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

Percentage Accurate: 72.2% → 82.1%

Time: 35.3s

Alternatives: 25

Speedup: 0.5×

• 58.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 72.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 82.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right) + \left(b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\right)\\ \mathbf{if}\;t_1 \leq \infty:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{{\left(a \cdot \left(c \cdot j - x \cdot t\right)\right)}^{3}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (* j (- (* a c) (* y i)))
          (- (* b (- (* t i) (* z c))) (* x (- (* t a) (* y z)))))))
   (if (<= t_1 INFINITY) t_1 (cbrt (pow (* a (- (* c j) (* x t))) 3.0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((a * c) - (y * i))) + ((b * ((t * i) - (z * c))) - (x * ((t * a) - (y * z))));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = cbrt(pow((a * ((c * j) - (x * t))), 3.0));
	}
	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 = (j * ((a * c) - (y * i))) + ((b * ((t * i) - (z * c))) - (x * ((t * a) - (y * z))));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = Math.cbrt(Math.pow((a * ((c * j) - (x * t))), 3.0));
	}
	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(Float64(b * Float64(Float64(t * i) - Float64(z * c))) - Float64(x * Float64(Float64(t * a) - Float64(y * z)))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = cbrt((Float64(a * Float64(Float64(c * j) - Float64(x * t))) ^ 3.0));
	end
	return 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[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[Power[N[Power[N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision], 1/3], $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 91.3%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in a around inf 49.5%

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

      1. +-commutative 49.5%

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

      2. mul-1-neg 49.5%

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

      3. unsub-neg 49.5%

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

      4. *-commutative 49.5%

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

   5. Simplified 49.5%

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

      1. add-cbrt-cube 51.2%

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

      2. pow3 51.2%

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

      3. *-commutative 51.2%

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

      4. *-commutative 51.2%

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

   7. Applied egg-rr 51.2%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \cdot \left(a \cdot c - y \cdot i\right) + \left(b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\right) \leq \infty:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + \left(b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{{\left(a \cdot \left(c \cdot j - x \cdot t\right)\right)}^{3}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 81.1% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $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 91.3%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in a around inf 49.5%

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

      1. +-commutative 49.5%

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

      2. mul-1-neg 49.5%

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

      3. unsub-neg 49.5%

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

      4. *-commutative 49.5%

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

   5. Simplified 49.5%

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

4. Final simplification 82.3%

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

Alternative 3: 60.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_3 := a \cdot \left(c \cdot j - x \cdot t\right) + t_1\\ t_4 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -2.6 \cdot 10^{-24}:\\ \;\;\;\;t_4 - j \cdot \left(y \cdot i\right)\\ \mathbf{elif}\;x \leq -1.22 \cdot 10^{-266}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-295}:\\ \;\;\;\;t_2 + y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 1.92 \cdot 10^{-280}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 10^{-148}:\\ \;\;\;\;t_2 + i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+116}:\\ \;\;\;\;t_4 + t_2\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+169}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

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))))
        (t_3 (+ (* a (- (* c j) (* x t))) t_1))
        (t_4 (* x (- (* y z) (* t a)))))
   (if (<= x -2.6e-24)
     (- t_4 (* j (* y i)))
     (if (<= x -1.22e-266)
       t_3
       (if (<= x 2.2e-295)
         (+ t_2 (* y (* x z)))
         (if (<= x 1.92e-280)
           t_1
           (if (<= x 1e-148)
             (+ t_2 (* i (* t b)))
             (if (<= x 1.7e+116)
               (+ t_4 t_2)
               (if (<= x 2.3e+169) t_3 t_4)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = j * ((a * c) - (y * i));
	double t_3 = (a * ((c * j) - (x * t))) + t_1;
	double t_4 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -2.6e-24) {
		tmp = t_4 - (j * (y * i));
	} else if (x <= -1.22e-266) {
		tmp = t_3;
	} else if (x <= 2.2e-295) {
		tmp = t_2 + (y * (x * z));
	} else if (x <= 1.92e-280) {
		tmp = t_1;
	} else if (x <= 1e-148) {
		tmp = t_2 + (i * (t * b));
	} else if (x <= 1.7e+116) {
		tmp = t_4 + t_2;
	} else if (x <= 2.3e+169) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = j * ((a * c) - (y * i))
    t_3 = (a * ((c * j) - (x * t))) + t_1
    t_4 = x * ((y * z) - (t * a))
    if (x <= (-2.6d-24)) then
        tmp = t_4 - (j * (y * i))
    else if (x <= (-1.22d-266)) then
        tmp = t_3
    else if (x <= 2.2d-295) then
        tmp = t_2 + (y * (x * z))
    else if (x <= 1.92d-280) then
        tmp = t_1
    else if (x <= 1d-148) then
        tmp = t_2 + (i * (t * b))
    else if (x <= 1.7d+116) then
        tmp = t_4 + t_2
    else if (x <= 2.3d+169) then
        tmp = t_3
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = j * ((a * c) - (y * i));
	double t_3 = (a * ((c * j) - (x * t))) + t_1;
	double t_4 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -2.6e-24) {
		tmp = t_4 - (j * (y * i));
	} else if (x <= -1.22e-266) {
		tmp = t_3;
	} else if (x <= 2.2e-295) {
		tmp = t_2 + (y * (x * z));
	} else if (x <= 1.92e-280) {
		tmp = t_1;
	} else if (x <= 1e-148) {
		tmp = t_2 + (i * (t * b));
	} else if (x <= 1.7e+116) {
		tmp = t_4 + t_2;
	} else if (x <= 2.3e+169) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	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))
	t_3 = (a * ((c * j) - (x * t))) + t_1
	t_4 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -2.6e-24:
		tmp = t_4 - (j * (y * i))
	elif x <= -1.22e-266:
		tmp = t_3
	elif x <= 2.2e-295:
		tmp = t_2 + (y * (x * z))
	elif x <= 1.92e-280:
		tmp = t_1
	elif x <= 1e-148:
		tmp = t_2 + (i * (t * b))
	elif x <= 1.7e+116:
		tmp = t_4 + t_2
	elif x <= 2.3e+169:
		tmp = t_3
	else:
		tmp = t_4
	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)))
	t_3 = Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) + t_1)
	t_4 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -2.6e-24)
		tmp = Float64(t_4 - Float64(j * Float64(y * i)));
	elseif (x <= -1.22e-266)
		tmp = t_3;
	elseif (x <= 2.2e-295)
		tmp = Float64(t_2 + Float64(y * Float64(x * z)));
	elseif (x <= 1.92e-280)
		tmp = t_1;
	elseif (x <= 1e-148)
		tmp = Float64(t_2 + Float64(i * Float64(t * b)));
	elseif (x <= 1.7e+116)
		tmp = Float64(t_4 + t_2);
	elseif (x <= 2.3e+169)
		tmp = t_3;
	else
		tmp = t_4;
	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));
	t_3 = (a * ((c * j) - (x * t))) + t_1;
	t_4 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -2.6e-24)
		tmp = t_4 - (j * (y * i));
	elseif (x <= -1.22e-266)
		tmp = t_3;
	elseif (x <= 2.2e-295)
		tmp = t_2 + (y * (x * z));
	elseif (x <= 1.92e-280)
		tmp = t_1;
	elseif (x <= 1e-148)
		tmp = t_2 + (i * (t * b));
	elseif (x <= 1.7e+116)
		tmp = t_4 + t_2;
	elseif (x <= 2.3e+169)
		tmp = t_3;
	else
		tmp = t_4;
	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]}, Block[{t$95$3 = N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.6e-24], N[(t$95$4 - N[(j * N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.22e-266], t$95$3, If[LessEqual[x, 2.2e-295], N[(t$95$2 + N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.92e-280], t$95$1, If[LessEqual[x, 1e-148], N[(t$95$2 + N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.7e+116], N[(t$95$4 + t$95$2), $MachinePrecision], If[LessEqual[x, 2.3e+169], t$95$3, t$95$4]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if x < -2.6e-24

   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. Add Preprocessing

   3. Taylor expanded in b around 0 71.4%

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

   4. Taylor expanded in a around 0 74.4%

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

      1. associate-*r* 74.4%

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

      2. neg-mul-1 74.4%

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

      3. *-commutative 74.4%

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

   6. Simplified 74.4%

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

   if -2.6e-24 < x < -1.22000000000000002e-266 or 1.70000000000000011e116 < x < 2.2999999999999999e169

   1. Initial program 83.7%

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

   3. Taylor expanded in y around 0 78.6%

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

      1. mul-1-neg 78.6%

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

      2. distribute-rgt-neg-in 78.6%

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

      3. mul-1-neg 78.6%

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

      4. distribute-lft-in 80.4%

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

      5. +-commutative 80.4%

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

      6. mul-1-neg 80.4%

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

      7. unsub-neg 80.4%

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

      8. *-commutative 80.4%

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

   5. Simplified 80.4%

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

   if -1.22000000000000002e-266 < x < 2.2000000000000002e-295

   1. Initial program 55.0%

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

   3. Taylor expanded in b around 0 55.1%

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

   4. Taylor expanded in y around inf 62.7%

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

      1. associate-*r* 6.8%

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

      2. *-commutative 6.8%

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

      3. associate-*r* 6.8%

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

   6. Simplified 77.9%

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

   if 2.2000000000000002e-295 < x < 1.92e-280

   1. Initial program 80.0%

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

   3. Taylor expanded in b around inf 80.9%

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

   if 1.92e-280 < x < 9.99999999999999936e-149

   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. Step-by-step derivation

      1. +-commutative 73.1%

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

      2. fma-def 73.1%

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

      3. *-commutative 73.1%

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

      4. sub-neg 73.1%

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

      5. sub-neg 73.1%

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

      6. *-commutative 73.1%

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

   3. Simplified 73.1%

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

   5. Taylor expanded in i around inf 80.0%

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

      1. *-commutative 80.0%

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

      2. associate-*l* 77.3%

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

      3. *-commutative 77.3%

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

   7. Simplified 77.3%

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

      1. fma-udef 77.3%

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

      2. *-commutative 77.3%

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

      3. *-commutative 77.3%

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

   9. Applied egg-rr 77.3%

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

   if 9.99999999999999936e-149 < x < 1.70000000000000011e116

   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 b around 0 77.8%

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

   if 2.2999999999999999e169 < x

   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 x around inf 87.0%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-24}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - j \cdot \left(y \cdot i\right)\\ \mathbf{elif}\;x \leq -1.22 \cdot 10^{-266}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-295}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 1.92 \cdot 10^{-280}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 10^{-148}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+116}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+169}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 67.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right) + t_1\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_4 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;j \leq -1.75 \cdot 10^{+182}:\\ \;\;\;\;t_3 + i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;j \leq -6.5 \cdot 10^{-5}:\\ \;\;\;\;t_4 + t_3\\ \mathbf{elif}\;j \leq -1.8 \cdot 10^{-211}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -1.3 \cdot 10^{-246}:\\ \;\;\;\;t_4 - j \cdot \left(y \cdot i\right)\\ \mathbf{elif}\;j \leq -6.3 \cdot 10^{-257}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 8.2 \cdot 10^{+49}:\\ \;\;\;\;t_1 - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_3 + y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c))))
        (t_2 (+ (* a (- (* c j) (* x t))) t_1))
        (t_3 (* j (- (* a c) (* y i))))
        (t_4 (* x (- (* y z) (* t a)))))
   (if (<= j -1.75e+182)
     (+ t_3 (* i (* t b)))
     (if (<= j -6.5e-5)
       (+ t_4 t_3)
       (if (<= j -1.8e-211)
         t_2
         (if (<= j -1.3e-246)
           (- t_4 (* j (* y i)))
           (if (<= j -6.3e-257)
             t_2
             (if (<= j 8.2e+49)
               (- t_1 (* x (- (* t a) (* y z))))
               (+ t_3 (* y (* x z)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = (a * ((c * j) - (x * t))) + t_1;
	double t_3 = j * ((a * c) - (y * i));
	double t_4 = x * ((y * z) - (t * a));
	double tmp;
	if (j <= -1.75e+182) {
		tmp = t_3 + (i * (t * b));
	} else if (j <= -6.5e-5) {
		tmp = t_4 + t_3;
	} else if (j <= -1.8e-211) {
		tmp = t_2;
	} else if (j <= -1.3e-246) {
		tmp = t_4 - (j * (y * i));
	} else if (j <= -6.3e-257) {
		tmp = t_2;
	} else if (j <= 8.2e+49) {
		tmp = t_1 - (x * ((t * a) - (y * z)));
	} else {
		tmp = t_3 + (y * (x * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = (a * ((c * j) - (x * t))) + t_1
    t_3 = j * ((a * c) - (y * i))
    t_4 = x * ((y * z) - (t * a))
    if (j <= (-1.75d+182)) then
        tmp = t_3 + (i * (t * b))
    else if (j <= (-6.5d-5)) then
        tmp = t_4 + t_3
    else if (j <= (-1.8d-211)) then
        tmp = t_2
    else if (j <= (-1.3d-246)) then
        tmp = t_4 - (j * (y * i))
    else if (j <= (-6.3d-257)) then
        tmp = t_2
    else if (j <= 8.2d+49) then
        tmp = t_1 - (x * ((t * a) - (y * z)))
    else
        tmp = t_3 + (y * (x * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = (a * ((c * j) - (x * t))) + t_1;
	double t_3 = j * ((a * c) - (y * i));
	double t_4 = x * ((y * z) - (t * a));
	double tmp;
	if (j <= -1.75e+182) {
		tmp = t_3 + (i * (t * b));
	} else if (j <= -6.5e-5) {
		tmp = t_4 + t_3;
	} else if (j <= -1.8e-211) {
		tmp = t_2;
	} else if (j <= -1.3e-246) {
		tmp = t_4 - (j * (y * i));
	} else if (j <= -6.3e-257) {
		tmp = t_2;
	} else if (j <= 8.2e+49) {
		tmp = t_1 - (x * ((t * a) - (y * z)));
	} else {
		tmp = t_3 + (y * (x * z));
	}
	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))) + t_1
	t_3 = j * ((a * c) - (y * i))
	t_4 = x * ((y * z) - (t * a))
	tmp = 0
	if j <= -1.75e+182:
		tmp = t_3 + (i * (t * b))
	elif j <= -6.5e-5:
		tmp = t_4 + t_3
	elif j <= -1.8e-211:
		tmp = t_2
	elif j <= -1.3e-246:
		tmp = t_4 - (j * (y * i))
	elif j <= -6.3e-257:
		tmp = t_2
	elif j <= 8.2e+49:
		tmp = t_1 - (x * ((t * a) - (y * z)))
	else:
		tmp = t_3 + (y * (x * z))
	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(Float64(a * Float64(Float64(c * j) - Float64(x * t))) + t_1)
	t_3 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_4 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (j <= -1.75e+182)
		tmp = Float64(t_3 + Float64(i * Float64(t * b)));
	elseif (j <= -6.5e-5)
		tmp = Float64(t_4 + t_3);
	elseif (j <= -1.8e-211)
		tmp = t_2;
	elseif (j <= -1.3e-246)
		tmp = Float64(t_4 - Float64(j * Float64(y * i)));
	elseif (j <= -6.3e-257)
		tmp = t_2;
	elseif (j <= 8.2e+49)
		tmp = Float64(t_1 - Float64(x * Float64(Float64(t * a) - Float64(y * z))));
	else
		tmp = Float64(t_3 + Float64(y * Float64(x * z)));
	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))) + t_1;
	t_3 = j * ((a * c) - (y * i));
	t_4 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (j <= -1.75e+182)
		tmp = t_3 + (i * (t * b));
	elseif (j <= -6.5e-5)
		tmp = t_4 + t_3;
	elseif (j <= -1.8e-211)
		tmp = t_2;
	elseif (j <= -1.3e-246)
		tmp = t_4 - (j * (y * i));
	elseif (j <= -6.3e-257)
		tmp = t_2;
	elseif (j <= 8.2e+49)
		tmp = t_1 - (x * ((t * a) - (y * z)));
	else
		tmp = t_3 + (y * (x * z));
	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[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.75e+182], N[(t$95$3 + N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -6.5e-5], N[(t$95$4 + t$95$3), $MachinePrecision], If[LessEqual[j, -1.8e-211], t$95$2, If[LessEqual[j, -1.3e-246], N[(t$95$4 - N[(j * N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -6.3e-257], t$95$2, If[LessEqual[j, 8.2e+49], N[(t$95$1 - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$3 + N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -1.75000000000000011e182

   1. Initial program 53.6%

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

      1. +-commutative 53.6%

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

      2. fma-def 53.6%

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

      3. *-commutative 53.6%

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

      4. sub-neg 53.6%

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

      5. sub-neg 53.6%

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

      6. *-commutative 53.6%

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

   3. Simplified 53.6%

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

   5. Taylor expanded in i around inf 68.4%

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

      1. *-commutative 68.4%

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

      2. associate-*l* 75.9%

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

      3. *-commutative 75.9%

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

   7. Simplified 75.9%

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

      1. fma-udef 75.9%

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

      2. *-commutative 75.9%

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

      3. *-commutative 75.9%

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

   9. Applied egg-rr 75.9%

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

   if -1.75000000000000011e182 < j < -6.49999999999999943e-5

   1. Initial program 81.3%

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

   3. Taylor expanded in b around 0 92.2%

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

   if -6.49999999999999943e-5 < j < -1.7999999999999999e-211 or -1.2999999999999999e-246 < j < -6.29999999999999993e-257

   1. Initial program 65.8%

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

   3. Taylor expanded in y around 0 65.9%

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

      1. mul-1-neg 65.9%

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

      2. distribute-rgt-neg-in 65.9%

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

      3. mul-1-neg 65.9%

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

      4. distribute-lft-in 65.9%

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

      5. +-commutative 65.9%

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

      6. mul-1-neg 65.9%

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

      7. unsub-neg 65.9%

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

      8. *-commutative 65.9%

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

   5. Simplified 65.9%

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

   if -1.7999999999999999e-211 < j < -1.2999999999999999e-246

   1. Initial program 74.6%

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

   3. Taylor expanded in b around 0 87.1%

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

   4. Taylor expanded in a around 0 99.6%

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

      1. associate-*r* 99.6%

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

      2. neg-mul-1 99.6%

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

      3. *-commutative 99.6%

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

   6. Simplified 99.6%

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

   if -6.29999999999999993e-257 < j < 8.2e49

   1. Initial program 76.0%

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

   3. Taylor expanded in j around 0 77.5%

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

   if 8.2e49 < j

   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 b around 0 73.0%

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

   4. Taylor expanded in y around inf 75.1%

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

      1. associate-*r* 15.0%

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

      2. *-commutative 15.0%

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

      3. associate-*r* 13.1%

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

   6. Simplified 77.0%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.75 \cdot 10^{+182}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;j \leq -6.5 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -1.8 \cdot 10^{-211}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -1.3 \cdot 10^{-246}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - j \cdot \left(y \cdot i\right)\\ \mathbf{elif}\;j \leq -6.3 \cdot 10^{-257}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 8.2 \cdot 10^{+49}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + y \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 48.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_3 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_4 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;a \leq -2.9 \cdot 10^{+55}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-98}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-190}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-215}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.08 \cdot 10^{-237}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-271}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;a \leq 440:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+65}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+70}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z)))
        (t_2 (* b (- (* t i) (* z c))))
        (t_3 (* a (- (* c j) (* x t))))
        (t_4 (* c (- (* a j) (* z b)))))
   (if (<= a -2.9e+55)
     t_3
     (if (<= a -6.2e-37)
       t_1
       (if (<= a -3.2e-98)
         t_4
         (if (<= a -5e-190)
           t_1
           (if (<= a -1.2e-215)
             t_2
             (if (<= a -1.08e-237)
               (* y (* x z))
               (if (<= a -2.4e-271)
                 (* (* y i) (- j))
                 (if (<= a 440.0)
                   t_2
                   (if (<= a 8.2e+65)
                     t_4
                     (if (<= a 5.5e+70) (* i (* y (- j))) t_3))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double t_2 = b * ((t * i) - (z * c));
	double t_3 = a * ((c * j) - (x * t));
	double t_4 = c * ((a * j) - (z * b));
	double tmp;
	if (a <= -2.9e+55) {
		tmp = t_3;
	} else if (a <= -6.2e-37) {
		tmp = t_1;
	} else if (a <= -3.2e-98) {
		tmp = t_4;
	} else if (a <= -5e-190) {
		tmp = t_1;
	} else if (a <= -1.2e-215) {
		tmp = t_2;
	} else if (a <= -1.08e-237) {
		tmp = y * (x * z);
	} else if (a <= -2.4e-271) {
		tmp = (y * i) * -j;
	} else if (a <= 440.0) {
		tmp = t_2;
	} else if (a <= 8.2e+65) {
		tmp = t_4;
	} else if (a <= 5.5e+70) {
		tmp = i * (y * -j);
	} 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) :: t_4
    real(8) :: tmp
    t_1 = x * (y * z)
    t_2 = b * ((t * i) - (z * c))
    t_3 = a * ((c * j) - (x * t))
    t_4 = c * ((a * j) - (z * b))
    if (a <= (-2.9d+55)) then
        tmp = t_3
    else if (a <= (-6.2d-37)) then
        tmp = t_1
    else if (a <= (-3.2d-98)) then
        tmp = t_4
    else if (a <= (-5d-190)) then
        tmp = t_1
    else if (a <= (-1.2d-215)) then
        tmp = t_2
    else if (a <= (-1.08d-237)) then
        tmp = y * (x * z)
    else if (a <= (-2.4d-271)) then
        tmp = (y * i) * -j
    else if (a <= 440.0d0) then
        tmp = t_2
    else if (a <= 8.2d+65) then
        tmp = t_4
    else if (a <= 5.5d+70) then
        tmp = i * (y * -j)
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double t_2 = b * ((t * i) - (z * c));
	double t_3 = a * ((c * j) - (x * t));
	double t_4 = c * ((a * j) - (z * b));
	double tmp;
	if (a <= -2.9e+55) {
		tmp = t_3;
	} else if (a <= -6.2e-37) {
		tmp = t_1;
	} else if (a <= -3.2e-98) {
		tmp = t_4;
	} else if (a <= -5e-190) {
		tmp = t_1;
	} else if (a <= -1.2e-215) {
		tmp = t_2;
	} else if (a <= -1.08e-237) {
		tmp = y * (x * z);
	} else if (a <= -2.4e-271) {
		tmp = (y * i) * -j;
	} else if (a <= 440.0) {
		tmp = t_2;
	} else if (a <= 8.2e+65) {
		tmp = t_4;
	} else if (a <= 5.5e+70) {
		tmp = i * (y * -j);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	t_2 = b * ((t * i) - (z * c))
	t_3 = a * ((c * j) - (x * t))
	t_4 = c * ((a * j) - (z * b))
	tmp = 0
	if a <= -2.9e+55:
		tmp = t_3
	elif a <= -6.2e-37:
		tmp = t_1
	elif a <= -3.2e-98:
		tmp = t_4
	elif a <= -5e-190:
		tmp = t_1
	elif a <= -1.2e-215:
		tmp = t_2
	elif a <= -1.08e-237:
		tmp = y * (x * z)
	elif a <= -2.4e-271:
		tmp = (y * i) * -j
	elif a <= 440.0:
		tmp = t_2
	elif a <= 8.2e+65:
		tmp = t_4
	elif a <= 5.5e+70:
		tmp = i * (y * -j)
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(y * z))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_3 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_4 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (a <= -2.9e+55)
		tmp = t_3;
	elseif (a <= -6.2e-37)
		tmp = t_1;
	elseif (a <= -3.2e-98)
		tmp = t_4;
	elseif (a <= -5e-190)
		tmp = t_1;
	elseif (a <= -1.2e-215)
		tmp = t_2;
	elseif (a <= -1.08e-237)
		tmp = Float64(y * Float64(x * z));
	elseif (a <= -2.4e-271)
		tmp = Float64(Float64(y * i) * Float64(-j));
	elseif (a <= 440.0)
		tmp = t_2;
	elseif (a <= 8.2e+65)
		tmp = t_4;
	elseif (a <= 5.5e+70)
		tmp = Float64(i * Float64(y * Float64(-j)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (y * z);
	t_2 = b * ((t * i) - (z * c));
	t_3 = a * ((c * j) - (x * t));
	t_4 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (a <= -2.9e+55)
		tmp = t_3;
	elseif (a <= -6.2e-37)
		tmp = t_1;
	elseif (a <= -3.2e-98)
		tmp = t_4;
	elseif (a <= -5e-190)
		tmp = t_1;
	elseif (a <= -1.2e-215)
		tmp = t_2;
	elseif (a <= -1.08e-237)
		tmp = y * (x * z);
	elseif (a <= -2.4e-271)
		tmp = (y * i) * -j;
	elseif (a <= 440.0)
		tmp = t_2;
	elseif (a <= 8.2e+65)
		tmp = t_4;
	elseif (a <= 5.5e+70)
		tmp = i * (y * -j);
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.9e+55], t$95$3, If[LessEqual[a, -6.2e-37], t$95$1, If[LessEqual[a, -3.2e-98], t$95$4, If[LessEqual[a, -5e-190], t$95$1, If[LessEqual[a, -1.2e-215], t$95$2, If[LessEqual[a, -1.08e-237], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.4e-271], N[(N[(y * i), $MachinePrecision] * (-j)), $MachinePrecision], If[LessEqual[a, 440.0], t$95$2, If[LessEqual[a, 8.2e+65], t$95$4, If[LessEqual[a, 5.5e+70], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if a < -2.8999999999999999e55 or 5.49999999999999986e70 < a

   1. Initial program 59.4%

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

   3. Taylor expanded in a around inf 73.1%

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

      1. +-commutative 73.1%

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

      2. mul-1-neg 73.1%

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

      3. unsub-neg 73.1%

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

      4. *-commutative 73.1%

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

   5. Simplified 73.1%

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

   if -2.8999999999999999e55 < a < -6.19999999999999987e-37 or -3.2000000000000001e-98 < a < -5.00000000000000034e-190

   1. Initial program 75.5%

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

   3. Taylor expanded in x around inf 64.0%

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

   4. Taylor expanded in y around inf 55.2%

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

   if -6.19999999999999987e-37 < a < -3.2000000000000001e-98 or 440 < a < 8.2000000000000003e65

   1. Initial program 75.6%

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

   3. Taylor expanded in c around inf 71.2%

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

      1. *-commutative 71.2%

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

   5. Simplified 71.2%

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

   if -5.00000000000000034e-190 < a < -1.20000000000000005e-215 or -2.4000000000000002e-271 < a < 440

   1. Initial program 85.0%

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

   3. Taylor expanded in b around inf 52.7%

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

   if -1.20000000000000005e-215 < a < -1.07999999999999996e-237

   1. Initial program 34.6%

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

   3. Taylor expanded in x around inf 66.6%

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

   4. Taylor expanded in y around inf 66.7%

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

      1. associate-*r* 67.0%

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

      2. *-commutative 67.0%

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

      3. associate-*r* 67.0%

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

   6. Simplified 67.0%

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

   if -1.07999999999999996e-237 < a < -2.4000000000000002e-271

   1. Initial program 100.0%

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

      1. add-cube-cbrt 100.0%

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

      2. pow3 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in j around inf 100.0%

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

      1. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in a around 0 75.6%

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

      1. *-commutative 75.6%

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

      2. *-commutative 75.6%

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

      3. associate-*l* 100.0%

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

      4. associate-*r* 100.0%

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

      5. *-commutative 100.0%

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

      6. *-commutative 100.0%

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

      7. mul-1-neg 100.0%

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

      8. distribute-rgt-neg-in 100.0%

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

   10. Simplified 100.0%

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

   if 8.2000000000000003e65 < a < 5.49999999999999986e70

   1. Initial program 99.6%

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

      1. add-cube-cbrt 99.6%

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

      2. pow3 99.6%

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in y around inf 75.1%

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

      1. mul-1-neg 75.1%

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

      2. distribute-rgt-neg-in 75.1%

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

      3. *-commutative 75.1%

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

      4. distribute-rgt-neg-in 75.1%

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

   7. Simplified 75.1%

      \[\leadsto \color{blue}{i \cdot \left(y \cdot \left(-j\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{+55}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-37}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-98}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-190}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-215}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq -1.08 \cdot 10^{-237}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-271}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;a \leq 440:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+65}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+70}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -2.4 \cdot 10^{-9}:\\ \;\;\;\;t_3 - j \cdot \left(y \cdot i\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-150}:\\ \;\;\;\;\left(y \cdot \left(x \cdot z\right) + t_1\right) + t_2\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+114}:\\ \;\;\;\;t_3 + t_2\\ \mathbf{else}:\\ \;\;\;\;t_1 - x \cdot \left(t \cdot a - y \cdot z\right)\\ \end{array} \end{array} \]

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))))
        (t_3 (* x (- (* y z) (* t a)))))
   (if (<= x -2.4e-9)
     (- t_3 (* j (* y i)))
     (if (<= x 5.2e-150)
       (+ (+ (* y (* x z)) t_1) t_2)
       (if (<= x 1.4e+114) (+ t_3 t_2) (- t_1 (* x (- (* t a) (* y z)))))))))

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 t_3 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -2.4e-9) {
		tmp = t_3 - (j * (y * i));
	} else if (x <= 5.2e-150) {
		tmp = ((y * (x * z)) + t_1) + t_2;
	} else if (x <= 1.4e+114) {
		tmp = t_3 + t_2;
	} else {
		tmp = t_1 - (x * ((t * a) - (y * z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = j * ((a * c) - (y * i))
    t_3 = x * ((y * z) - (t * a))
    if (x <= (-2.4d-9)) then
        tmp = t_3 - (j * (y * i))
    else if (x <= 5.2d-150) then
        tmp = ((y * (x * z)) + t_1) + t_2
    else if (x <= 1.4d+114) then
        tmp = t_3 + t_2
    else
        tmp = t_1 - (x * ((t * a) - (y * z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = j * ((a * c) - (y * i));
	double t_3 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -2.4e-9) {
		tmp = t_3 - (j * (y * i));
	} else if (x <= 5.2e-150) {
		tmp = ((y * (x * z)) + t_1) + t_2;
	} else if (x <= 1.4e+114) {
		tmp = t_3 + t_2;
	} else {
		tmp = t_1 - (x * ((t * a) - (y * z)));
	}
	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))
	t_3 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -2.4e-9:
		tmp = t_3 - (j * (y * i))
	elif x <= 5.2e-150:
		tmp = ((y * (x * z)) + t_1) + t_2
	elif x <= 1.4e+114:
		tmp = t_3 + t_2
	else:
		tmp = t_1 - (x * ((t * a) - (y * z)))
	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)))
	t_3 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -2.4e-9)
		tmp = Float64(t_3 - Float64(j * Float64(y * i)));
	elseif (x <= 5.2e-150)
		tmp = Float64(Float64(Float64(y * Float64(x * z)) + t_1) + t_2);
	elseif (x <= 1.4e+114)
		tmp = Float64(t_3 + t_2);
	else
		tmp = Float64(t_1 - Float64(x * Float64(Float64(t * a) - Float64(y * z))));
	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));
	t_3 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -2.4e-9)
		tmp = t_3 - (j * (y * i));
	elseif (x <= 5.2e-150)
		tmp = ((y * (x * z)) + t_1) + t_2;
	elseif (x <= 1.4e+114)
		tmp = t_3 + t_2;
	else
		tmp = t_1 - (x * ((t * a) - (y * z)));
	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]}, Block[{t$95$3 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.4e-9], N[(t$95$3 - N[(j * N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.2e-150], N[(N[(N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[x, 1.4e+114], N[(t$95$3 + t$95$2), $MachinePrecision], N[(t$95$1 - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.4e-9

   1. Initial program 66.5%

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

   3. Taylor expanded in b around 0 72.3%

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

   4. Taylor expanded in a around 0 75.5%

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

      1. associate-*r* 75.5%

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

      2. neg-mul-1 75.5%

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

      3. *-commutative 75.5%

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

   6. Simplified 75.5%

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

   if -2.4e-9 < x < 5.1999999999999995e-150

   1. Initial program 76.8%

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

   3. Taylor expanded in y around inf 77.9%

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

      1. *-commutative 77.9%

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

      2. associate-*l* 83.3%

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

   5. Simplified 83.3%

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

   if 5.1999999999999995e-150 < x < 1.4e114

   1. Initial program 67.8%

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

   3. Taylor expanded in b around 0 76.5%

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

   if 1.4e114 < x

   1. Initial program 73.4%

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

   3. Taylor expanded in j around 0 83.5%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-9}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - j \cdot \left(y \cdot i\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-150}:\\ \;\;\;\;\left(y \cdot \left(x \cdot z\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+114}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 48.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z\right)\\ t_3 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.95 \cdot 10^{+58}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-35}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-80}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-159}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.15 \cdot 10^{-190}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-214}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-239}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-271}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c))))
        (t_2 (* x (* y z)))
        (t_3 (* a (- (* c j) (* x t)))))
   (if (<= a -1.95e+58)
     t_3
     (if (<= a -1.7e-35)
       t_2
       (if (<= a -3.5e-80)
         t_3
         (if (<= a -1.05e-159)
           t_1
           (if (<= a -4.15e-190)
             t_2
             (if (<= a -1.4e-214)
               t_1
               (if (<= a -1.2e-239)
                 (* y (* x z))
                 (if (<= a -2.4e-271)
                   (* (* y i) (- j))
                   (if (<= a 6.5e-26) t_1 t_3)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = x * (y * z);
	double t_3 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.95e+58) {
		tmp = t_3;
	} else if (a <= -1.7e-35) {
		tmp = t_2;
	} else if (a <= -3.5e-80) {
		tmp = t_3;
	} else if (a <= -1.05e-159) {
		tmp = t_1;
	} else if (a <= -4.15e-190) {
		tmp = t_2;
	} else if (a <= -1.4e-214) {
		tmp = t_1;
	} else if (a <= -1.2e-239) {
		tmp = y * (x * z);
	} else if (a <= -2.4e-271) {
		tmp = (y * i) * -j;
	} else if (a <= 6.5e-26) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = x * (y * z)
    t_3 = a * ((c * j) - (x * t))
    if (a <= (-1.95d+58)) then
        tmp = t_3
    else if (a <= (-1.7d-35)) then
        tmp = t_2
    else if (a <= (-3.5d-80)) then
        tmp = t_3
    else if (a <= (-1.05d-159)) then
        tmp = t_1
    else if (a <= (-4.15d-190)) then
        tmp = t_2
    else if (a <= (-1.4d-214)) then
        tmp = t_1
    else if (a <= (-1.2d-239)) then
        tmp = y * (x * z)
    else if (a <= (-2.4d-271)) then
        tmp = (y * i) * -j
    else if (a <= 6.5d-26) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = x * (y * z);
	double t_3 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.95e+58) {
		tmp = t_3;
	} else if (a <= -1.7e-35) {
		tmp = t_2;
	} else if (a <= -3.5e-80) {
		tmp = t_3;
	} else if (a <= -1.05e-159) {
		tmp = t_1;
	} else if (a <= -4.15e-190) {
		tmp = t_2;
	} else if (a <= -1.4e-214) {
		tmp = t_1;
	} else if (a <= -1.2e-239) {
		tmp = y * (x * z);
	} else if (a <= -2.4e-271) {
		tmp = (y * i) * -j;
	} else if (a <= 6.5e-26) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = x * (y * z)
	t_3 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -1.95e+58:
		tmp = t_3
	elif a <= -1.7e-35:
		tmp = t_2
	elif a <= -3.5e-80:
		tmp = t_3
	elif a <= -1.05e-159:
		tmp = t_1
	elif a <= -4.15e-190:
		tmp = t_2
	elif a <= -1.4e-214:
		tmp = t_1
	elif a <= -1.2e-239:
		tmp = y * (x * z)
	elif a <= -2.4e-271:
		tmp = (y * i) * -j
	elif a <= 6.5e-26:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(x * Float64(y * z))
	t_3 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -1.95e+58)
		tmp = t_3;
	elseif (a <= -1.7e-35)
		tmp = t_2;
	elseif (a <= -3.5e-80)
		tmp = t_3;
	elseif (a <= -1.05e-159)
		tmp = t_1;
	elseif (a <= -4.15e-190)
		tmp = t_2;
	elseif (a <= -1.4e-214)
		tmp = t_1;
	elseif (a <= -1.2e-239)
		tmp = Float64(y * Float64(x * z));
	elseif (a <= -2.4e-271)
		tmp = Float64(Float64(y * i) * Float64(-j));
	elseif (a <= 6.5e-26)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = x * (y * z);
	t_3 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -1.95e+58)
		tmp = t_3;
	elseif (a <= -1.7e-35)
		tmp = t_2;
	elseif (a <= -3.5e-80)
		tmp = t_3;
	elseif (a <= -1.05e-159)
		tmp = t_1;
	elseif (a <= -4.15e-190)
		tmp = t_2;
	elseif (a <= -1.4e-214)
		tmp = t_1;
	elseif (a <= -1.2e-239)
		tmp = y * (x * z);
	elseif (a <= -2.4e-271)
		tmp = (y * i) * -j;
	elseif (a <= 6.5e-26)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.95e+58], t$95$3, If[LessEqual[a, -1.7e-35], t$95$2, If[LessEqual[a, -3.5e-80], t$95$3, If[LessEqual[a, -1.05e-159], t$95$1, If[LessEqual[a, -4.15e-190], t$95$2, If[LessEqual[a, -1.4e-214], t$95$1, If[LessEqual[a, -1.2e-239], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.4e-271], N[(N[(y * i), $MachinePrecision] * (-j)), $MachinePrecision], If[LessEqual[a, 6.5e-26], t$95$1, t$95$3]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.95000000000000005e58 or -1.7000000000000001e-35 < a < -3.50000000000000015e-80 or 6.5e-26 < a

   1. Initial program 64.1%

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

   3. Taylor expanded in a around inf 67.9%

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

      1. +-commutative 67.9%

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

      2. mul-1-neg 67.9%

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

      3. unsub-neg 67.9%

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

      4. *-commutative 67.9%

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

   5. Simplified 67.9%

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

   if -1.95000000000000005e58 < a < -1.7000000000000001e-35 or -1.05e-159 < a < -4.15000000000000002e-190

   1. Initial program 86.7%

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

   3. Taylor expanded in x around inf 74.2%

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

   4. Taylor expanded in y around inf 65.9%

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

   if -3.50000000000000015e-80 < a < -1.05e-159 or -4.15000000000000002e-190 < a < -1.4000000000000001e-214 or -2.4000000000000002e-271 < a < 6.5e-26

   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. Add Preprocessing

   3. Taylor expanded in b around inf 52.8%

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

   if -1.4000000000000001e-214 < a < -1.19999999999999996e-239

   1. Initial program 34.6%

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

   3. Taylor expanded in x around inf 66.6%

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

   4. Taylor expanded in y around inf 66.7%

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

      1. associate-*r* 67.0%

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

      2. *-commutative 67.0%

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

      3. associate-*r* 67.0%

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

   6. Simplified 67.0%

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

   if -1.19999999999999996e-239 < a < -2.4000000000000002e-271

   1. Initial program 100.0%

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

      1. add-cube-cbrt 100.0%

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

      2. pow3 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in j around inf 100.0%

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

      1. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in a around 0 75.6%

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

      1. *-commutative 75.6%

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

      2. *-commutative 75.6%

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

      3. associate-*l* 100.0%

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

      4. associate-*r* 100.0%

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

      5. *-commutative 100.0%

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

      6. *-commutative 100.0%

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

      7. mul-1-neg 100.0%

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

      8. distribute-rgt-neg-in 100.0%

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

   10. Simplified 100.0%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.95 \cdot 10^{+58}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-35}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-80}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-159}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq -4.15 \cdot 10^{-190}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-214}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-239}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-271}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-26}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 48.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_3 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -3.4 \cdot 10^{+54}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-100}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq -8.8 \cdot 10^{-189}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-214}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-236}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-271}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;a \leq 58000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+89}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z)))
        (t_2 (* b (- (* t i) (* z c))))
        (t_3 (* a (- (* c j) (* x t)))))
   (if (<= a -3.4e+54)
     t_3
     (if (<= a -1.4e-35)
       t_1
       (if (<= a -4.4e-100)
         (* c (- (* a j) (* z b)))
         (if (<= a -8.8e-189)
           t_1
           (if (<= a -2.6e-214)
             t_2
             (if (<= a -9e-236)
               (* y (* x z))
               (if (<= a -2.4e-271)
                 (* (* y i) (- j))
                 (if (<= a 58000.0)
                   t_2
                   (if (<= a 1.25e+89) (* j (- (* a c) (* y i))) t_3)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double t_2 = b * ((t * i) - (z * c));
	double t_3 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -3.4e+54) {
		tmp = t_3;
	} else if (a <= -1.4e-35) {
		tmp = t_1;
	} else if (a <= -4.4e-100) {
		tmp = c * ((a * j) - (z * b));
	} else if (a <= -8.8e-189) {
		tmp = t_1;
	} else if (a <= -2.6e-214) {
		tmp = t_2;
	} else if (a <= -9e-236) {
		tmp = y * (x * z);
	} else if (a <= -2.4e-271) {
		tmp = (y * i) * -j;
	} else if (a <= 58000.0) {
		tmp = t_2;
	} else if (a <= 1.25e+89) {
		tmp = j * ((a * c) - (y * i));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * (y * z)
    t_2 = b * ((t * i) - (z * c))
    t_3 = a * ((c * j) - (x * t))
    if (a <= (-3.4d+54)) then
        tmp = t_3
    else if (a <= (-1.4d-35)) then
        tmp = t_1
    else if (a <= (-4.4d-100)) then
        tmp = c * ((a * j) - (z * b))
    else if (a <= (-8.8d-189)) then
        tmp = t_1
    else if (a <= (-2.6d-214)) then
        tmp = t_2
    else if (a <= (-9d-236)) then
        tmp = y * (x * z)
    else if (a <= (-2.4d-271)) then
        tmp = (y * i) * -j
    else if (a <= 58000.0d0) then
        tmp = t_2
    else if (a <= 1.25d+89) then
        tmp = j * ((a * c) - (y * i))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double t_2 = b * ((t * i) - (z * c));
	double t_3 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -3.4e+54) {
		tmp = t_3;
	} else if (a <= -1.4e-35) {
		tmp = t_1;
	} else if (a <= -4.4e-100) {
		tmp = c * ((a * j) - (z * b));
	} else if (a <= -8.8e-189) {
		tmp = t_1;
	} else if (a <= -2.6e-214) {
		tmp = t_2;
	} else if (a <= -9e-236) {
		tmp = y * (x * z);
	} else if (a <= -2.4e-271) {
		tmp = (y * i) * -j;
	} else if (a <= 58000.0) {
		tmp = t_2;
	} else if (a <= 1.25e+89) {
		tmp = j * ((a * c) - (y * i));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	t_2 = b * ((t * i) - (z * c))
	t_3 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -3.4e+54:
		tmp = t_3
	elif a <= -1.4e-35:
		tmp = t_1
	elif a <= -4.4e-100:
		tmp = c * ((a * j) - (z * b))
	elif a <= -8.8e-189:
		tmp = t_1
	elif a <= -2.6e-214:
		tmp = t_2
	elif a <= -9e-236:
		tmp = y * (x * z)
	elif a <= -2.4e-271:
		tmp = (y * i) * -j
	elif a <= 58000.0:
		tmp = t_2
	elif a <= 1.25e+89:
		tmp = j * ((a * c) - (y * i))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(y * z))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_3 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -3.4e+54)
		tmp = t_3;
	elseif (a <= -1.4e-35)
		tmp = t_1;
	elseif (a <= -4.4e-100)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (a <= -8.8e-189)
		tmp = t_1;
	elseif (a <= -2.6e-214)
		tmp = t_2;
	elseif (a <= -9e-236)
		tmp = Float64(y * Float64(x * z));
	elseif (a <= -2.4e-271)
		tmp = Float64(Float64(y * i) * Float64(-j));
	elseif (a <= 58000.0)
		tmp = t_2;
	elseif (a <= 1.25e+89)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (y * z);
	t_2 = b * ((t * i) - (z * c));
	t_3 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -3.4e+54)
		tmp = t_3;
	elseif (a <= -1.4e-35)
		tmp = t_1;
	elseif (a <= -4.4e-100)
		tmp = c * ((a * j) - (z * b));
	elseif (a <= -8.8e-189)
		tmp = t_1;
	elseif (a <= -2.6e-214)
		tmp = t_2;
	elseif (a <= -9e-236)
		tmp = y * (x * z);
	elseif (a <= -2.4e-271)
		tmp = (y * i) * -j;
	elseif (a <= 58000.0)
		tmp = t_2;
	elseif (a <= 1.25e+89)
		tmp = j * ((a * c) - (y * i));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.4e+54], t$95$3, If[LessEqual[a, -1.4e-35], t$95$1, If[LessEqual[a, -4.4e-100], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -8.8e-189], t$95$1, If[LessEqual[a, -2.6e-214], t$95$2, If[LessEqual[a, -9e-236], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.4e-271], N[(N[(y * i), $MachinePrecision] * (-j)), $MachinePrecision], If[LessEqual[a, 58000.0], t$95$2, If[LessEqual[a, 1.25e+89], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if a < -3.4000000000000001e54 or 1.24999999999999996e89 < a

   1. Initial program 58.3%

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

   3. Taylor expanded in a around inf 74.1%

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

      1. +-commutative 74.1%

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

      2. mul-1-neg 74.1%

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

      3. unsub-neg 74.1%

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

      4. *-commutative 74.1%

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

   5. Simplified 74.1%

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

   if -3.4000000000000001e54 < a < -1.4e-35 or -4.39999999999999978e-100 < a < -8.80000000000000076e-189

   1. Initial program 75.5%

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

   3. Taylor expanded in x around inf 64.0%

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

   4. Taylor expanded in y around inf 55.2%

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

   if -1.4e-35 < a < -4.39999999999999978e-100

   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 c around inf 69.6%

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

      1. *-commutative 69.6%

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

   5. Simplified 69.6%

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

   if -8.80000000000000076e-189 < a < -2.6e-214 or -2.4000000000000002e-271 < a < 58000

   1. Initial program 85.0%

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

   3. Taylor expanded in b around inf 52.7%

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

   if -2.6e-214 < a < -8.99999999999999997e-236

   1. Initial program 34.6%

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

   3. Taylor expanded in x around inf 66.6%

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

   4. Taylor expanded in y around inf 66.7%

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

      1. associate-*r* 67.0%

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

      2. *-commutative 67.0%

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

      3. associate-*r* 67.0%

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

   6. Simplified 67.0%

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

   if -8.99999999999999997e-236 < a < -2.4000000000000002e-271

   1. Initial program 100.0%

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

      1. add-cube-cbrt 100.0%

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

      2. pow3 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in j around inf 100.0%

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

      1. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in a around 0 75.6%

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

      1. *-commutative 75.6%

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

      2. *-commutative 75.6%

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

      3. associate-*l* 100.0%

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

      4. associate-*r* 100.0%

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

      5. *-commutative 100.0%

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

      6. *-commutative 100.0%

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

      7. mul-1-neg 100.0%

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

      8. distribute-rgt-neg-in 100.0%

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

   10. Simplified 100.0%

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

   if 58000 < a < 1.24999999999999996e89

   1. Initial program 89.0%

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

   3. Taylor expanded in j around inf 67.9%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+54}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-35}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-100}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq -8.8 \cdot 10^{-189}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-214}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-236}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-271}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;a \leq 58000:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+89}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 61.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -1.4 \cdot 10^{-25}:\\ \;\;\;\;t_2 - j \cdot \left(y \cdot i\right)\\ \mathbf{elif}\;x \leq -6.9 \cdot 10^{-196}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-149}:\\ \;\;\;\;t_1 + i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+108}:\\ \;\;\;\;t_2 + t_1\\ \mathbf{else}:\\ \;\;\;\;t_2 - z \cdot \left(b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))) (t_2 (* x (- (* y z) (* t a)))))
   (if (<= x -1.4e-25)
     (- t_2 (* j (* y i)))
     (if (<= x -6.9e-196)
       (+ (* a (* c j)) (* b (- (* t i) (* z c))))
       (if (<= x 7.2e-149)
         (+ t_1 (* i (* t b)))
         (if (<= x 1.4e+108) (+ t_2 t_1) (- t_2 (* 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 = j * ((a * c) - (y * i));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.4e-25) {
		tmp = t_2 - (j * (y * i));
	} else if (x <= -6.9e-196) {
		tmp = (a * (c * j)) + (b * ((t * i) - (z * c)));
	} else if (x <= 7.2e-149) {
		tmp = t_1 + (i * (t * b));
	} else if (x <= 1.4e+108) {
		tmp = t_2 + t_1;
	} else {
		tmp = t_2 - (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) :: t_2
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = x * ((y * z) - (t * a))
    if (x <= (-1.4d-25)) then
        tmp = t_2 - (j * (y * i))
    else if (x <= (-6.9d-196)) then
        tmp = (a * (c * j)) + (b * ((t * i) - (z * c)))
    else if (x <= 7.2d-149) then
        tmp = t_1 + (i * (t * b))
    else if (x <= 1.4d+108) then
        tmp = t_2 + t_1
    else
        tmp = t_2 - (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 = j * ((a * c) - (y * i));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.4e-25) {
		tmp = t_2 - (j * (y * i));
	} else if (x <= -6.9e-196) {
		tmp = (a * (c * j)) + (b * ((t * i) - (z * c)));
	} else if (x <= 7.2e-149) {
		tmp = t_1 + (i * (t * b));
	} else if (x <= 1.4e+108) {
		tmp = t_2 + t_1;
	} else {
		tmp = t_2 - (z * (b * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -1.4e-25:
		tmp = t_2 - (j * (y * i))
	elif x <= -6.9e-196:
		tmp = (a * (c * j)) + (b * ((t * i) - (z * c)))
	elif x <= 7.2e-149:
		tmp = t_1 + (i * (t * b))
	elif x <= 1.4e+108:
		tmp = t_2 + t_1
	else:
		tmp = t_2 - (z * (b * c))
	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(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -1.4e-25)
		tmp = Float64(t_2 - Float64(j * Float64(y * i)));
	elseif (x <= -6.9e-196)
		tmp = Float64(Float64(a * Float64(c * j)) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	elseif (x <= 7.2e-149)
		tmp = Float64(t_1 + Float64(i * Float64(t * b)));
	elseif (x <= 1.4e+108)
		tmp = Float64(t_2 + t_1);
	else
		tmp = Float64(t_2 - 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 = j * ((a * c) - (y * i));
	t_2 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -1.4e-25)
		tmp = t_2 - (j * (y * i));
	elseif (x <= -6.9e-196)
		tmp = (a * (c * j)) + (b * ((t * i) - (z * c)));
	elseif (x <= 7.2e-149)
		tmp = t_1 + (i * (t * b));
	elseif (x <= 1.4e+108)
		tmp = t_2 + t_1;
	else
		tmp = t_2 - (z * (b * c));
	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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.4e-25], N[(t$95$2 - N[(j * N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6.9e-196], N[(N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.2e-149], N[(t$95$1 + N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.4e+108], N[(t$95$2 + t$95$1), $MachinePrecision], N[(t$95$2 - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.39999999999999994e-25

   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. Add Preprocessing

   3. Taylor expanded in b around 0 71.4%

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

   4. Taylor expanded in a around 0 74.4%

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

      1. associate-*r* 74.4%

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

      2. neg-mul-1 74.4%

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

      3. *-commutative 74.4%

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

   6. Simplified 74.4%

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

   if -1.39999999999999994e-25 < x < -6.89999999999999958e-196

   1. Initial program 87.2%

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

   3. Taylor expanded in y around inf 87.0%

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

      1. *-commutative 87.0%

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

      2. associate-*l* 89.9%

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

   5. Simplified 89.9%

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

   6. Taylor expanded in y around 0 74.7%

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

      1. *-commutative 74.7%

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

      2. *-commutative 74.7%

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

      3. *-commutative 74.7%

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

   8. Simplified 74.7%

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

   if -6.89999999999999958e-196 < x < 7.2000000000000004e-149

   1. Initial program 69.8%

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

      1. +-commutative 69.8%

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

      2. fma-def 69.8%

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

      3. *-commutative 69.8%

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

      4. sub-neg 69.8%

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

      5. sub-neg 69.8%

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

      6. *-commutative 69.8%

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

   3. Simplified 69.8%

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

   5. Taylor expanded in i around inf 68.3%

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

      1. *-commutative 68.3%

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

      2. associate-*l* 67.0%

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

      3. *-commutative 67.0%

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

   7. Simplified 67.0%

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

      1. fma-udef 67.0%

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

      2. *-commutative 67.0%

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

      3. *-commutative 67.0%

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

   9. Applied egg-rr 67.0%

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

   if 7.2000000000000004e-149 < x < 1.3999999999999999e108

   1. Initial program 69.7%

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

   3. Taylor expanded in b around 0 77.0%

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

   if 1.3999999999999999e108 < x

   1. Initial program 71.9%

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

      1. add-cube-cbrt 71.7%

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

      2. pow3 71.7%

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

   4. Applied egg-rr 71.7%

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

   5. Taylor expanded in i around 0 77.7%

      \[\leadsto \color{blue}{\left(a \cdot \left(c \cdot j\right) + \left(i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + {1}^{0.3333333333333333} \cdot \left(x \cdot \left(y \cdot z - a \cdot t\right)\right)\right)\right) - b \cdot \left(c \cdot z\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 77.7%

         \[\leadsto \left(a \cdot \left(c \cdot j\right) + \left(i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + {1}^{0.3333333333333333} \cdot \left(x \cdot \left(y \cdot z - a \cdot t\right)\right)\right)\right) - \color{blue}{\left(b \cdot c\right) \cdot z} \]

      2. fma-def 77.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, c \cdot j, i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + {1}^{0.3333333333333333} \cdot \left(x \cdot \left(y \cdot z - a \cdot t\right)\right)\right)} - \left(b \cdot c\right) \cdot z \]

      3. *-commutative 77.7%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{j \cdot c}, i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + {1}^{0.3333333333333333} \cdot \left(x \cdot \left(y \cdot z - a \cdot t\right)\right)\right) - \left(b \cdot c\right) \cdot z \]

      4. fma-def 87.7%

         \[\leadsto \mathsf{fma}\left(a, j \cdot c, \color{blue}{\mathsf{fma}\left(i, -1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right), {1}^{0.3333333333333333} \cdot \left(x \cdot \left(y \cdot z - a \cdot t\right)\right)\right)}\right) - \left(b \cdot c\right) \cdot z \]

      5. distribute-lft-out-- 87.7%

         \[\leadsto \mathsf{fma}\left(a, j \cdot c, \mathsf{fma}\left(i, \color{blue}{-1 \cdot \left(j \cdot y - b \cdot t\right)}, {1}^{0.3333333333333333} \cdot \left(x \cdot \left(y \cdot z - a \cdot t\right)\right)\right)\right) - \left(b \cdot c\right) \cdot z \]

      6. *-commutative 87.7%

         \[\leadsto \mathsf{fma}\left(a, j \cdot c, \mathsf{fma}\left(i, -1 \cdot \left(\color{blue}{y \cdot j} - b \cdot t\right), {1}^{0.3333333333333333} \cdot \left(x \cdot \left(y \cdot z - a \cdot t\right)\right)\right)\right) - \left(b \cdot c\right) \cdot z \]

      7. *-commutative 87.7%

         \[\leadsto \mathsf{fma}\left(a, j \cdot c, \mathsf{fma}\left(i, -1 \cdot \left(y \cdot j - \color{blue}{t \cdot b}\right), {1}^{0.3333333333333333} \cdot \left(x \cdot \left(y \cdot z - a \cdot t\right)\right)\right)\right) - \left(b \cdot c\right) \cdot z \]

      8. pow-base-1 87.7%

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

      9. *-commutative 87.7%

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

   7. Simplified 87.7%

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

   8. Taylor expanded in x around inf 76.4%

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

      1. *-commutative 76.4%

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

   10. Simplified 76.4%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-25}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - j \cdot \left(y \cdot i\right)\\ \mathbf{elif}\;x \leq -6.9 \cdot 10^{-196}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-149}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+108}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 62.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;x \leq -6.7 \cdot 10^{-9}:\\ \;\;\;\;t_1 - j \cdot \left(y \cdot i\right)\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-283}:\\ \;\;\;\;t_2 + \left(y \cdot \left(x \cdot z\right) - z \cdot \left(b \cdot c\right)\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-148}:\\ \;\;\;\;t_2 + i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{+113}:\\ \;\;\;\;t_1 + t_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (* j (- (* a c) (* y i)))))
   (if (<= x -6.7e-9)
     (- t_1 (* j (* y i)))
     (if (<= x 3.5e-283)
       (+ t_2 (- (* y (* x z)) (* z (* b c))))
       (if (<= x 2.2e-148)
         (+ t_2 (* i (* t b)))
         (if (<= x 7.4e+113)
           (+ t_1 t_2)
           (- (* b (- (* t i) (* z c))) (* x (- (* t a) (* y z))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (x <= -6.7e-9) {
		tmp = t_1 - (j * (y * i));
	} else if (x <= 3.5e-283) {
		tmp = t_2 + ((y * (x * z)) - (z * (b * c)));
	} else if (x <= 2.2e-148) {
		tmp = t_2 + (i * (t * b));
	} else if (x <= 7.4e+113) {
		tmp = t_1 + t_2;
	} else {
		tmp = (b * ((t * i) - (z * c))) - (x * ((t * a) - (y * z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = j * ((a * c) - (y * i))
    if (x <= (-6.7d-9)) then
        tmp = t_1 - (j * (y * i))
    else if (x <= 3.5d-283) then
        tmp = t_2 + ((y * (x * z)) - (z * (b * c)))
    else if (x <= 2.2d-148) then
        tmp = t_2 + (i * (t * b))
    else if (x <= 7.4d+113) then
        tmp = t_1 + t_2
    else
        tmp = (b * ((t * i) - (z * c))) - (x * ((t * a) - (y * z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (x <= -6.7e-9) {
		tmp = t_1 - (j * (y * i));
	} else if (x <= 3.5e-283) {
		tmp = t_2 + ((y * (x * z)) - (z * (b * c)));
	} else if (x <= 2.2e-148) {
		tmp = t_2 + (i * (t * b));
	} else if (x <= 7.4e+113) {
		tmp = t_1 + t_2;
	} else {
		tmp = (b * ((t * i) - (z * c))) - (x * ((t * a) - (y * z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = j * ((a * c) - (y * i))
	tmp = 0
	if x <= -6.7e-9:
		tmp = t_1 - (j * (y * i))
	elif x <= 3.5e-283:
		tmp = t_2 + ((y * (x * z)) - (z * (b * c)))
	elif x <= 2.2e-148:
		tmp = t_2 + (i * (t * b))
	elif x <= 7.4e+113:
		tmp = t_1 + t_2
	else:
		tmp = (b * ((t * i) - (z * c))) - (x * ((t * a) - (y * z)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (x <= -6.7e-9)
		tmp = Float64(t_1 - Float64(j * Float64(y * i)));
	elseif (x <= 3.5e-283)
		tmp = Float64(t_2 + Float64(Float64(y * Float64(x * z)) - Float64(z * Float64(b * c))));
	elseif (x <= 2.2e-148)
		tmp = Float64(t_2 + Float64(i * Float64(t * b)));
	elseif (x <= 7.4e+113)
		tmp = Float64(t_1 + t_2);
	else
		tmp = Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) - Float64(x * Float64(Float64(t * a) - Float64(y * z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (x <= -6.7e-9)
		tmp = t_1 - (j * (y * i));
	elseif (x <= 3.5e-283)
		tmp = t_2 + ((y * (x * z)) - (z * (b * c)));
	elseif (x <= 2.2e-148)
		tmp = t_2 + (i * (t * b));
	elseif (x <= 7.4e+113)
		tmp = t_1 + t_2;
	else
		tmp = (b * ((t * i) - (z * c))) - (x * ((t * a) - (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.7e-9], N[(t$95$1 - N[(j * N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.5e-283], N[(t$95$2 + N[(N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision] - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.2e-148], N[(t$95$2 + N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.4e+113], N[(t$95$1 + t$95$2), $MachinePrecision], N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -6.69999999999999961e-9

   1. Initial program 66.5%

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

   3. Taylor expanded in b around 0 72.3%

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

   4. Taylor expanded in a around 0 75.5%

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

      1. associate-*r* 75.5%

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

      2. neg-mul-1 75.5%

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

      3. *-commutative 75.5%

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

   6. Simplified 75.5%

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

   if -6.69999999999999961e-9 < x < 3.4999999999999999e-283

   1. Initial program 78.7%

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

   3. Taylor expanded in y around inf 78.7%

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

      1. *-commutative 78.7%

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

      2. associate-*l* 85.0%

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

   5. Simplified 85.0%

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

   6. Taylor expanded in c around inf 72.3%

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

      1. *-commutative 72.3%

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

      2. *-commutative 72.3%

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

      3. associate-*l* 70.7%

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

   8. Simplified 70.7%

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

   if 3.4999999999999999e-283 < x < 2.20000000000000017e-148

   1. Initial program 71.6%

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

      1. +-commutative 71.6%

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

      2. fma-def 71.6%

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

      3. *-commutative 71.6%

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

      4. sub-neg 71.6%

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

      5. sub-neg 71.6%

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

      6. *-commutative 71.6%

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

   3. Simplified 71.6%

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

   5. Taylor expanded in i around inf 78.0%

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

      1. *-commutative 78.0%

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

      2. associate-*l* 75.5%

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

      3. *-commutative 75.5%

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

   7. Simplified 75.5%

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

      1. fma-udef 75.5%

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

      2. *-commutative 75.5%

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

      3. *-commutative 75.5%

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

   9. Applied egg-rr 75.5%

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

   if 2.20000000000000017e-148 < x < 7.3999999999999996e113

   1. Initial program 68.4%

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

   3. Taylor expanded in b around 0 77.4%

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

   if 7.3999999999999996e113 < x

   1. Initial program 73.4%

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

   3. Taylor expanded in j around 0 83.5%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.7 \cdot 10^{-9}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - j \cdot \left(y \cdot i\right)\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-283}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + \left(y \cdot \left(x \cdot z\right) - z \cdot \left(b \cdot c\right)\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-148}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{+113}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := t_1 + y \cdot \left(x \cdot z\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -1.95 \cdot 10^{+149}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -8.5:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-194}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 2.65 \cdot 10^{+42}:\\ \;\;\;\;t_1 + i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+115}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+193}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i))))
        (t_2 (+ t_1 (* y (* x z))))
        (t_3 (* x (- (* y z) (* t a)))))
   (if (<= x -1.95e+149)
     t_3
     (if (<= x -8.5)
       t_2
       (if (<= x -2.6e-194)
         (+ (* a (* c j)) (* b (- (* t i) (* z c))))
         (if (<= x 2.65e+42)
           (+ t_1 (* i (* t b)))
           (if (<= x 5e+115)
             t_2
             (if (<= x 2.2e+193) (* t (- (* b i) (* x a))) t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = t_1 + (y * (x * z));
	double t_3 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.95e+149) {
		tmp = t_3;
	} else if (x <= -8.5) {
		tmp = t_2;
	} else if (x <= -2.6e-194) {
		tmp = (a * (c * j)) + (b * ((t * i) - (z * c)));
	} else if (x <= 2.65e+42) {
		tmp = t_1 + (i * (t * b));
	} else if (x <= 5e+115) {
		tmp = t_2;
	} else if (x <= 2.2e+193) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = t_1 + (y * (x * z))
    t_3 = x * ((y * z) - (t * a))
    if (x <= (-1.95d+149)) then
        tmp = t_3
    else if (x <= (-8.5d0)) then
        tmp = t_2
    else if (x <= (-2.6d-194)) then
        tmp = (a * (c * j)) + (b * ((t * i) - (z * c)))
    else if (x <= 2.65d+42) then
        tmp = t_1 + (i * (t * b))
    else if (x <= 5d+115) then
        tmp = t_2
    else if (x <= 2.2d+193) then
        tmp = t * ((b * i) - (x * a))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = t_1 + (y * (x * z));
	double t_3 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.95e+149) {
		tmp = t_3;
	} else if (x <= -8.5) {
		tmp = t_2;
	} else if (x <= -2.6e-194) {
		tmp = (a * (c * j)) + (b * ((t * i) - (z * c)));
	} else if (x <= 2.65e+42) {
		tmp = t_1 + (i * (t * b));
	} else if (x <= 5e+115) {
		tmp = t_2;
	} else if (x <= 2.2e+193) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = t_1 + (y * (x * z))
	t_3 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -1.95e+149:
		tmp = t_3
	elif x <= -8.5:
		tmp = t_2
	elif x <= -2.6e-194:
		tmp = (a * (c * j)) + (b * ((t * i) - (z * c)))
	elif x <= 2.65e+42:
		tmp = t_1 + (i * (t * b))
	elif x <= 5e+115:
		tmp = t_2
	elif x <= 2.2e+193:
		tmp = t * ((b * i) - (x * a))
	else:
		tmp = t_3
	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_1 + Float64(y * Float64(x * z)))
	t_3 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -1.95e+149)
		tmp = t_3;
	elseif (x <= -8.5)
		tmp = t_2;
	elseif (x <= -2.6e-194)
		tmp = Float64(Float64(a * Float64(c * j)) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	elseif (x <= 2.65e+42)
		tmp = Float64(t_1 + Float64(i * Float64(t * b)));
	elseif (x <= 5e+115)
		tmp = t_2;
	elseif (x <= 2.2e+193)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = t_1 + (y * (x * z));
	t_3 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -1.95e+149)
		tmp = t_3;
	elseif (x <= -8.5)
		tmp = t_2;
	elseif (x <= -2.6e-194)
		tmp = (a * (c * j)) + (b * ((t * i) - (z * c)));
	elseif (x <= 2.65e+42)
		tmp = t_1 + (i * (t * b));
	elseif (x <= 5e+115)
		tmp = t_2;
	elseif (x <= 2.2e+193)
		tmp = t * ((b * i) - (x * a));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.95e+149], t$95$3, If[LessEqual[x, -8.5], t$95$2, If[LessEqual[x, -2.6e-194], N[(N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.65e+42], N[(t$95$1 + N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5e+115], t$95$2, If[LessEqual[x, 2.2e+193], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.95e149 or 2.19999999999999986e193 < x

   1. Initial program 65.5%

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

   3. Taylor expanded in x around inf 80.1%

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

   if -1.95e149 < x < -8.5 or 2.65000000000000014e42 < x < 5.00000000000000008e115

   1. Initial program 69.3%

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

   3. Taylor expanded in b around 0 78.7%

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

   4. Taylor expanded in y around inf 75.3%

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

      1. associate-*r* 37.2%

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

      2. *-commutative 37.2%

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

      3. associate-*r* 37.1%

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

   6. Simplified 75.3%

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

   if -8.5 < x < -2.60000000000000002e-194

   1. Initial program 84.3%

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

   3. Taylor expanded in y around inf 81.5%

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

      1. *-commutative 81.5%

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

      2. associate-*l* 83.8%

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

   5. Simplified 83.8%

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

   6. Taylor expanded in y around 0 68.9%

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

      1. *-commutative 68.9%

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

      2. *-commutative 68.9%

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

      3. *-commutative 68.9%

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

   8. Simplified 68.9%

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

   if -2.60000000000000002e-194 < x < 2.65000000000000014e42

   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. Step-by-step derivation

      1. +-commutative 71.1%

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

      2. fma-def 71.1%

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

      3. *-commutative 71.1%

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

      4. sub-neg 71.1%

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

      5. sub-neg 71.1%

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

      6. *-commutative 71.1%

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

   3. Simplified 71.1%

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

   5. Taylor expanded in i around inf 60.4%

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

      1. *-commutative 60.4%

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

      2. associate-*l* 61.7%

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

      3. *-commutative 61.7%

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

   7. Simplified 61.7%

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

      1. fma-udef 61.7%

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

      2. *-commutative 61.7%

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

      3. *-commutative 61.7%

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

   9. Applied egg-rr 61.7%

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

   if 5.00000000000000008e115 < x < 2.19999999999999986e193

   1. Initial program 74.7%

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

   3. Taylor expanded in t around inf 70.1%

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

      1. distribute-lft-out-- 70.1%

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

      2. *-commutative 70.1%

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

   5. Simplified 70.1%

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

   6. Taylor expanded in t around 0 70.1%

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

      1. mul-1-neg 70.1%

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

      2. *-commutative 70.1%

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

      3. *-commutative 70.1%

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

      4. cancel-sign-sub-inv 70.1%

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

      5. fma-def 70.1%

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

      6. distribute-rgt-neg-out 70.1%

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

      7. *-commutative 70.1%

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

      8. distribute-rgt-neg-in 70.1%

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

      9. fma-def 70.1%

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

      10. +-commutative 70.1%

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

      11. distribute-neg-in 70.1%

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

      12. remove-double-neg 70.1%

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

      13. *-commutative 70.1%

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

      14. *-commutative 70.1%

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

   8. Simplified 70.1%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{+149}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -8.5:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-194}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 2.65 \cdot 10^{+42}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+115}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+193}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 50.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right) + i \cdot \left(t \cdot b\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;j \leq -2.7 \cdot 10^{+147}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 10^{-232}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 1.35 \cdot 10^{-80}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 2.7 \cdot 10^{+64}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* j (- (* a c) (* y i))) (* i (* t b))))
        (t_2 (* x (- (* y z) (* t a)))))
   (if (<= j -2.7e+147)
     t_1
     (if (<= j 1e-232)
       t_2
       (if (<= j 1.35e-80)
         (* z (- (* x y) (* b c)))
         (if (<= j 2.7e+64) 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 = (j * ((a * c) - (y * i))) + (i * (t * b));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (j <= -2.7e+147) {
		tmp = t_1;
	} else if (j <= 1e-232) {
		tmp = t_2;
	} else if (j <= 1.35e-80) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 2.7e+64) {
		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 = (j * ((a * c) - (y * i))) + (i * (t * b))
    t_2 = x * ((y * z) - (t * a))
    if (j <= (-2.7d+147)) then
        tmp = t_1
    else if (j <= 1d-232) then
        tmp = t_2
    else if (j <= 1.35d-80) then
        tmp = z * ((x * y) - (b * c))
    else if (j <= 2.7d+64) 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 = (j * ((a * c) - (y * i))) + (i * (t * b));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (j <= -2.7e+147) {
		tmp = t_1;
	} else if (j <= 1e-232) {
		tmp = t_2;
	} else if (j <= 1.35e-80) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 2.7e+64) {
		tmp = t_2;
	} 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))) + (i * (t * b))
	t_2 = x * ((y * z) - (t * a))
	tmp = 0
	if j <= -2.7e+147:
		tmp = t_1
	elif j <= 1e-232:
		tmp = t_2
	elif j <= 1.35e-80:
		tmp = z * ((x * y) - (b * c))
	elif j <= 2.7e+64:
		tmp = t_2
	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(i * Float64(t * b)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (j <= -2.7e+147)
		tmp = t_1;
	elseif (j <= 1e-232)
		tmp = t_2;
	elseif (j <= 1.35e-80)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (j <= 2.7e+64)
		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 = (j * ((a * c) - (y * i))) + (i * (t * b));
	t_2 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (j <= -2.7e+147)
		tmp = t_1;
	elseif (j <= 1e-232)
		tmp = t_2;
	elseif (j <= 1.35e-80)
		tmp = z * ((x * y) - (b * c));
	elseif (j <= 2.7e+64)
		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[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.7e+147], t$95$1, If[LessEqual[j, 1e-232], t$95$2, If[LessEqual[j, 1.35e-80], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.7e+64], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -2.69999999999999998e147 or 2.7e64 < j

   1. Initial program 67.4%

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

      1. +-commutative 67.4%

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

      2. fma-def 68.6%

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

      3. *-commutative 68.6%

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

      4. sub-neg 68.6%

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

      5. sub-neg 68.6%

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

      6. *-commutative 68.6%

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

   3. Simplified 68.6%

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

   5. Taylor expanded in i around inf 75.4%

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

      1. *-commutative 75.4%

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

      2. associate-*l* 77.7%

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

      3. *-commutative 77.7%

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

   7. Simplified 77.7%

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

      1. fma-udef 77.7%

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

      2. *-commutative 77.7%

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

      3. *-commutative 77.7%

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

   9. Applied egg-rr 77.7%

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

   if -2.69999999999999998e147 < j < 1.00000000000000002e-232 or 1.3500000000000001e-80 < j < 2.7e64

   1. Initial program 73.2%

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

   3. Taylor expanded in x around inf 56.7%

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

   if 1.00000000000000002e-232 < j < 1.3500000000000001e-80

   1. Initial program 75.9%

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

   3. Taylor expanded in z around inf 67.1%

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

      1. *-commutative 67.1%

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

      2. *-commutative 67.1%

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

   5. Simplified 67.1%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.7 \cdot 10^{+147}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;j \leq 10^{-232}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 1.35 \cdot 10^{-80}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 2.7 \cdot 10^{+64}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + i \cdot \left(t \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 57.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := t_1 + y \cdot \left(x \cdot z\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -2.3 \cdot 10^{+149}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-182}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+41}:\\ \;\;\;\;t_1 + i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+118}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+193}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i))))
        (t_2 (+ t_1 (* y (* x z))))
        (t_3 (* x (- (* y z) (* t a)))))
   (if (<= x -2.3e+149)
     t_3
     (if (<= x -4.2e-182)
       t_2
       (if (<= x 1.3e+41)
         (+ t_1 (* i (* t b)))
         (if (<= x 1.8e+118)
           t_2
           (if (<= x 7.5e+193) (* t (- (* b i) (* x a))) t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = t_1 + (y * (x * z));
	double t_3 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -2.3e+149) {
		tmp = t_3;
	} else if (x <= -4.2e-182) {
		tmp = t_2;
	} else if (x <= 1.3e+41) {
		tmp = t_1 + (i * (t * b));
	} else if (x <= 1.8e+118) {
		tmp = t_2;
	} else if (x <= 7.5e+193) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = t_1 + (y * (x * z))
    t_3 = x * ((y * z) - (t * a))
    if (x <= (-2.3d+149)) then
        tmp = t_3
    else if (x <= (-4.2d-182)) then
        tmp = t_2
    else if (x <= 1.3d+41) then
        tmp = t_1 + (i * (t * b))
    else if (x <= 1.8d+118) then
        tmp = t_2
    else if (x <= 7.5d+193) then
        tmp = t * ((b * i) - (x * a))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = t_1 + (y * (x * z));
	double t_3 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -2.3e+149) {
		tmp = t_3;
	} else if (x <= -4.2e-182) {
		tmp = t_2;
	} else if (x <= 1.3e+41) {
		tmp = t_1 + (i * (t * b));
	} else if (x <= 1.8e+118) {
		tmp = t_2;
	} else if (x <= 7.5e+193) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = t_1 + (y * (x * z))
	t_3 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -2.3e+149:
		tmp = t_3
	elif x <= -4.2e-182:
		tmp = t_2
	elif x <= 1.3e+41:
		tmp = t_1 + (i * (t * b))
	elif x <= 1.8e+118:
		tmp = t_2
	elif x <= 7.5e+193:
		tmp = t * ((b * i) - (x * a))
	else:
		tmp = t_3
	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_1 + Float64(y * Float64(x * z)))
	t_3 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -2.3e+149)
		tmp = t_3;
	elseif (x <= -4.2e-182)
		tmp = t_2;
	elseif (x <= 1.3e+41)
		tmp = Float64(t_1 + Float64(i * Float64(t * b)));
	elseif (x <= 1.8e+118)
		tmp = t_2;
	elseif (x <= 7.5e+193)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = t_1 + (y * (x * z));
	t_3 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -2.3e+149)
		tmp = t_3;
	elseif (x <= -4.2e-182)
		tmp = t_2;
	elseif (x <= 1.3e+41)
		tmp = t_1 + (i * (t * b));
	elseif (x <= 1.8e+118)
		tmp = t_2;
	elseif (x <= 7.5e+193)
		tmp = t * ((b * i) - (x * a));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.3e+149], t$95$3, If[LessEqual[x, -4.2e-182], t$95$2, If[LessEqual[x, 1.3e+41], N[(t$95$1 + N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.8e+118], t$95$2, If[LessEqual[x, 7.5e+193], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.2999999999999998e149 or 7.5000000000000008e193 < x

   1. Initial program 65.5%

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

   3. Taylor expanded in x around inf 80.1%

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

   if -2.2999999999999998e149 < x < -4.2000000000000001e-182 or 1.3e41 < x < 1.8e118

   1. Initial program 74.5%

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

   3. Taylor expanded in b around 0 70.1%

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

   4. Taylor expanded in y around inf 66.8%

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

      1. associate-*r* 31.5%

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

      2. *-commutative 31.5%

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

      3. associate-*r* 31.4%

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

   6. Simplified 67.9%

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

   if -4.2000000000000001e-182 < x < 1.3e41

   1. Initial program 72.3%

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

      1. +-commutative 72.3%

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

      2. fma-def 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. sub-neg 72.3%

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

      6. *-commutative 72.3%

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

   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 i around inf 62.1%

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

      1. *-commutative 62.1%

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

      2. associate-*l* 62.3%

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

      3. *-commutative 62.3%

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

   7. Simplified 62.3%

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

      1. fma-udef 62.3%

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

      2. *-commutative 62.3%

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

      3. *-commutative 62.3%

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

   9. Applied egg-rr 62.3%

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

   if 1.8e118 < x < 7.5000000000000008e193

   1. Initial program 74.7%

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

   3. Taylor expanded in t around inf 70.1%

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

      1. distribute-lft-out-- 70.1%

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

      2. *-commutative 70.1%

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

   5. Simplified 70.1%

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

   6. Taylor expanded in t around 0 70.1%

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

      1. mul-1-neg 70.1%

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

      2. *-commutative 70.1%

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

      3. *-commutative 70.1%

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

      4. cancel-sign-sub-inv 70.1%

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

      5. fma-def 70.1%

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

      6. distribute-rgt-neg-out 70.1%

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

      7. *-commutative 70.1%

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

      8. distribute-rgt-neg-in 70.1%

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

      9. fma-def 70.1%

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

      10. +-commutative 70.1%

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

      11. distribute-neg-in 70.1%

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

      12. remove-double-neg 70.1%

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

      13. *-commutative 70.1%

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

      14. *-commutative 70.1%

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

   8. Simplified 70.1%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+149}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-182}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+41}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+118}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+193}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 59.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -1.15 \cdot 10^{+149}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -155:\\ \;\;\;\;t_1 + y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-195}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{+48}:\\ \;\;\;\;t_1 + i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_2 - z \cdot \left(b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))) (t_2 (* x (- (* y z) (* t a)))))
   (if (<= x -1.15e+149)
     t_2
     (if (<= x -155.0)
       (+ t_1 (* y (* x z)))
       (if (<= x -2.9e-195)
         (+ (* a (* c j)) (* b (- (* t i) (* z c))))
         (if (<= x 5.4e+48) (+ t_1 (* i (* t b))) (- t_2 (* 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 = j * ((a * c) - (y * i));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.15e+149) {
		tmp = t_2;
	} else if (x <= -155.0) {
		tmp = t_1 + (y * (x * z));
	} else if (x <= -2.9e-195) {
		tmp = (a * (c * j)) + (b * ((t * i) - (z * c)));
	} else if (x <= 5.4e+48) {
		tmp = t_1 + (i * (t * b));
	} else {
		tmp = t_2 - (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) :: t_2
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = x * ((y * z) - (t * a))
    if (x <= (-1.15d+149)) then
        tmp = t_2
    else if (x <= (-155.0d0)) then
        tmp = t_1 + (y * (x * z))
    else if (x <= (-2.9d-195)) then
        tmp = (a * (c * j)) + (b * ((t * i) - (z * c)))
    else if (x <= 5.4d+48) then
        tmp = t_1 + (i * (t * b))
    else
        tmp = t_2 - (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 = j * ((a * c) - (y * i));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.15e+149) {
		tmp = t_2;
	} else if (x <= -155.0) {
		tmp = t_1 + (y * (x * z));
	} else if (x <= -2.9e-195) {
		tmp = (a * (c * j)) + (b * ((t * i) - (z * c)));
	} else if (x <= 5.4e+48) {
		tmp = t_1 + (i * (t * b));
	} else {
		tmp = t_2 - (z * (b * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -1.15e+149:
		tmp = t_2
	elif x <= -155.0:
		tmp = t_1 + (y * (x * z))
	elif x <= -2.9e-195:
		tmp = (a * (c * j)) + (b * ((t * i) - (z * c)))
	elif x <= 5.4e+48:
		tmp = t_1 + (i * (t * b))
	else:
		tmp = t_2 - (z * (b * c))
	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(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -1.15e+149)
		tmp = t_2;
	elseif (x <= -155.0)
		tmp = Float64(t_1 + Float64(y * Float64(x * z)));
	elseif (x <= -2.9e-195)
		tmp = Float64(Float64(a * Float64(c * j)) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	elseif (x <= 5.4e+48)
		tmp = Float64(t_1 + Float64(i * Float64(t * b)));
	else
		tmp = Float64(t_2 - 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 = j * ((a * c) - (y * i));
	t_2 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -1.15e+149)
		tmp = t_2;
	elseif (x <= -155.0)
		tmp = t_1 + (y * (x * z));
	elseif (x <= -2.9e-195)
		tmp = (a * (c * j)) + (b * ((t * i) - (z * c)));
	elseif (x <= 5.4e+48)
		tmp = t_1 + (i * (t * b));
	else
		tmp = t_2 - (z * (b * c));
	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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.15e+149], t$95$2, If[LessEqual[x, -155.0], N[(t$95$1 + N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.9e-195], N[(N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.4e+48], N[(t$95$1 + N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$2 - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.1499999999999999e149

   1. Initial program 59.9%

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

   3. Taylor expanded in x around inf 72.0%

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

   if -1.1499999999999999e149 < x < -155

   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 74.3%

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

   4. Taylor expanded in y around inf 74.9%

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

      1. associate-*r* 36.5%

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

      2. *-commutative 36.5%

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

      3. associate-*r* 33.4%

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

   6. Simplified 75.0%

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

   if -155 < x < -2.9000000000000002e-195

   1. Initial program 84.3%

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

   3. Taylor expanded in y around inf 81.5%

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

      1. *-commutative 81.5%

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

      2. associate-*l* 83.8%

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

   5. Simplified 83.8%

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

   6. Taylor expanded in y around 0 68.9%

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

      1. *-commutative 68.9%

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

      2. *-commutative 68.9%

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

      3. *-commutative 68.9%

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

   8. Simplified 68.9%

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

   if -2.9000000000000002e-195 < x < 5.40000000000000007e48

   1. Initial program 70.9%

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

      1. +-commutative 70.9%

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

      2. fma-def 70.9%

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

      3. *-commutative 70.9%

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

      4. sub-neg 70.9%

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

      5. sub-neg 70.9%

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

      6. *-commutative 70.9%

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

   3. Simplified 70.9%

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

   5. Taylor expanded in i around inf 60.6%

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

      1. *-commutative 60.6%

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

      2. associate-*l* 61.9%

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

      3. *-commutative 61.9%

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

   7. Simplified 61.9%

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

      1. fma-udef 61.9%

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

      2. *-commutative 61.9%

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

      3. *-commutative 61.9%

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

   9. Applied egg-rr 61.9%

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

   if 5.40000000000000007e48 < x

   1. Initial program 69.8%

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

      1. add-cube-cbrt 69.6%

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

      2. pow3 69.6%

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

   4. Applied egg-rr 69.6%

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

   5. Taylor expanded in i around 0 75.6%

      \[\leadsto \color{blue}{\left(a \cdot \left(c \cdot j\right) + \left(i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + {1}^{0.3333333333333333} \cdot \left(x \cdot \left(y \cdot z - a \cdot t\right)\right)\right)\right) - b \cdot \left(c \cdot z\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 77.0%

         \[\leadsto \left(a \cdot \left(c \cdot j\right) + \left(i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + {1}^{0.3333333333333333} \cdot \left(x \cdot \left(y \cdot z - a \cdot t\right)\right)\right)\right) - \color{blue}{\left(b \cdot c\right) \cdot z} \]

      2. fma-def 78.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, c \cdot j, i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + {1}^{0.3333333333333333} \cdot \left(x \cdot \left(y \cdot z - a \cdot t\right)\right)\right)} - \left(b \cdot c\right) \cdot z \]

      3. *-commutative 78.5%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{j \cdot c}, i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + {1}^{0.3333333333333333} \cdot \left(x \cdot \left(y \cdot z - a \cdot t\right)\right)\right) - \left(b \cdot c\right) \cdot z \]

      4. fma-def 86.1%

         \[\leadsto \mathsf{fma}\left(a, j \cdot c, \color{blue}{\mathsf{fma}\left(i, -1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right), {1}^{0.3333333333333333} \cdot \left(x \cdot \left(y \cdot z - a \cdot t\right)\right)\right)}\right) - \left(b \cdot c\right) \cdot z \]

      5. distribute-lft-out-- 86.1%

         \[\leadsto \mathsf{fma}\left(a, j \cdot c, \mathsf{fma}\left(i, \color{blue}{-1 \cdot \left(j \cdot y - b \cdot t\right)}, {1}^{0.3333333333333333} \cdot \left(x \cdot \left(y \cdot z - a \cdot t\right)\right)\right)\right) - \left(b \cdot c\right) \cdot z \]

      6. *-commutative 86.1%

         \[\leadsto \mathsf{fma}\left(a, j \cdot c, \mathsf{fma}\left(i, -1 \cdot \left(\color{blue}{y \cdot j} - b \cdot t\right), {1}^{0.3333333333333333} \cdot \left(x \cdot \left(y \cdot z - a \cdot t\right)\right)\right)\right) - \left(b \cdot c\right) \cdot z \]

      7. *-commutative 86.1%

         \[\leadsto \mathsf{fma}\left(a, j \cdot c, \mathsf{fma}\left(i, -1 \cdot \left(y \cdot j - \color{blue}{t \cdot b}\right), {1}^{0.3333333333333333} \cdot \left(x \cdot \left(y \cdot z - a \cdot t\right)\right)\right)\right) - \left(b \cdot c\right) \cdot z \]

      8. pow-base-1 86.1%

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

      9. *-commutative 86.1%

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

   7. Simplified 86.1%

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

   8. Taylor expanded in x around inf 74.9%

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

      1. *-commutative 74.9%

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

   10. Simplified 74.9%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+149}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -155:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-195}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{+48}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 58.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := t_1 - j \cdot \left(y \cdot i\right)\\ \mathbf{if}\;x \leq -4 \cdot 10^{-33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-195}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-145}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{+108}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1 - z \cdot \left(b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (- t_1 (* j (* y i)))))
   (if (<= x -4e-33)
     t_2
     (if (<= x -3e-195)
       (+ (* a (* c j)) (* b (- (* t i) (* z c))))
       (if (<= x 2.05e-145)
         (+ (* j (- (* a c) (* y i))) (* i (* t b)))
         (if (<= x 1.95e+108) t_2 (- t_1 (* 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 = x * ((y * z) - (t * a));
	double t_2 = t_1 - (j * (y * i));
	double tmp;
	if (x <= -4e-33) {
		tmp = t_2;
	} else if (x <= -3e-195) {
		tmp = (a * (c * j)) + (b * ((t * i) - (z * c)));
	} else if (x <= 2.05e-145) {
		tmp = (j * ((a * c) - (y * i))) + (i * (t * b));
	} else if (x <= 1.95e+108) {
		tmp = t_2;
	} else {
		tmp = t_1 - (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) :: t_2
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = t_1 - (j * (y * i))
    if (x <= (-4d-33)) then
        tmp = t_2
    else if (x <= (-3d-195)) then
        tmp = (a * (c * j)) + (b * ((t * i) - (z * c)))
    else if (x <= 2.05d-145) then
        tmp = (j * ((a * c) - (y * i))) + (i * (t * b))
    else if (x <= 1.95d+108) then
        tmp = t_2
    else
        tmp = t_1 - (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 = x * ((y * z) - (t * a));
	double t_2 = t_1 - (j * (y * i));
	double tmp;
	if (x <= -4e-33) {
		tmp = t_2;
	} else if (x <= -3e-195) {
		tmp = (a * (c * j)) + (b * ((t * i) - (z * c)));
	} else if (x <= 2.05e-145) {
		tmp = (j * ((a * c) - (y * i))) + (i * (t * b));
	} else if (x <= 1.95e+108) {
		tmp = t_2;
	} else {
		tmp = t_1 - (z * (b * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = t_1 - (j * (y * i))
	tmp = 0
	if x <= -4e-33:
		tmp = t_2
	elif x <= -3e-195:
		tmp = (a * (c * j)) + (b * ((t * i) - (z * c)))
	elif x <= 2.05e-145:
		tmp = (j * ((a * c) - (y * i))) + (i * (t * b))
	elif x <= 1.95e+108:
		tmp = t_2
	else:
		tmp = t_1 - (z * (b * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(t_1 - Float64(j * Float64(y * i)))
	tmp = 0.0
	if (x <= -4e-33)
		tmp = t_2;
	elseif (x <= -3e-195)
		tmp = Float64(Float64(a * Float64(c * j)) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	elseif (x <= 2.05e-145)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(i * Float64(t * b)));
	elseif (x <= 1.95e+108)
		tmp = t_2;
	else
		tmp = Float64(t_1 - 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 = x * ((y * z) - (t * a));
	t_2 = t_1 - (j * (y * i));
	tmp = 0.0;
	if (x <= -4e-33)
		tmp = t_2;
	elseif (x <= -3e-195)
		tmp = (a * (c * j)) + (b * ((t * i) - (z * c)));
	elseif (x <= 2.05e-145)
		tmp = (j * ((a * c) - (y * i))) + (i * (t * b));
	elseif (x <= 1.95e+108)
		tmp = t_2;
	else
		tmp = t_1 - (z * (b * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - N[(j * N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4e-33], t$95$2, If[LessEqual[x, -3e-195], N[(N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.05e-145], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.95e+108], t$95$2, N[(t$95$1 - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.0000000000000002e-33 or 2.0499999999999999e-145 < x < 1.94999999999999992e108

   1. Initial program 68.2%

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

   3. Taylor expanded in b around 0 73.6%

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

   4. Taylor expanded in a around 0 71.2%

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

      1. associate-*r* 71.2%

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

      2. neg-mul-1 71.2%

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

      3. *-commutative 71.2%

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

   6. Simplified 71.2%

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

   if -4.0000000000000002e-33 < x < -3e-195

   1. Initial program 87.2%

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

   3. Taylor expanded in y around inf 87.0%

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

      1. *-commutative 87.0%

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

      2. associate-*l* 89.9%

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

   5. Simplified 89.9%

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

   6. Taylor expanded in y around 0 74.7%

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

      1. *-commutative 74.7%

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

      2. *-commutative 74.7%

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

      3. *-commutative 74.7%

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

   8. Simplified 74.7%

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

   if -3e-195 < x < 2.0499999999999999e-145

   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-def 70.3%

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

      3. *-commutative 70.3%

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

      4. sub-neg 70.3%

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

      5. sub-neg 70.3%

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

      6. *-commutative 70.3%

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

   3. Simplified 70.3%

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

   5. Taylor expanded in i around inf 68.9%

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

      1. *-commutative 68.9%

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

      2. associate-*l* 67.5%

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

      3. *-commutative 67.5%

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

   7. Simplified 67.5%

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

      1. fma-udef 67.5%

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

      2. *-commutative 67.5%

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

      3. *-commutative 67.5%

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

   9. Applied egg-rr 67.5%

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

   if 1.94999999999999992e108 < x

   1. Initial program 71.9%

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

      1. add-cube-cbrt 71.7%

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

      2. pow3 71.7%

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

   4. Applied egg-rr 71.7%

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

   5. Taylor expanded in i around 0 77.7%

      \[\leadsto \color{blue}{\left(a \cdot \left(c \cdot j\right) + \left(i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + {1}^{0.3333333333333333} \cdot \left(x \cdot \left(y \cdot z - a \cdot t\right)\right)\right)\right) - b \cdot \left(c \cdot z\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 77.7%

         \[\leadsto \left(a \cdot \left(c \cdot j\right) + \left(i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + {1}^{0.3333333333333333} \cdot \left(x \cdot \left(y \cdot z - a \cdot t\right)\right)\right)\right) - \color{blue}{\left(b \cdot c\right) \cdot z} \]

      2. fma-def 77.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, c \cdot j, i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + {1}^{0.3333333333333333} \cdot \left(x \cdot \left(y \cdot z - a \cdot t\right)\right)\right)} - \left(b \cdot c\right) \cdot z \]

      3. *-commutative 77.7%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{j \cdot c}, i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right) + {1}^{0.3333333333333333} \cdot \left(x \cdot \left(y \cdot z - a \cdot t\right)\right)\right) - \left(b \cdot c\right) \cdot z \]

      4. fma-def 87.7%

         \[\leadsto \mathsf{fma}\left(a, j \cdot c, \color{blue}{\mathsf{fma}\left(i, -1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right), {1}^{0.3333333333333333} \cdot \left(x \cdot \left(y \cdot z - a \cdot t\right)\right)\right)}\right) - \left(b \cdot c\right) \cdot z \]

      5. distribute-lft-out-- 87.7%

         \[\leadsto \mathsf{fma}\left(a, j \cdot c, \mathsf{fma}\left(i, \color{blue}{-1 \cdot \left(j \cdot y - b \cdot t\right)}, {1}^{0.3333333333333333} \cdot \left(x \cdot \left(y \cdot z - a \cdot t\right)\right)\right)\right) - \left(b \cdot c\right) \cdot z \]

      6. *-commutative 87.7%

         \[\leadsto \mathsf{fma}\left(a, j \cdot c, \mathsf{fma}\left(i, -1 \cdot \left(\color{blue}{y \cdot j} - b \cdot t\right), {1}^{0.3333333333333333} \cdot \left(x \cdot \left(y \cdot z - a \cdot t\right)\right)\right)\right) - \left(b \cdot c\right) \cdot z \]

      7. *-commutative 87.7%

         \[\leadsto \mathsf{fma}\left(a, j \cdot c, \mathsf{fma}\left(i, -1 \cdot \left(y \cdot j - \color{blue}{t \cdot b}\right), {1}^{0.3333333333333333} \cdot \left(x \cdot \left(y \cdot z - a \cdot t\right)\right)\right)\right) - \left(b \cdot c\right) \cdot z \]

      8. pow-base-1 87.7%

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

      9. *-commutative 87.7%

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

   7. Simplified 87.7%

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

   8. Taylor expanded in x around inf 76.4%

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

      1. *-commutative 76.4%

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

   10. Simplified 76.4%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-33}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - j \cdot \left(y \cdot i\right)\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-195}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-145}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{+108}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - j \cdot \left(y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 50.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -2 \cdot 10^{+224}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -2.7 \cdot 10^{+207}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -2.6 \cdot 10^{+104}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 1.2 \cdot 10^{-231}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 2.75 \cdot 10^{-81}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 6.5 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (* j (- (* a c) (* y i)))))
   (if (<= j -2e+224)
     t_2
     (if (<= j -2.7e+207)
       (* b (- (* t i) (* z c)))
       (if (<= j -2.6e+104)
         t_2
         (if (<= j 1.2e-231)
           t_1
           (if (<= j 2.75e-81)
             (* z (- (* x y) (* b c)))
             (if (<= j 6.5e+51) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -2e+224) {
		tmp = t_2;
	} else if (j <= -2.7e+207) {
		tmp = b * ((t * i) - (z * c));
	} else if (j <= -2.6e+104) {
		tmp = t_2;
	} else if (j <= 1.2e-231) {
		tmp = t_1;
	} else if (j <= 2.75e-81) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 6.5e+51) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = j * ((a * c) - (y * i))
    if (j <= (-2d+224)) then
        tmp = t_2
    else if (j <= (-2.7d+207)) then
        tmp = b * ((t * i) - (z * c))
    else if (j <= (-2.6d+104)) then
        tmp = t_2
    else if (j <= 1.2d-231) then
        tmp = t_1
    else if (j <= 2.75d-81) then
        tmp = z * ((x * y) - (b * c))
    else if (j <= 6.5d+51) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -2e+224) {
		tmp = t_2;
	} else if (j <= -2.7e+207) {
		tmp = b * ((t * i) - (z * c));
	} else if (j <= -2.6e+104) {
		tmp = t_2;
	} else if (j <= 1.2e-231) {
		tmp = t_1;
	} else if (j <= 2.75e-81) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 6.5e+51) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -2e+224:
		tmp = t_2
	elif j <= -2.7e+207:
		tmp = b * ((t * i) - (z * c))
	elif j <= -2.6e+104:
		tmp = t_2
	elif j <= 1.2e-231:
		tmp = t_1
	elif j <= 2.75e-81:
		tmp = z * ((x * y) - (b * c))
	elif j <= 6.5e+51:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -2e+224)
		tmp = t_2;
	elseif (j <= -2.7e+207)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (j <= -2.6e+104)
		tmp = t_2;
	elseif (j <= 1.2e-231)
		tmp = t_1;
	elseif (j <= 2.75e-81)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (j <= 6.5e+51)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -2e+224)
		tmp = t_2;
	elseif (j <= -2.7e+207)
		tmp = b * ((t * i) - (z * c));
	elseif (j <= -2.6e+104)
		tmp = t_2;
	elseif (j <= 1.2e-231)
		tmp = t_1;
	elseif (j <= 2.75e-81)
		tmp = z * ((x * y) - (b * c));
	elseif (j <= 6.5e+51)
		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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2e+224], t$95$2, If[LessEqual[j, -2.7e+207], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.6e+104], t$95$2, If[LessEqual[j, 1.2e-231], t$95$1, If[LessEqual[j, 2.75e-81], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6.5e+51], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.99999999999999994e224 or -2.70000000000000025e207 < j < -2.6e104 or 6.5e51 < j

   1. Initial program 68.2%

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

   3. Taylor expanded in j around inf 77.1%

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

   if -1.99999999999999994e224 < j < -2.70000000000000025e207

   1. Initial program 66.7%

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

   3. Taylor expanded in b around inf 84.3%

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

   if -2.6e104 < j < 1.19999999999999996e-231 or 2.75000000000000013e-81 < j < 6.5e51

   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 x around inf 57.0%

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

   if 1.19999999999999996e-231 < j < 2.75000000000000013e-81

   1. Initial program 75.9%

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

   3. Taylor expanded in z around inf 67.1%

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

      1. *-commutative 67.1%

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

      2. *-commutative 67.1%

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

   5. Simplified 67.1%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2 \cdot 10^{+224}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -2.7 \cdot 10^{+207}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -2.6 \cdot 10^{+104}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 1.2 \cdot 10^{-231}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 2.75 \cdot 10^{-81}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 6.5 \cdot 10^{+51}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 50.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -2 \cdot 10^{+224}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -2.7 \cdot 10^{+207}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -7.5 \cdot 10^{+103} \lor \neg \left(j \leq 1.25 \cdot 10^{+51}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (<= j -2e+224)
     t_1
     (if (<= j -2.7e+207)
       (* b (- (* t i) (* z c)))
       (if (or (<= j -7.5e+103) (not (<= j 1.25e+51)))
         t_1
         (* x (- (* y z) (* t a))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -2e+224) {
		tmp = t_1;
	} else if (j <= -2.7e+207) {
		tmp = b * ((t * i) - (z * c));
	} else if ((j <= -7.5e+103) || !(j <= 1.25e+51)) {
		tmp = t_1;
	} else {
		tmp = x * ((y * z) - (t * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    if (j <= (-2d+224)) then
        tmp = t_1
    else if (j <= (-2.7d+207)) then
        tmp = b * ((t * i) - (z * c))
    else if ((j <= (-7.5d+103)) .or. (.not. (j <= 1.25d+51))) then
        tmp = t_1
    else
        tmp = x * ((y * z) - (t * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -2e+224) {
		tmp = t_1;
	} else if (j <= -2.7e+207) {
		tmp = b * ((t * i) - (z * c));
	} else if ((j <= -7.5e+103) || !(j <= 1.25e+51)) {
		tmp = t_1;
	} else {
		tmp = x * ((y * z) - (t * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -2e+224:
		tmp = t_1
	elif j <= -2.7e+207:
		tmp = b * ((t * i) - (z * c))
	elif (j <= -7.5e+103) or not (j <= 1.25e+51):
		tmp = t_1
	else:
		tmp = x * ((y * z) - (t * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -2e+224)
		tmp = t_1;
	elseif (j <= -2.7e+207)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif ((j <= -7.5e+103) || !(j <= 1.25e+51))
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -2e+224)
		tmp = t_1;
	elseif (j <= -2.7e+207)
		tmp = b * ((t * i) - (z * c));
	elseif ((j <= -7.5e+103) || ~((j <= 1.25e+51)))
		tmp = t_1;
	else
		tmp = x * ((y * z) - (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2e+224], t$95$1, If[LessEqual[j, -2.7e+207], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[j, -7.5e+103], N[Not[LessEqual[j, 1.25e+51]], $MachinePrecision]], t$95$1, N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.99999999999999994e224 or -2.70000000000000025e207 < j < -7.49999999999999922e103 or 1.25e51 < j

   1. Initial program 68.2%

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

   3. Taylor expanded in j around inf 77.1%

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

   if -1.99999999999999994e224 < j < -2.70000000000000025e207

   1. Initial program 66.7%

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

   3. Taylor expanded in b around inf 84.3%

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

   if -7.49999999999999922e103 < j < 1.25e51

   1. Initial program 73.7%

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

   3. Taylor expanded in x around inf 55.5%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2 \cdot 10^{+224}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -2.7 \cdot 10^{+207}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -7.5 \cdot 10^{+103} \lor \neg \left(j \leq 1.25 \cdot 10^{+51}\right):\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 28.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot t\right) \cdot \left(-a\right)\\ t_2 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;j \leq -3.5 \cdot 10^{+142}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -1.9 \cdot 10^{-128}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 1.15 \cdot 10^{-296}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 3.15 \cdot 10^{-53}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 3.6 \cdot 10^{+77}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* x t) (- a))) (t_2 (* a (* c j))))
   (if (<= j -3.5e+142)
     t_2
     (if (<= j -1.9e-128)
       (* y (* x z))
       (if (<= j 1.15e-296)
         t_1
         (if (<= j 3.15e-53) (* x (* y z)) (if (<= j 3.6e+77) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * t) * -a;
	double t_2 = a * (c * j);
	double tmp;
	if (j <= -3.5e+142) {
		tmp = t_2;
	} else if (j <= -1.9e-128) {
		tmp = y * (x * z);
	} else if (j <= 1.15e-296) {
		tmp = t_1;
	} else if (j <= 3.15e-53) {
		tmp = x * (y * z);
	} else if (j <= 3.6e+77) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * t) * -a
    t_2 = a * (c * j)
    if (j <= (-3.5d+142)) then
        tmp = t_2
    else if (j <= (-1.9d-128)) then
        tmp = y * (x * z)
    else if (j <= 1.15d-296) then
        tmp = t_1
    else if (j <= 3.15d-53) then
        tmp = x * (y * z)
    else if (j <= 3.6d+77) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * t) * -a;
	double t_2 = a * (c * j);
	double tmp;
	if (j <= -3.5e+142) {
		tmp = t_2;
	} else if (j <= -1.9e-128) {
		tmp = y * (x * z);
	} else if (j <= 1.15e-296) {
		tmp = t_1;
	} else if (j <= 3.15e-53) {
		tmp = x * (y * z);
	} else if (j <= 3.6e+77) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (x * t) * -a
	t_2 = a * (c * j)
	tmp = 0
	if j <= -3.5e+142:
		tmp = t_2
	elif j <= -1.9e-128:
		tmp = y * (x * z)
	elif j <= 1.15e-296:
		tmp = t_1
	elif j <= 3.15e-53:
		tmp = x * (y * z)
	elif j <= 3.6e+77:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(x * t) * Float64(-a))
	t_2 = Float64(a * Float64(c * j))
	tmp = 0.0
	if (j <= -3.5e+142)
		tmp = t_2;
	elseif (j <= -1.9e-128)
		tmp = Float64(y * Float64(x * z));
	elseif (j <= 1.15e-296)
		tmp = t_1;
	elseif (j <= 3.15e-53)
		tmp = Float64(x * Float64(y * z));
	elseif (j <= 3.6e+77)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (x * t) * -a;
	t_2 = a * (c * j);
	tmp = 0.0;
	if (j <= -3.5e+142)
		tmp = t_2;
	elseif (j <= -1.9e-128)
		tmp = y * (x * z);
	elseif (j <= 1.15e-296)
		tmp = t_1;
	elseif (j <= 3.15e-53)
		tmp = x * (y * z);
	elseif (j <= 3.6e+77)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(x * t), $MachinePrecision] * (-a)), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.5e+142], t$95$2, If[LessEqual[j, -1.9e-128], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.15e-296], t$95$1, If[LessEqual[j, 3.15e-53], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.6e+77], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -3.49999999999999997e142 or 3.5999999999999998e77 < j

   1. Initial program 68.3%

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

      1. add-cube-cbrt 68.3%

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

      2. pow3 68.3%

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

   4. Applied egg-rr 68.3%

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

   5. Taylor expanded in a around inf 49.3%

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

      1. *-commutative 49.3%

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

   7. Simplified 49.3%

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

   if -3.49999999999999997e142 < j < -1.9000000000000001e-128

   1. Initial program 76.8%

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

   3. Taylor expanded in x around inf 59.4%

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

   4. Taylor expanded in y around inf 44.3%

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

      1. associate-*r* 45.4%

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

      2. *-commutative 45.4%

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

      3. associate-*r* 47.4%

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

   6. Simplified 47.4%

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

   if -1.9000000000000001e-128 < j < 1.15000000000000002e-296 or 3.14999999999999989e-53 < j < 3.5999999999999998e77

   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 a around inf 44.6%

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

      1. +-commutative 44.6%

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

      2. mul-1-neg 44.6%

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

      3. unsub-neg 44.6%

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

      4. *-commutative 44.6%

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

   5. Simplified 44.6%

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

   6. Taylor expanded in j around 0 38.9%

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

      1. associate-*r* 38.9%

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

      2. neg-mul-1 38.9%

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

   8. Simplified 38.9%

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

   if 1.15000000000000002e-296 < j < 3.14999999999999989e-53

   1. Initial program 77.3%

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

   3. Taylor expanded in x around inf 57.0%

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

   4. Taylor expanded in y around inf 46.5%

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

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.5 \cdot 10^{+142}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq -1.9 \cdot 10^{-128}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 1.15 \cdot 10^{-296}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;j \leq 3.15 \cdot 10^{-53}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 3.6 \cdot 10^{+77}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 28.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;j \leq -2.6 \cdot 10^{+142}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -5.3 \cdot 10^{-126}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 9 \cdot 10^{-301}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;j \leq 1.16 \cdot 10^{-58}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 7.2 \cdot 10^{+77}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))))
   (if (<= j -2.6e+142)
     t_1
     (if (<= j -5.3e-126)
       (* y (* x z))
       (if (<= j 9e-301)
         (* (* x t) (- a))
         (if (<= j 1.16e-58)
           (* x (* y z))
           (if (<= j 7.2e+77) (* (* t a) (- x)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double tmp;
	if (j <= -2.6e+142) {
		tmp = t_1;
	} else if (j <= -5.3e-126) {
		tmp = y * (x * z);
	} else if (j <= 9e-301) {
		tmp = (x * t) * -a;
	} else if (j <= 1.16e-58) {
		tmp = x * (y * z);
	} else if (j <= 7.2e+77) {
		tmp = (t * a) * -x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (c * j)
    if (j <= (-2.6d+142)) then
        tmp = t_1
    else if (j <= (-5.3d-126)) then
        tmp = y * (x * z)
    else if (j <= 9d-301) then
        tmp = (x * t) * -a
    else if (j <= 1.16d-58) then
        tmp = x * (y * z)
    else if (j <= 7.2d+77) then
        tmp = (t * a) * -x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double tmp;
	if (j <= -2.6e+142) {
		tmp = t_1;
	} else if (j <= -5.3e-126) {
		tmp = y * (x * z);
	} else if (j <= 9e-301) {
		tmp = (x * t) * -a;
	} else if (j <= 1.16e-58) {
		tmp = x * (y * z);
	} else if (j <= 7.2e+77) {
		tmp = (t * a) * -x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	tmp = 0
	if j <= -2.6e+142:
		tmp = t_1
	elif j <= -5.3e-126:
		tmp = y * (x * z)
	elif j <= 9e-301:
		tmp = (x * t) * -a
	elif j <= 1.16e-58:
		tmp = x * (y * z)
	elif j <= 7.2e+77:
		tmp = (t * a) * -x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	tmp = 0.0
	if (j <= -2.6e+142)
		tmp = t_1;
	elseif (j <= -5.3e-126)
		tmp = Float64(y * Float64(x * z));
	elseif (j <= 9e-301)
		tmp = Float64(Float64(x * t) * Float64(-a));
	elseif (j <= 1.16e-58)
		tmp = Float64(x * Float64(y * z));
	elseif (j <= 7.2e+77)
		tmp = Float64(Float64(t * a) * Float64(-x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (c * j);
	tmp = 0.0;
	if (j <= -2.6e+142)
		tmp = t_1;
	elseif (j <= -5.3e-126)
		tmp = y * (x * z);
	elseif (j <= 9e-301)
		tmp = (x * t) * -a;
	elseif (j <= 1.16e-58)
		tmp = x * (y * z);
	elseif (j <= 7.2e+77)
		tmp = (t * a) * -x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.6e+142], t$95$1, If[LessEqual[j, -5.3e-126], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 9e-301], N[(N[(x * t), $MachinePrecision] * (-a)), $MachinePrecision], If[LessEqual[j, 1.16e-58], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7.2e+77], N[(N[(t * a), $MachinePrecision] * (-x)), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -2.60000000000000021e142 or 7.1999999999999996e77 < j

   1. Initial program 68.3%

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

      1. add-cube-cbrt 68.3%

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

      2. pow3 68.3%

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

   4. Applied egg-rr 68.3%

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

   5. Taylor expanded in a around inf 49.3%

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

      1. *-commutative 49.3%

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

   7. Simplified 49.3%

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

   if -2.60000000000000021e142 < j < -5.29999999999999995e-126

   1. Initial program 76.8%

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

   3. Taylor expanded in x around inf 59.4%

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

   4. Taylor expanded in y around inf 44.3%

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

      1. associate-*r* 45.4%

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

      2. *-commutative 45.4%

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

      3. associate-*r* 47.4%

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

   6. Simplified 47.4%

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

   if -5.29999999999999995e-126 < j < 9.00000000000000039e-301

   1. Initial program 71.0%

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

   3. Taylor expanded in a around inf 42.4%

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

      1. +-commutative 42.4%

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

      2. mul-1-neg 42.4%

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

      3. unsub-neg 42.4%

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

      4. *-commutative 42.4%

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

   5. Simplified 42.4%

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

   6. Taylor expanded in j around 0 38.8%

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

      1. associate-*r* 38.8%

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

      2. neg-mul-1 38.8%

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

   8. Simplified 38.8%

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

   if 9.00000000000000039e-301 < j < 1.16000000000000007e-58

   1. Initial program 77.3%

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

   3. Taylor expanded in x around inf 57.0%

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

   4. Taylor expanded in y around inf 46.5%

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

   if 1.16000000000000007e-58 < j < 7.1999999999999996e77

   1. Initial program 66.1%

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

   3. Taylor expanded in a around inf 47.2%

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

      1. +-commutative 47.2%

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

      2. mul-1-neg 47.2%

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

      3. unsub-neg 47.2%

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

      4. *-commutative 47.2%

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

   5. Simplified 47.2%

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

   6. Taylor expanded in j around 0 39.1%

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

      1. mul-1-neg 39.1%

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

      2. associate-*r* 41.5%

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

      3. *-commutative 41.5%

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

      4. distribute-rgt-neg-in 41.5%

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

      5. *-commutative 41.5%

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

   8. Simplified 41.5%

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

4. Final simplification 45.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.6 \cdot 10^{+142}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq -5.3 \cdot 10^{-126}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 9 \cdot 10^{-301}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;j \leq 1.16 \cdot 10^{-58}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 7.2 \cdot 10^{+77}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 40.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+127}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{+65}:\\ \;\;\;\;-i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+209}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -1.9e+127)
   (* x (* y z))
   (if (<= y -1.2e+65)
     (- (* i (* y j)))
     (if (<= y 1.35e+209) (* a (- (* c j) (* x t))) (* y (* x z))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -1.9e+127) {
		tmp = x * (y * z);
	} else if (y <= -1.2e+65) {
		tmp = -(i * (y * j));
	} else if (y <= 1.35e+209) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-1.9d+127)) then
        tmp = x * (y * z)
    else if (y <= (-1.2d+65)) then
        tmp = -(i * (y * j))
    else if (y <= 1.35d+209) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = y * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -1.9e+127) {
		tmp = x * (y * z);
	} else if (y <= -1.2e+65) {
		tmp = -(i * (y * j));
	} else if (y <= 1.35e+209) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -1.9e+127:
		tmp = x * (y * z)
	elif y <= -1.2e+65:
		tmp = -(i * (y * j))
	elif y <= 1.35e+209:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -1.9e+127)
		tmp = Float64(x * Float64(y * z));
	elseif (y <= -1.2e+65)
		tmp = Float64(-Float64(i * Float64(y * j)));
	elseif (y <= 1.35e+209)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -1.9e+127)
		tmp = x * (y * z);
	elseif (y <= -1.2e+65)
		tmp = -(i * (y * j));
	elseif (y <= 1.35e+209)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -1.9e+127], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.2e+65], (-N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), If[LessEqual[y, 1.35e+209], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.8999999999999999e127

   1. Initial program 66.1%

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

   3. Taylor expanded in x around inf 62.7%

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

   4. Taylor expanded in y around inf 58.2%

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

   if -1.8999999999999999e127 < y < -1.2000000000000001e65

   1. Initial program 72.6%

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

      1. add-cube-cbrt 72.3%

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

      2. pow3 72.3%

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

   4. Applied egg-rr 72.3%

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

   5. Taylor expanded in y around inf 63.2%

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

      1. mul-1-neg 63.2%

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

      2. distribute-rgt-neg-in 63.2%

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

      3. *-commutative 63.2%

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

      4. distribute-rgt-neg-in 63.2%

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

   7. Simplified 63.2%

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

   if -1.2000000000000001e65 < y < 1.35e209

   1. Initial program 75.9%

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

   3. Taylor expanded in a around inf 52.0%

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

      1. +-commutative 52.0%

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

      2. mul-1-neg 52.0%

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

      3. unsub-neg 52.0%

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

      4. *-commutative 52.0%

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

   5. Simplified 52.0%

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

   if 1.35e209 < y

   1. Initial program 48.2%

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

   3. Taylor expanded in x around inf 53.4%

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

   4. Taylor expanded in y around inf 53.5%

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

      1. associate-*r* 53.7%

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

      2. *-commutative 53.7%

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

      3. associate-*r* 57.8%

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

   6. Simplified 57.8%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+127}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{+65}:\\ \;\;\;\;-i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+209}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 29.5% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{-96} \lor \neg \left(a \leq 2 \cdot 10^{-31}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -2.4e-96) (not (<= a 2e-31))) (* 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 ((a <= -2.4e-96) || !(a <= 2e-31)) {
		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 ((a <= (-2.4d-96)) .or. (.not. (a <= 2d-31))) 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 ((a <= -2.4e-96) || !(a <= 2e-31)) {
		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 (a <= -2.4e-96) or not (a <= 2e-31):
		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 ((a <= -2.4e-96) || !(a <= 2e-31))
		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 ((a <= -2.4e-96) || ~((a <= 2e-31)))
		tmp = a * (c * j);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -2.4e-96], N[Not[LessEqual[a, 2e-31]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.40000000000000019e-96 or 2e-31 < a

   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. Step-by-step derivation

      1. add-cube-cbrt 66.8%

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

      2. pow3 66.9%

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

   4. Applied egg-rr 66.9%

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

   5. Taylor expanded in a around inf 34.3%

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

      1. *-commutative 34.3%

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

   7. Simplified 34.3%

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

   if -2.40000000000000019e-96 < a < 2e-31

   1. Initial program 79.0%

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

      1. add-cube-cbrt 78.8%

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

      2. pow3 78.7%

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

   4. Applied egg-rr 78.7%

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

   5. Taylor expanded in t around inf 29.2%

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

      1. *-commutative 29.2%

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

   7. Simplified 29.2%

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

4. Final simplification 32.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{-96} \lor \neg \left(a \leq 2 \cdot 10^{-31}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 30.0% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{-100} \lor \neg \left(a \leq 1.04 \cdot 10^{-32}\right):\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -1.9e-100) (not (<= a 1.04e-32))) (* j (* a c)) (* 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 ((a <= -1.9e-100) || !(a <= 1.04e-32)) {
		tmp = j * (a * c);
	} 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 ((a <= (-1.9d-100)) .or. (.not. (a <= 1.04d-32))) then
        tmp = j * (a * c)
    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 ((a <= -1.9e-100) || !(a <= 1.04e-32)) {
		tmp = j * (a * c);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (a <= -1.9e-100) or not (a <= 1.04e-32):
		tmp = j * (a * c)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -1.9e-100) || !(a <= 1.04e-32))
		tmp = Float64(j * Float64(a * c));
	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 ((a <= -1.9e-100) || ~((a <= 1.04e-32)))
		tmp = j * (a * c);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -1.9e-100], N[Not[LessEqual[a, 1.04e-32]], $MachinePrecision]], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.89999999999999999e-100 or 1.03999999999999998e-32 < a

   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. Step-by-step derivation

      1. add-cube-cbrt 66.8%

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

      2. pow3 66.9%

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

   4. Applied egg-rr 66.9%

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

   5. Taylor expanded in j around inf 46.4%

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

      1. *-commutative 46.4%

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

   7. Simplified 46.4%

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

   8. Taylor expanded in a around inf 34.3%

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

      1. associate-*r* 35.8%

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

      2. *-commutative 35.8%

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

   10. Simplified 35.8%

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

   if -1.89999999999999999e-100 < a < 1.03999999999999998e-32

   1. Initial program 79.0%

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

      1. add-cube-cbrt 78.8%

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

      2. pow3 78.7%

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

   4. Applied egg-rr 78.7%

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

   5. Taylor expanded in t around inf 29.2%

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

      1. *-commutative 29.2%

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

   7. Simplified 29.2%

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

4. Final simplification 33.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{-100} \lor \neg \left(a \leq 1.04 \cdot 10^{-32}\right):\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 29.4% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.1 \cdot 10^{+144} \lor \neg \left(j \leq 12500000\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -1.1e+144) (not (<= j 12500000.0)))
   (* a (* c j))
   (* x (* y z))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -1.1e+144) || !(j <= 12500000.0)) {
		tmp = a * (c * j);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((j <= (-1.1d+144)) .or. (.not. (j <= 12500000.0d0))) then
        tmp = a * (c * j)
    else
        tmp = x * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -1.1e+144) || !(j <= 12500000.0)) {
		tmp = a * (c * j);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -1.1e+144) or not (j <= 12500000.0):
		tmp = a * (c * j)
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -1.1e+144) || !(j <= 12500000.0))
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -1.1e+144) || ~((j <= 12500000.0)))
		tmp = a * (c * j);
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -1.1e+144], N[Not[LessEqual[j, 12500000.0]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -1.09999999999999994e144 or 1.25e7 < j

   1. Initial program 66.7%

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

      1. add-cube-cbrt 66.6%

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

      2. pow3 66.6%

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

   4. Applied egg-rr 66.6%

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

   5. Taylor expanded in a around inf 42.5%

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

      1. *-commutative 42.5%

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

   7. Simplified 42.5%

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

   if -1.09999999999999994e144 < j < 1.25e7

   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 x around inf 56.1%

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

   4. Taylor expanded in y around inf 35.3%

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

4. Final simplification 38.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.1 \cdot 10^{+144} \lor \neg \left(j \leq 12500000\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 29.6% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -6.5 \cdot 10^{+142} \lor \neg \left(j \leq 15000000\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -6.5e+142) (not (<= j 15000000.0)))
   (* a (* c j))
   (* y (* x z))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -6.5e+142) || !(j <= 15000000.0)) {
		tmp = a * (c * j);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((j <= (-6.5d+142)) .or. (.not. (j <= 15000000.0d0))) then
        tmp = a * (c * j)
    else
        tmp = y * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -6.5e+142) || !(j <= 15000000.0)) {
		tmp = a * (c * j);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -6.5e+142) or not (j <= 15000000.0):
		tmp = a * (c * j)
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -6.5e+142) || !(j <= 15000000.0))
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -6.5e+142) || ~((j <= 15000000.0)))
		tmp = a * (c * j);
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -6.5e+142], N[Not[LessEqual[j, 15000000.0]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -6.4999999999999997e142 or 1.5e7 < j

   1. Initial program 66.7%

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

      1. add-cube-cbrt 66.6%

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

      2. pow3 66.6%

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

   4. Applied egg-rr 66.6%

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

   5. Taylor expanded in a around inf 42.5%

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

      1. *-commutative 42.5%

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

   7. Simplified 42.5%

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

   if -6.4999999999999997e142 < j < 1.5e7

   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 x around inf 56.1%

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

   4. Taylor expanded in y around inf 35.3%

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

      1. associate-*r* 32.0%

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

      2. *-commutative 32.0%

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

      3. associate-*r* 35.8%

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

   6. Simplified 35.8%

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

4. Final simplification 38.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -6.5 \cdot 10^{+142} \lor \neg \left(j \leq 15000000\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 23.2% accurate, 5.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 71.7%

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

   1. add-cube-cbrt 71.5%

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

   2. pow3 71.5%

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

4. Applied egg-rr 71.5%

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

5. Taylor expanded in a around inf 22.9%

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

   1. *-commutative 22.9%

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

7. Simplified 22.9%

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

8. Final simplification 22.9%

   \[\leadsto a \cdot \left(c \cdot j\right) \]
9. Add Preprocessing

Developer target: 58.9% 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 2024010 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

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

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