blue}{y \cdot j}\right) \]

   10. Simplified 100.0%

       \[\leadsto \color{blue}{i \cdot \left(b \cdot t - y \cdot j\right)} \]

   11. Taylor expanded in b around inf 100.0%

       \[\leadsto i \cdot \color{blue}{\left(b \cdot t\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{-39}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-82}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{-69}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+68}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+180}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{+280}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 58.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -7.2 \cdot 10^{+141}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{+97}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq -1.56 \cdot 10^{+57} \lor \neg \left(t \leq 6 \cdot 10^{+172}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - z \cdot \left(b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* b i) (* x a)))))
   (if (<= t -7.2e+141)
     t_1
     (if (<= t -4.5e+97)
       (* y (- (* x z) (* i j)))
       (if (or (<= t -1.56e+57) (not (<= t 6e+172)))
         t_1
         (- (* j (- (* a c) (* y i))) (* z (* b 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 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -7.2e+141) {
		tmp = t_1;
	} else if (t <= -4.5e+97) {
		tmp = y * ((x * z) - (i * j));
	} else if ((t <= -1.56e+57) || !(t <= 6e+172)) {
		tmp = t_1;
	} else {
		tmp = (j * ((a * c) - (y * i))) - (z * (b * 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 = t * ((b * i) - (x * a))
    if (t <= (-7.2d+141)) then
        tmp = t_1
    else if (t <= (-4.5d+97)) then
        tmp = y * ((x * z) - (i * j))
    else if ((t <= (-1.56d+57)) .or. (.not. (t <= 6d+172))) then
        tmp = t_1
    else
        tmp = (j * ((a * c) - (y * i))) - (z * (b * 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 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -7.2e+141) {
		tmp = t_1;
	} else if (t <= -4.5e+97) {
		tmp = y * ((x * z) - (i * j));
	} else if ((t <= -1.56e+57) || !(t <= 6e+172)) {
		tmp = t_1;
	} else {
		tmp = (j * ((a * c) - (y * i))) - (z * (b * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((b * i) - (x * a))
	tmp = 0
	if t <= -7.2e+141:
		tmp = t_1
	elif t <= -4.5e+97:
		tmp = y * ((x * z) - (i * j))
	elif (t <= -1.56e+57) or not (t <= 6e+172):
		tmp = t_1
	else:
		tmp = (j * ((a * c) - (y * i))) - (z * (b * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	tmp = 0.0
	if (t <= -7.2e+141)
		tmp = t_1;
	elseif (t <= -4.5e+97)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif ((t <= -1.56e+57) || !(t <= 6e+172))
		tmp = t_1;
	else
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) - Float64(z * Float64(b * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -7.2e+141)
		tmp = t_1;
	elseif (t <= -4.5e+97)
		tmp = y * ((x * z) - (i * j));
	elseif ((t <= -1.56e+57) || ~((t <= 6e+172)))
		tmp = t_1;
	else
		tmp = (j * ((a * c) - (y * i))) - (z * (b * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.2e+141], t$95$1, If[LessEqual[t, -4.5e+97], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -1.56e+57], N[Not[LessEqual[t, 6e+172]], $MachinePrecision]], t$95$1, N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.2000000000000003e141 or -4.49999999999999976e97 < t < -1.55999999999999998e57 or 5.9999999999999998e172 < t

   1. Initial program 71.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 81.7%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 81.7%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x - b \cdot i\right)\right)} \]

      2. *-commutative 81.7%

         \[\leadsto t \cdot \left(-1 \cdot \left(a \cdot x - \color{blue}{i \cdot b}\right)\right) \]

   5. Simplified 81.7%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x - i \cdot b\right)\right)} \]

   if -7.2000000000000003e141 < t < -4.49999999999999976e97

   1. Initial program 75.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 87.8%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 87.8%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 87.8%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 87.8%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 87.8%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

      5. *-commutative 87.8%

         \[\leadsto y \cdot \left(z \cdot x - \color{blue}{j \cdot i}\right) \]

   5. Simplified 87.8%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - j \cdot i\right)} \]

   if -1.55999999999999998e57 < t < 5.9999999999999998e172

   1. Initial program 77.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 77.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-define 78.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 78.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. sub-neg 78.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}\right) \]

      5. *-commutative 78.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z + \left(-\color{blue}{i \cdot t}\right)\right)\right) \]

      6. sub-neg 78.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - i \cdot t\right)}\right) \]

      7. *-commutative 78.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) \]

      8. *-commutative 78.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) \]

   3. Simplified 78.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf 75.0%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \left(y \cdot z - a \cdot t\right) + \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x}\right)\right)}\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 75.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-x \cdot \left(-1 \cdot \left(y \cdot z - a \cdot t\right) + \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x}\right)}\right) \]

      2. distribute-rgt-neg-in 75.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{x \cdot \left(-\left(-1 \cdot \left(y \cdot z - a \cdot t\right) + \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x}\right)\right)}\right) \]

      3. +-commutative 75.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\color{blue}{\left(\frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + -1 \cdot \left(y \cdot z - a \cdot t\right)\right)}\right)\right) \]

      4. mul-1-neg 75.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\left(\frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + \color{blue}{\left(-\left(y \cdot z - a \cdot t\right)\right)}\right)\right)\right) \]

      5. unsub-neg 75.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\color{blue}{\left(\frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} - \left(y \cdot z - a \cdot t\right)\right)}\right)\right) \]

      6. associate-/l* 73.2%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\left(\color{blue}{b \cdot \frac{c \cdot z - i \cdot t}{x}} - \left(y \cdot z - a \cdot t\right)\right)\right)\right) \]

   7. Simplified 73.2%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{x \cdot \left(-\left(b \cdot \frac{c \cdot z - i \cdot t}{x} - \left(y \cdot z - a \cdot t\right)\right)\right)}\right) \]

   8. Taylor expanded in x around 0 67.0%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right) + j \cdot \left(a \cdot c - i \cdot y\right)} \]
   9. Step-by-step derivation

      1. +-commutative 67.0%

         \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + -1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right)} \]

      2. *-commutative 67.0%

         \[\leadsto j \cdot \left(\color{blue}{c \cdot a} - i \cdot y\right) + -1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      3. sub-neg 67.0%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot a + \left(-i \cdot y\right)\right)} + -1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      4. sub-neg 67.0%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot a - i \cdot y\right)} + -1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      5. mul-1-neg 67.0%

         \[\leadsto j \cdot \left(c \cdot a - i \cdot y\right) + \color{blue}{\left(-b \cdot \left(c \cdot z - i \cdot t\right)\right)} \]

      6. unsub-neg 67.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   10. Simplified 67.0%

       \[\leadsto \color{blue}{j \cdot \left(c \cdot a - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   11. Taylor expanded in c around inf 61.0%

       \[\leadsto j \cdot \left(c \cdot a - i \cdot y\right) - \color{blue}{b \cdot \left(c \cdot z\right)} \]
   12. Step-by-step derivation

       1. associate-*r* 62.2%

          \[\leadsto j \cdot \left(c \cdot a - i \cdot y\right) - \color{blue}{\left(b \cdot c\right) \cdot z} \]

       2. *-commutative 62.2%

          \[\leadsto j \cdot \left(c \cdot a - i \cdot y\right) - \color{blue}{\left(c \cdot b\right)} \cdot z \]

   13. Simplified 62.2%

       \[\leadsto j \cdot \left(c \cdot a - i \cdot y\right) - \color{blue}{\left(c \cdot b\right) \cdot z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+141}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{+97}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq -1.56 \cdot 10^{+57} \lor \neg \left(t \leq 6 \cdot 10^{+172}\right):\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - z \cdot \left(b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 68.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{+156}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-34}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-12}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) + a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* y (- (* x z) (* i j))) (* z (* b c)))))
   (if (<= y -4.5e+156)
     t_1
     (if (<= y -6.5e-34)
       (+ (* j (- (* a c) (* y i))) (* x (- (* y z) (* t a))))
       (if (<= y 2.5e-12)
         (+ (* b (- (* t i) (* z c))) (* a (- (* c j) (* x t))))
         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 = (y * ((x * z) - (i * j))) - (z * (b * c));
	double tmp;
	if (y <= -4.5e+156) {
		tmp = t_1;
	} else if (y <= -6.5e-34) {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else if (y <= 2.5e-12) {
		tmp = (b * ((t * i) - (z * c))) + (a * ((c * j) - (x * t)));
	} 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 = (y * ((x * z) - (i * j))) - (z * (b * c))
    if (y <= (-4.5d+156)) then
        tmp = t_1
    else if (y <= (-6.5d-34)) then
        tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
    else if (y <= 2.5d-12) then
        tmp = (b * ((t * i) - (z * c))) + (a * ((c * j) - (x * t)))
    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 = (y * ((x * z) - (i * j))) - (z * (b * c));
	double tmp;
	if (y <= -4.5e+156) {
		tmp = t_1;
	} else if (y <= -6.5e-34) {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else if (y <= 2.5e-12) {
		tmp = (b * ((t * i) - (z * c))) + (a * ((c * j) - (x * t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (y * ((x * z) - (i * j))) - (z * (b * c))
	tmp = 0
	if y <= -4.5e+156:
		tmp = t_1
	elif y <= -6.5e-34:
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
	elif y <= 2.5e-12:
		tmp = (b * ((t * i) - (z * c))) + (a * ((c * j) - (x * t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) - Float64(z * Float64(b * c)))
	tmp = 0.0
	if (y <= -4.5e+156)
		tmp = t_1;
	elseif (y <= -6.5e-34)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	elseif (y <= 2.5e-12)
		tmp = Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) + Float64(a * Float64(Float64(c * j) - Float64(x * t))));
	else
		tmp = t_1;
	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))) - (z * (b * c));
	tmp = 0.0;
	if (y <= -4.5e+156)
		tmp = t_1;
	elseif (y <= -6.5e-34)
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	elseif (y <= 2.5e-12)
		tmp = (b * ((t * i) - (z * c))) + (a * ((c * j) - (x * t)));
	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[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.5e+156], t$95$1, If[LessEqual[y, -6.5e-34], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e-12], N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.50000000000000031e156 or 2.49999999999999985e-12 < y

   1. Initial program 71.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 64.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   5. Simplified 71.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - j \cdot i\right) + b \cdot \left(i \cdot t - c \cdot z\right)} \]

   6. Taylor expanded in t around 0 76.5%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right) + y \cdot \left(x \cdot z - i \cdot j\right)} \]
   7. Step-by-step derivation

      1. neg-mul-1 76.5%

         \[\leadsto \color{blue}{\left(-b \cdot \left(c \cdot z\right)\right)} + y \cdot \left(x \cdot z - i \cdot j\right) \]

      2. +-commutative 76.5%

         \[\leadsto \color{blue}{y \cdot \left(x \cdot z - i \cdot j\right) + \left(-b \cdot \left(c \cdot z\right)\right)} \]

      3. *-commutative 76.5%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) + \left(-b \cdot \left(c \cdot z\right)\right) \]

      4. *-commutative 76.5%

         \[\leadsto y \cdot \left(z \cdot x - \color{blue}{j \cdot i}\right) + \left(-b \cdot \left(c \cdot z\right)\right) \]

      5. sub-neg 76.5%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + \left(-j \cdot i\right)\right)} + \left(-b \cdot \left(c \cdot z\right)\right) \]

      6. sub-neg 76.5%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - j \cdot i\right)} + \left(-b \cdot \left(c \cdot z\right)\right) \]

      7. unsub-neg 76.5%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x - j \cdot i\right) - b \cdot \left(c \cdot z\right)} \]

      8. associate-*r* 79.8%

         \[\leadsto y \cdot \left(z \cdot x - j \cdot i\right) - \color{blue}{\left(b \cdot c\right) \cdot z} \]

      9. *-commutative 79.8%

         \[\leadsto y \cdot \left(z \cdot x - j \cdot i\right) - \color{blue}{\left(c \cdot b\right)} \cdot z \]

   8. Simplified 79.8%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - j \cdot i\right) - \left(c \cdot b\right) \cdot z} \]

   if -4.50000000000000031e156 < y < -6.49999999999999985e-34

   1. Initial program 86.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 78.3%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   if -6.49999999999999985e-34 < y < 2.49999999999999985e-12

   1. Initial program 75.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 70.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(c \cdot j\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   4. Step-by-step derivation

      1. cancel-sign-sub-inv 70.1%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(c \cdot j\right)\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot t\right)} \]

      2. *-commutative 70.1%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(t \cdot x\right) \cdot a\right)} + a \cdot \left(c \cdot j\right)\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot t\right) \]

      3. associate-*r* 70.1%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right) \cdot a} + a \cdot \left(c \cdot j\right)\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot t\right) \]

      4. *-commutative 70.1%

         \[\leadsto \left(\left(-1 \cdot \left(t \cdot x\right)\right) \cdot a + \color{blue}{\left(c \cdot j\right) \cdot a}\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot t\right) \]

      5. distribute-rgt-in 71.6%

         \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} + \left(-b\right) \cdot \left(c \cdot z - i \cdot t\right) \]

      6. +-commutative 71.6%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} + \left(-b\right) \cdot \left(c \cdot z - i \cdot t\right) \]

      7. mul-1-neg 71.6%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot t\right) \]

      8. unsub-neg 71.6%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} + \left(-b\right) \cdot \left(c \cdot z - i \cdot t\right) \]

      9. *-commutative 71.6%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot t\right) \]

      10. distribute-lft-neg-in 71.6%

          \[\leadsto a \cdot \left(j \cdot c - t \cdot x\right) + \color{blue}{\left(-b \cdot \left(c \cdot z - i \cdot t\right)\right)} \]

      11. sub-neg 71.6%

          \[\leadsto a \cdot \left(j \cdot c - t \cdot x\right) + \left(-b \cdot \color{blue}{\left(c \cdot z + \left(-i \cdot t\right)\right)}\right) \]

      12. distribute-rgt-neg-out 71.6%

          \[\leadsto a \cdot \left(j \cdot c - t \cdot x\right) + \left(-b \cdot \left(c \cdot z + \color{blue}{i \cdot \left(-t\right)}\right)\right) \]

      13. distribute-lft-out 69.4%

          \[\leadsto a \cdot \left(j \cdot c - t \cdot x\right) + \left(-\color{blue}{\left(b \cdot \left(c \cdot z\right) + b \cdot \left(i \cdot \left(-t\right)\right)\right)}\right) \]

      14. +-commutative 69.4%

          \[\leadsto a \cdot \left(j \cdot c - t \cdot x\right) + \left(-\color{blue}{\left(b \cdot \left(i \cdot \left(-t\right)\right) + b \cdot \left(c \cdot z\right)\right)}\right) \]

      15. distribute-rgt-neg-out 69.4%

          \[\leadsto a \cdot \left(j \cdot c - t \cdot x\right) + \left(-\left(b \cdot \color{blue}{\left(-i \cdot t\right)} + b \cdot \left(c \cdot z\right)\right)\right) \]

      16. distribute-rgt-neg-in 69.4%

          \[\leadsto a \cdot \left(j \cdot c - t \cdot x\right) + \left(-\left(\color{blue}{\left(-b \cdot \left(i \cdot t\right)\right)} + b \cdot \left(c \cdot z\right)\right)\right) \]

      17. mul-1-neg 69.4%

          \[\leadsto a \cdot \left(j \cdot c - t \cdot x\right) + \left(-\left(\color{blue}{-1 \cdot \left(b \cdot \left(i \cdot t\right)\right)} + b \cdot \left(c \cdot z\right)\right)\right) \]

   5. Simplified 71.6%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right) + b \cdot \left(i \cdot t - c \cdot z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+156}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-34}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-12}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) + a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - z \cdot \left(b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 67.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;a \leq -3.1 \cdot 10^{+33}:\\ \;\;\;\;t\_2 + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq -2.05 \cdot 10^{-84}:\\ \;\;\;\;t\_2 + t\_1\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+108}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_1 + a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* j (- (* a c) (* y i)))))
   (if (<= a -3.1e+33)
     (+ t_2 (* x (- (* y z) (* t a))))
     (if (<= a -2.05e-84)
       (+ t_2 t_1)
       (if (<= a 8.2e+108)
         (+ (* y (- (* x z) (* i j))) t_1)
         (+ t_1 (* a (- (* c j) (* x t)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (a <= -3.1e+33) {
		tmp = t_2 + (x * ((y * z) - (t * a)));
	} else if (a <= -2.05e-84) {
		tmp = t_2 + t_1;
	} else if (a <= 8.2e+108) {
		tmp = (y * ((x * z) - (i * j))) + t_1;
	} else {
		tmp = t_1 + (a * ((c * j) - (x * t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = j * ((a * c) - (y * i))
    if (a <= (-3.1d+33)) then
        tmp = t_2 + (x * ((y * z) - (t * a)))
    else if (a <= (-2.05d-84)) then
        tmp = t_2 + t_1
    else if (a <= 8.2d+108) then
        tmp = (y * ((x * z) - (i * j))) + t_1
    else
        tmp = t_1 + (a * ((c * j) - (x * t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (a <= -3.1e+33) {
		tmp = t_2 + (x * ((y * z) - (t * a)));
	} else if (a <= -2.05e-84) {
		tmp = t_2 + t_1;
	} else if (a <= 8.2e+108) {
		tmp = (y * ((x * z) - (i * j))) + t_1;
	} else {
		tmp = t_1 + (a * ((c * j) - (x * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = j * ((a * c) - (y * i))
	tmp = 0
	if a <= -3.1e+33:
		tmp = t_2 + (x * ((y * z) - (t * a)))
	elif a <= -2.05e-84:
		tmp = t_2 + t_1
	elif a <= 8.2e+108:
		tmp = (y * ((x * z) - (i * j))) + t_1
	else:
		tmp = t_1 + (a * ((c * j) - (x * t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (a <= -3.1e+33)
		tmp = Float64(t_2 + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	elseif (a <= -2.05e-84)
		tmp = Float64(t_2 + t_1);
	elseif (a <= 8.2e+108)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + t_1);
	else
		tmp = Float64(t_1 + Float64(a * Float64(Float64(c * j) - Float64(x * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (a <= -3.1e+33)
		tmp = t_2 + (x * ((y * z) - (t * a)));
	elseif (a <= -2.05e-84)
		tmp = t_2 + t_1;
	elseif (a <= 8.2e+108)
		tmp = (y * ((x * z) - (i * j))) + t_1;
	else
		tmp = t_1 + (a * ((c * j) - (x * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.1e+33], N[(t$95$2 + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.05e-84], N[(t$95$2 + t$95$1), $MachinePrecision], If[LessEqual[a, 8.2e+108], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(t$95$1 + N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.1e33

   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 b around 0 73.4%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   if -3.1e33 < a < -2.05000000000000003e-84

   1. Initial program 80.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 80.7%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   if -2.05000000000000003e-84 < a < 8.1999999999999998e108

   1. Initial program 79.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 75.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   5. Simplified 74.3%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - j \cdot i\right) + b \cdot \left(i \cdot t - c \cdot z\right)} \]

   if 8.1999999999999998e108 < a

   1. Initial program 60.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 77.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(c \cdot j\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   4. Step-by-step derivation

      1. cancel-sign-sub-inv 77.9%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(c \cdot j\right)\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot t\right)} \]

      2. *-commutative 77.9%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(t \cdot x\right) \cdot a\right)} + a \cdot \left(c \cdot j\right)\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot t\right) \]

      3. associate-*r* 77.9%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right) \cdot a} + a \cdot \left(c \cdot j\right)\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot t\right) \]

      4. *-commutative 77.9%

         \[\leadsto \left(\left(-1 \cdot \left(t \cdot x\right)\right) \cdot a + \color{blue}{\left(c \cdot j\right) \cdot a}\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot t\right) \]

      5. distribute-rgt-in 80.4%

         \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} + \left(-b\right) \cdot \left(c \cdot z - i \cdot t\right) \]

      6. +-commutative 80.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} + \left(-b\right) \cdot \left(c \cdot z - i \cdot t\right) \]

      7. mul-1-neg 80.4%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot t\right) \]

      8. unsub-neg 80.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} + \left(-b\right) \cdot \left(c \cdot z - i \cdot t\right) \]

      9. *-commutative 80.4%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot t\right) \]

      10. distribute-lft-neg-in 80.4%

          \[\leadsto a \cdot \left(j \cdot c - t \cdot x\right) + \color{blue}{\left(-b \cdot \left(c \cdot z - i \cdot t\right)\right)} \]

      11. sub-neg 80.4%

          \[\leadsto a \cdot \left(j \cdot c - t \cdot x\right) + \left(-b \cdot \color{blue}{\left(c \cdot z + \left(-i \cdot t\right)\right)}\right) \]

      12. distribute-rgt-neg-out 80.4%

          \[\leadsto a \cdot \left(j \cdot c - t \cdot x\right) + \left(-b \cdot \left(c \cdot z + \color{blue}{i \cdot \left(-t\right)}\right)\right) \]

      13. distribute-lft-out 77.9%

          \[\leadsto a \cdot \left(j \cdot c - t \cdot x\right) + \left(-\color{blue}{\left(b \cdot \left(c \cdot z\right) + b \cdot \left(i \cdot \left(-t\right)\right)\right)}\right) \]

      14. +-commutative 77.9%

          \[\leadsto a \cdot \left(j \cdot c - t \cdot x\right) + \left(-\color{blue}{\left(b \cdot \left(i \cdot \left(-t\right)\right) + b \cdot \left(c \cdot z\right)\right)}\right) \]

      15. distribute-rgt-neg-out 77.9%

          \[\leadsto a \cdot \left(j \cdot c - t \cdot x\right) + \left(-\left(b \cdot \color{blue}{\left(-i \cdot t\right)} + b \cdot \left(c \cdot z\right)\right)\right) \]

      16. distribute-rgt-neg-in 77.9%

          \[\leadsto a \cdot \left(j \cdot c - t \cdot x\right) + \left(-\left(\color{blue}{\left(-b \cdot \left(i \cdot t\right)\right)} + b \cdot \left(c \cdot z\right)\right)\right) \]

      17. mul-1-neg 77.9%

          \[\leadsto a \cdot \left(j \cdot c - t \cdot x\right) + \left(-\left(\color{blue}{-1 \cdot \left(b \cdot \left(i \cdot t\right)\right)} + b \cdot \left(c \cdot z\right)\right)\right) \]

   5. Simplified 80.4%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right) + b \cdot \left(i \cdot t - c \cdot z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{+33}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq -2.05 \cdot 10^{-84}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+108}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) + a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 29.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ t_2 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;y \leq -3.9 \cdot 10^{+81}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-304}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-192}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-10}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))) (t_2 (* x (* y z))))
   (if (<= y -3.9e+81)
     t_2
     (if (<= y -6.8e-119)
       t_1
       (if (<= y 8e-304)
         (* i (* t b))
         (if (<= y 6.2e-192) t_1 (if (<= y 1.1e-10) (* b (* t i)) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double t_2 = x * (y * z);
	double tmp;
	if (y <= -3.9e+81) {
		tmp = t_2;
	} else if (y <= -6.8e-119) {
		tmp = t_1;
	} else if (y <= 8e-304) {
		tmp = i * (t * b);
	} else if (y <= 6.2e-192) {
		tmp = t_1;
	} else if (y <= 1.1e-10) {
		tmp = b * (t * i);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (c * j)
    t_2 = x * (y * z)
    if (y <= (-3.9d+81)) then
        tmp = t_2
    else if (y <= (-6.8d-119)) then
        tmp = t_1
    else if (y <= 8d-304) then
        tmp = i * (t * b)
    else if (y <= 6.2d-192) then
        tmp = t_1
    else if (y <= 1.1d-10) then
        tmp = b * (t * i)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double t_2 = x * (y * z);
	double tmp;
	if (y <= -3.9e+81) {
		tmp = t_2;
	} else if (y <= -6.8e-119) {
		tmp = t_1;
	} else if (y <= 8e-304) {
		tmp = i * (t * b);
	} else if (y <= 6.2e-192) {
		tmp = t_1;
	} else if (y <= 1.1e-10) {
		tmp = b * (t * i);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	t_2 = x * (y * z)
	tmp = 0
	if y <= -3.9e+81:
		tmp = t_2
	elif y <= -6.8e-119:
		tmp = t_1
	elif y <= 8e-304:
		tmp = i * (t * b)
	elif y <= 6.2e-192:
		tmp = t_1
	elif y <= 1.1e-10:
		tmp = b * (t * i)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	t_2 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (y <= -3.9e+81)
		tmp = t_2;
	elseif (y <= -6.8e-119)
		tmp = t_1;
	elseif (y <= 8e-304)
		tmp = Float64(i * Float64(t * b));
	elseif (y <= 6.2e-192)
		tmp = t_1;
	elseif (y <= 1.1e-10)
		tmp = Float64(b * Float64(t * i));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (c * j);
	t_2 = x * (y * z);
	tmp = 0.0;
	if (y <= -3.9e+81)
		tmp = t_2;
	elseif (y <= -6.8e-119)
		tmp = t_1;
	elseif (y <= 8e-304)
		tmp = i * (t * b);
	elseif (y <= 6.2e-192)
		tmp = t_1;
	elseif (y <= 1.1e-10)
		tmp = b * (t * i);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.9e+81], t$95$2, If[LessEqual[y, -6.8e-119], t$95$1, If[LessEqual[y, 8e-304], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.2e-192], t$95$1, If[LessEqual[y, 1.1e-10], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.9000000000000001e81 or 1.09999999999999995e-10 < y

   1. Initial program 71.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 50.8%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 50.8%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

      2. *-commutative 50.8%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) \]

   5. Simplified 50.8%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   6. Taylor expanded in y around 0 44.7%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right) + x \cdot \left(y \cdot z\right)} \]

   7. Taylor expanded in b around 0 37.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   if -3.9000000000000001e81 < y < -6.80000000000000047e-119 or 7.99999999999999977e-304 < y < 6.2000000000000001e-192

   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 53.4%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 53.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 53.4%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 53.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 53.4%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 53.4%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around inf 40.0%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

   if -6.80000000000000047e-119 < y < 7.99999999999999977e-304

   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. Step-by-step derivation

      1. +-commutative 79.8%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-define 84.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 84.8%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. sub-neg 84.8%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}\right) \]

      5. *-commutative 84.8%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z + \left(-\color{blue}{i \cdot t}\right)\right)\right) \]

      6. sub-neg 84.8%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - i \cdot t\right)}\right) \]

      7. *-commutative 84.8%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) \]

      8. *-commutative 84.8%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) \]

   3. Simplified 84.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf 85.1%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \left(y \cdot z - a \cdot t\right) + \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x}\right)\right)}\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 85.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-x \cdot \left(-1 \cdot \left(y \cdot z - a \cdot t\right) + \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x}\right)}\right) \]

      2. distribute-rgt-neg-in 85.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{x \cdot \left(-\left(-1 \cdot \left(y \cdot z - a \cdot t\right) + \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x}\right)\right)}\right) \]

      3. +-commutative 85.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\color{blue}{\left(\frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + -1 \cdot \left(y \cdot z - a \cdot t\right)\right)}\right)\right) \]

      4. mul-1-neg 85.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\left(\frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + \color{blue}{\left(-\left(y \cdot z - a \cdot t\right)\right)}\right)\right)\right) \]

      5. unsub-neg 85.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\color{blue}{\left(\frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} - \left(y \cdot z - a \cdot t\right)\right)}\right)\right) \]

      6. associate-/l* 82.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\left(\color{blue}{b \cdot \frac{c \cdot z - i \cdot t}{x}} - \left(y \cdot z - a \cdot t\right)\right)\right)\right) \]

   7. Simplified 82.7%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{x \cdot \left(-\left(b \cdot \frac{c \cdot z - i \cdot t}{x} - \left(y \cdot z - a \cdot t\right)\right)\right)}\right) \]

   8. Taylor expanded in i around inf 60.1%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]
   9. Step-by-step derivation

      1. +-commutative 60.1%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      2. mul-1-neg 60.1%

         \[\leadsto i \cdot \left(b \cdot t + \color{blue}{\left(-j \cdot y\right)}\right) \]

      3. unsub-neg 60.1%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t - j \cdot y\right)} \]

      4. *-commutative 60.1%

         \[\leadsto i \cdot \left(b \cdot t - \color{blue}{y \cdot j}\right) \]

   10. Simplified 60.1%

       \[\leadsto \color{blue}{i \cdot \left(b \cdot t - y \cdot j\right)} \]

   11. Taylor expanded in b around inf 57.7%

       \[\leadsto i \cdot \color{blue}{\left(b \cdot t\right)} \]

   if 6.2000000000000001e-192 < y < 1.09999999999999995e-10

   1. Initial program 80.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 80.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-define 80.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 80.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. sub-neg 80.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}\right) \]

      5. *-commutative 80.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z + \left(-\color{blue}{i \cdot t}\right)\right)\right) \]

      6. sub-neg 80.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - i \cdot t\right)}\right) \]

      7. *-commutative 80.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) \]

      8. *-commutative 80.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) \]

   3. Simplified 80.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf 74.3%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \left(y \cdot z - a \cdot t\right) + \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x}\right)\right)}\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 74.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-x \cdot \left(-1 \cdot \left(y \cdot z - a \cdot t\right) + \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x}\right)}\right) \]

      2. distribute-rgt-neg-in 74.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{x \cdot \left(-\left(-1 \cdot \left(y \cdot z - a \cdot t\right) + \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x}\right)\right)}\right) \]

      3. +-commutative 74.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\color{blue}{\left(\frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + -1 \cdot \left(y \cdot z - a \cdot t\right)\right)}\right)\right) \]

      4. mul-1-neg 74.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\left(\frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + \color{blue}{\left(-\left(y \cdot z - a \cdot t\right)\right)}\right)\right)\right) \]

      5. unsub-neg 74.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\color{blue}{\left(\frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} - \left(y \cdot z - a \cdot t\right)\right)}\right)\right) \]

      6. associate-/l* 72.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\left(\color{blue}{b \cdot \frac{c \cdot z - i \cdot t}{x}} - \left(y \cdot z - a \cdot t\right)\right)\right)\right) \]

   7. Simplified 72.0%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{x \cdot \left(-\left(b \cdot \frac{c \cdot z - i \cdot t}{x} - \left(y \cdot z - a \cdot t\right)\right)\right)}\right) \]

   8. Taylor expanded in x around 0 68.7%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right) + j \cdot \left(a \cdot c - i \cdot y\right)} \]
   9. Step-by-step derivation

      1. +-commutative 68.7%

         \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + -1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right)} \]

      2. *-commutative 68.7%

         \[\leadsto j \cdot \left(\color{blue}{c \cdot a} - i \cdot y\right) + -1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      3. sub-neg 68.7%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot a + \left(-i \cdot y\right)\right)} + -1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      4. sub-neg 68.7%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot a - i \cdot y\right)} + -1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      5. mul-1-neg 68.7%

         \[\leadsto j \cdot \left(c \cdot a - i \cdot y\right) + \color{blue}{\left(-b \cdot \left(c \cdot z - i \cdot t\right)\right)} \]

      6. unsub-neg 68.7%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   10. Simplified 68.7%

       \[\leadsto \color{blue}{j \cdot \left(c \cdot a - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   11. Taylor expanded in t around inf 32.9%

       \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 40.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+81}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-119}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-304}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-192}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-10}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 51.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -2.3 \cdot 10^{+25}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 10^{-81}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{+107}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 -2.3e+25)
     t_2
     (if (<= a 2.7e-92)
       t_1
       (if (<= a 1e-81) (* x (* y z)) (if (<= a 9.6e+107) 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 <= -2.3e+25) {
		tmp = t_2;
	} else if (a <= 2.7e-92) {
		tmp = t_1;
	} else if (a <= 1e-81) {
		tmp = x * (y * z);
	} else if (a <= 9.6e+107) {
		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 <= (-2.3d+25)) then
        tmp = t_2
    else if (a <= 2.7d-92) then
        tmp = t_1
    else if (a <= 1d-81) then
        tmp = x * (y * z)
    else if (a <= 9.6d+107) 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 <= -2.3e+25) {
		tmp = t_2;
	} else if (a <= 2.7e-92) {
		tmp = t_1;
	} else if (a <= 1e-81) {
		tmp = x * (y * z);
	} else if (a <= 9.6e+107) {
		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 <= -2.3e+25:
		tmp = t_2
	elif a <= 2.7e-92:
		tmp = t_1
	elif a <= 1e-81:
		tmp = x * (y * z)
	elif a <= 9.6e+107:
		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 <= -2.3e+25)
		tmp = t_2;
	elseif (a <= 2.7e-92)
		tmp = t_1;
	elseif (a <= 1e-81)
		tmp = Float64(x * Float64(y * z));
	elseif (a <= 9.6e+107)
		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 <= -2.3e+25)
		tmp = t_2;
	elseif (a <= 2.7e-92)
		tmp = t_1;
	elseif (a <= 1e-81)
		tmp = x * (y * z);
	elseif (a <= 9.6e+107)
		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, -2.3e+25], t$95$2, If[LessEqual[a, 2.7e-92], t$95$1, If[LessEqual[a, 1e-81], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.6e+107], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.2999999999999998e25 or 9.6000000000000002e107 < a

   1. Initial program 68.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 61.1%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 61.1%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 61.1%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 61.1%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 61.1%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 61.1%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   if -2.2999999999999998e25 < a < 2.69999999999999995e-92 or 9.9999999999999996e-82 < a < 9.6000000000000002e107

   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 b around inf 54.2%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]

   if 2.69999999999999995e-92 < a < 9.9999999999999996e-82

   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 z around inf 84.5%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 84.5%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

      2. *-commutative 84.5%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) \]

   5. Simplified 84.5%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   6. Taylor expanded in y around 0 99.5%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right) + x \cdot \left(y \cdot z\right)} \]

   7. Taylor expanded in b around 0 95.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{+25}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-92}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 10^{-81}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{+107}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 52.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -1.7 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 8.5 \cdot 10^{-84}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 1.75 \cdot 10^{+52}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j)))))
   (if (<= i -1.7e+25)
     t_1
     (if (<= i 8.5e-84)
       (* c (- (* a j) (* z b)))
       (if (<= i 1.75e+52) (* b (- (* t i) (* z c))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -1.7e+25) {
		tmp = t_1;
	} else if (i <= 8.5e-84) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 1.75e+52) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * ((t * b) - (y * j))
    if (i <= (-1.7d+25)) then
        tmp = t_1
    else if (i <= 8.5d-84) then
        tmp = c * ((a * j) - (z * b))
    else if (i <= 1.75d+52) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -1.7e+25) {
		tmp = t_1;
	} else if (i <= 8.5e-84) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 1.75e+52) {
		tmp = b * ((t * i) - (z * c));
	} 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 <= -1.7e+25:
		tmp = t_1
	elif i <= 8.5e-84:
		tmp = c * ((a * j) - (z * b))
	elif i <= 1.75e+52:
		tmp = b * ((t * i) - (z * c))
	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 <= -1.7e+25)
		tmp = t_1;
	elseif (i <= 8.5e-84)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (i <= 1.75e+52)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -1.7e+25)
		tmp = t_1;
	elseif (i <= 8.5e-84)
		tmp = c * ((a * j) - (z * b));
	elseif (i <= 1.75e+52)
		tmp = b * ((t * i) - (z * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.7e+25], t$95$1, If[LessEqual[i, 8.5e-84], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.75e+52], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if i < -1.69999999999999992e25 or 1.75e52 < i

   1. Initial program 70.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 70.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-define 72.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 72.3%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. sub-neg 72.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}\right) \]

      5. *-commutative 72.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z + \left(-\color{blue}{i \cdot t}\right)\right)\right) \]

      6. sub-neg 72.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - i \cdot t\right)}\right) \]

      7. *-commutative 72.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) \]

      8. *-commutative 72.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) \]

   3. Simplified 72.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf 71.3%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \left(y \cdot z - a \cdot t\right) + \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x}\right)\right)}\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 71.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-x \cdot \left(-1 \cdot \left(y \cdot z - a \cdot t\right) + \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x}\right)}\right) \]

      2. distribute-rgt-neg-in 71.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{x \cdot \left(-\left(-1 \cdot \left(y \cdot z - a \cdot t\right) + \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x}\right)\right)}\right) \]

      3. +-commutative 71.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\color{blue}{\left(\frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + -1 \cdot \left(y \cdot z - a \cdot t\right)\right)}\right)\right) \]

      4. mul-1-neg 71.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\left(\frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + \color{blue}{\left(-\left(y \cdot z - a \cdot t\right)\right)}\right)\right)\right) \]

      5. unsub-neg 71.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\color{blue}{\left(\frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} - \left(y \cdot z - a \cdot t\right)\right)}\right)\right) \]

      6. associate-/l* 70.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\left(\color{blue}{b \cdot \frac{c \cdot z - i \cdot t}{x}} - \left(y \cdot z - a \cdot t\right)\right)\right)\right) \]

   7. Simplified 70.3%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{x \cdot \left(-\left(b \cdot \frac{c \cdot z - i \cdot t}{x} - \left(y \cdot z - a \cdot t\right)\right)\right)}\right) \]

   8. Taylor expanded in i around inf 69.7%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]
   9. Step-by-step derivation

      1. +-commutative 69.7%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      2. mul-1-neg 69.7%

         \[\leadsto i \cdot \left(b \cdot t + \color{blue}{\left(-j \cdot y\right)}\right) \]

      3. unsub-neg 69.7%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t - j \cdot y\right)} \]

      4. *-commutative 69.7%

         \[\leadsto i \cdot \left(b \cdot t - \color{blue}{y \cdot j}\right) \]

   10. Simplified 69.7%

       \[\leadsto \color{blue}{i \cdot \left(b \cdot t - y \cdot j\right)} \]

   if -1.69999999999999992e25 < i < 8.4999999999999994e-84

   1. Initial program 80.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 48.0%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 48.0%

         \[\leadsto c \cdot \left(\color{blue}{j \cdot a} - b \cdot z\right) \]

   5. Simplified 48.0%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a - b \cdot z\right)} \]

   if 8.4999999999999994e-84 < i < 1.75e52

   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 b around inf 52.7%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.7 \cdot 10^{+25}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq 8.5 \cdot 10^{-84}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 1.75 \cdot 10^{+52}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 29.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{-48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-136}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-66}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* z c) (- b))))
   (if (<= z -2.6e-48)
     t_1
     (if (<= z -6.6e-136)
       (* a (* c j))
       (if (<= z 8.6e-66) (* 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 = (z * c) * -b;
	double tmp;
	if (z <= -2.6e-48) {
		tmp = t_1;
	} else if (z <= -6.6e-136) {
		tmp = a * (c * j);
	} else if (z <= 8.6e-66) {
		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 = (z * c) * -b
    if (z <= (-2.6d-48)) then
        tmp = t_1
    else if (z <= (-6.6d-136)) then
        tmp = a * (c * j)
    else if (z <= 8.6d-66) 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 = (z * c) * -b;
	double tmp;
	if (z <= -2.6e-48) {
		tmp = t_1;
	} else if (z <= -6.6e-136) {
		tmp = a * (c * j);
	} else if (z <= 8.6e-66) {
		tmp = i * (t * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (z * c) * -b
	tmp = 0
	if z <= -2.6e-48:
		tmp = t_1
	elif z <= -6.6e-136:
		tmp = a * (c * j)
	elif z <= 8.6e-66:
		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(Float64(z * c) * Float64(-b))
	tmp = 0.0
	if (z <= -2.6e-48)
		tmp = t_1;
	elseif (z <= -6.6e-136)
		tmp = Float64(a * Float64(c * j));
	elseif (z <= 8.6e-66)
		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 = (z * c) * -b;
	tmp = 0.0;
	if (z <= -2.6e-48)
		tmp = t_1;
	elseif (z <= -6.6e-136)
		tmp = a * (c * j);
	elseif (z <= 8.6e-66)
		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[(N[(z * c), $MachinePrecision] * (-b)), $MachinePrecision]}, If[LessEqual[z, -2.6e-48], t$95$1, If[LessEqual[z, -6.6e-136], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.6e-66], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.59999999999999987e-48 or 8.60000000000000027e-66 < z

   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. Step-by-step derivation

      1. +-commutative 72.6%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-define 73.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 73.9%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. sub-neg 73.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}\right) \]

      5. *-commutative 73.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z + \left(-\color{blue}{i \cdot t}\right)\right)\right) \]

      6. sub-neg 73.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - i \cdot t\right)}\right) \]

      7. *-commutative 73.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) \]

      8. *-commutative 73.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) \]

   3. Simplified 73.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf 71.0%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \left(y \cdot z - a \cdot t\right) + \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x}\right)\right)}\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 71.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-x \cdot \left(-1 \cdot \left(y \cdot z - a \cdot t\right) + \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x}\right)}\right) \]

      2. distribute-rgt-neg-in 71.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{x \cdot \left(-\left(-1 \cdot \left(y \cdot z - a \cdot t\right) + \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x}\right)\right)}\right) \]

      3. +-commutative 71.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\color{blue}{\left(\frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + -1 \cdot \left(y \cdot z - a \cdot t\right)\right)}\right)\right) \]

      4. mul-1-neg 71.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\left(\frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + \color{blue}{\left(-\left(y \cdot z - a \cdot t\right)\right)}\right)\right)\right) \]

      5. unsub-neg 71.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\color{blue}{\left(\frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} - \left(y \cdot z - a \cdot t\right)\right)}\right)\right) \]

      6. associate-/l* 69.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\left(\color{blue}{b \cdot \frac{c \cdot z - i \cdot t}{x}} - \left(y \cdot z - a \cdot t\right)\right)\right)\right) \]

   7. Simplified 69.7%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{x \cdot \left(-\left(b \cdot \frac{c \cdot z - i \cdot t}{x} - \left(y \cdot z - a \cdot t\right)\right)\right)}\right) \]

   8. Taylor expanded in x around 0 64.2%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right) + j \cdot \left(a \cdot c - i \cdot y\right)} \]
   9. Step-by-step derivation

      1. +-commutative 64.2%

         \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + -1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right)} \]

      2. *-commutative 64.2%

         \[\leadsto j \cdot \left(\color{blue}{c \cdot a} - i \cdot y\right) + -1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      3. sub-neg 64.2%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot a + \left(-i \cdot y\right)\right)} + -1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      4. sub-neg 64.2%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot a - i \cdot y\right)} + -1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      5. mul-1-neg 64.2%

         \[\leadsto j \cdot \left(c \cdot a - i \cdot y\right) + \color{blue}{\left(-b \cdot \left(c \cdot z - i \cdot t\right)\right)} \]

      6. unsub-neg 64.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   10. Simplified 64.2%

       \[\leadsto \color{blue}{j \cdot \left(c \cdot a - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   11. Taylor expanded in z around inf 36.8%

       \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} \]
   12. Step-by-step derivation

       1. neg-mul-1 36.8%

          \[\leadsto \color{blue}{-b \cdot \left(c \cdot z\right)} \]

       2. distribute-rgt-neg-in 36.8%

          \[\leadsto \color{blue}{b \cdot \left(-c \cdot z\right)} \]

       3. distribute-rgt-neg-in 36.8%

          \[\leadsto b \cdot \color{blue}{\left(c \cdot \left(-z\right)\right)} \]

   13. Simplified 36.8%

       \[\leadsto \color{blue}{b \cdot \left(c \cdot \left(-z\right)\right)} \]

   if -2.59999999999999987e-48 < z < -6.60000000000000035e-136

   1. Initial program 77.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 64.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 64.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 64.0%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 64.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 64.0%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 64.0%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around inf 45.5%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

   if -6.60000000000000035e-136 < z < 8.60000000000000027e-66

   1. Initial program 79.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 79.6%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-define 81.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 81.9%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. sub-neg 81.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}\right) \]

      5. *-commutative 81.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z + \left(-\color{blue}{i \cdot t}\right)\right)\right) \]

      6. sub-neg 81.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - i \cdot t\right)}\right) \]

      7. *-commutative 81.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) \]

      8. *-commutative 81.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) \]

   3. Simplified 81.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf 79.6%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \left(y \cdot z - a \cdot t\right) + \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x}\right)\right)}\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 79.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-x \cdot \left(-1 \cdot \left(y \cdot z - a \cdot t\right) + \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x}\right)}\right) \]

      2. distribute-rgt-neg-in 79.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{x \cdot \left(-\left(-1 \cdot \left(y \cdot z - a \cdot t\right) + \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x}\right)\right)}\right) \]

      3. +-commutative 79.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\color{blue}{\left(\frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + -1 \cdot \left(y \cdot z - a \cdot t\right)\right)}\right)\right) \]

      4. mul-1-neg 79.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\left(\frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + \color{blue}{\left(-\left(y \cdot z - a \cdot t\right)\right)}\right)\right)\right) \]

      5. unsub-neg 79.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\color{blue}{\left(\frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} - \left(y \cdot z - a \cdot t\right)\right)}\right)\right) \]

      6. associate-/l* 78.4%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\left(\color{blue}{b \cdot \frac{c \cdot z - i \cdot t}{x}} - \left(y \cdot z - a \cdot t\right)\right)\right)\right) \]

   7. Simplified 78.4%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{x \cdot \left(-\left(b \cdot \frac{c \cdot z - i \cdot t}{x} - \left(y \cdot z - a \cdot t\right)\right)\right)}\right) \]

   8. Taylor expanded in i around inf 62.2%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]
   9. Step-by-step derivation

      1. +-commutative 62.2%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      2. mul-1-neg 62.2%

         \[\leadsto i \cdot \left(b \cdot t + \color{blue}{\left(-j \cdot y\right)}\right) \]

      3. unsub-neg 62.2%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t - j \cdot y\right)} \]

      4. *-commutative 62.2%

         \[\leadsto i \cdot \left(b \cdot t - \color{blue}{y \cdot j}\right) \]

   10. Simplified 62.2%

       \[\leadsto \color{blue}{i \cdot \left(b \cdot t - y \cdot j\right)} \]

   11. Taylor expanded in b around inf 38.4%

       \[\leadsto i \cdot \color{blue}{\left(b \cdot t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 37.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-48}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-136}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-66}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 29.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-46}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-137}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-66}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -2.9e-46)
   (* (* z c) (- b))
   (if (<= z -1.4e-137)
     (* a (* c j))
     (if (<= z 8.8e-66) (* i (* t b)) (* c (* z (- b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -2.9e-46) {
		tmp = (z * c) * -b;
	} else if (z <= -1.4e-137) {
		tmp = a * (c * j);
	} else if (z <= 8.8e-66) {
		tmp = i * (t * b);
	} else {
		tmp = c * (z * -b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-2.9d-46)) then
        tmp = (z * c) * -b
    else if (z <= (-1.4d-137)) then
        tmp = a * (c * j)
    else if (z <= 8.8d-66) then
        tmp = i * (t * b)
    else
        tmp = c * (z * -b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -2.9e-46) {
		tmp = (z * c) * -b;
	} else if (z <= -1.4e-137) {
		tmp = a * (c * j);
	} else if (z <= 8.8e-66) {
		tmp = i * (t * b);
	} else {
		tmp = c * (z * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -2.9e-46:
		tmp = (z * c) * -b
	elif z <= -1.4e-137:
		tmp = a * (c * j)
	elif z <= 8.8e-66:
		tmp = i * (t * b)
	else:
		tmp = c * (z * -b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -2.9e-46)
		tmp = Float64(Float64(z * c) * Float64(-b));
	elseif (z <= -1.4e-137)
		tmp = Float64(a * Float64(c * j));
	elseif (z <= 8.8e-66)
		tmp = Float64(i * Float64(t * b));
	else
		tmp = Float64(c * Float64(z * Float64(-b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -2.9e-46)
		tmp = (z * c) * -b;
	elseif (z <= -1.4e-137)
		tmp = a * (c * j);
	elseif (z <= 8.8e-66)
		tmp = i * (t * b);
	else
		tmp = c * (z * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -2.9e-46], N[(N[(z * c), $MachinePrecision] * (-b)), $MachinePrecision], If[LessEqual[z, -1.4e-137], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.8e-66], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.90000000000000005e-46

   1. Initial program 76.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 76.9%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-define 79.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 79.4%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. sub-neg 79.4%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}\right) \]

      5. *-commutative 79.4%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z + \left(-\color{blue}{i \cdot t}\right)\right)\right) \]

      6. sub-neg 79.4%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - i \cdot t\right)}\right) \]

      7. *-commutative 79.4%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) \]

      8. *-commutative 79.4%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) \]

   3. Simplified 79.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf 77.1%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \left(y \cdot z - a \cdot t\right) + \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x}\right)\right)}\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 77.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-x \cdot \left(-1 \cdot \left(y \cdot z - a \cdot t\right) + \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x}\right)}\right) \]

      2. distribute-rgt-neg-in 77.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{x \cdot \left(-\left(-1 \cdot \left(y \cdot z - a \cdot t\right) + \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x}\right)\right)}\right) \]

      3. +-commutative 77.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\color{blue}{\left(\frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + -1 \cdot \left(y \cdot z - a \cdot t\right)\right)}\right)\right) \]

      4. mul-1-neg 77.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\left(\frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + \color{blue}{\left(-\left(y \cdot z - a \cdot t\right)\right)}\right)\right)\right) \]

      5. unsub-neg 77.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\color{blue}{\left(\frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} - \left(y \cdot z - a \cdot t\right)\right)}\right)\right) \]

      6. associate-/l* 77.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\left(\color{blue}{b \cdot \frac{c \cdot z - i \cdot t}{x}} - \left(y \cdot z - a \cdot t\right)\right)\right)\right) \]

   7. Simplified 77.1%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{x \cdot \left(-\left(b \cdot \frac{c \cdot z - i \cdot t}{x} - \left(y \cdot z - a \cdot t\right)\right)\right)}\right) \]

   8. Taylor expanded in x around 0 64.6%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right) + j \cdot \left(a \cdot c - i \cdot y\right)} \]
   9. Step-by-step derivation

      1. +-commutative 64.6%

         \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + -1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right)} \]

      2. *-commutative 64.6%

         \[\leadsto j \cdot \left(\color{blue}{c \cdot a} - i \cdot y\right) + -1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      3. sub-neg 64.6%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot a + \left(-i \cdot y\right)\right)} + -1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      4. sub-neg 64.6%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot a - i \cdot y\right)} + -1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      5. mul-1-neg 64.6%

         \[\leadsto j \cdot \left(c \cdot a - i \cdot y\right) + \color{blue}{\left(-b \cdot \left(c \cdot z - i \cdot t\right)\right)} \]

      6. unsub-neg 64.6%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   10. Simplified 64.6%

       \[\leadsto \color{blue}{j \cdot \left(c \cdot a - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   11. Taylor expanded in z around inf 39.5%

       \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} \]
   12. Step-by-step derivation

       1. neg-mul-1 39.5%

          \[\leadsto \color{blue}{-b \cdot \left(c \cdot z\right)} \]

       2. distribute-rgt-neg-in 39.5%

          \[\leadsto \color{blue}{b \cdot \left(-c \cdot z\right)} \]

       3. distribute-rgt-neg-in 39.5%

          \[\leadsto b \cdot \color{blue}{\left(c \cdot \left(-z\right)\right)} \]

   13. Simplified 39.5%

       \[\leadsto \color{blue}{b \cdot \left(c \cdot \left(-z\right)\right)} \]

   if -2.90000000000000005e-46 < z < -1.3999999999999999e-137

   1. Initial program 77.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 64.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 64.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 64.0%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 64.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 64.0%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 64.0%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around inf 45.5%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

   if -1.3999999999999999e-137 < z < 8.8000000000000004e-66

   1. Initial program 79.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 79.6%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-define 81.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 81.9%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. sub-neg 81.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}\right) \]

      5. *-commutative 81.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z + \left(-\color{blue}{i \cdot t}\right)\right)\right) \]

      6. sub-neg 81.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - i \cdot t\right)}\right) \]

      7. *-commutative 81.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) \]

      8. *-commutative 81.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) \]

   3. Simplified 81.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf 79.6%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \left(y \cdot z - a \cdot t\right) + \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x}\right)\right)}\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 79.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-x \cdot \left(-1 \cdot \left(y \cdot z - a \cdot t\right) + \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x}\right)}\right) \]

      2. distribute-rgt-neg-in 79.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{x \cdot \left(-\left(-1 \cdot \left(y \cdot z - a \cdot t\right) + \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x}\right)\right)}\right) \]

      3. +-commutative 79.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\color{blue}{\left(\frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + -1 \cdot \left(y \cdot z - a \cdot t\right)\right)}\right)\right) \]

      4. mul-1-neg 79.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\left(\frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + \color{blue}{\left(-\left(y \cdot z - a \cdot t\right)\right)}\right)\right)\right) \]

      5. unsub-neg 79.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\color{blue}{\left(\frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} - \left(y \cdot z - a \cdot t\right)\right)}\right)\right) \]

      6. associate-/l* 78.4%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\left(\color{blue}{b \cdot \frac{c \cdot z - i \cdot t}{x}} - \left(y \cdot z - a \cdot t\right)\right)\right)\right) \]

   7. Simplified 78.4%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{x \cdot \left(-\left(b \cdot \frac{c \cdot z - i \cdot t}{x} - \left(y \cdot z - a \cdot t\right)\right)\right)}\right) \]

   8. Taylor expanded in i around inf 62.2%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]
   9. Step-by-step derivation

      1. +-commutative 62.2%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      2. mul-1-neg 62.2%

         \[\leadsto i \cdot \left(b \cdot t + \color{blue}{\left(-j \cdot y\right)}\right) \]

      3. unsub-neg 62.2%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t - j \cdot y\right)} \]

      4. *-commutative 62.2%

         \[\leadsto i \cdot \left(b \cdot t - \color{blue}{y \cdot j}\right) \]

   10. Simplified 62.2%

       \[\leadsto \color{blue}{i \cdot \left(b \cdot t - y \cdot j\right)} \]

   11. Taylor expanded in b around inf 38.4%

       \[\leadsto i \cdot \color{blue}{\left(b \cdot t\right)} \]

   if 8.8000000000000004e-66 < z

   1. Initial program 67.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 67.5%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-define 67.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 67.5%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. sub-neg 67.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}\right) \]

      5. *-commutative 67.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z + \left(-\color{blue}{i \cdot t}\right)\right)\right) \]

      6. sub-neg 67.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - i \cdot t\right)}\right) \]

      7. *-commutative 67.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) \]

      8. *-commutative 67.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) \]

   3. Simplified 67.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf 63.9%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \left(y \cdot z - a \cdot t\right) + \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x}\right)\right)}\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 63.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-x \cdot \left(-1 \cdot \left(y \cdot z - a \cdot t\right) + \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x}\right)}\right) \]

      2. distribute-rgt-neg-in 63.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{x \cdot \left(-\left(-1 \cdot \left(y \cdot z - a \cdot t\right) + \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x}\right)\right)}\right) \]

      3. +-commutative 63.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\color{blue}{\left(\frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + -1 \cdot \left(y \cdot z - a \cdot t\right)\right)}\right)\right) \]

      4. mul-1-neg 63.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\left(\frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + \color{blue}{\left(-\left(y \cdot z - a \cdot t\right)\right)}\right)\right)\right) \]

      5. unsub-neg 63.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\color{blue}{\left(\frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} - \left(y \cdot z - a \cdot t\right)\right)}\right)\right) \]

      6. associate-/l* 61.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\left(\color{blue}{b \cdot \frac{c \cdot z - i \cdot t}{x}} - \left(y \cdot z - a \cdot t\right)\right)\right)\right) \]

   7. Simplified 61.1%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{x \cdot \left(-\left(b \cdot \frac{c \cdot z - i \cdot t}{x} - \left(y \cdot z - a \cdot t\right)\right)\right)}\right) \]

   8. Taylor expanded in x around 0 63.8%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right) + j \cdot \left(a \cdot c - i \cdot y\right)} \]
   9. Step-by-step derivation

      1. +-commutative 63.8%

         \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + -1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right)} \]

      2. *-commutative 63.8%

         \[\leadsto j \cdot \left(\color{blue}{c \cdot a} - i \cdot y\right) + -1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      3. sub-neg 63.8%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot a + \left(-i \cdot y\right)\right)} + -1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      4. sub-neg 63.8%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot a - i \cdot y\right)} + -1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      5. mul-1-neg 63.8%

         \[\leadsto j \cdot \left(c \cdot a - i \cdot y\right) + \color{blue}{\left(-b \cdot \left(c \cdot z - i \cdot t\right)\right)} \]

      6. unsub-neg 63.8%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   10. Simplified 63.8%

       \[\leadsto \color{blue}{j \cdot \left(c \cdot a - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   11. Taylor expanded in c around inf 59.8%

       \[\leadsto j \cdot \left(c \cdot a - i \cdot y\right) - \color{blue}{b \cdot \left(c \cdot z\right)} \]
   12. Step-by-step derivation

       1. associate-*r* 66.8%

          \[\leadsto j \cdot \left(c \cdot a - i \cdot y\right) - \color{blue}{\left(b \cdot c\right) \cdot z} \]

       2. *-commutative 66.8%

          \[\leadsto j \cdot \left(c \cdot a - i \cdot y\right) - \color{blue}{\left(c \cdot b\right)} \cdot z \]

   13. Simplified 66.8%

       \[\leadsto j \cdot \left(c \cdot a - i \cdot y\right) - \color{blue}{\left(c \cdot b\right) \cdot z} \]

   14. Taylor expanded in j around 0 33.6%

       \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} \]
   15. Step-by-step derivation

       1. mul-1-neg 33.6%

          \[\leadsto \color{blue}{-b \cdot \left(c \cdot z\right)} \]

       2. *-commutative 33.6%

          \[\leadsto -b \cdot \color{blue}{\left(z \cdot c\right)} \]

       3. associate-*l* 36.4%

          \[\leadsto -\color{blue}{\left(b \cdot z\right) \cdot c} \]

       4. *-commutative 36.4%

          \[\leadsto -\color{blue}{c \cdot \left(b \cdot z\right)} \]

       5. distribute-rgt-neg-in 36.4%

          \[\leadsto \color{blue}{c \cdot \left(-b \cdot z\right)} \]

       6. distribute-rgt-neg-in 36.4%

          \[\leadsto c \cdot \color{blue}{\left(b \cdot \left(-z\right)\right)} \]

   16. Simplified 36.4%

       \[\leadsto \color{blue}{c \cdot \left(b \cdot \left(-z\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 38.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-46}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-137}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-66}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 29.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{-48} \lor \neg \left(t \leq 2.6 \cdot 10^{-34}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -1.55e-48) (not (<= t 2.6e-34))) (* b (* t i)) (* a (* c j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -1.55e-48) || !(t <= 2.6e-34)) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((t <= (-1.55d-48)) .or. (.not. (t <= 2.6d-34))) then
        tmp = b * (t * i)
    else
        tmp = a * (c * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -1.55e-48) || !(t <= 2.6e-34)) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -1.55e-48) or not (t <= 2.6e-34):
		tmp = b * (t * i)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -1.55e-48) || !(t <= 2.6e-34))
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(a * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -1.55e-48) || ~((t <= 2.6e-34)))
		tmp = b * (t * i);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -1.55e-48], N[Not[LessEqual[t, 2.6e-34]], $MachinePrecision]], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.55000000000000008e-48 or 2.5999999999999999e-34 < t

   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. Step-by-step derivation

      1. +-commutative 75.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-define 76.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 76.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. sub-neg 76.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}\right) \]

      5. *-commutative 76.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z + \left(-\color{blue}{i \cdot t}\right)\right)\right) \]

      6. sub-neg 76.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - i \cdot t\right)}\right) \]

      7. *-commutative 76.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) \]

      8. *-commutative 76.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) \]

   3. Simplified 76.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf 74.1%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \left(y \cdot z - a \cdot t\right) + \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x}\right)\right)}\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 74.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-x \cdot \left(-1 \cdot \left(y \cdot z - a \cdot t\right) + \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x}\right)}\right) \]

      2. distribute-rgt-neg-in 74.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{x \cdot \left(-\left(-1 \cdot \left(y \cdot z - a \cdot t\right) + \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x}\right)\right)}\right) \]

      3. +-commutative 74.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\color{blue}{\left(\frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + -1 \cdot \left(y \cdot z - a \cdot t\right)\right)}\right)\right) \]

      4. mul-1-neg 74.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\left(\frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + \color{blue}{\left(-\left(y \cdot z - a \cdot t\right)\right)}\right)\right)\right) \]

      5. unsub-neg 74.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\color{blue}{\left(\frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} - \left(y \cdot z - a \cdot t\right)\right)}\right)\right) \]

      6. associate-/l* 73.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\left(\color{blue}{b \cdot \frac{c \cdot z - i \cdot t}{x}} - \left(y \cdot z - a \cdot t\right)\right)\right)\right) \]

   7. Simplified 73.3%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{x \cdot \left(-\left(b \cdot \frac{c \cdot z - i \cdot t}{x} - \left(y \cdot z - a \cdot t\right)\right)\right)}\right) \]

   8. Taylor expanded in x around 0 62.5%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right) + j \cdot \left(a \cdot c - i \cdot y\right)} \]
   9. Step-by-step derivation

      1. +-commutative 62.5%

         \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + -1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right)} \]

      2. *-commutative 62.5%

         \[\leadsto j \cdot \left(\color{blue}{c \cdot a} - i \cdot y\right) + -1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      3. sub-neg 62.5%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot a + \left(-i \cdot y\right)\right)} + -1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      4. sub-neg 62.5%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot a - i \cdot y\right)} + -1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      5. mul-1-neg 62.5%

         \[\leadsto j \cdot \left(c \cdot a - i \cdot y\right) + \color{blue}{\left(-b \cdot \left(c \cdot z - i \cdot t\right)\right)} \]

      6. unsub-neg 62.5%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   10. Simplified 62.5%

       \[\leadsto \color{blue}{j \cdot \left(c \cdot a - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   11. Taylor expanded in t around inf 34.8%

       \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]

   if -1.55000000000000008e-48 < t < 2.5999999999999999e-34

   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 a around inf 31.1%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 31.1%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 31.1%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 31.1%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 31.1%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 31.1%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around inf 27.3%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 31.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{-48} \lor \neg \left(t \leq 2.6 \cdot 10^{-34}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 29.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{-48}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{-37}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -1.7e-48)
   (* i (* t b))
   (if (<= t 5.1e-37) (* 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 (t <= -1.7e-48) {
		tmp = i * (t * b);
	} else if (t <= 5.1e-37) {
		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 (t <= (-1.7d-48)) then
        tmp = i * (t * b)
    else if (t <= 5.1d-37) 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 (t <= -1.7e-48) {
		tmp = i * (t * b);
	} else if (t <= 5.1e-37) {
		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 t <= -1.7e-48:
		tmp = i * (t * b)
	elif t <= 5.1e-37:
		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 (t <= -1.7e-48)
		tmp = Float64(i * Float64(t * b));
	elseif (t <= 5.1e-37)
		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 (t <= -1.7e-48)
		tmp = i * (t * b);
	elseif (t <= 5.1e-37)
		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[LessEqual[t, -1.7e-48], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.1e-37], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.70000000000000014e-48

   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. Step-by-step derivation

      1. +-commutative 75.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-define 75.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 75.3%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. sub-neg 75.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}\right) \]

      5. *-commutative 75.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z + \left(-\color{blue}{i \cdot t}\right)\right)\right) \]

      6. sub-neg 75.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - i \cdot t\right)}\right) \]

      7. *-commutative 75.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) \]

      8. *-commutative 75.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) \]

   3. Simplified 75.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf 73.0%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \left(y \cdot z - a \cdot t\right) + \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x}\right)\right)}\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 73.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-x \cdot \left(-1 \cdot \left(y \cdot z - a \cdot t\right) + \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x}\right)}\right) \]

      2. distribute-rgt-neg-in 73.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{x \cdot \left(-\left(-1 \cdot \left(y \cdot z - a \cdot t\right) + \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x}\right)\right)}\right) \]

      3. +-commutative 73.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\color{blue}{\left(\frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + -1 \cdot \left(y \cdot z - a \cdot t\right)\right)}\right)\right) \]

      4. mul-1-neg 73.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\left(\frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + \color{blue}{\left(-\left(y \cdot z - a \cdot t\right)\right)}\right)\right)\right) \]

      5. unsub-neg 73.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\color{blue}{\left(\frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} - \left(y \cdot z - a \cdot t\right)\right)}\right)\right) \]

      6. associate-/l* 70.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\left(\color{blue}{b \cdot \frac{c \cdot z - i \cdot t}{x}} - \left(y \cdot z - a \cdot t\right)\right)\right)\right) \]

   7. Simplified 70.5%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{x \cdot \left(-\left(b \cdot \frac{c \cdot z - i \cdot t}{x} - \left(y \cdot z - a \cdot t\right)\right)\right)}\right) \]

   8. Taylor expanded in i around inf 44.9%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]
   9. Step-by-step derivation

      1. +-commutative 44.9%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      2. mul-1-neg 44.9%

         \[\leadsto i \cdot \left(b \cdot t + \color{blue}{\left(-j \cdot y\right)}\right) \]

      3. unsub-neg 44.9%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t - j \cdot y\right)} \]

      4. *-commutative 44.9%

         \[\leadsto i \cdot \left(b \cdot t - \color{blue}{y \cdot j}\right) \]

   10. Simplified 44.9%

       \[\leadsto \color{blue}{i \cdot \left(b \cdot t - y \cdot j\right)} \]

   11. Taylor expanded in b around inf 33.5%

       \[\leadsto i \cdot \color{blue}{\left(b \cdot t\right)} \]

   if -1.70000000000000014e-48 < t < 5.1000000000000001e-37

   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 a around inf 31.1%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 31.1%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 31.1%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 31.1%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 31.1%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 31.1%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around inf 27.3%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

   if 5.1000000000000001e-37 < t

   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. Step-by-step derivation

      1. +-commutative 75.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-define 78.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 78.5%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. sub-neg 78.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}\right) \]

      5. *-commutative 78.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z + \left(-\color{blue}{i \cdot t}\right)\right)\right) \]

      6. sub-neg 78.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - i \cdot t\right)}\right) \]

      7. *-commutative 78.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) \]

      8. *-commutative 78.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) \]

   3. Simplified 78.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf 75.5%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \left(y \cdot z - a \cdot t\right) + \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x}\right)\right)}\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 75.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-x \cdot \left(-1 \cdot \left(y \cdot z - a \cdot t\right) + \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x}\right)}\right) \]

      2. distribute-rgt-neg-in 75.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{x \cdot \left(-\left(-1 \cdot \left(y \cdot z - a \cdot t\right) + \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x}\right)\right)}\right) \]

      3. +-commutative 75.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\color{blue}{\left(\frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + -1 \cdot \left(y \cdot z - a \cdot t\right)\right)}\right)\right) \]

      4. mul-1-neg 75.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\left(\frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + \color{blue}{\left(-\left(y \cdot z - a \cdot t\right)\right)}\right)\right)\right) \]

      5. unsub-neg 75.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\color{blue}{\left(\frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} - \left(y \cdot z - a \cdot t\right)\right)}\right)\right) \]

      6. associate-/l* 77.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(-\left(\color{blue}{b \cdot \frac{c \cdot z - i \cdot t}{x}} - \left(y \cdot z - a \cdot t\right)\right)\right)\right) \]

   7. Simplified 77.0%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{x \cdot \left(-\left(b \cdot \frac{c \cdot z - i \cdot t}{x} - \left(y \cdot z - a \cdot t\right)\right)\right)}\right) \]

   8. Taylor expanded in x around 0 63.9%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right) + j \cdot \left(a \cdot c - i \cdot y\right)} \]
   9. Step-by-step derivation

      1. +-commutative 63.9%

         \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + -1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right)} \]

      2. *-commutative 63.9%

         \[\leadsto j \cdot \left(\color{blue}{c \cdot a} - i \cdot y\right) + -1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      3. sub-neg 63.9%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot a + \left(-i \cdot y\right)\right)} + -1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      4. sub-neg 63.9%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot a - i \cdot y\right)} + -1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      5. mul-1-neg 63.9%

         \[\leadsto j \cdot \left(c \cdot a - i \cdot y\right) + \color{blue}{\left(-b \cdot \left(c \cdot z - i \cdot t\right)\right)} \]

      6. unsub-neg 63.9%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   10. Simplified 63.9%

       \[\leadsto \color{blue}{j \cdot \left(c \cdot a - i \cdot y\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   11. Taylor expanded in t around inf 42.1%

       \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 32.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{-48}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{-37}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 22.5% 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 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 a around inf 34.0%

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
4. Step-by-step derivation

   1. +-commutative 34.0%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

   2. mul-1-neg 34.0%

      \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

   3. unsub-neg 34.0%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. *-commutative 34.0%

      \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

5. Simplified 34.0%

   \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

6. Taylor expanded in j around inf 22.4%

   \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

7. Final simplification 22.4%

   \[\leadsto a \cdot \left(c \cdot j\right) \]
8. Add Preprocessing

Developer target: 60.2% 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 2024095 
(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)))))