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

Percentage Accurate: 74.4% → 83.6%

Time: 25.5s

Alternatives: 28

Speedup: 0.5×

• 57.7% 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: 74.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 83.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot c - x \cdot y\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;t_2 \leq \infty:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;z \cdot \sqrt[3]{\left(x \cdot y - b \cdot c\right) \cdot \left(t_1 \cdot t_1\right)}\\ \end{array} \end{array} \]

FPCore

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

C

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

Java

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, Infinity], t$95$2, N[(z * N[Power[N[(N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision] * N[(t$95$1 * t$95$1), $MachinePrecision]), $MachinePrecision], 1/3], $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 91.4%

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

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

   1. Initial program 0.0%

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

      1. associate-+l- 0.0%

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

      2. *-commutative 0.0%

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

      3. sub-neg 0.0%

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

      4. sub-neg 0.0%

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

      5. *-commutative 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in z around inf 49.0%

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

      1. add-cbrt-cube 55.6%

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

      2. fma-neg 55.6%

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

      3. *-commutative 55.6%

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

      4. fma-neg 55.6%

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

      5. *-commutative 55.6%

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

      6. fma-neg 57.3%

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

      7. *-commutative 57.3%

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

   6. Applied egg-rr 57.3%

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

      1. associate-*l* 57.3%

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

      2. fma-neg 55.6%

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

      3. *-commutative 55.6%

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

      4. *-commutative 55.6%

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

      5. fma-neg 55.6%

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

      6. *-commutative 55.6%

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

      7. *-commutative 55.6%

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

      8. fma-neg 55.6%

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

      9. *-commutative 55.6%

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

      10. *-commutative 55.6%

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

   8. Simplified 55.6%

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

4. Final simplification 83.3%

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

Alternative 2: 83.1% accurate, 0.5× speedup

Math

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

FPCore

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

Python

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

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(t * i) - Float64(z * c)))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + 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 = ((x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))) + (j * ((a * c) - (y * i)));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = (y * ((x * z) - (i * j))) + (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[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 91.4%

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

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

   1. Initial program 0.0%

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

      1. +-commutative 0.0%

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

      2. fma-def 12.1%

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

      3. *-commutative 12.1%

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

      4. *-commutative 12.1%

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

   3. Simplified 12.1%

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

   4. Taylor expanded in b around 0 24.1%

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

   5. Taylor expanded in a around -inf 41.5%

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

      1. +-commutative 41.5%

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

      2. mul-1-neg 41.5%

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

      3. unsub-neg 41.5%

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

      4. associate-*r* 39.8%

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

      5. *-commutative 39.8%

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

      6. associate-*r* 38.1%

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

      7. neg-mul-1 38.1%

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

      8. distribute-rgt-neg-in 38.1%

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

      9. mul-1-neg 38.1%

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

      10. distribute-lft-in 50.1%

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

      11. +-commutative 50.1%

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

      12. mul-1-neg 50.1%

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

      13. unsub-neg 50.1%

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

      14. *-commutative 50.1%

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

      15. *-commutative 50.1%

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

   7. Simplified 50.1%

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

4. Final simplification 82.1%

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

Alternative 3: 63.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right) + a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;b \leq -5 \cdot 10^{+41}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) + t_1\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{-272}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 10^{-202}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-115}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{-54}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{+54}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1 - y \cdot \left(i \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c))))
        (t_2 (+ (* y (- (* x z) (* i j))) (* a (- (* c j) (* x t))))))
   (if (<= b -5e+41)
     (+ (* z (* x y)) t_1)
     (if (<= b 3.5e-272)
       t_2
       (if (<= b 1e-202)
         (* t (- (* b i) (* x a)))
         (if (<= b 8e-115)
           t_2
           (if (<= b 7.5e-54)
             (* z (- (* x y) (* b c)))
             (if (<= b 4.6e+54) t_2 (- t_1 (* y (* i j)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = (y * ((x * z) - (i * j))) + (a * ((c * j) - (x * t)));
	double tmp;
	if (b <= -5e+41) {
		tmp = (z * (x * y)) + t_1;
	} else if (b <= 3.5e-272) {
		tmp = t_2;
	} else if (b <= 1e-202) {
		tmp = t * ((b * i) - (x * a));
	} else if (b <= 8e-115) {
		tmp = t_2;
	} else if (b <= 7.5e-54) {
		tmp = z * ((x * y) - (b * c));
	} else if (b <= 4.6e+54) {
		tmp = t_2;
	} else {
		tmp = t_1 - (y * (i * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = (y * ((x * z) - (i * j))) + (a * ((c * j) - (x * t)))
    if (b <= (-5d+41)) then
        tmp = (z * (x * y)) + t_1
    else if (b <= 3.5d-272) then
        tmp = t_2
    else if (b <= 1d-202) then
        tmp = t * ((b * i) - (x * a))
    else if (b <= 8d-115) then
        tmp = t_2
    else if (b <= 7.5d-54) then
        tmp = z * ((x * y) - (b * c))
    else if (b <= 4.6d+54) then
        tmp = t_2
    else
        tmp = t_1 - (y * (i * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = (y * ((x * z) - (i * j))) + (a * ((c * j) - (x * t)));
	double tmp;
	if (b <= -5e+41) {
		tmp = (z * (x * y)) + t_1;
	} else if (b <= 3.5e-272) {
		tmp = t_2;
	} else if (b <= 1e-202) {
		tmp = t * ((b * i) - (x * a));
	} else if (b <= 8e-115) {
		tmp = t_2;
	} else if (b <= 7.5e-54) {
		tmp = z * ((x * y) - (b * c));
	} else if (b <= 4.6e+54) {
		tmp = t_2;
	} else {
		tmp = t_1 - (y * (i * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = (y * ((x * z) - (i * j))) + (a * ((c * j) - (x * t)))
	tmp = 0
	if b <= -5e+41:
		tmp = (z * (x * y)) + t_1
	elif b <= 3.5e-272:
		tmp = t_2
	elif b <= 1e-202:
		tmp = t * ((b * i) - (x * a))
	elif b <= 8e-115:
		tmp = t_2
	elif b <= 7.5e-54:
		tmp = z * ((x * y) - (b * c))
	elif b <= 4.6e+54:
		tmp = t_2
	else:
		tmp = t_1 - (y * (i * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(a * Float64(Float64(c * j) - Float64(x * t))))
	tmp = 0.0
	if (b <= -5e+41)
		tmp = Float64(Float64(z * Float64(x * y)) + t_1);
	elseif (b <= 3.5e-272)
		tmp = t_2;
	elseif (b <= 1e-202)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (b <= 8e-115)
		tmp = t_2;
	elseif (b <= 7.5e-54)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (b <= 4.6e+54)
		tmp = t_2;
	else
		tmp = Float64(t_1 - Float64(y * Float64(i * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = (y * ((x * z) - (i * j))) + (a * ((c * j) - (x * t)));
	tmp = 0.0;
	if (b <= -5e+41)
		tmp = (z * (x * y)) + t_1;
	elseif (b <= 3.5e-272)
		tmp = t_2;
	elseif (b <= 1e-202)
		tmp = t * ((b * i) - (x * a));
	elseif (b <= 8e-115)
		tmp = t_2;
	elseif (b <= 7.5e-54)
		tmp = z * ((x * y) - (b * c));
	elseif (b <= 4.6e+54)
		tmp = t_2;
	else
		tmp = t_1 - (y * (i * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5e+41], N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[b, 3.5e-272], t$95$2, If[LessEqual[b, 1e-202], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8e-115], t$95$2, If[LessEqual[b, 7.5e-54], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.6e+54], t$95$2, N[(t$95$1 - N[(y * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -5.00000000000000022e41

   1. Initial program 69.4%

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

      1. +-commutative 69.4%

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

      2. fma-def 74.0%

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

      3. *-commutative 74.0%

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

      4. *-commutative 74.0%

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

   3. Simplified 74.0%

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

   4. Taylor expanded in a around 0 72.7%

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

   5. Taylor expanded in j around 0 69.9%

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

      1. *-commutative 69.9%

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

      2. associate-*r* 74.3%

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

      3. *-commutative 74.3%

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

      4. *-commutative 74.3%

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

      5. *-commutative 74.3%

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

      6. *-commutative 74.3%

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

   7. Simplified 74.3%

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

   if -5.00000000000000022e41 < b < 3.4999999999999997e-272 or 1e-202 < b < 8.0000000000000004e-115 or 7.5000000000000005e-54 < b < 4.59999999999999988e54

   1. Initial program 71.8%

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

      1. +-commutative 71.8%

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

      2. fma-def 74.3%

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

      3. *-commutative 74.3%

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

      4. *-commutative 74.3%

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

   3. Simplified 74.3%

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

   4. Taylor expanded in b around 0 69.3%

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

   5. Taylor expanded in a around -inf 68.1%

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

      1. +-commutative 68.1%

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

      2. mul-1-neg 68.1%

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

      3. unsub-neg 68.1%

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

      4. associate-*r* 68.4%

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

      5. *-commutative 68.4%

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

      6. associate-*r* 69.7%

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

      7. neg-mul-1 69.7%

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

      8. distribute-rgt-neg-in 69.7%

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

      9. mul-1-neg 69.7%

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

      10. distribute-lft-in 74.0%

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

      11. +-commutative 74.0%

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

      12. mul-1-neg 74.0%

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

      13. unsub-neg 74.0%

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

      14. *-commutative 74.0%

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

      15. *-commutative 74.0%

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

   7. Simplified 74.0%

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

   if 3.4999999999999997e-272 < b < 1e-202

   1. Initial program 56.3%

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

      1. associate-+l- 56.3%

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

      2. *-commutative 56.3%

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

      3. sub-neg 56.3%

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

      4. sub-neg 56.3%

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

      5. *-commutative 56.3%

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

   3. Simplified 56.3%

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

   4. Taylor expanded in t around inf 75.7%

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

      1. distribute-lft-out-- 75.7%

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

      2. associate-*r* 75.7%

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

      3. mul-1-neg 75.7%

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

      4. *-commutative 75.7%

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

   6. Simplified 75.7%

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

   if 8.0000000000000004e-115 < b < 7.5000000000000005e-54

   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. Step-by-step derivation

      1. associate-+l- 65.5%

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

      2. *-commutative 65.5%

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

      3. sub-neg 65.5%

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

      4. sub-neg 65.5%

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

      5. *-commutative 65.5%

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

   3. Simplified 65.5%

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

   4. Taylor expanded in z around inf 82.0%

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

   if 4.59999999999999988e54 < b

   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. Step-by-step derivation

      1. +-commutative 76.0%

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

      2. fma-def 76.0%

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

      3. *-commutative 76.0%

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

      4. *-commutative 76.0%

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

   3. Simplified 76.0%

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

   4. Taylor expanded in a around 0 67.3%

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

   5. Taylor expanded in x around 0 74.0%

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

      1. *-commutative 74.0%

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

      2. *-commutative 74.0%

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

      3. *-commutative 74.0%

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

      4. mul-1-neg 74.0%

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

      5. associate-*r* 76.1%

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

      6. *-commutative 76.1%

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

      7. associate-*r* 76.1%

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

      8. distribute-rgt-neg-in 76.1%

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

      9. *-commutative 76.1%

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

      10. distribute-rgt-neg-in 76.1%

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

   7. Simplified 76.1%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+41}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{-272}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 10^{-202}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-115}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{-54}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{+54}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - y \cdot \left(i \cdot j\right)\\ \end{array} \]

Alternative 4: 63.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_3 := t_2 + a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;b \leq -1.3 \cdot 10^{+37}:\\ \;\;\;\;t_2 + t_1\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{-272}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 10^{-202}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-115}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-54}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{+54}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1 - y \cdot \left(i \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c))))
        (t_2 (* y (- (* x z) (* i j))))
        (t_3 (+ t_2 (* a (- (* c j) (* x t))))))
   (if (<= b -1.3e+37)
     (+ t_2 t_1)
     (if (<= b 3.5e-272)
       t_3
       (if (<= b 1e-202)
         (* t (- (* b i) (* x a)))
         (if (<= b 8e-115)
           t_3
           (if (<= b 7e-54)
             (* z (- (* x y) (* b c)))
             (if (<= b 1.25e+54) t_3 (- t_1 (* y (* i j)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = t_2 + (a * ((c * j) - (x * t)));
	double tmp;
	if (b <= -1.3e+37) {
		tmp = t_2 + t_1;
	} else if (b <= 3.5e-272) {
		tmp = t_3;
	} else if (b <= 1e-202) {
		tmp = t * ((b * i) - (x * a));
	} else if (b <= 8e-115) {
		tmp = t_3;
	} else if (b <= 7e-54) {
		tmp = z * ((x * y) - (b * c));
	} else if (b <= 1.25e+54) {
		tmp = t_3;
	} else {
		tmp = t_1 - (y * (i * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = y * ((x * z) - (i * j))
    t_3 = t_2 + (a * ((c * j) - (x * t)))
    if (b <= (-1.3d+37)) then
        tmp = t_2 + t_1
    else if (b <= 3.5d-272) then
        tmp = t_3
    else if (b <= 1d-202) then
        tmp = t * ((b * i) - (x * a))
    else if (b <= 8d-115) then
        tmp = t_3
    else if (b <= 7d-54) then
        tmp = z * ((x * y) - (b * c))
    else if (b <= 1.25d+54) then
        tmp = t_3
    else
        tmp = t_1 - (y * (i * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = t_2 + (a * ((c * j) - (x * t)));
	double tmp;
	if (b <= -1.3e+37) {
		tmp = t_2 + t_1;
	} else if (b <= 3.5e-272) {
		tmp = t_3;
	} else if (b <= 1e-202) {
		tmp = t * ((b * i) - (x * a));
	} else if (b <= 8e-115) {
		tmp = t_3;
	} else if (b <= 7e-54) {
		tmp = z * ((x * y) - (b * c));
	} else if (b <= 1.25e+54) {
		tmp = t_3;
	} else {
		tmp = t_1 - (y * (i * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = y * ((x * z) - (i * j))
	t_3 = t_2 + (a * ((c * j) - (x * t)))
	tmp = 0
	if b <= -1.3e+37:
		tmp = t_2 + t_1
	elif b <= 3.5e-272:
		tmp = t_3
	elif b <= 1e-202:
		tmp = t * ((b * i) - (x * a))
	elif b <= 8e-115:
		tmp = t_3
	elif b <= 7e-54:
		tmp = z * ((x * y) - (b * c))
	elif b <= 1.25e+54:
		tmp = t_3
	else:
		tmp = t_1 - (y * (i * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_3 = Float64(t_2 + Float64(a * Float64(Float64(c * j) - Float64(x * t))))
	tmp = 0.0
	if (b <= -1.3e+37)
		tmp = Float64(t_2 + t_1);
	elseif (b <= 3.5e-272)
		tmp = t_3;
	elseif (b <= 1e-202)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (b <= 8e-115)
		tmp = t_3;
	elseif (b <= 7e-54)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (b <= 1.25e+54)
		tmp = t_3;
	else
		tmp = Float64(t_1 - Float64(y * Float64(i * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = y * ((x * z) - (i * j));
	t_3 = t_2 + (a * ((c * j) - (x * t)));
	tmp = 0.0;
	if (b <= -1.3e+37)
		tmp = t_2 + t_1;
	elseif (b <= 3.5e-272)
		tmp = t_3;
	elseif (b <= 1e-202)
		tmp = t * ((b * i) - (x * a));
	elseif (b <= 8e-115)
		tmp = t_3;
	elseif (b <= 7e-54)
		tmp = z * ((x * y) - (b * c));
	elseif (b <= 1.25e+54)
		tmp = t_3;
	else
		tmp = t_1 - (y * (i * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.3e+37], N[(t$95$2 + t$95$1), $MachinePrecision], If[LessEqual[b, 3.5e-272], t$95$3, If[LessEqual[b, 1e-202], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8e-115], t$95$3, If[LessEqual[b, 7e-54], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.25e+54], t$95$3, N[(t$95$1 - N[(y * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.3e37

   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. associate-+l- 70.3%

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

      2. *-commutative 70.3%

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

      3. sub-neg 70.3%

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

      4. sub-neg 70.3%

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

      5. *-commutative 70.3%

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

   3. Simplified 70.3%

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

      1. add-cube-cbrt 70.3%

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

      2. pow3 70.3%

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

      3. *-commutative 70.3%

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

   5. Applied egg-rr 70.3%

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

   6. Taylor expanded in a around 0 73.5%

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

      1. neg-mul-1 73.5%

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

      2. distribute-rgt-neg-in 73.5%

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

      3. mul-1-neg 73.5%

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

      4. pow-base-1 73.5%

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

      5. *-lft-identity 73.5%

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

      6. distribute-lft-in 75.0%

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

      7. +-commutative 75.0%

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

      8. mul-1-neg 75.0%

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

      9. unsub-neg 75.0%

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

      10. *-commutative 75.0%

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

      11. *-commutative 75.0%

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

      12. *-commutative 75.0%

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

      13. *-commutative 75.0%

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

      14. *-commutative 75.0%

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

   8. Simplified 75.0%

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

   if -1.3e37 < b < 3.4999999999999997e-272 or 1e-202 < b < 8.0000000000000004e-115 or 6.99999999999999964e-54 < b < 1.25000000000000001e54

   1. Initial program 71.3%

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

      1. +-commutative 71.3%

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

      2. fma-def 73.9%

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

      3. *-commutative 73.9%

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

      4. *-commutative 73.9%

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

   3. Simplified 73.9%

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

   4. Taylor expanded in b around 0 69.6%

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

   5. Taylor expanded in a around -inf 68.4%

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

      1. +-commutative 68.4%

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

      2. mul-1-neg 68.4%

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

      3. unsub-neg 68.4%

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

      4. associate-*r* 68.7%

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

      5. *-commutative 68.7%

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

      6. associate-*r* 70.0%

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

      7. neg-mul-1 70.0%

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

      8. distribute-rgt-neg-in 70.0%

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

      9. mul-1-neg 70.0%

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

      10. distribute-lft-in 74.4%

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

      11. +-commutative 74.4%

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

      12. mul-1-neg 74.4%

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

      13. unsub-neg 74.4%

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

      14. *-commutative 74.4%

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

      15. *-commutative 74.4%

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

   7. Simplified 74.4%

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

   if 3.4999999999999997e-272 < b < 1e-202

   1. Initial program 56.3%

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

      1. associate-+l- 56.3%

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

      2. *-commutative 56.3%

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

      3. sub-neg 56.3%

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

      4. sub-neg 56.3%

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

      5. *-commutative 56.3%

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

   3. Simplified 56.3%

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

   4. Taylor expanded in t around inf 75.7%

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

      1. distribute-lft-out-- 75.7%

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

      2. associate-*r* 75.7%

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

      3. mul-1-neg 75.7%

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

      4. *-commutative 75.7%

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

   6. Simplified 75.7%

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

   if 8.0000000000000004e-115 < b < 6.99999999999999964e-54

   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. Step-by-step derivation

      1. associate-+l- 65.5%

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

      2. *-commutative 65.5%

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

      3. sub-neg 65.5%

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

      4. sub-neg 65.5%

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

      5. *-commutative 65.5%

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

   3. Simplified 65.5%

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

   4. Taylor expanded in z around inf 82.0%

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

   if 1.25000000000000001e54 < b

   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. Step-by-step derivation

      1. +-commutative 76.0%

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

      2. fma-def 76.0%

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

      3. *-commutative 76.0%

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

      4. *-commutative 76.0%

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

   3. Simplified 76.0%

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

   4. Taylor expanded in a around 0 67.3%

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

   5. Taylor expanded in x around 0 74.0%

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

      1. *-commutative 74.0%

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

      2. *-commutative 74.0%

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

      3. *-commutative 74.0%

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

      4. mul-1-neg 74.0%

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

      5. associate-*r* 76.1%

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

      6. *-commutative 76.1%

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

      7. associate-*r* 76.1%

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

      8. distribute-rgt-neg-in 76.1%

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

      9. *-commutative 76.1%

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

      10. distribute-rgt-neg-in 76.1%

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

   7. Simplified 76.1%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{+37}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{-272}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 10^{-202}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-115}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-54}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{+54}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - y \cdot \left(i \cdot j\right)\\ \end{array} \]

Alternative 5: 66.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := \left(c \cdot \left(a \cdot j\right) - x \cdot \left(t \cdot a - y \cdot z\right)\right) - c \cdot \left(z \cdot b\right)\\ t_3 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_4 := t_3 + a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;b \leq -4.9 \cdot 10^{+36}:\\ \;\;\;\;t_3 + t_1\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{-240}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq 5.1 \cdot 10^{-210}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-133}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-40}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c))))
        (t_2 (- (- (* c (* a j)) (* x (- (* t a) (* y z)))) (* c (* z b))))
        (t_3 (* y (- (* x z) (* i j))))
        (t_4 (+ t_3 (* a (- (* c j) (* x t))))))
   (if (<= b -4.9e+36)
     (+ t_3 t_1)
     (if (<= b -2.9e-240)
       t_4
       (if (<= b 5.1e-210)
         t_2
         (if (<= b 1.6e-133)
           t_4
           (if (<= b 1.4e-40) t_2 (+ (* j (- (* a c) (* y i))) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = ((c * (a * j)) - (x * ((t * a) - (y * z)))) - (c * (z * b));
	double t_3 = y * ((x * z) - (i * j));
	double t_4 = t_3 + (a * ((c * j) - (x * t)));
	double tmp;
	if (b <= -4.9e+36) {
		tmp = t_3 + t_1;
	} else if (b <= -2.9e-240) {
		tmp = t_4;
	} else if (b <= 5.1e-210) {
		tmp = t_2;
	} else if (b <= 1.6e-133) {
		tmp = t_4;
	} else if (b <= 1.4e-40) {
		tmp = t_2;
	} else {
		tmp = (j * ((a * c) - (y * i))) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = ((c * (a * j)) - (x * ((t * a) - (y * z)))) - (c * (z * b))
    t_3 = y * ((x * z) - (i * j))
    t_4 = t_3 + (a * ((c * j) - (x * t)))
    if (b <= (-4.9d+36)) then
        tmp = t_3 + t_1
    else if (b <= (-2.9d-240)) then
        tmp = t_4
    else if (b <= 5.1d-210) then
        tmp = t_2
    else if (b <= 1.6d-133) then
        tmp = t_4
    else if (b <= 1.4d-40) then
        tmp = t_2
    else
        tmp = (j * ((a * c) - (y * i))) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = ((c * (a * j)) - (x * ((t * a) - (y * z)))) - (c * (z * b));
	double t_3 = y * ((x * z) - (i * j));
	double t_4 = t_3 + (a * ((c * j) - (x * t)));
	double tmp;
	if (b <= -4.9e+36) {
		tmp = t_3 + t_1;
	} else if (b <= -2.9e-240) {
		tmp = t_4;
	} else if (b <= 5.1e-210) {
		tmp = t_2;
	} else if (b <= 1.6e-133) {
		tmp = t_4;
	} else if (b <= 1.4e-40) {
		tmp = t_2;
	} else {
		tmp = (j * ((a * c) - (y * i))) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = ((c * (a * j)) - (x * ((t * a) - (y * z)))) - (c * (z * b))
	t_3 = y * ((x * z) - (i * j))
	t_4 = t_3 + (a * ((c * j) - (x * t)))
	tmp = 0
	if b <= -4.9e+36:
		tmp = t_3 + t_1
	elif b <= -2.9e-240:
		tmp = t_4
	elif b <= 5.1e-210:
		tmp = t_2
	elif b <= 1.6e-133:
		tmp = t_4
	elif b <= 1.4e-40:
		tmp = t_2
	else:
		tmp = (j * ((a * c) - (y * i))) + t_1
	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(Float64(c * Float64(a * j)) - Float64(x * Float64(Float64(t * a) - Float64(y * z)))) - Float64(c * Float64(z * b)))
	t_3 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_4 = Float64(t_3 + Float64(a * Float64(Float64(c * j) - Float64(x * t))))
	tmp = 0.0
	if (b <= -4.9e+36)
		tmp = Float64(t_3 + t_1);
	elseif (b <= -2.9e-240)
		tmp = t_4;
	elseif (b <= 5.1e-210)
		tmp = t_2;
	elseif (b <= 1.6e-133)
		tmp = t_4;
	elseif (b <= 1.4e-40)
		tmp = t_2;
	else
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + t_1);
	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 = ((c * (a * j)) - (x * ((t * a) - (y * z)))) - (c * (z * b));
	t_3 = y * ((x * z) - (i * j));
	t_4 = t_3 + (a * ((c * j) - (x * t)));
	tmp = 0.0;
	if (b <= -4.9e+36)
		tmp = t_3 + t_1;
	elseif (b <= -2.9e-240)
		tmp = t_4;
	elseif (b <= 5.1e-210)
		tmp = t_2;
	elseif (b <= 1.6e-133)
		tmp = t_4;
	elseif (b <= 1.4e-40)
		tmp = t_2;
	else
		tmp = (j * ((a * c) - (y * i))) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 + N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.9e+36], N[(t$95$3 + t$95$1), $MachinePrecision], If[LessEqual[b, -2.9e-240], t$95$4, If[LessEqual[b, 5.1e-210], t$95$2, If[LessEqual[b, 1.6e-133], t$95$4, If[LessEqual[b, 1.4e-40], t$95$2, N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -4.89999999999999981e36

   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. associate-+l- 70.3%

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

      2. *-commutative 70.3%

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

      3. sub-neg 70.3%

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

      4. sub-neg 70.3%

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

      5. *-commutative 70.3%

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

   3. Simplified 70.3%

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

      1. add-cube-cbrt 70.3%

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

      2. pow3 70.3%

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

      3. *-commutative 70.3%

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

   5. Applied egg-rr 70.3%

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

   6. Taylor expanded in a around 0 73.5%

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

      1. neg-mul-1 73.5%

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

      2. distribute-rgt-neg-in 73.5%

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

      3. mul-1-neg 73.5%

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

      4. pow-base-1 73.5%

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

      5. *-lft-identity 73.5%

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

      6. distribute-lft-in 75.0%

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

      7. +-commutative 75.0%

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

      8. mul-1-neg 75.0%

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

      9. unsub-neg 75.0%

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

      10. *-commutative 75.0%

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

      11. *-commutative 75.0%

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

      12. *-commutative 75.0%

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

      13. *-commutative 75.0%

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

      14. *-commutative 75.0%

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

   8. Simplified 75.0%

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

   if -4.89999999999999981e36 < b < -2.9000000000000002e-240 or 5.09999999999999995e-210 < b < 1.60000000000000006e-133

   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 73.0%

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

      3. *-commutative 73.0%

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

      4. *-commutative 73.0%

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

   3. Simplified 73.0%

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

   4. Taylor expanded in b around 0 70.0%

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

   5. Taylor expanded in a around -inf 73.9%

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

      1. +-commutative 73.9%

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

      2. mul-1-neg 73.9%

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

      3. unsub-neg 73.9%

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

      4. associate-*r* 73.9%

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

      5. *-commutative 73.9%

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

      6. associate-*r* 78.1%

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

      7. neg-mul-1 78.1%

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

      8. distribute-rgt-neg-in 78.1%

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

      9. mul-1-neg 78.1%

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

      10. distribute-lft-in 79.5%

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

      11. +-commutative 79.5%

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

      12. mul-1-neg 79.5%

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

      13. unsub-neg 79.5%

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

      14. *-commutative 79.5%

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

      15. *-commutative 79.5%

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

   7. Simplified 79.5%

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

   if -2.9000000000000002e-240 < b < 5.09999999999999995e-210 or 1.60000000000000006e-133 < b < 1.4e-40

   1. Initial program 61.4%

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

      1. associate-+l- 61.4%

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

      2. *-commutative 61.4%

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

      3. sub-neg 61.4%

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

      4. sub-neg 61.4%

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

      5. *-commutative 61.4%

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

   3. Simplified 61.4%

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

   4. Taylor expanded in i around 0 76.3%

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

   if 1.4e-40 < b

   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. Step-by-step derivation

      1. +-commutative 79.0%

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

      2. fma-def 79.0%

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

      3. *-commutative 79.0%

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

      4. *-commutative 79.0%

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

   3. Simplified 79.0%

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

   4. Taylor expanded in x around 0 83.8%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.9 \cdot 10^{+36}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{-240}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 5.1 \cdot 10^{-210}:\\ \;\;\;\;\left(c \cdot \left(a \cdot j\right) - x \cdot \left(t \cdot a - y \cdot z\right)\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-133}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-40}:\\ \;\;\;\;\left(c \cdot \left(a \cdot j\right) - x \cdot \left(t \cdot a - y \cdot z\right)\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 6: 50.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right) - y \cdot \left(i \cdot j\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -7 \cdot 10^{+90}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -1.4 \cdot 10^{+52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -2.5 \cdot 10^{-140}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq -2.3 \cdot 10^{-305}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 6.5 \cdot 10^{-38}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 3.55 \cdot 10^{+158}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* x (- (* y z) (* t a))) (* y (* i j))))
        (t_2 (* j (- (* a c) (* y i)))))
   (if (<= j -7e+90)
     t_2
     (if (<= j -1.4e+52)
       t_1
       (if (<= j -2.5e-140)
         (* c (- (* a j) (* z b)))
         (if (<= j -2.3e-305)
           (* t (- (* b i) (* x a)))
           (if (<= j 6.5e-38)
             (* z (- (* x y) (* b c)))
             (if (<= j 3.55e+158) 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))) - (y * (i * j));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -7e+90) {
		tmp = t_2;
	} else if (j <= -1.4e+52) {
		tmp = t_1;
	} else if (j <= -2.5e-140) {
		tmp = c * ((a * j) - (z * b));
	} else if (j <= -2.3e-305) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 6.5e-38) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 3.55e+158) {
		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))) - (y * (i * j))
    t_2 = j * ((a * c) - (y * i))
    if (j <= (-7d+90)) then
        tmp = t_2
    else if (j <= (-1.4d+52)) then
        tmp = t_1
    else if (j <= (-2.5d-140)) then
        tmp = c * ((a * j) - (z * b))
    else if (j <= (-2.3d-305)) then
        tmp = t * ((b * i) - (x * a))
    else if (j <= 6.5d-38) then
        tmp = z * ((x * y) - (b * c))
    else if (j <= 3.55d+158) 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))) - (y * (i * j));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -7e+90) {
		tmp = t_2;
	} else if (j <= -1.4e+52) {
		tmp = t_1;
	} else if (j <= -2.5e-140) {
		tmp = c * ((a * j) - (z * b));
	} else if (j <= -2.3e-305) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 6.5e-38) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 3.55e+158) {
		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))) - (y * (i * j))
	t_2 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -7e+90:
		tmp = t_2
	elif j <= -1.4e+52:
		tmp = t_1
	elif j <= -2.5e-140:
		tmp = c * ((a * j) - (z * b))
	elif j <= -2.3e-305:
		tmp = t * ((b * i) - (x * a))
	elif j <= 6.5e-38:
		tmp = z * ((x * y) - (b * c))
	elif j <= 3.55e+158:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(y * Float64(i * j)))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -7e+90)
		tmp = t_2;
	elseif (j <= -1.4e+52)
		tmp = t_1;
	elseif (j <= -2.5e-140)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (j <= -2.3e-305)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (j <= 6.5e-38)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (j <= 3.55e+158)
		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))) - (y * (i * j));
	t_2 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -7e+90)
		tmp = t_2;
	elseif (j <= -1.4e+52)
		tmp = t_1;
	elseif (j <= -2.5e-140)
		tmp = c * ((a * j) - (z * b));
	elseif (j <= -2.3e-305)
		tmp = t * ((b * i) - (x * a));
	elseif (j <= 6.5e-38)
		tmp = z * ((x * y) - (b * c));
	elseif (j <= 3.55e+158)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -7e+90], t$95$2, If[LessEqual[j, -1.4e+52], t$95$1, If[LessEqual[j, -2.5e-140], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.3e-305], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6.5e-38], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.55e+158], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -6.9999999999999997e90 or 3.5499999999999998e158 < j

   1. Initial program 69.2%

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

      1. associate-+l- 69.2%

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

      2. *-commutative 69.2%

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

      3. sub-neg 69.2%

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

      4. sub-neg 69.2%

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

      5. *-commutative 69.2%

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

   3. Simplified 69.2%

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

      1. add-cube-cbrt 69.2%

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

      2. pow3 69.2%

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

      3. *-commutative 69.2%

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

   5. Applied egg-rr 69.2%

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

   6. Taylor expanded in j around -inf 75.9%

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

   if -6.9999999999999997e90 < j < -1.4e52 or 6.49999999999999949e-38 < j < 3.5499999999999998e158

   1. Initial program 71.2%

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

      1. +-commutative 71.2%

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

      2. fma-def 80.8%

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

      3. *-commutative 80.8%

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

      4. *-commutative 80.8%

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

   3. Simplified 80.8%

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

   4. Taylor expanded in b around 0 69.6%

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

   5. Taylor expanded in c around 0 63.9%

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

      1. *-commutative 63.9%

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

      2. *-commutative 63.9%

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

      3. *-commutative 63.9%

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

      4. associate-*r* 69.7%

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

      5. *-commutative 69.7%

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

      6. associate-*r* 71.6%

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

      7. neg-mul-1 71.6%

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

      8. unsub-neg 71.6%

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

      9. *-commutative 71.6%

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

      10. *-commutative 71.6%

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

      11. *-commutative 71.6%

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

   7. Simplified 71.6%

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

   if -1.4e52 < j < -2.50000000000000007e-140

   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. associate-+l- 70.3%

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

      2. *-commutative 70.3%

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

      3. sub-neg 70.3%

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

      4. sub-neg 70.3%

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

      5. *-commutative 70.3%

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

   3. Simplified 70.3%

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

   4. Taylor expanded in c around inf 57.0%

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

      1. *-commutative 57.0%

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

   6. Simplified 57.0%

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

   if -2.50000000000000007e-140 < j < -2.3e-305

   1. Initial program 69.1%

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

      1. associate-+l- 69.1%

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

      2. *-commutative 69.1%

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

      3. sub-neg 69.1%

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

      4. sub-neg 69.1%

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

      5. *-commutative 69.1%

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

   3. Simplified 69.1%

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

   4. Taylor expanded in t around inf 63.8%

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

      1. distribute-lft-out-- 63.8%

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

      2. associate-*r* 63.8%

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

      3. mul-1-neg 63.8%

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

      4. *-commutative 63.8%

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

   6. Simplified 63.8%

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

   if -2.3e-305 < j < 6.49999999999999949e-38

   1. Initial program 73.5%

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

      1. associate-+l- 73.5%

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

      2. *-commutative 73.5%

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

      3. sub-neg 73.5%

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

      4. sub-neg 73.5%

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

      5. *-commutative 73.5%

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

   3. Simplified 73.5%

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

   4. Taylor expanded in z around inf 66.8%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -7 \cdot 10^{+90}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -1.4 \cdot 10^{+52}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;j \leq -2.5 \cdot 10^{-140}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq -2.3 \cdot 10^{-305}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 6.5 \cdot 10^{-38}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 3.55 \cdot 10^{+158}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 7: 60.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -5.2 \cdot 10^{+75}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 1.25 \cdot 10^{-28}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 19000:\\ \;\;\;\;t_1 - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;j \leq 4.4 \cdot 10^{+111}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + t_2\\ \end{array} \end{array} \]

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 -5.2e+75)
     t_2
     (if (<= j 1.25e-28)
       (+ (* z (* x y)) (* b (- (* t i) (* z c))))
       (if (<= j 19000.0)
         (- t_1 (* y (* i j)))
         (if (<= j 4.4e+111)
           (+ (* y (- (* x z) (* i j))) (* i (* t 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 = x * ((y * z) - (t * a));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -5.2e+75) {
		tmp = t_2;
	} else if (j <= 1.25e-28) {
		tmp = (z * (x * y)) + (b * ((t * i) - (z * c)));
	} else if (j <= 19000.0) {
		tmp = t_1 - (y * (i * j));
	} else if (j <= 4.4e+111) {
		tmp = (y * ((x * z) - (i * j))) + (i * (t * b));
	} else {
		tmp = t_1 + 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 <= (-5.2d+75)) then
        tmp = t_2
    else if (j <= 1.25d-28) then
        tmp = (z * (x * y)) + (b * ((t * i) - (z * c)))
    else if (j <= 19000.0d0) then
        tmp = t_1 - (y * (i * j))
    else if (j <= 4.4d+111) then
        tmp = (y * ((x * z) - (i * j))) + (i * (t * b))
    else
        tmp = t_1 + 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 <= -5.2e+75) {
		tmp = t_2;
	} else if (j <= 1.25e-28) {
		tmp = (z * (x * y)) + (b * ((t * i) - (z * c)));
	} else if (j <= 19000.0) {
		tmp = t_1 - (y * (i * j));
	} else if (j <= 4.4e+111) {
		tmp = (y * ((x * z) - (i * j))) + (i * (t * b));
	} else {
		tmp = t_1 + 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 <= -5.2e+75:
		tmp = t_2
	elif j <= 1.25e-28:
		tmp = (z * (x * y)) + (b * ((t * i) - (z * c)))
	elif j <= 19000.0:
		tmp = t_1 - (y * (i * j))
	elif j <= 4.4e+111:
		tmp = (y * ((x * z) - (i * j))) + (i * (t * b))
	else:
		tmp = t_1 + 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 <= -5.2e+75)
		tmp = t_2;
	elseif (j <= 1.25e-28)
		tmp = Float64(Float64(z * Float64(x * y)) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	elseif (j <= 19000.0)
		tmp = Float64(t_1 - Float64(y * Float64(i * j)));
	elseif (j <= 4.4e+111)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(i * Float64(t * b)));
	else
		tmp = Float64(t_1 + 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 <= -5.2e+75)
		tmp = t_2;
	elseif (j <= 1.25e-28)
		tmp = (z * (x * y)) + (b * ((t * i) - (z * c)));
	elseif (j <= 19000.0)
		tmp = t_1 - (y * (i * j));
	elseif (j <= 4.4e+111)
		tmp = (y * ((x * z) - (i * j))) + (i * (t * b));
	else
		tmp = t_1 + 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, -5.2e+75], t$95$2, If[LessEqual[j, 1.25e-28], N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 19000.0], N[(t$95$1 - N[(y * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.4e+111], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + t$95$2), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -5.1999999999999997e75

   1. Initial program 69.4%

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

      1. associate-+l- 69.4%

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

      2. *-commutative 69.4%

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

      3. sub-neg 69.4%

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

      4. sub-neg 69.4%

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

      5. *-commutative 69.4%

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

   3. Simplified 69.4%

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

      1. add-cube-cbrt 69.4%

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

      2. pow3 69.4%

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

      3. *-commutative 69.4%

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

   5. Applied egg-rr 69.4%

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

   6. Taylor expanded in j around -inf 69.9%

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

   if -5.1999999999999997e75 < j < 1.25e-28

   1. Initial program 72.9%

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

      1. +-commutative 72.9%

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

      2. fma-def 72.9%

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

      3. *-commutative 72.9%

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

      4. *-commutative 72.9%

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

   3. Simplified 72.9%

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

   4. Taylor expanded in a around 0 65.6%

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

   5. Taylor expanded in j around 0 64.1%

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

      1. *-commutative 64.1%

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

      2. associate-*r* 68.1%

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

      3. *-commutative 68.1%

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

      4. *-commutative 68.1%

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

      5. *-commutative 68.1%

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

      6. *-commutative 68.1%

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

   7. Simplified 68.1%

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

   if 1.25e-28 < j < 19000

   1. Initial program 59.8%

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

      1. +-commutative 59.8%

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

      2. fma-def 59.8%

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

      3. *-commutative 59.8%

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

      4. *-commutative 59.8%

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

   3. Simplified 59.8%

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

   4. Taylor expanded in b around 0 79.8%

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

   5. Taylor expanded in c around 0 90.2%

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

      1. *-commutative 90.2%

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

      2. *-commutative 90.2%

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

      3. *-commutative 90.2%

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

      4. associate-*r* 90.2%

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

      5. *-commutative 90.2%

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

      6. associate-*r* 90.2%

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

      7. neg-mul-1 90.2%

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

      8. unsub-neg 90.2%

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

      9. *-commutative 90.2%

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

      10. *-commutative 90.2%

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

      11. *-commutative 90.2%

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

   7. Simplified 90.2%

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

   if 19000 < j < 4.39999999999999997e111

   1. Initial program 70.5%

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

      1. associate-+l- 70.5%

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

      2. *-commutative 70.5%

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

      3. sub-neg 70.5%

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

      4. sub-neg 70.5%

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

      5. *-commutative 70.5%

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

   3. Simplified 70.5%

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

      1. add-cube-cbrt 70.4%

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

      2. pow3 70.4%

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

      3. *-commutative 70.4%

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

   5. Applied egg-rr 70.4%

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

   6. Taylor expanded in a around 0 76.6%

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

      1. neg-mul-1 76.6%

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

      2. distribute-rgt-neg-in 76.6%

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

      3. mul-1-neg 76.6%

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

      4. pow-base-1 76.6%

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

      5. *-lft-identity 76.6%

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

      6. distribute-lft-in 82.5%

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

      7. +-commutative 82.5%

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

      8. mul-1-neg 82.5%

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

      9. unsub-neg 82.5%

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

      10. *-commutative 82.5%

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

      11. *-commutative 82.5%

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

      12. *-commutative 82.5%

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

      13. *-commutative 82.5%

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

      14. *-commutative 82.5%

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

   8. Simplified 82.5%

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

   9. Taylor expanded in c around 0 82.4%

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

       1. associate-*r* 82.4%

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

       2. neg-mul-1 82.4%

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

   11. Simplified 82.4%

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

   if 4.39999999999999997e111 < j

   1. Initial program 67.6%

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

      1. +-commutative 67.6%

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

      2. fma-def 74.2%

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

      3. *-commutative 74.2%

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

      4. *-commutative 74.2%

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

   3. Simplified 74.2%

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

   4. Taylor expanded in b around 0 74.5%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -5.2 \cdot 10^{+75}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 1.25 \cdot 10^{-28}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 19000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;j \leq 4.4 \cdot 10^{+111}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 8: 67.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;x \leq -2.9 \cdot 10^{+161}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -4.4 \cdot 10^{+88}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + t_3\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{+92}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + t_1\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+179}:\\ \;\;\;\;t_2 + t_1\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+218}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c))))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (* a (- (* c j) (* x t)))))
   (if (<= x -2.9e+161)
     t_2
     (if (<= x -4.4e+88)
       (+ (* y (- (* x z) (* i j))) t_3)
       (if (<= x 2.55e+92)
         (+ (* j (- (* a c) (* y i))) t_1)
         (if (<= x 4.2e+179) (+ t_2 t_1) (if (<= x 8e+218) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = a * ((c * j) - (x * t));
	double tmp;
	if (x <= -2.9e+161) {
		tmp = t_2;
	} else if (x <= -4.4e+88) {
		tmp = (y * ((x * z) - (i * j))) + t_3;
	} else if (x <= 2.55e+92) {
		tmp = (j * ((a * c) - (y * i))) + t_1;
	} else if (x <= 4.2e+179) {
		tmp = t_2 + t_1;
	} else if (x <= 8e+218) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = x * ((y * z) - (t * a))
    t_3 = a * ((c * j) - (x * t))
    if (x <= (-2.9d+161)) then
        tmp = t_2
    else if (x <= (-4.4d+88)) then
        tmp = (y * ((x * z) - (i * j))) + t_3
    else if (x <= 2.55d+92) then
        tmp = (j * ((a * c) - (y * i))) + t_1
    else if (x <= 4.2d+179) then
        tmp = t_2 + t_1
    else if (x <= 8d+218) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = a * ((c * j) - (x * t));
	double tmp;
	if (x <= -2.9e+161) {
		tmp = t_2;
	} else if (x <= -4.4e+88) {
		tmp = (y * ((x * z) - (i * j))) + t_3;
	} else if (x <= 2.55e+92) {
		tmp = (j * ((a * c) - (y * i))) + t_1;
	} else if (x <= 4.2e+179) {
		tmp = t_2 + t_1;
	} else if (x <= 8e+218) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = x * ((y * z) - (t * a))
	t_3 = a * ((c * j) - (x * t))
	tmp = 0
	if x <= -2.9e+161:
		tmp = t_2
	elif x <= -4.4e+88:
		tmp = (y * ((x * z) - (i * j))) + t_3
	elif x <= 2.55e+92:
		tmp = (j * ((a * c) - (y * i))) + t_1
	elif x <= 4.2e+179:
		tmp = t_2 + t_1
	elif x <= 8e+218:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_3 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (x <= -2.9e+161)
		tmp = t_2;
	elseif (x <= -4.4e+88)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + t_3);
	elseif (x <= 2.55e+92)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + t_1);
	elseif (x <= 4.2e+179)
		tmp = Float64(t_2 + t_1);
	elseif (x <= 8e+218)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = x * ((y * z) - (t * a));
	t_3 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (x <= -2.9e+161)
		tmp = t_2;
	elseif (x <= -4.4e+88)
		tmp = (y * ((x * z) - (i * j))) + t_3;
	elseif (x <= 2.55e+92)
		tmp = (j * ((a * c) - (y * i))) + t_1;
	elseif (x <= 4.2e+179)
		tmp = t_2 + t_1;
	elseif (x <= 8e+218)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.9e+161], t$95$2, If[LessEqual[x, -4.4e+88], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision], If[LessEqual[x, 2.55e+92], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[x, 4.2e+179], N[(t$95$2 + t$95$1), $MachinePrecision], If[LessEqual[x, 8e+218], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -2.90000000000000016e161 or 8.00000000000000066e218 < x

   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. associate-+l- 70.9%

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

      2. *-commutative 70.9%

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

      3. sub-neg 70.9%

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

      4. sub-neg 70.9%

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

      5. *-commutative 70.9%

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

   3. Simplified 70.9%

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

   4. Taylor expanded in x around inf 83.9%

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

   if -2.90000000000000016e161 < x < -4.40000000000000017e88

   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. Step-by-step derivation

      1. +-commutative 64.1%

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

      2. fma-def 64.1%

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

      3. *-commutative 64.1%

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

      4. *-commutative 64.1%

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

   3. Simplified 64.1%

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

   4. Taylor expanded in b around 0 70.1%

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

   5. Taylor expanded in a around -inf 76.6%

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

      1. +-commutative 76.6%

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

      2. mul-1-neg 76.6%

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

      3. unsub-neg 76.6%

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

      4. associate-*r* 83.9%

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

      5. *-commutative 83.9%

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

      6. associate-*r* 76.7%

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

      7. neg-mul-1 76.7%

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

      8. distribute-rgt-neg-in 76.7%

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

      9. mul-1-neg 76.7%

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

      10. distribute-lft-in 83.9%

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

      11. +-commutative 83.9%

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

      12. mul-1-neg 83.9%

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

      13. unsub-neg 83.9%

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

      14. *-commutative 83.9%

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

      15. *-commutative 83.9%

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

   7. Simplified 83.9%

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

   if -4.40000000000000017e88 < x < 2.5500000000000001e92

   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 72.9%

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

      3. *-commutative 72.9%

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

      4. *-commutative 72.9%

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

   3. Simplified 72.9%

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

   4. Taylor expanded in x around 0 70.3%

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

   if 2.5500000000000001e92 < x < 4.1999999999999997e179

   1. Initial program 77.1%

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

      1. associate-+l- 77.1%

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

      2. *-commutative 77.1%

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

      3. sub-neg 77.1%

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

      4. sub-neg 77.1%

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

      5. *-commutative 77.1%

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

   3. Simplified 77.1%

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

   4. Taylor expanded in j around 0 86.2%

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

   if 4.1999999999999997e179 < x < 8.00000000000000066e218

   1. Initial program 42.9%

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

      1. associate-+l- 42.9%

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

      2. *-commutative 42.9%

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

      3. sub-neg 42.9%

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

      4. sub-neg 42.9%

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

      5. *-commutative 42.9%

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

   3. Simplified 42.9%

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

   4. Taylor expanded in a around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

   6. Simplified 100.0%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+161}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -4.4 \cdot 10^{+88}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{+92}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+179}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+218}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]

Alternative 9: 67.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -4.8 \cdot 10^{+159}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{+89}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+116}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= x -4.8e+159)
     t_1
     (if (<= x -1.2e+89)
       (+ (* y (- (* x z) (* i j))) (* a (- (* c j) (* x t))))
       (if (<= x 8.5e+116)
         (+ (* j (- (* a c) (* y i))) (* b (- (* t i) (* z c))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -4.8e+159) {
		tmp = t_1;
	} else if (x <= -1.2e+89) {
		tmp = (y * ((x * z) - (i * j))) + (a * ((c * j) - (x * t)));
	} else if (x <= 8.5e+116) {
		tmp = (j * ((a * c) - (y * i))) + (b * ((t * i) - (z * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (x <= (-4.8d+159)) then
        tmp = t_1
    else if (x <= (-1.2d+89)) then
        tmp = (y * ((x * z) - (i * j))) + (a * ((c * j) - (x * t)))
    else if (x <= 8.5d+116) then
        tmp = (j * ((a * c) - (y * i))) + (b * ((t * i) - (z * c)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -4.8e+159) {
		tmp = t_1;
	} else if (x <= -1.2e+89) {
		tmp = (y * ((x * z) - (i * j))) + (a * ((c * j) - (x * t)));
	} else if (x <= 8.5e+116) {
		tmp = (j * ((a * c) - (y * i))) + (b * ((t * i) - (z * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -4.8e+159:
		tmp = t_1
	elif x <= -1.2e+89:
		tmp = (y * ((x * z) - (i * j))) + (a * ((c * j) - (x * t)))
	elif x <= 8.5e+116:
		tmp = (j * ((a * c) - (y * i))) + (b * ((t * i) - (z * c)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -4.8e+159)
		tmp = t_1;
	elseif (x <= -1.2e+89)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(a * Float64(Float64(c * j) - Float64(x * t))));
	elseif (x <= 8.5e+116)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -4.8e+159)
		tmp = t_1;
	elseif (x <= -1.2e+89)
		tmp = (y * ((x * z) - (i * j))) + (a * ((c * j) - (x * t)));
	elseif (x <= 8.5e+116)
		tmp = (j * ((a * c) - (y * i))) + (b * ((t * i) - (z * c)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.8e+159], t$95$1, If[LessEqual[x, -1.2e+89], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.5e+116], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.8e159 or 8.5000000000000002e116 < x

   1. Initial program 67.5%

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

      1. associate-+l- 67.5%

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

      2. *-commutative 67.5%

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

      3. sub-neg 67.5%

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

      4. sub-neg 67.5%

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

      5. *-commutative 67.5%

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

   3. Simplified 67.5%

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

   4. Taylor expanded in x around inf 80.8%

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

   if -4.8e159 < x < -1.20000000000000002e89

   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. Step-by-step derivation

      1. +-commutative 64.1%

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

      2. fma-def 64.1%

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

      3. *-commutative 64.1%

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

      4. *-commutative 64.1%

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

   3. Simplified 64.1%

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

   4. Taylor expanded in b around 0 70.1%

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

   5. Taylor expanded in a around -inf 76.6%

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

      1. +-commutative 76.6%

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

      2. mul-1-neg 76.6%

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

      3. unsub-neg 76.6%

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

      4. associate-*r* 83.9%

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

      5. *-commutative 83.9%

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

      6. associate-*r* 76.7%

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

      7. neg-mul-1 76.7%

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

      8. distribute-rgt-neg-in 76.7%

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

      9. mul-1-neg 76.7%

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

      10. distribute-lft-in 83.9%

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

      11. +-commutative 83.9%

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

      12. mul-1-neg 83.9%

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

      13. unsub-neg 83.9%

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

      14. *-commutative 83.9%

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

      15. *-commutative 83.9%

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

   7. Simplified 83.9%

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

   if -1.20000000000000002e89 < x < 8.5000000000000002e116

   1. Initial program 72.8%

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

      1. +-commutative 72.8%

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

      2. fma-def 74.0%

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

      3. *-commutative 74.0%

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

      4. *-commutative 74.0%

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

   3. Simplified 74.0%

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

   4. Taylor expanded in x around 0 69.8%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+159}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{+89}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+116}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]

Alternative 10: 49.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -2.4 \cdot 10^{+84}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -8.2 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -2.2 \cdot 10^{+16}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;j \leq -2.6 \cdot 10^{-166}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -2.9 \cdot 10^{-304}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 5.5 \cdot 10^{-38}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 2.85 \cdot 10^{+158}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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 -2.4e+84)
     t_2
     (if (<= j -8.2e+33)
       t_1
       (if (<= j -2.2e+16)
         (* a (- (* c j) (* x t)))
         (if (<= j -2.6e-166)
           (* b (- (* t i) (* z c)))
           (if (<= j -2.9e-304)
             t_1
             (if (<= j 5.5e-38)
               (* z (- (* x y) (* b c)))
               (if (<= j 2.85e+158) 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 <= -2.4e+84) {
		tmp = t_2;
	} else if (j <= -8.2e+33) {
		tmp = t_1;
	} else if (j <= -2.2e+16) {
		tmp = a * ((c * j) - (x * t));
	} else if (j <= -2.6e-166) {
		tmp = b * ((t * i) - (z * c));
	} else if (j <= -2.9e-304) {
		tmp = t_1;
	} else if (j <= 5.5e-38) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 2.85e+158) {
		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 <= (-2.4d+84)) then
        tmp = t_2
    else if (j <= (-8.2d+33)) then
        tmp = t_1
    else if (j <= (-2.2d+16)) then
        tmp = a * ((c * j) - (x * t))
    else if (j <= (-2.6d-166)) then
        tmp = b * ((t * i) - (z * c))
    else if (j <= (-2.9d-304)) then
        tmp = t_1
    else if (j <= 5.5d-38) then
        tmp = z * ((x * y) - (b * c))
    else if (j <= 2.85d+158) 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 <= -2.4e+84) {
		tmp = t_2;
	} else if (j <= -8.2e+33) {
		tmp = t_1;
	} else if (j <= -2.2e+16) {
		tmp = a * ((c * j) - (x * t));
	} else if (j <= -2.6e-166) {
		tmp = b * ((t * i) - (z * c));
	} else if (j <= -2.9e-304) {
		tmp = t_1;
	} else if (j <= 5.5e-38) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 2.85e+158) {
		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 <= -2.4e+84:
		tmp = t_2
	elif j <= -8.2e+33:
		tmp = t_1
	elif j <= -2.2e+16:
		tmp = a * ((c * j) - (x * t))
	elif j <= -2.6e-166:
		tmp = b * ((t * i) - (z * c))
	elif j <= -2.9e-304:
		tmp = t_1
	elif j <= 5.5e-38:
		tmp = z * ((x * y) - (b * c))
	elif j <= 2.85e+158:
		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 <= -2.4e+84)
		tmp = t_2;
	elseif (j <= -8.2e+33)
		tmp = t_1;
	elseif (j <= -2.2e+16)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (j <= -2.6e-166)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (j <= -2.9e-304)
		tmp = t_1;
	elseif (j <= 5.5e-38)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (j <= 2.85e+158)
		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 <= -2.4e+84)
		tmp = t_2;
	elseif (j <= -8.2e+33)
		tmp = t_1;
	elseif (j <= -2.2e+16)
		tmp = a * ((c * j) - (x * t));
	elseif (j <= -2.6e-166)
		tmp = b * ((t * i) - (z * c));
	elseif (j <= -2.9e-304)
		tmp = t_1;
	elseif (j <= 5.5e-38)
		tmp = z * ((x * y) - (b * c));
	elseif (j <= 2.85e+158)
		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, -2.4e+84], t$95$2, If[LessEqual[j, -8.2e+33], t$95$1, If[LessEqual[j, -2.2e+16], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.6e-166], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.9e-304], t$95$1, If[LessEqual[j, 5.5e-38], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.85e+158], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -2.4e84 or 2.8500000000000001e158 < j

   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. Step-by-step derivation

      1. associate-+l- 68.7%

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

      2. *-commutative 68.7%

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

      3. sub-neg 68.7%

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

      4. sub-neg 68.7%

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

      5. *-commutative 68.7%

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

   3. Simplified 68.7%

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

      1. add-cube-cbrt 68.7%

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

      2. pow3 68.7%

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

      3. *-commutative 68.7%

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

   5. Applied egg-rr 68.7%

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

   6. Taylor expanded in j around -inf 75.4%

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

   if -2.4e84 < j < -8.1999999999999999e33 or -2.59999999999999989e-166 < j < -2.9e-304 or 5.50000000000000005e-38 < j < 2.8500000000000001e158

   1. Initial program 71.4%

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

      1. associate-+l- 71.4%

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

      2. *-commutative 71.4%

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

      3. sub-neg 71.4%

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

      4. sub-neg 71.4%

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

      5. *-commutative 71.4%

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

   3. Simplified 71.4%

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

   4. Taylor expanded in x around inf 63.5%

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

   if -8.1999999999999999e33 < j < -2.2e16

   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. Step-by-step derivation

      1. associate-+l- 100.0%

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

      2. *-commutative 100.0%

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

      3. sub-neg 100.0%

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

      4. sub-neg 100.0%

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

      5. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around inf 75.3%

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

      1. +-commutative 75.3%

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

      2. mul-1-neg 75.3%

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

      3. unsub-neg 75.3%

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

   6. Simplified 75.3%

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

   if -2.2e16 < j < -2.59999999999999989e-166

   1. Initial program 66.4%

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

      1. associate-+l- 66.4%

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

      2. *-commutative 66.4%

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

      3. sub-neg 66.4%

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

      4. sub-neg 66.4%

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

      5. *-commutative 66.4%

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

   3. Simplified 66.4%

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

   4. Taylor expanded in b around inf 59.6%

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

   if -2.9e-304 < j < 5.50000000000000005e-38

   1. Initial program 73.5%

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

      1. associate-+l- 73.5%

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

      2. *-commutative 73.5%

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

      3. sub-neg 73.5%

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

      4. sub-neg 73.5%

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

      5. *-commutative 73.5%

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

   3. Simplified 73.5%

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

   4. Taylor expanded in z around inf 66.8%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.4 \cdot 10^{+84}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -8.2 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq -2.2 \cdot 10^{+16}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;j \leq -2.6 \cdot 10^{-166}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -2.9 \cdot 10^{-304}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 5.5 \cdot 10^{-38}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 2.85 \cdot 10^{+158}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 11: 48.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.9 \cdot 10^{+84}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -7 \cdot 10^{+50}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -57000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -8.5 \cdot 10^{-140}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq -6.4 \cdot 10^{-304}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 4.4 \cdot 10^{-38}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 3.2 \cdot 10^{+158}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* b i) (* x a))))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (* j (- (* a c) (* y i)))))
   (if (<= j -1.9e+84)
     t_3
     (if (<= j -7e+50)
       t_2
       (if (<= j -57000000.0)
         t_1
         (if (<= j -8.5e-140)
           (* c (- (* a j) (* z b)))
           (if (<= j -6.4e-304)
             t_1
             (if (<= j 4.4e-38)
               (* z (- (* x y) (* b c)))
               (if (<= j 3.2e+158) t_2 t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -1.9e+84) {
		tmp = t_3;
	} else if (j <= -7e+50) {
		tmp = t_2;
	} else if (j <= -57000000.0) {
		tmp = t_1;
	} else if (j <= -8.5e-140) {
		tmp = c * ((a * j) - (z * b));
	} else if (j <= -6.4e-304) {
		tmp = t_1;
	} else if (j <= 4.4e-38) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 3.2e+158) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = t * ((b * i) - (x * a))
    t_2 = x * ((y * z) - (t * a))
    t_3 = j * ((a * c) - (y * i))
    if (j <= (-1.9d+84)) then
        tmp = t_3
    else if (j <= (-7d+50)) then
        tmp = t_2
    else if (j <= (-57000000.0d0)) then
        tmp = t_1
    else if (j <= (-8.5d-140)) then
        tmp = c * ((a * j) - (z * b))
    else if (j <= (-6.4d-304)) then
        tmp = t_1
    else if (j <= 4.4d-38) then
        tmp = z * ((x * y) - (b * c))
    else if (j <= 3.2d+158) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -1.9e+84) {
		tmp = t_3;
	} else if (j <= -7e+50) {
		tmp = t_2;
	} else if (j <= -57000000.0) {
		tmp = t_1;
	} else if (j <= -8.5e-140) {
		tmp = c * ((a * j) - (z * b));
	} else if (j <= -6.4e-304) {
		tmp = t_1;
	} else if (j <= 4.4e-38) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 3.2e+158) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((b * i) - (x * a))
	t_2 = x * ((y * z) - (t * a))
	t_3 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -1.9e+84:
		tmp = t_3
	elif j <= -7e+50:
		tmp = t_2
	elif j <= -57000000.0:
		tmp = t_1
	elif j <= -8.5e-140:
		tmp = c * ((a * j) - (z * b))
	elif j <= -6.4e-304:
		tmp = t_1
	elif j <= 4.4e-38:
		tmp = z * ((x * y) - (b * c))
	elif j <= 3.2e+158:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_3 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -1.9e+84)
		tmp = t_3;
	elseif (j <= -7e+50)
		tmp = t_2;
	elseif (j <= -57000000.0)
		tmp = t_1;
	elseif (j <= -8.5e-140)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (j <= -6.4e-304)
		tmp = t_1;
	elseif (j <= 4.4e-38)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (j <= 3.2e+158)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((b * i) - (x * a));
	t_2 = x * ((y * z) - (t * a));
	t_3 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -1.9e+84)
		tmp = t_3;
	elseif (j <= -7e+50)
		tmp = t_2;
	elseif (j <= -57000000.0)
		tmp = t_1;
	elseif (j <= -8.5e-140)
		tmp = c * ((a * j) - (z * b));
	elseif (j <= -6.4e-304)
		tmp = t_1;
	elseif (j <= 4.4e-38)
		tmp = z * ((x * y) - (b * c));
	elseif (j <= 3.2e+158)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.9e+84], t$95$3, If[LessEqual[j, -7e+50], t$95$2, If[LessEqual[j, -57000000.0], t$95$1, If[LessEqual[j, -8.5e-140], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -6.4e-304], t$95$1, If[LessEqual[j, 4.4e-38], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.2e+158], t$95$2, t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -1.9e84 or 3.19999999999999995e158 < j

   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. Step-by-step derivation

      1. associate-+l- 68.7%

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

      2. *-commutative 68.7%

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

      3. sub-neg 68.7%

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

      4. sub-neg 68.7%

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

      5. *-commutative 68.7%

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

   3. Simplified 68.7%

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

      1. add-cube-cbrt 68.7%

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

      2. pow3 68.7%

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

      3. *-commutative 68.7%

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

   5. Applied egg-rr 68.7%

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

   6. Taylor expanded in j around -inf 75.4%

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

   if -1.9e84 < j < -7.00000000000000012e50 or 4.40000000000000015e-38 < j < 3.19999999999999995e158

   1. Initial program 72.6%

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

      1. associate-+l- 72.6%

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

      2. *-commutative 72.6%

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

      3. sub-neg 72.6%

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

      4. sub-neg 72.6%

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

      5. *-commutative 72.6%

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

   3. Simplified 72.6%

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

   4. Taylor expanded in x around inf 67.5%

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

   if -7.00000000000000012e50 < j < -5.7e7 or -8.49999999999999997e-140 < j < -6.39999999999999998e-304

   1. Initial program 71.3%

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

      1. associate-+l- 71.3%

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

      2. *-commutative 71.3%

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

      3. sub-neg 71.3%

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

      4. sub-neg 71.3%

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

      5. *-commutative 71.3%

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

   3. Simplified 71.3%

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

   4. Taylor expanded in t around inf 61.8%

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

      1. distribute-lft-out-- 61.8%

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

      2. associate-*r* 61.8%

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

      3. mul-1-neg 61.8%

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

      4. *-commutative 61.8%

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

   6. Simplified 61.8%

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

   if -5.7e7 < j < -8.49999999999999997e-140

   1. Initial program 67.3%

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

      1. associate-+l- 67.3%

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

      2. *-commutative 67.3%

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

      3. sub-neg 67.3%

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

      4. sub-neg 67.3%

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

      5. *-commutative 67.3%

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

   3. Simplified 67.3%

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

   4. Taylor expanded in c around inf 59.6%

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

      1. *-commutative 59.6%

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

   6. Simplified 59.6%

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

   if -6.39999999999999998e-304 < j < 4.40000000000000015e-38

   1. Initial program 73.5%

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

      1. associate-+l- 73.5%

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

      2. *-commutative 73.5%

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

      3. sub-neg 73.5%

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

      4. sub-neg 73.5%

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

      5. *-commutative 73.5%

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

   3. Simplified 73.5%

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

   4. Taylor expanded in z around inf 66.8%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.9 \cdot 10^{+84}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -7 \cdot 10^{+50}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq -57000000:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq -8.5 \cdot 10^{-140}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq -6.4 \cdot 10^{-304}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 4.4 \cdot 10^{-38}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 3.2 \cdot 10^{+158}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 12: 48.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -3.8 \cdot 10^{+84}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -1.05 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -0.0011:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;j \leq -5.5 \cdot 10^{-143}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq -7 \cdot 10^{-303}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 7.5 \cdot 10^{-38}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 2.85 \cdot 10^{+158}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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 -3.8e+84)
     t_2
     (if (<= j -1.05e+51)
       t_1
       (if (<= j -0.0011)
         (* i (- (* t b) (* y j)))
         (if (<= j -5.5e-143)
           (* c (- (* a j) (* z b)))
           (if (<= j -7e-303)
             (* t (- (* b i) (* x a)))
             (if (<= j 7.5e-38)
               (* z (- (* x y) (* b c)))
               (if (<= j 2.85e+158) 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 <= -3.8e+84) {
		tmp = t_2;
	} else if (j <= -1.05e+51) {
		tmp = t_1;
	} else if (j <= -0.0011) {
		tmp = i * ((t * b) - (y * j));
	} else if (j <= -5.5e-143) {
		tmp = c * ((a * j) - (z * b));
	} else if (j <= -7e-303) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 7.5e-38) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 2.85e+158) {
		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 <= (-3.8d+84)) then
        tmp = t_2
    else if (j <= (-1.05d+51)) then
        tmp = t_1
    else if (j <= (-0.0011d0)) then
        tmp = i * ((t * b) - (y * j))
    else if (j <= (-5.5d-143)) then
        tmp = c * ((a * j) - (z * b))
    else if (j <= (-7d-303)) then
        tmp = t * ((b * i) - (x * a))
    else if (j <= 7.5d-38) then
        tmp = z * ((x * y) - (b * c))
    else if (j <= 2.85d+158) 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 <= -3.8e+84) {
		tmp = t_2;
	} else if (j <= -1.05e+51) {
		tmp = t_1;
	} else if (j <= -0.0011) {
		tmp = i * ((t * b) - (y * j));
	} else if (j <= -5.5e-143) {
		tmp = c * ((a * j) - (z * b));
	} else if (j <= -7e-303) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 7.5e-38) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 2.85e+158) {
		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 <= -3.8e+84:
		tmp = t_2
	elif j <= -1.05e+51:
		tmp = t_1
	elif j <= -0.0011:
		tmp = i * ((t * b) - (y * j))
	elif j <= -5.5e-143:
		tmp = c * ((a * j) - (z * b))
	elif j <= -7e-303:
		tmp = t * ((b * i) - (x * a))
	elif j <= 7.5e-38:
		tmp = z * ((x * y) - (b * c))
	elif j <= 2.85e+158:
		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 <= -3.8e+84)
		tmp = t_2;
	elseif (j <= -1.05e+51)
		tmp = t_1;
	elseif (j <= -0.0011)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (j <= -5.5e-143)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (j <= -7e-303)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (j <= 7.5e-38)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (j <= 2.85e+158)
		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 <= -3.8e+84)
		tmp = t_2;
	elseif (j <= -1.05e+51)
		tmp = t_1;
	elseif (j <= -0.0011)
		tmp = i * ((t * b) - (y * j));
	elseif (j <= -5.5e-143)
		tmp = c * ((a * j) - (z * b));
	elseif (j <= -7e-303)
		tmp = t * ((b * i) - (x * a));
	elseif (j <= 7.5e-38)
		tmp = z * ((x * y) - (b * c));
	elseif (j <= 2.85e+158)
		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, -3.8e+84], t$95$2, If[LessEqual[j, -1.05e+51], t$95$1, If[LessEqual[j, -0.0011], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -5.5e-143], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -7e-303], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7.5e-38], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.85e+158], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -3.8000000000000001e84 or 2.8500000000000001e158 < j

   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. Step-by-step derivation

      1. associate-+l- 68.7%

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

      2. *-commutative 68.7%

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

      3. sub-neg 68.7%

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

      4. sub-neg 68.7%

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

      5. *-commutative 68.7%

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

   3. Simplified 68.7%

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

      1. add-cube-cbrt 68.7%

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

      2. pow3 68.7%

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

      3. *-commutative 68.7%

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

   5. Applied egg-rr 68.7%

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

   6. Taylor expanded in j around -inf 75.4%

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

   if -3.8000000000000001e84 < j < -1.0500000000000001e51 or 7.5e-38 < j < 2.8500000000000001e158

   1. Initial program 72.6%

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

      1. associate-+l- 72.6%

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

      2. *-commutative 72.6%

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

      3. sub-neg 72.6%

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

      4. sub-neg 72.6%

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

      5. *-commutative 72.6%

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

   3. Simplified 72.6%

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

   4. Taylor expanded in x around inf 67.5%

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

   if -1.0500000000000001e51 < j < -0.00110000000000000007

   1. Initial program 82.1%

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

      1. associate-+l- 82.1%

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

      2. *-commutative 82.1%

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

      3. sub-neg 82.1%

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

      4. sub-neg 82.1%

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

      5. *-commutative 82.1%

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

   3. Simplified 82.1%

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

   4. Taylor expanded in i around inf 47.5%

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

      1. distribute-lft-out-- 47.5%

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

      2. *-commutative 47.5%

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

   6. Simplified 47.5%

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

   if -0.00110000000000000007 < j < -5.50000000000000041e-143

   1. Initial program 65.1%

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

      1. associate-+l- 65.1%

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

      2. *-commutative 65.1%

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

      3. sub-neg 65.1%

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

      4. sub-neg 65.1%

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

      5. *-commutative 65.1%

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

   3. Simplified 65.1%

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

   4. Taylor expanded in c around inf 62.5%

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

      1. *-commutative 62.5%

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

   6. Simplified 62.5%

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

   if -5.50000000000000041e-143 < j < -7e-303

   1. Initial program 69.1%

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

      1. associate-+l- 69.1%

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

      2. *-commutative 69.1%

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

      3. sub-neg 69.1%

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

      4. sub-neg 69.1%

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

      5. *-commutative 69.1%

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

   3. Simplified 69.1%

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

   4. Taylor expanded in t around inf 63.8%

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

      1. distribute-lft-out-- 63.8%

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

      2. associate-*r* 63.8%

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

      3. mul-1-neg 63.8%

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

      4. *-commutative 63.8%

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

   6. Simplified 63.8%

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

   if -7e-303 < j < 7.5e-38

   1. Initial program 73.5%

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

      1. associate-+l- 73.5%

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

      2. *-commutative 73.5%

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

      3. sub-neg 73.5%

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

      4. sub-neg 73.5%

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

      5. *-commutative 73.5%

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

   3. Simplified 73.5%

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

   4. Taylor expanded in z around inf 66.8%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.8 \cdot 10^{+84}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -1.05 \cdot 10^{+51}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq -0.0011:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;j \leq -5.5 \cdot 10^{-143}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq -7 \cdot 10^{-303}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 7.5 \cdot 10^{-38}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 2.85 \cdot 10^{+158}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 13: 58.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := z \cdot \left(x \cdot y\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -9.8 \cdot 10^{+74}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 1.45 \cdot 10^{-28}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 2.25 \cdot 10^{-9}:\\ \;\;\;\;t_1 - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;j \leq 1.14 \cdot 10^{+107}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{+161}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (+ (* z (* x y)) (* b (- (* t i) (* z c)))))
        (t_3 (* j (- (* a c) (* y i)))))
   (if (<= j -9.8e+74)
     t_3
     (if (<= j 1.45e-28)
       t_2
       (if (<= j 2.25e-9)
         (- t_1 (* y (* i j)))
         (if (<= j 1.14e+107) t_2 (if (<= j 4.5e+161) 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 = x * ((y * z) - (t * a));
	double t_2 = (z * (x * y)) + (b * ((t * i) - (z * c)));
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -9.8e+74) {
		tmp = t_3;
	} else if (j <= 1.45e-28) {
		tmp = t_2;
	} else if (j <= 2.25e-9) {
		tmp = t_1 - (y * (i * j));
	} else if (j <= 1.14e+107) {
		tmp = t_2;
	} else if (j <= 4.5e+161) {
		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 = x * ((y * z) - (t * a))
    t_2 = (z * (x * y)) + (b * ((t * i) - (z * c)))
    t_3 = j * ((a * c) - (y * i))
    if (j <= (-9.8d+74)) then
        tmp = t_3
    else if (j <= 1.45d-28) then
        tmp = t_2
    else if (j <= 2.25d-9) then
        tmp = t_1 - (y * (i * j))
    else if (j <= 1.14d+107) then
        tmp = t_2
    else if (j <= 4.5d+161) 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 = x * ((y * z) - (t * a));
	double t_2 = (z * (x * y)) + (b * ((t * i) - (z * c)));
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -9.8e+74) {
		tmp = t_3;
	} else if (j <= 1.45e-28) {
		tmp = t_2;
	} else if (j <= 2.25e-9) {
		tmp = t_1 - (y * (i * j));
	} else if (j <= 1.14e+107) {
		tmp = t_2;
	} else if (j <= 4.5e+161) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = (z * (x * y)) + (b * ((t * i) - (z * c)))
	t_3 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -9.8e+74:
		tmp = t_3
	elif j <= 1.45e-28:
		tmp = t_2
	elif j <= 2.25e-9:
		tmp = t_1 - (y * (i * j))
	elif j <= 1.14e+107:
		tmp = t_2
	elif j <= 4.5e+161:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(Float64(z * Float64(x * y)) + Float64(b * Float64(Float64(t * i) - Float64(z * c))))
	t_3 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -9.8e+74)
		tmp = t_3;
	elseif (j <= 1.45e-28)
		tmp = t_2;
	elseif (j <= 2.25e-9)
		tmp = Float64(t_1 - Float64(y * Float64(i * j)));
	elseif (j <= 1.14e+107)
		tmp = t_2;
	elseif (j <= 4.5e+161)
		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 = x * ((y * z) - (t * a));
	t_2 = (z * (x * y)) + (b * ((t * i) - (z * c)));
	t_3 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -9.8e+74)
		tmp = t_3;
	elseif (j <= 1.45e-28)
		tmp = t_2;
	elseif (j <= 2.25e-9)
		tmp = t_1 - (y * (i * j));
	elseif (j <= 1.14e+107)
		tmp = t_2;
	elseif (j <= 4.5e+161)
		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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -9.8e+74], t$95$3, If[LessEqual[j, 1.45e-28], t$95$2, If[LessEqual[j, 2.25e-9], N[(t$95$1 - N[(y * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.14e+107], t$95$2, If[LessEqual[j, 4.5e+161], t$95$1, t$95$3]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -9.7999999999999998e74 or 4.49999999999999992e161 < j

   1. Initial program 69.1%

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

      1. associate-+l- 69.1%

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

      2. *-commutative 69.1%

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

      3. sub-neg 69.1%

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

      4. sub-neg 69.1%

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

      5. *-commutative 69.1%

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

   3. Simplified 69.1%

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

      1. add-cube-cbrt 69.1%

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

      2. pow3 69.1%

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

      3. *-commutative 69.1%

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

   5. Applied egg-rr 69.1%

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

   6. Taylor expanded in j around -inf 75.7%

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

   if -9.7999999999999998e74 < j < 1.45000000000000006e-28 or 2.24999999999999988e-9 < j < 1.1399999999999999e107

   1. Initial program 73.3%

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

      1. +-commutative 73.3%

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

      2. fma-def 74.5%

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

      3. *-commutative 74.5%

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

      4. *-commutative 74.5%

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

   3. Simplified 74.5%

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

   4. Taylor expanded in a around 0 66.8%

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

   5. Taylor expanded in j around 0 64.9%

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

      1. *-commutative 64.9%

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

      2. associate-*r* 69.0%

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

      3. *-commutative 69.0%

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

      4. *-commutative 69.0%

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

      5. *-commutative 69.0%

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

      6. *-commutative 69.0%

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

   7. Simplified 69.0%

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

   if 1.45000000000000006e-28 < j < 2.24999999999999988e-9

   1. Initial program 55.4%

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

      1. +-commutative 55.4%

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

      2. fma-def 55.4%

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

      3. *-commutative 55.4%

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

      4. *-commutative 55.4%

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

   3. Simplified 55.4%

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

   4. Taylor expanded in b around 0 77.6%

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

   5. Taylor expanded in c around 0 89.1%

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

      1. *-commutative 89.1%

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

      2. *-commutative 89.1%

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

      3. *-commutative 89.1%

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

      4. associate-*r* 89.1%

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

      5. *-commutative 89.1%

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

      6. associate-*r* 89.1%

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

      7. neg-mul-1 89.1%

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

      8. unsub-neg 89.1%

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

      9. *-commutative 89.1%

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

      10. *-commutative 89.1%

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

      11. *-commutative 89.1%

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

   7. Simplified 89.1%

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

   if 1.1399999999999999e107 < j < 4.49999999999999992e161

   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. Step-by-step derivation

      1. associate-+l- 58.3%

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

      2. *-commutative 58.3%

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

      3. sub-neg 58.3%

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

      4. sub-neg 58.3%

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

      5. *-commutative 58.3%

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

   3. Simplified 58.3%

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

   4. Taylor expanded in x around inf 84.0%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -9.8 \cdot 10^{+74}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 1.45 \cdot 10^{-28}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 2.25 \cdot 10^{-9}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;j \leq 1.14 \cdot 10^{+107}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{+161}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 14: 58.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -9.5 \cdot 10^{+76}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 1.6 \cdot 10^{-28}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 88000:\\ \;\;\;\;t_1 - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;j \leq 1.15 \cdot 10^{+105}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;j \leq 2.85 \cdot 10^{+158}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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 -9.5e+76)
     t_2
     (if (<= j 1.6e-28)
       (+ (* z (* x y)) (* b (- (* t i) (* z c))))
       (if (<= j 88000.0)
         (- t_1 (* y (* i j)))
         (if (<= j 1.15e+105)
           (+ (* y (- (* x z) (* i j))) (* i (* t b)))
           (if (<= j 2.85e+158) 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 <= -9.5e+76) {
		tmp = t_2;
	} else if (j <= 1.6e-28) {
		tmp = (z * (x * y)) + (b * ((t * i) - (z * c)));
	} else if (j <= 88000.0) {
		tmp = t_1 - (y * (i * j));
	} else if (j <= 1.15e+105) {
		tmp = (y * ((x * z) - (i * j))) + (i * (t * b));
	} else if (j <= 2.85e+158) {
		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 <= (-9.5d+76)) then
        tmp = t_2
    else if (j <= 1.6d-28) then
        tmp = (z * (x * y)) + (b * ((t * i) - (z * c)))
    else if (j <= 88000.0d0) then
        tmp = t_1 - (y * (i * j))
    else if (j <= 1.15d+105) then
        tmp = (y * ((x * z) - (i * j))) + (i * (t * b))
    else if (j <= 2.85d+158) 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 <= -9.5e+76) {
		tmp = t_2;
	} else if (j <= 1.6e-28) {
		tmp = (z * (x * y)) + (b * ((t * i) - (z * c)));
	} else if (j <= 88000.0) {
		tmp = t_1 - (y * (i * j));
	} else if (j <= 1.15e+105) {
		tmp = (y * ((x * z) - (i * j))) + (i * (t * b));
	} else if (j <= 2.85e+158) {
		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 <= -9.5e+76:
		tmp = t_2
	elif j <= 1.6e-28:
		tmp = (z * (x * y)) + (b * ((t * i) - (z * c)))
	elif j <= 88000.0:
		tmp = t_1 - (y * (i * j))
	elif j <= 1.15e+105:
		tmp = (y * ((x * z) - (i * j))) + (i * (t * b))
	elif j <= 2.85e+158:
		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 <= -9.5e+76)
		tmp = t_2;
	elseif (j <= 1.6e-28)
		tmp = Float64(Float64(z * Float64(x * y)) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	elseif (j <= 88000.0)
		tmp = Float64(t_1 - Float64(y * Float64(i * j)));
	elseif (j <= 1.15e+105)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(i * Float64(t * b)));
	elseif (j <= 2.85e+158)
		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 <= -9.5e+76)
		tmp = t_2;
	elseif (j <= 1.6e-28)
		tmp = (z * (x * y)) + (b * ((t * i) - (z * c)));
	elseif (j <= 88000.0)
		tmp = t_1 - (y * (i * j));
	elseif (j <= 1.15e+105)
		tmp = (y * ((x * z) - (i * j))) + (i * (t * b));
	elseif (j <= 2.85e+158)
		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, -9.5e+76], t$95$2, If[LessEqual[j, 1.6e-28], N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 88000.0], N[(t$95$1 - N[(y * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.15e+105], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.85e+158], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -9.5000000000000003e76 or 2.8500000000000001e158 < j

   1. Initial program 69.1%

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

      1. associate-+l- 69.1%

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

      2. *-commutative 69.1%

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

      3. sub-neg 69.1%

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

      4. sub-neg 69.1%

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

      5. *-commutative 69.1%

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

   3. Simplified 69.1%

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

      1. add-cube-cbrt 69.1%

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

      2. pow3 69.1%

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

      3. *-commutative 69.1%

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

   5. Applied egg-rr 69.1%

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

   6. Taylor expanded in j around -inf 75.7%

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

   if -9.5000000000000003e76 < j < 1.59999999999999991e-28

   1. Initial program 72.9%

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

      1. +-commutative 72.9%

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

      2. fma-def 72.9%

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

      3. *-commutative 72.9%

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

      4. *-commutative 72.9%

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

   3. Simplified 72.9%

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

   4. Taylor expanded in a around 0 65.6%

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

   5. Taylor expanded in j around 0 64.1%

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

      1. *-commutative 64.1%

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

      2. associate-*r* 68.1%

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

      3. *-commutative 68.1%

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

      4. *-commutative 68.1%

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

      5. *-commutative 68.1%

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

      6. *-commutative 68.1%

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

   7. Simplified 68.1%

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

   if 1.59999999999999991e-28 < j < 88000

   1. Initial program 59.8%

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

      1. +-commutative 59.8%

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

      2. fma-def 59.8%

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

      3. *-commutative 59.8%

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

      4. *-commutative 59.8%

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

   3. Simplified 59.8%

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

   4. Taylor expanded in b around 0 79.8%

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

   5. Taylor expanded in c around 0 90.2%

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

      1. *-commutative 90.2%

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

      2. *-commutative 90.2%

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

      3. *-commutative 90.2%

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

      4. associate-*r* 90.2%

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

      5. *-commutative 90.2%

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

      6. associate-*r* 90.2%

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

      7. neg-mul-1 90.2%

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

      8. unsub-neg 90.2%

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

      9. *-commutative 90.2%

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

      10. *-commutative 90.2%

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

      11. *-commutative 90.2%

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

   7. Simplified 90.2%

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

   if 88000 < j < 1.1499999999999999e105

   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. Step-by-step derivation

      1. associate-+l- 73.2%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 73.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 73.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 73.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 73.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 73.2%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 73.2%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      2. pow3 73.2%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      3. *-commutative 73.2%

         \[\leadsto {\left(\sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right)}\right)}^{3} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   5. Applied egg-rr 73.2%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right)}\right)}^{3}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   6. Taylor expanded in a around 0 86.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot \left(i \cdot j\right)\right) + {1}^{0.3333333333333333} \cdot \left(y \cdot \left(z \cdot x\right)\right)\right) - \left(c \cdot z - i \cdot t\right) \cdot b} \]
   7. Step-by-step derivation

      1. neg-mul-1 86.6%

         \[\leadsto \left(\color{blue}{\left(-y \cdot \left(i \cdot j\right)\right)} + {1}^{0.3333333333333333} \cdot \left(y \cdot \left(z \cdot x\right)\right)\right) - \left(c \cdot z - i \cdot t\right) \cdot b \]

      2. distribute-rgt-neg-in 86.6%

         \[\leadsto \left(\color{blue}{y \cdot \left(-i \cdot j\right)} + {1}^{0.3333333333333333} \cdot \left(y \cdot \left(z \cdot x\right)\right)\right) - \left(c \cdot z - i \cdot t\right) \cdot b \]

      3. mul-1-neg 86.6%

         \[\leadsto \left(y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)} + {1}^{0.3333333333333333} \cdot \left(y \cdot \left(z \cdot x\right)\right)\right) - \left(c \cdot z - i \cdot t\right) \cdot b \]

      4. pow-base-1 86.6%

         \[\leadsto \left(y \cdot \left(-1 \cdot \left(i \cdot j\right)\right) + \color{blue}{1} \cdot \left(y \cdot \left(z \cdot x\right)\right)\right) - \left(c \cdot z - i \cdot t\right) \cdot b \]

      5. *-lft-identity 86.6%

         \[\leadsto \left(y \cdot \left(-1 \cdot \left(i \cdot j\right)\right) + \color{blue}{y \cdot \left(z \cdot x\right)}\right) - \left(c \cdot z - i \cdot t\right) \cdot b \]

      6. distribute-lft-in 86.6%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} - \left(c \cdot z - i \cdot t\right) \cdot b \]

      7. +-commutative 86.6%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} - \left(c \cdot z - i \cdot t\right) \cdot b \]

      8. mul-1-neg 86.6%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) - \left(c \cdot z - i \cdot t\right) \cdot b \]

      9. unsub-neg 86.6%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} - \left(c \cdot z - i \cdot t\right) \cdot b \]

      10. *-commutative 86.6%

          \[\leadsto y \cdot \left(\color{blue}{x \cdot z} - i \cdot j\right) - \left(c \cdot z - i \cdot t\right) \cdot b \]

      11. *-commutative 86.6%

          \[\leadsto y \cdot \left(x \cdot z - \color{blue}{j \cdot i}\right) - \left(c \cdot z - i \cdot t\right) \cdot b \]

      12. *-commutative 86.6%

          \[\leadsto y \cdot \left(x \cdot z - j \cdot i\right) - \color{blue}{b \cdot \left(c \cdot z - i \cdot t\right)} \]

      13. *-commutative 86.6%

          \[\leadsto y \cdot \left(x \cdot z - j \cdot i\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right) \]

      14. *-commutative 86.6%

          \[\leadsto y \cdot \left(x \cdot z - j \cdot i\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right) \]

   8. Simplified 86.6%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z - j \cdot i\right) - b \cdot \left(z \cdot c - t \cdot i\right)} \]

   9. Taylor expanded in c around 0 86.6%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - -1 \cdot \left(i \cdot \left(t \cdot b\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 86.6%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - \color{blue}{\left(-1 \cdot i\right) \cdot \left(t \cdot b\right)} \]

       2. neg-mul-1 86.6%

          \[\leadsto y \cdot \left(z \cdot x - i \cdot j\right) - \color{blue}{\left(-i\right)} \cdot \left(t \cdot b\right) \]

   11. Simplified 86.6%

       \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - \left(-i\right) \cdot \left(t \cdot b\right)} \]

   if 1.1499999999999999e105 < j < 2.8500000000000001e158

   1. Initial program 61.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 61.5%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 61.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 61.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 61.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 61.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 61.5%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in x around inf 77.6%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]
3. Recombined 5 regimes into one program.

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -9.5 \cdot 10^{+76}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 1.6 \cdot 10^{-28}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 88000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;j \leq 1.15 \cdot 10^{+105}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;j \leq 2.85 \cdot 10^{+158}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 15: 29.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(z \cdot \left(-b\right)\right)\\ t_2 := b \cdot \left(t \cdot i\right)\\ t_3 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;x \leq -1.3 \cdot 10^{+89}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.85 \cdot 10^{-221}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-139}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-72}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{+98}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{+136}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+149}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* z (- b)))) (t_2 (* b (* t i))) (t_3 (* z (* x y))))
   (if (<= x -1.3e+89)
     t_3
     (if (<= x -1.85e-221)
       t_1
       (if (<= x 1.05e-139)
         t_2
         (if (<= x 1.25e-72)
           (* j (* y (- i)))
           (if (<= x 6.6e+98)
             t_2
             (if (<= x 7.4e+136)
               (* a (* t (- x)))
               (if (<= x 6.2e+149) 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 = c * (z * -b);
	double t_2 = b * (t * i);
	double t_3 = z * (x * y);
	double tmp;
	if (x <= -1.3e+89) {
		tmp = t_3;
	} else if (x <= -1.85e-221) {
		tmp = t_1;
	} else if (x <= 1.05e-139) {
		tmp = t_2;
	} else if (x <= 1.25e-72) {
		tmp = j * (y * -i);
	} else if (x <= 6.6e+98) {
		tmp = t_2;
	} else if (x <= 7.4e+136) {
		tmp = a * (t * -x);
	} else if (x <= 6.2e+149) {
		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 = c * (z * -b)
    t_2 = b * (t * i)
    t_3 = z * (x * y)
    if (x <= (-1.3d+89)) then
        tmp = t_3
    else if (x <= (-1.85d-221)) then
        tmp = t_1
    else if (x <= 1.05d-139) then
        tmp = t_2
    else if (x <= 1.25d-72) then
        tmp = j * (y * -i)
    else if (x <= 6.6d+98) then
        tmp = t_2
    else if (x <= 7.4d+136) then
        tmp = a * (t * -x)
    else if (x <= 6.2d+149) 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 = c * (z * -b);
	double t_2 = b * (t * i);
	double t_3 = z * (x * y);
	double tmp;
	if (x <= -1.3e+89) {
		tmp = t_3;
	} else if (x <= -1.85e-221) {
		tmp = t_1;
	} else if (x <= 1.05e-139) {
		tmp = t_2;
	} else if (x <= 1.25e-72) {
		tmp = j * (y * -i);
	} else if (x <= 6.6e+98) {
		tmp = t_2;
	} else if (x <= 7.4e+136) {
		tmp = a * (t * -x);
	} else if (x <= 6.2e+149) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (z * -b)
	t_2 = b * (t * i)
	t_3 = z * (x * y)
	tmp = 0
	if x <= -1.3e+89:
		tmp = t_3
	elif x <= -1.85e-221:
		tmp = t_1
	elif x <= 1.05e-139:
		tmp = t_2
	elif x <= 1.25e-72:
		tmp = j * (y * -i)
	elif x <= 6.6e+98:
		tmp = t_2
	elif x <= 7.4e+136:
		tmp = a * (t * -x)
	elif x <= 6.2e+149:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(z * Float64(-b)))
	t_2 = Float64(b * Float64(t * i))
	t_3 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (x <= -1.3e+89)
		tmp = t_3;
	elseif (x <= -1.85e-221)
		tmp = t_1;
	elseif (x <= 1.05e-139)
		tmp = t_2;
	elseif (x <= 1.25e-72)
		tmp = Float64(j * Float64(y * Float64(-i)));
	elseif (x <= 6.6e+98)
		tmp = t_2;
	elseif (x <= 7.4e+136)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (x <= 6.2e+149)
		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 = c * (z * -b);
	t_2 = b * (t * i);
	t_3 = z * (x * y);
	tmp = 0.0;
	if (x <= -1.3e+89)
		tmp = t_3;
	elseif (x <= -1.85e-221)
		tmp = t_1;
	elseif (x <= 1.05e-139)
		tmp = t_2;
	elseif (x <= 1.25e-72)
		tmp = j * (y * -i);
	elseif (x <= 6.6e+98)
		tmp = t_2;
	elseif (x <= 7.4e+136)
		tmp = a * (t * -x);
	elseif (x <= 6.2e+149)
		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[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.3e+89], t$95$3, If[LessEqual[x, -1.85e-221], t$95$1, If[LessEqual[x, 1.05e-139], t$95$2, If[LessEqual[x, 1.25e-72], N[(j * N[(y * (-i)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.6e+98], t$95$2, If[LessEqual[x, 7.4e+136], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.2e+149], t$95$1, t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.3e89 or 6.19999999999999974e149 < x

   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. Step-by-step derivation

      1. associate-+l- 67.0%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 67.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 67.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 67.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 67.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 67.0%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in z around inf 62.7%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   5. Taylor expanded in y around inf 60.2%

      \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]

   if -1.3e89 < x < -1.84999999999999993e-221 or 7.4000000000000002e136 < x < 6.19999999999999974e149

   1. Initial program 69.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 69.5%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 69.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 69.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 69.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 69.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 69.5%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 69.4%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      2. pow3 69.4%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      3. *-commutative 69.4%

         \[\leadsto {\left(\sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right)}\right)}^{3} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   5. Applied egg-rr 69.4%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right)}\right)}^{3}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   6. Taylor expanded in z around inf 42.8%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(b \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 42.8%

         \[\leadsto \color{blue}{\left(-1 \cdot c\right) \cdot \left(b \cdot z\right)} \]

      2. neg-mul-1 42.8%

         \[\leadsto \color{blue}{\left(-c\right)} \cdot \left(b \cdot z\right) \]

      3. *-commutative 42.8%

         \[\leadsto \left(-c\right) \cdot \color{blue}{\left(z \cdot b\right)} \]

   8. Simplified 42.8%

      \[\leadsto \color{blue}{\left(-c\right) \cdot \left(z \cdot b\right)} \]

   if -1.84999999999999993e-221 < x < 1.05000000000000004e-139 or 1.2499999999999999e-72 < x < 6.60000000000000056e98

   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. Step-by-step derivation

      1. associate-+l- 73.7%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 73.7%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 73.7%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 73.7%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 73.7%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 73.7%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in b around inf 48.0%

      \[\leadsto \color{blue}{\left(i \cdot t - c \cdot z\right) \cdot b} \]

   5. Taylor expanded in i around inf 34.0%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 36.3%

         \[\leadsto \color{blue}{\left(i \cdot t\right) \cdot b} \]

      2. *-commutative 36.3%

         \[\leadsto \color{blue}{\left(t \cdot i\right)} \cdot b \]

   7. Simplified 36.3%

      \[\leadsto \color{blue}{\left(t \cdot i\right) \cdot b} \]

   if 1.05000000000000004e-139 < x < 1.2499999999999999e-72

   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. Step-by-step derivation

      1. associate-+l- 74.0%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 74.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 74.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 74.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 74.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 74.0%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 73.9%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      2. pow3 73.9%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      3. *-commutative 73.9%

         \[\leadsto {\left(\sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right)}\right)}^{3} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   5. Applied egg-rr 73.9%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right)}\right)}^{3}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   6. Taylor expanded in y around inf 49.4%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(i \cdot j\right)\right)} \]
   7. Step-by-step derivation

      1. neg-mul-1 49.4%

         \[\leadsto \color{blue}{-y \cdot \left(i \cdot j\right)} \]

      2. distribute-rgt-neg-in 49.4%

         \[\leadsto \color{blue}{y \cdot \left(-i \cdot j\right)} \]

      3. *-commutative 49.4%

         \[\leadsto y \cdot \left(-\color{blue}{j \cdot i}\right) \]

      4. distribute-rgt-neg-in 49.4%

         \[\leadsto y \cdot \color{blue}{\left(j \cdot \left(-i\right)\right)} \]

   8. Simplified 49.4%

      \[\leadsto \color{blue}{y \cdot \left(j \cdot \left(-i\right)\right)} \]

   9. Taylor expanded in y around 0 49.4%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(i \cdot j\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 49.4%

          \[\leadsto \color{blue}{-y \cdot \left(i \cdot j\right)} \]

       2. *-commutative 49.4%

          \[\leadsto -\color{blue}{\left(i \cdot j\right) \cdot y} \]

       3. distribute-lft-neg-in 49.4%

          \[\leadsto \color{blue}{\left(-i \cdot j\right) \cdot y} \]

       4. *-commutative 49.4%

          \[\leadsto \left(-\color{blue}{j \cdot i}\right) \cdot y \]

       5. distribute-rgt-neg-out 49.4%

          \[\leadsto \color{blue}{\left(j \cdot \left(-i\right)\right)} \cdot y \]

       6. associate-*l* 59.3%

          \[\leadsto \color{blue}{j \cdot \left(\left(-i\right) \cdot y\right)} \]

   11. Simplified 59.3%

       \[\leadsto \color{blue}{j \cdot \left(\left(-i\right) \cdot y\right)} \]

   if 6.60000000000000056e98 < x < 7.4000000000000002e136

   1. Initial program 79.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 79.7%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 79.7%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 79.7%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 79.7%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 79.7%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 79.7%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in a around inf 79.9%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 79.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 79.9%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 79.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 79.9%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around 0 60.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 60.9%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x\right)} \]

      2. neg-mul-1 60.9%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(t \cdot x\right) \]

   9. Simplified 60.9%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(t \cdot x\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+89}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq -1.85 \cdot 10^{-221}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-139}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-72}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{+98}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{+136}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+149}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 16: 29.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b\right)\\ t_2 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;x \leq -54000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-276}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{-141}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-73}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+98}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{+139}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;x \leq 4.9 \cdot 10^{+148}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* t b))) (t_2 (* z (* x y))))
   (if (<= x -54000000000.0)
     t_2
     (if (<= x 7.2e-276)
       (* c (* a j))
       (if (<= x 8.8e-141)
         t_1
         (if (<= x 9e-73)
           (* j (* y (- i)))
           (if (<= x 1.05e+98)
             (* b (* t i))
             (if (<= x 2.35e+139)
               (* a (* t (- x)))
               (if (<= x 4.9e+148) 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 = i * (t * b);
	double t_2 = z * (x * y);
	double tmp;
	if (x <= -54000000000.0) {
		tmp = t_2;
	} else if (x <= 7.2e-276) {
		tmp = c * (a * j);
	} else if (x <= 8.8e-141) {
		tmp = t_1;
	} else if (x <= 9e-73) {
		tmp = j * (y * -i);
	} else if (x <= 1.05e+98) {
		tmp = b * (t * i);
	} else if (x <= 2.35e+139) {
		tmp = a * (t * -x);
	} else if (x <= 4.9e+148) {
		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 = i * (t * b)
    t_2 = z * (x * y)
    if (x <= (-54000000000.0d0)) then
        tmp = t_2
    else if (x <= 7.2d-276) then
        tmp = c * (a * j)
    else if (x <= 8.8d-141) then
        tmp = t_1
    else if (x <= 9d-73) then
        tmp = j * (y * -i)
    else if (x <= 1.05d+98) then
        tmp = b * (t * i)
    else if (x <= 2.35d+139) then
        tmp = a * (t * -x)
    else if (x <= 4.9d+148) 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 = i * (t * b);
	double t_2 = z * (x * y);
	double tmp;
	if (x <= -54000000000.0) {
		tmp = t_2;
	} else if (x <= 7.2e-276) {
		tmp = c * (a * j);
	} else if (x <= 8.8e-141) {
		tmp = t_1;
	} else if (x <= 9e-73) {
		tmp = j * (y * -i);
	} else if (x <= 1.05e+98) {
		tmp = b * (t * i);
	} else if (x <= 2.35e+139) {
		tmp = a * (t * -x);
	} else if (x <= 4.9e+148) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (t * b)
	t_2 = z * (x * y)
	tmp = 0
	if x <= -54000000000.0:
		tmp = t_2
	elif x <= 7.2e-276:
		tmp = c * (a * j)
	elif x <= 8.8e-141:
		tmp = t_1
	elif x <= 9e-73:
		tmp = j * (y * -i)
	elif x <= 1.05e+98:
		tmp = b * (t * i)
	elif x <= 2.35e+139:
		tmp = a * (t * -x)
	elif x <= 4.9e+148:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(t * b))
	t_2 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (x <= -54000000000.0)
		tmp = t_2;
	elseif (x <= 7.2e-276)
		tmp = Float64(c * Float64(a * j));
	elseif (x <= 8.8e-141)
		tmp = t_1;
	elseif (x <= 9e-73)
		tmp = Float64(j * Float64(y * Float64(-i)));
	elseif (x <= 1.05e+98)
		tmp = Float64(b * Float64(t * i));
	elseif (x <= 2.35e+139)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (x <= 4.9e+148)
		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 = i * (t * b);
	t_2 = z * (x * y);
	tmp = 0.0;
	if (x <= -54000000000.0)
		tmp = t_2;
	elseif (x <= 7.2e-276)
		tmp = c * (a * j);
	elseif (x <= 8.8e-141)
		tmp = t_1;
	elseif (x <= 9e-73)
		tmp = j * (y * -i);
	elseif (x <= 1.05e+98)
		tmp = b * (t * i);
	elseif (x <= 2.35e+139)
		tmp = a * (t * -x);
	elseif (x <= 4.9e+148)
		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[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -54000000000.0], t$95$2, If[LessEqual[x, 7.2e-276], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.8e-141], t$95$1, If[LessEqual[x, 9e-73], N[(j * N[(y * (-i)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.05e+98], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.35e+139], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.9e+148], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -5.4e10 or 4.9e148 < x

   1. Initial program 66.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 66.9%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 66.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 66.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 66.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 66.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 66.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in z around inf 59.4%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   5. Taylor expanded in y around inf 55.2%

      \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]

   if -5.4e10 < x < 7.19999999999999988e-276

   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. Step-by-step derivation

      1. associate-+l- 71.0%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 71.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 71.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 71.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 71.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 71.0%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 71.0%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      2. pow3 71.0%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      3. *-commutative 71.0%

         \[\leadsto {\left(\sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right)}\right)}^{3} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   5. Applied egg-rr 71.0%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right)}\right)}^{3}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   6. Taylor expanded in a around inf 33.8%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]

   if 7.19999999999999988e-276 < x < 8.80000000000000037e-141 or 2.35e139 < x < 4.9e148

   1. Initial program 66.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 66.3%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 66.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 66.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 66.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 66.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 66.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 66.1%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      2. pow3 66.2%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      3. *-commutative 66.2%

         \[\leadsto {\left(\sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right)}\right)}^{3} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   5. Applied egg-rr 66.2%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right)}\right)}^{3}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   6. Taylor expanded in t around inf 46.5%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]

   if 8.80000000000000037e-141 < x < 9e-73

   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. Step-by-step derivation

      1. associate-+l- 74.0%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 74.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 74.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 74.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 74.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 74.0%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 73.9%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      2. pow3 73.9%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      3. *-commutative 73.9%

         \[\leadsto {\left(\sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right)}\right)}^{3} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   5. Applied egg-rr 73.9%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right)}\right)}^{3}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   6. Taylor expanded in y around inf 49.4%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(i \cdot j\right)\right)} \]
   7. Step-by-step derivation

      1. neg-mul-1 49.4%

         \[\leadsto \color{blue}{-y \cdot \left(i \cdot j\right)} \]

      2. distribute-rgt-neg-in 49.4%

         \[\leadsto \color{blue}{y \cdot \left(-i \cdot j\right)} \]

      3. *-commutative 49.4%

         \[\leadsto y \cdot \left(-\color{blue}{j \cdot i}\right) \]

      4. distribute-rgt-neg-in 49.4%

         \[\leadsto y \cdot \color{blue}{\left(j \cdot \left(-i\right)\right)} \]

   8. Simplified 49.4%

      \[\leadsto \color{blue}{y \cdot \left(j \cdot \left(-i\right)\right)} \]

   9. Taylor expanded in y around 0 49.4%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(i \cdot j\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 49.4%

          \[\leadsto \color{blue}{-y \cdot \left(i \cdot j\right)} \]

       2. *-commutative 49.4%

          \[\leadsto -\color{blue}{\left(i \cdot j\right) \cdot y} \]

       3. distribute-lft-neg-in 49.4%

          \[\leadsto \color{blue}{\left(-i \cdot j\right) \cdot y} \]

       4. *-commutative 49.4%

          \[\leadsto \left(-\color{blue}{j \cdot i}\right) \cdot y \]

       5. distribute-rgt-neg-out 49.4%

          \[\leadsto \color{blue}{\left(j \cdot \left(-i\right)\right)} \cdot y \]

       6. associate-*l* 59.3%

          \[\leadsto \color{blue}{j \cdot \left(\left(-i\right) \cdot y\right)} \]

   11. Simplified 59.3%

       \[\leadsto \color{blue}{j \cdot \left(\left(-i\right) \cdot y\right)} \]

   if 9e-73 < x < 1.05000000000000002e98

   1. Initial program 81.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 81.2%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 81.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 81.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 81.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 81.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 81.2%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in b around inf 46.0%

      \[\leadsto \color{blue}{\left(i \cdot t - c \cdot z\right) \cdot b} \]

   5. Taylor expanded in i around inf 30.4%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 33.3%

         \[\leadsto \color{blue}{\left(i \cdot t\right) \cdot b} \]

      2. *-commutative 33.3%

         \[\leadsto \color{blue}{\left(t \cdot i\right)} \cdot b \]

   7. Simplified 33.3%

      \[\leadsto \color{blue}{\left(t \cdot i\right) \cdot b} \]

   if 1.05000000000000002e98 < x < 2.35e139

   1. Initial program 79.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 79.7%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 79.7%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 79.7%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 79.7%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 79.7%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 79.7%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in a around inf 79.9%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 79.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 79.9%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 79.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 79.9%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around 0 60.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 60.9%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x\right)} \]

      2. neg-mul-1 60.9%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(t \cdot x\right) \]

   9. Simplified 60.9%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(t \cdot x\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 46.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -54000000000:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-276}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{-141}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-73}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+98}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{+139}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;x \leq 4.9 \cdot 10^{+148}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 17: 51.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_3 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -1.05 \cdot 10^{+89}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-190}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-167}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-45}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* a j) (* z b))))
        (t_2 (* b (- (* t i) (* z c))))
        (t_3 (* y (- (* x z) (* i j)))))
   (if (<= y -1.05e+89)
     t_3
     (if (<= y -1.9e-190)
       t_2
       (if (<= y 6.4e-167)
         t_1
         (if (<= y 6.5e-45) t_2 (if (<= y 1.02e+46) 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 = c * ((a * j) - (z * b));
	double t_2 = b * ((t * i) - (z * c));
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.05e+89) {
		tmp = t_3;
	} else if (y <= -1.9e-190) {
		tmp = t_2;
	} else if (y <= 6.4e-167) {
		tmp = t_1;
	} else if (y <= 6.5e-45) {
		tmp = t_2;
	} else if (y <= 1.02e+46) {
		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 = c * ((a * j) - (z * b))
    t_2 = b * ((t * i) - (z * c))
    t_3 = y * ((x * z) - (i * j))
    if (y <= (-1.05d+89)) then
        tmp = t_3
    else if (y <= (-1.9d-190)) then
        tmp = t_2
    else if (y <= 6.4d-167) then
        tmp = t_1
    else if (y <= 6.5d-45) then
        tmp = t_2
    else if (y <= 1.02d+46) 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 = c * ((a * j) - (z * b));
	double t_2 = b * ((t * i) - (z * c));
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.05e+89) {
		tmp = t_3;
	} else if (y <= -1.9e-190) {
		tmp = t_2;
	} else if (y <= 6.4e-167) {
		tmp = t_1;
	} else if (y <= 6.5e-45) {
		tmp = t_2;
	} else if (y <= 1.02e+46) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((a * j) - (z * b))
	t_2 = b * ((t * i) - (z * c))
	t_3 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -1.05e+89:
		tmp = t_3
	elif y <= -1.9e-190:
		tmp = t_2
	elif y <= 6.4e-167:
		tmp = t_1
	elif y <= 6.5e-45:
		tmp = t_2
	elif y <= 1.02e+46:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_3 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -1.05e+89)
		tmp = t_3;
	elseif (y <= -1.9e-190)
		tmp = t_2;
	elseif (y <= 6.4e-167)
		tmp = t_1;
	elseif (y <= 6.5e-45)
		tmp = t_2;
	elseif (y <= 1.02e+46)
		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 = c * ((a * j) - (z * b));
	t_2 = b * ((t * i) - (z * c));
	t_3 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -1.05e+89)
		tmp = t_3;
	elseif (y <= -1.9e-190)
		tmp = t_2;
	elseif (y <= 6.4e-167)
		tmp = t_1;
	elseif (y <= 6.5e-45)
		tmp = t_2;
	elseif (y <= 1.02e+46)
		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[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.05e+89], t$95$3, If[LessEqual[y, -1.9e-190], t$95$2, If[LessEqual[y, 6.4e-167], t$95$1, If[LessEqual[y, 6.5e-45], t$95$2, If[LessEqual[y, 1.02e+46], t$95$1, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.04999999999999993e89 or 1.0199999999999999e46 < y

   1. Initial program 62.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 62.0%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 62.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 62.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 62.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 62.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 62.0%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in y around inf 66.0%

      \[\leadsto \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y} \]
   5. Step-by-step derivation

      1. *-commutative 66.0%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 66.0%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 66.0%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 66.0%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   if -1.04999999999999993e89 < y < -1.8999999999999999e-190 or 6.4000000000000003e-167 < y < 6.4999999999999995e-45

   1. Initial program 77.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 77.8%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 77.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 77.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 77.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 77.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 77.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in b around inf 59.8%

      \[\leadsto \color{blue}{\left(i \cdot t - c \cdot z\right) \cdot b} \]

   if -1.8999999999999999e-190 < y < 6.4000000000000003e-167 or 6.4999999999999995e-45 < y < 1.0199999999999999e46

   1. Initial program 76.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 76.6%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 76.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 76.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 76.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 76.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 76.6%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in c around inf 65.1%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]
   5. Step-by-step derivation

      1. *-commutative 65.1%

         \[\leadsto c \cdot \left(\color{blue}{j \cdot a} - z \cdot b\right) \]

   6. Simplified 65.1%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a - z \cdot b\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+89}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-190}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-167}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-45}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+46}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]

Alternative 18: 41.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.8 \cdot 10^{-29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-260}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-143}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* x y))) (t_2 (* a (- (* c j) (* x t)))))
   (if (<= a -1.8e-29)
     t_2
     (if (<= a 1.75e-260)
       t_1
       (if (<= a 1.1e-143) (* i (* t b)) (if (<= a 2.1e+44) 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 = z * (x * y);
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.8e-29) {
		tmp = t_2;
	} else if (a <= 1.75e-260) {
		tmp = t_1;
	} else if (a <= 1.1e-143) {
		tmp = i * (t * b);
	} else if (a <= 2.1e+44) {
		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 = z * (x * y)
    t_2 = a * ((c * j) - (x * t))
    if (a <= (-1.8d-29)) then
        tmp = t_2
    else if (a <= 1.75d-260) then
        tmp = t_1
    else if (a <= 1.1d-143) then
        tmp = i * (t * b)
    else if (a <= 2.1d+44) 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 = z * (x * y);
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.8e-29) {
		tmp = t_2;
	} else if (a <= 1.75e-260) {
		tmp = t_1;
	} else if (a <= 1.1e-143) {
		tmp = i * (t * b);
	} else if (a <= 2.1e+44) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (x * y)
	t_2 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -1.8e-29:
		tmp = t_2
	elif a <= 1.75e-260:
		tmp = t_1
	elif a <= 1.1e-143:
		tmp = i * (t * b)
	elif a <= 2.1e+44:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(x * y))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -1.8e-29)
		tmp = t_2;
	elseif (a <= 1.75e-260)
		tmp = t_1;
	elseif (a <= 1.1e-143)
		tmp = Float64(i * Float64(t * b));
	elseif (a <= 2.1e+44)
		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 = z * (x * y);
	t_2 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -1.8e-29)
		tmp = t_2;
	elseif (a <= 1.75e-260)
		tmp = t_1;
	elseif (a <= 1.1e-143)
		tmp = i * (t * b);
	elseif (a <= 2.1e+44)
		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[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.8e-29], t$95$2, If[LessEqual[a, 1.75e-260], t$95$1, If[LessEqual[a, 1.1e-143], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.1e+44], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.79999999999999987e-29 or 2.09999999999999987e44 < a

   1. Initial program 61.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 61.9%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 61.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 61.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 61.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 61.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 61.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in a around inf 62.6%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 62.6%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 62.6%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 62.6%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 62.6%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   if -1.79999999999999987e-29 < a < 1.75e-260 or 1.09999999999999995e-143 < a < 2.09999999999999987e44

   1. Initial program 79.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 79.8%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 79.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 79.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 79.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 79.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 79.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in z around inf 51.6%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   5. Taylor expanded in y around inf 38.3%

      \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]

   if 1.75e-260 < a < 1.09999999999999995e-143

   1. Initial program 86.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 86.4%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 86.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 86.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 86.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 86.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 86.4%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 86.2%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      2. pow3 86.2%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      3. *-commutative 86.2%

         \[\leadsto {\left(\sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right)}\right)}^{3} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   5. Applied egg-rr 86.2%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right)}\right)}^{3}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   6. Taylor expanded in t around inf 42.4%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{-29}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-260}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-143}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+44}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]

Alternative 19: 28.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;x \leq -16000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{-277}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-139}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{-73}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;x \leq 5.7 \cdot 10^{+110}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* x y))))
   (if (<= x -16000000.0)
     t_1
     (if (<= x 8.8e-277)
       (* c (* a j))
       (if (<= x 1.15e-139)
         (* i (* t b))
         (if (<= x 2.35e-73)
           (* j (* y (- i)))
           (if (<= x 5.7e+110) (* a (* c j)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (x * y);
	double tmp;
	if (x <= -16000000.0) {
		tmp = t_1;
	} else if (x <= 8.8e-277) {
		tmp = c * (a * j);
	} else if (x <= 1.15e-139) {
		tmp = i * (t * b);
	} else if (x <= 2.35e-73) {
		tmp = j * (y * -i);
	} else if (x <= 5.7e+110) {
		tmp = a * (c * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (x * y)
    if (x <= (-16000000.0d0)) then
        tmp = t_1
    else if (x <= 8.8d-277) then
        tmp = c * (a * j)
    else if (x <= 1.15d-139) then
        tmp = i * (t * b)
    else if (x <= 2.35d-73) then
        tmp = j * (y * -i)
    else if (x <= 5.7d+110) then
        tmp = a * (c * j)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (x * y);
	double tmp;
	if (x <= -16000000.0) {
		tmp = t_1;
	} else if (x <= 8.8e-277) {
		tmp = c * (a * j);
	} else if (x <= 1.15e-139) {
		tmp = i * (t * b);
	} else if (x <= 2.35e-73) {
		tmp = j * (y * -i);
	} else if (x <= 5.7e+110) {
		tmp = a * (c * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (x * y)
	tmp = 0
	if x <= -16000000.0:
		tmp = t_1
	elif x <= 8.8e-277:
		tmp = c * (a * j)
	elif x <= 1.15e-139:
		tmp = i * (t * b)
	elif x <= 2.35e-73:
		tmp = j * (y * -i)
	elif x <= 5.7e+110:
		tmp = a * (c * j)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (x <= -16000000.0)
		tmp = t_1;
	elseif (x <= 8.8e-277)
		tmp = Float64(c * Float64(a * j));
	elseif (x <= 1.15e-139)
		tmp = Float64(i * Float64(t * b));
	elseif (x <= 2.35e-73)
		tmp = Float64(j * Float64(y * Float64(-i)));
	elseif (x <= 5.7e+110)
		tmp = Float64(a * Float64(c * j));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * (x * y);
	tmp = 0.0;
	if (x <= -16000000.0)
		tmp = t_1;
	elseif (x <= 8.8e-277)
		tmp = c * (a * j);
	elseif (x <= 1.15e-139)
		tmp = i * (t * b);
	elseif (x <= 2.35e-73)
		tmp = j * (y * -i);
	elseif (x <= 5.7e+110)
		tmp = a * (c * j);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -16000000.0], t$95$1, If[LessEqual[x, 8.8e-277], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.15e-139], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.35e-73], N[(j * N[(y * (-i)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.7e+110], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.6e7 or 5.7000000000000002e110 < x

   1. Initial program 67.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 67.5%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 67.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 67.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 67.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 67.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 67.5%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in z around inf 56.4%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   5. Taylor expanded in y around inf 51.6%

      \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]

   if -1.6e7 < x < 8.79999999999999983e-277

   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. Step-by-step derivation

      1. associate-+l- 71.0%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 71.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 71.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 71.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 71.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 71.0%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 71.0%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      2. pow3 71.0%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      3. *-commutative 71.0%

         \[\leadsto {\left(\sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right)}\right)}^{3} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   5. Applied egg-rr 71.0%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right)}\right)}^{3}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   6. Taylor expanded in a around inf 33.8%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]

   if 8.79999999999999983e-277 < x < 1.15000000000000006e-139

   1. Initial program 63.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 63.5%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 63.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 63.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 63.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 63.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 63.5%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 63.4%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      2. pow3 63.4%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      3. *-commutative 63.4%

         \[\leadsto {\left(\sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right)}\right)}^{3} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   5. Applied egg-rr 63.4%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right)}\right)}^{3}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   6. Taylor expanded in t around inf 43.5%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]

   if 1.15000000000000006e-139 < x < 2.34999999999999997e-73

   1. Initial program 72.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 72.6%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 72.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 72.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 72.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 72.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 72.6%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 72.4%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      2. pow3 72.4%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      3. *-commutative 72.4%

         \[\leadsto {\left(\sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right)}\right)}^{3} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   5. Applied egg-rr 72.4%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right)}\right)}^{3}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   6. Taylor expanded in y around inf 52.1%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(i \cdot j\right)\right)} \]
   7. Step-by-step derivation

      1. neg-mul-1 52.1%

         \[\leadsto \color{blue}{-y \cdot \left(i \cdot j\right)} \]

      2. distribute-rgt-neg-in 52.1%

         \[\leadsto \color{blue}{y \cdot \left(-i \cdot j\right)} \]

      3. *-commutative 52.1%

         \[\leadsto y \cdot \left(-\color{blue}{j \cdot i}\right) \]

      4. distribute-rgt-neg-in 52.1%

         \[\leadsto y \cdot \color{blue}{\left(j \cdot \left(-i\right)\right)} \]

   8. Simplified 52.1%

      \[\leadsto \color{blue}{y \cdot \left(j \cdot \left(-i\right)\right)} \]

   9. Taylor expanded in y around 0 52.1%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(i \cdot j\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 52.1%

          \[\leadsto \color{blue}{-y \cdot \left(i \cdot j\right)} \]

       2. *-commutative 52.1%

          \[\leadsto -\color{blue}{\left(i \cdot j\right) \cdot y} \]

       3. distribute-lft-neg-in 52.1%

          \[\leadsto \color{blue}{\left(-i \cdot j\right) \cdot y} \]

       4. *-commutative 52.1%

          \[\leadsto \left(-\color{blue}{j \cdot i}\right) \cdot y \]

       5. distribute-rgt-neg-out 52.1%

          \[\leadsto \color{blue}{\left(j \cdot \left(-i\right)\right)} \cdot y \]

       6. associate-*l* 62.5%

          \[\leadsto \color{blue}{j \cdot \left(\left(-i\right) \cdot y\right)} \]

   11. Simplified 62.5%

       \[\leadsto \color{blue}{j \cdot \left(\left(-i\right) \cdot y\right)} \]

   if 2.34999999999999997e-73 < x < 5.7000000000000002e110

   1. Initial program 83.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 83.8%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 83.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 83.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 83.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 83.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 83.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in a around inf 45.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 45.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 45.5%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 45.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 45.5%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around inf 33.8%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 33.8%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   9. Simplified 33.8%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -16000000:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{-277}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-139}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{-73}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;x \leq 5.7 \cdot 10^{+110}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 20: 41.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+266}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{+115} \lor \neg \left(y \leq 2.05 \cdot 10^{+49}\right):\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -1.85e+266)
   (* i (* y (- j)))
   (if (or (<= y -3.1e+115) (not (<= y 2.05e+49)))
     (* z (* x y))
     (* c (- (* a j) (* z b))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -1.85e+266) {
		tmp = i * (y * -j);
	} else if ((y <= -3.1e+115) || !(y <= 2.05e+49)) {
		tmp = z * (x * y);
	} else {
		tmp = c * ((a * j) - (z * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-1.85d+266)) then
        tmp = i * (y * -j)
    else if ((y <= (-3.1d+115)) .or. (.not. (y <= 2.05d+49))) then
        tmp = z * (x * y)
    else
        tmp = c * ((a * j) - (z * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -1.85e+266) {
		tmp = i * (y * -j);
	} else if ((y <= -3.1e+115) || !(y <= 2.05e+49)) {
		tmp = z * (x * y);
	} else {
		tmp = c * ((a * j) - (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -1.85e+266:
		tmp = i * (y * -j)
	elif (y <= -3.1e+115) or not (y <= 2.05e+49):
		tmp = z * (x * y)
	else:
		tmp = c * ((a * j) - (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -1.85e+266)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif ((y <= -3.1e+115) || !(y <= 2.05e+49))
		tmp = Float64(z * Float64(x * y));
	else
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -1.85e+266)
		tmp = i * (y * -j);
	elseif ((y <= -3.1e+115) || ~((y <= 2.05e+49)))
		tmp = z * (x * y);
	else
		tmp = c * ((a * j) - (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -1.85e+266], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -3.1e+115], N[Not[LessEqual[y, 2.05e+49]], $MachinePrecision]], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.85e266

   1. Initial program 41.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 41.7%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 41.7%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 41.7%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 41.7%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 41.7%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 41.7%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 41.7%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      2. pow3 41.7%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      3. *-commutative 41.7%

         \[\leadsto {\left(\sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right)}\right)}^{3} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   5. Applied egg-rr 41.7%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right)}\right)}^{3}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   6. Taylor expanded in y around inf 67.4%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(i \cdot j\right)\right)} \]
   7. Step-by-step derivation

      1. neg-mul-1 67.4%

         \[\leadsto \color{blue}{-y \cdot \left(i \cdot j\right)} \]

      2. distribute-rgt-neg-in 67.4%

         \[\leadsto \color{blue}{y \cdot \left(-i \cdot j\right)} \]

      3. *-commutative 67.4%

         \[\leadsto y \cdot \left(-\color{blue}{j \cdot i}\right) \]

      4. distribute-rgt-neg-in 67.4%

         \[\leadsto y \cdot \color{blue}{\left(j \cdot \left(-i\right)\right)} \]

   8. Simplified 67.4%

      \[\leadsto \color{blue}{y \cdot \left(j \cdot \left(-i\right)\right)} \]

   9. Taylor expanded in j around 0 75.3%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(y \cdot j\right)\right)} \]

   if -1.85e266 < y < -3.10000000000000005e115 or 2.05e49 < y

   1. Initial program 64.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 64.9%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 64.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 64.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 64.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 64.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 64.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in z around inf 50.5%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   5. Taylor expanded in y around inf 49.7%

      \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]

   if -3.10000000000000005e115 < y < 2.05e49

   1. Initial program 76.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 76.6%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 76.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 76.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 76.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 76.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 76.6%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in c around inf 54.8%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]
   5. Step-by-step derivation

      1. *-commutative 54.8%

         \[\leadsto c \cdot \left(\color{blue}{j \cdot a} - z \cdot b\right) \]

   6. Simplified 54.8%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a - z \cdot b\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+266}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{+115} \lor \neg \left(y \leq 2.05 \cdot 10^{+49}\right):\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 21: 51.0% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+113} \lor \neg \left(y \leq 2.65 \cdot 10^{+47}\right):\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= y -3.8e+113) (not (<= y 2.65e+47)))
   (* y (- (* x z) (* i j)))
   (* c (- (* a j) (* z b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((y <= -3.8e+113) || !(y <= 2.65e+47)) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = c * ((a * j) - (z * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((y <= (-3.8d+113)) .or. (.not. (y <= 2.65d+47))) then
        tmp = y * ((x * z) - (i * j))
    else
        tmp = c * ((a * j) - (z * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((y <= -3.8e+113) || !(y <= 2.65e+47)) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = c * ((a * j) - (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (y <= -3.8e+113) or not (y <= 2.65e+47):
		tmp = y * ((x * z) - (i * j))
	else:
		tmp = c * ((a * j) - (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((y <= -3.8e+113) || !(y <= 2.65e+47))
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	else
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((y <= -3.8e+113) || ~((y <= 2.65e+47)))
		tmp = y * ((x * z) - (i * j));
	else
		tmp = c * ((a * j) - (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[y, -3.8e+113], N[Not[LessEqual[y, 2.65e+47]], $MachinePrecision]], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.8000000000000003e113 or 2.65e47 < y

   1. Initial program 62.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 62.3%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 62.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 62.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 62.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 62.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 62.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in y around inf 67.5%

      \[\leadsto \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y} \]
   5. Step-by-step derivation

      1. *-commutative 67.5%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 67.5%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 67.5%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 67.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   if -3.8000000000000003e113 < y < 2.65e47

   1. Initial program 76.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 76.6%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 76.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 76.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 76.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 76.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 76.6%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in c around inf 54.8%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]
   5. Step-by-step derivation

      1. *-commutative 54.8%

         \[\leadsto c \cdot \left(\color{blue}{j \cdot a} - z \cdot b\right) \]

   6. Simplified 54.8%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a - z \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+113} \lor \neg \left(y \leq 2.65 \cdot 10^{+47}\right):\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 22: 50.3% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -7.4 \cdot 10^{+74} \lor \neg \left(j \leq 3.3 \cdot 10^{+138}\right):\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -7.4e+74) (not (<= j 3.3e+138)))
   (* j (- (* a c) (* y i)))
   (* z (- (* x y) (* b c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -7.4e+74) || !(j <= 3.3e+138)) {
		tmp = j * ((a * c) - (y * i));
	} else {
		tmp = z * ((x * y) - (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) :: tmp
    if ((j <= (-7.4d+74)) .or. (.not. (j <= 3.3d+138))) then
        tmp = j * ((a * c) - (y * i))
    else
        tmp = z * ((x * y) - (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 tmp;
	if ((j <= -7.4e+74) || !(j <= 3.3e+138)) {
		tmp = j * ((a * c) - (y * i));
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -7.4e+74) or not (j <= 3.3e+138):
		tmp = j * ((a * c) - (y * i))
	else:
		tmp = z * ((x * y) - (b * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -7.4e+74) || !(j <= 3.3e+138))
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	else
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -7.4e+74) || ~((j <= 3.3e+138)))
		tmp = j * ((a * c) - (y * i));
	else
		tmp = z * ((x * y) - (b * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -7.4e+74], N[Not[LessEqual[j, 3.3e+138]], $MachinePrecision]], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -7.4000000000000002e74 or 3.29999999999999978e138 < j

   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. Step-by-step derivation

      1. associate-+l- 71.0%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 71.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 71.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 71.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 71.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 71.0%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 71.0%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      2. pow3 71.0%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      3. *-commutative 71.0%

         \[\leadsto {\left(\sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right)}\right)}^{3} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   5. Applied egg-rr 71.0%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right)}\right)}^{3}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   6. Taylor expanded in j around -inf 73.6%

      \[\leadsto \color{blue}{\left(c \cdot a - i \cdot y\right) \cdot j} \]

   if -7.4000000000000002e74 < j < 3.29999999999999978e138

   1. Initial program 70.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 70.6%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 70.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 70.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 70.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 70.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 70.6%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in z around inf 55.2%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -7.4 \cdot 10^{+74} \lor \neg \left(j \leq 3.3 \cdot 10^{+138}\right):\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]

Alternative 23: 30.0% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;x \leq -2000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-277}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+58}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* x z))))
   (if (<= x -2000000000.0)
     t_1
     (if (<= x 2.2e-277)
       (* c (* a j))
       (if (<= x 1.55e+58) (* i (* t b)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (x * z);
	double tmp;
	if (x <= -2000000000.0) {
		tmp = t_1;
	} else if (x <= 2.2e-277) {
		tmp = c * (a * j);
	} else if (x <= 1.55e+58) {
		tmp = i * (t * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (x * z)
    if (x <= (-2000000000.0d0)) then
        tmp = t_1
    else if (x <= 2.2d-277) then
        tmp = c * (a * j)
    else if (x <= 1.55d+58) then
        tmp = i * (t * b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (x * z);
	double tmp;
	if (x <= -2000000000.0) {
		tmp = t_1;
	} else if (x <= 2.2e-277) {
		tmp = c * (a * j);
	} else if (x <= 1.55e+58) {
		tmp = i * (t * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (x * z)
	tmp = 0
	if x <= -2000000000.0:
		tmp = t_1
	elif x <= 2.2e-277:
		tmp = c * (a * j)
	elif x <= 1.55e+58:
		tmp = i * (t * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(x * z))
	tmp = 0.0
	if (x <= -2000000000.0)
		tmp = t_1;
	elseif (x <= 2.2e-277)
		tmp = Float64(c * Float64(a * j));
	elseif (x <= 1.55e+58)
		tmp = Float64(i * Float64(t * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * (x * z);
	tmp = 0.0;
	if (x <= -2000000000.0)
		tmp = t_1;
	elseif (x <= 2.2e-277)
		tmp = c * (a * j);
	elseif (x <= 1.55e+58)
		tmp = i * (t * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2000000000.0], t$95$1, If[LessEqual[x, 2.2e-277], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.55e+58], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2e9 or 1.55e58 < x

   1. Initial program 69.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 69.4%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 69.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 69.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 69.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 69.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 69.4%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in z around inf 54.4%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   5. Taylor expanded in y around inf 43.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if -2e9 < x < 2.19999999999999996e-277

   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. Step-by-step derivation

      1. associate-+l- 71.0%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 71.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 71.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 71.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 71.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 71.0%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 71.0%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      2. pow3 71.0%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      3. *-commutative 71.0%

         \[\leadsto {\left(\sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right)}\right)}^{3} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   5. Applied egg-rr 71.0%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right)}\right)}^{3}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   6. Taylor expanded in a around inf 33.8%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]

   if 2.19999999999999996e-277 < x < 1.55e58

   1. Initial program 72.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 72.6%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 72.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 72.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 72.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 72.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 72.6%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 72.5%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      2. pow3 72.5%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      3. *-commutative 72.5%

         \[\leadsto {\left(\sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right)}\right)}^{3} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   5. Applied egg-rr 72.5%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right)}\right)}^{3}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   6. Taylor expanded in t around inf 35.4%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 38.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2000000000:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-277}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+58}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 24: 30.2% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;x \leq -50000000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-276}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;x \leq 5.3 \cdot 10^{+54}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* x z))))
   (if (<= x -50000000000000.0)
     t_1
     (if (<= x 2.05e-276)
       (* c (* a j))
       (if (<= x 5.3e+54) (* b (* t i)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (x * z);
	double tmp;
	if (x <= -50000000000000.0) {
		tmp = t_1;
	} else if (x <= 2.05e-276) {
		tmp = c * (a * j);
	} else if (x <= 5.3e+54) {
		tmp = b * (t * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (x * z)
    if (x <= (-50000000000000.0d0)) then
        tmp = t_1
    else if (x <= 2.05d-276) then
        tmp = c * (a * j)
    else if (x <= 5.3d+54) then
        tmp = b * (t * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (x * z);
	double tmp;
	if (x <= -50000000000000.0) {
		tmp = t_1;
	} else if (x <= 2.05e-276) {
		tmp = c * (a * j);
	} else if (x <= 5.3e+54) {
		tmp = b * (t * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (x * z)
	tmp = 0
	if x <= -50000000000000.0:
		tmp = t_1
	elif x <= 2.05e-276:
		tmp = c * (a * j)
	elif x <= 5.3e+54:
		tmp = b * (t * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(x * z))
	tmp = 0.0
	if (x <= -50000000000000.0)
		tmp = t_1;
	elseif (x <= 2.05e-276)
		tmp = Float64(c * Float64(a * j));
	elseif (x <= 5.3e+54)
		tmp = Float64(b * Float64(t * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * (x * z);
	tmp = 0.0;
	if (x <= -50000000000000.0)
		tmp = t_1;
	elseif (x <= 2.05e-276)
		tmp = c * (a * j);
	elseif (x <= 5.3e+54)
		tmp = b * (t * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -50000000000000.0], t$95$1, If[LessEqual[x, 2.05e-276], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.3e+54], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5e13 or 5.30000000000000018e54 < x

   1. Initial program 69.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 69.4%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 69.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 69.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 69.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 69.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 69.4%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in z around inf 54.4%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   5. Taylor expanded in y around inf 43.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if -5e13 < x < 2.05e-276

   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. Step-by-step derivation

      1. associate-+l- 71.0%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 71.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 71.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 71.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 71.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 71.0%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 71.0%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      2. pow3 71.0%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      3. *-commutative 71.0%

         \[\leadsto {\left(\sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right)}\right)}^{3} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   5. Applied egg-rr 71.0%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right)}\right)}^{3}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   6. Taylor expanded in a around inf 33.8%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]

   if 2.05e-276 < x < 5.30000000000000018e54

   1. Initial program 72.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 72.6%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 72.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 72.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 72.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 72.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 72.6%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in b around inf 52.9%

      \[\leadsto \color{blue}{\left(i \cdot t - c \cdot z\right) \cdot b} \]

   5. Taylor expanded in i around inf 35.4%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 36.6%

         \[\leadsto \color{blue}{\left(i \cdot t\right) \cdot b} \]

      2. *-commutative 36.6%

         \[\leadsto \color{blue}{\left(t \cdot i\right)} \cdot b \]

   7. Simplified 36.6%

      \[\leadsto \color{blue}{\left(t \cdot i\right) \cdot b} \]
3. Recombined 3 regimes into one program.

4. Final simplification 39.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -50000000000000:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-276}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;x \leq 5.3 \cdot 10^{+54}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 25: 29.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;x \leq -850000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-277}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+60}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* x y))))
   (if (<= x -850000.0)
     t_1
     (if (<= x 6.8e-277)
       (* c (* a j))
       (if (<= x 2.9e+60) (* b (* t i)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (x * y);
	double tmp;
	if (x <= -850000.0) {
		tmp = t_1;
	} else if (x <= 6.8e-277) {
		tmp = c * (a * j);
	} else if (x <= 2.9e+60) {
		tmp = b * (t * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (x * y)
    if (x <= (-850000.0d0)) then
        tmp = t_1
    else if (x <= 6.8d-277) then
        tmp = c * (a * j)
    else if (x <= 2.9d+60) then
        tmp = b * (t * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (x * y);
	double tmp;
	if (x <= -850000.0) {
		tmp = t_1;
	} else if (x <= 6.8e-277) {
		tmp = c * (a * j);
	} else if (x <= 2.9e+60) {
		tmp = b * (t * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (x * y)
	tmp = 0
	if x <= -850000.0:
		tmp = t_1
	elif x <= 6.8e-277:
		tmp = c * (a * j)
	elif x <= 2.9e+60:
		tmp = b * (t * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (x <= -850000.0)
		tmp = t_1;
	elseif (x <= 6.8e-277)
		tmp = Float64(c * Float64(a * j));
	elseif (x <= 2.9e+60)
		tmp = Float64(b * Float64(t * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * (x * y);
	tmp = 0.0;
	if (x <= -850000.0)
		tmp = t_1;
	elseif (x <= 6.8e-277)
		tmp = c * (a * j);
	elseif (x <= 2.9e+60)
		tmp = b * (t * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -850000.0], t$95$1, If[LessEqual[x, 6.8e-277], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.9e+60], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.5e5 or 2.9e60 < x

   1. Initial program 69.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 69.4%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 69.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 69.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 69.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 69.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 69.4%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in z around inf 54.4%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   5. Taylor expanded in y around inf 48.5%

      \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]

   if -8.5e5 < x < 6.79999999999999964e-277

   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. Step-by-step derivation

      1. associate-+l- 71.0%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 71.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 71.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 71.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 71.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 71.0%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 71.0%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      2. pow3 71.0%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      3. *-commutative 71.0%

         \[\leadsto {\left(\sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right)}\right)}^{3} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   5. Applied egg-rr 71.0%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right)}\right)}^{3}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   6. Taylor expanded in a around inf 33.8%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]

   if 6.79999999999999964e-277 < x < 2.9e60

   1. Initial program 72.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 72.6%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 72.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 72.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 72.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 72.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 72.6%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in b around inf 52.9%

      \[\leadsto \color{blue}{\left(i \cdot t - c \cdot z\right) \cdot b} \]

   5. Taylor expanded in i around inf 35.4%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 36.6%

         \[\leadsto \color{blue}{\left(i \cdot t\right) \cdot b} \]

      2. *-commutative 36.6%

         \[\leadsto \color{blue}{\left(t \cdot i\right)} \cdot b \]

   7. Simplified 36.6%

      \[\leadsto \color{blue}{\left(t \cdot i\right) \cdot b} \]
3. Recombined 3 regimes into one program.

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -850000:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-277}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+60}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 26: 30.0% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.25 \cdot 10^{+55} \lor \neg \left(a \leq 1.32 \cdot 10^{+47}\right):\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -1.25e+55) (not (<= a 1.32e+47))) (* c (* a j)) (* i (* t b))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -1.25e+55) || !(a <= 1.32e+47)) {
		tmp = c * (a * j);
	} else {
		tmp = i * (t * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((a <= (-1.25d+55)) .or. (.not. (a <= 1.32d+47))) then
        tmp = c * (a * j)
    else
        tmp = i * (t * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -1.25e+55) || !(a <= 1.32e+47)) {
		tmp = c * (a * j);
	} else {
		tmp = i * (t * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (a <= -1.25e+55) or not (a <= 1.32e+47):
		tmp = c * (a * j)
	else:
		tmp = i * (t * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -1.25e+55) || !(a <= 1.32e+47))
		tmp = Float64(c * Float64(a * j));
	else
		tmp = Float64(i * Float64(t * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((a <= -1.25e+55) || ~((a <= 1.32e+47)))
		tmp = c * (a * j);
	else
		tmp = i * (t * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -1.25e+55], N[Not[LessEqual[a, 1.32e+47]], $MachinePrecision]], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.25000000000000011e55 or 1.31999999999999992e47 < a

   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. Step-by-step derivation

      1. associate-+l- 59.9%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 59.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 59.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 59.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 59.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 59.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 59.8%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      2. pow3 59.8%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      3. *-commutative 59.8%

         \[\leadsto {\left(\sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right)}\right)}^{3} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   5. Applied egg-rr 59.8%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right)}\right)}^{3}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   6. Taylor expanded in a around inf 46.0%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]

   if -1.25000000000000011e55 < a < 1.31999999999999992e47

   1. Initial program 79.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 79.7%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 79.7%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 79.7%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 79.7%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 79.7%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 79.7%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 79.5%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      2. pow3 79.5%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      3. *-commutative 79.5%

         \[\leadsto {\left(\sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right)}\right)}^{3} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   5. Applied egg-rr 79.5%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right)}\right)}^{3}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   6. Taylor expanded in t around inf 26.5%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 35.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.25 \cdot 10^{+55} \lor \neg \left(a \leq 1.32 \cdot 10^{+47}\right):\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \]

Alternative 27: 22.1% 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 70.7%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
2. Step-by-step derivation

   1. associate-+l- 70.7%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

   2. *-commutative 70.7%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

   3. sub-neg 70.7%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

   4. sub-neg 70.7%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

   5. *-commutative 70.7%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

3. Simplified 70.7%

   \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

4. Taylor expanded in a around inf 38.2%

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
5. Step-by-step derivation

   1. +-commutative 38.2%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

   2. mul-1-neg 38.2%

      \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

   3. unsub-neg 38.2%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

6. Simplified 38.2%

   \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

7. Taylor expanded in c around inf 23.2%

   \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
8. Step-by-step derivation

   1. *-commutative 23.2%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

9. Simplified 23.2%

   \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

10. Final simplification 23.2%

    \[\leadsto a \cdot \left(c \cdot j\right) \]

Alternative 28: 22.0% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ c \cdot \left(a \cdot j\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* c (* a j)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return c * (a * 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 = c * (a * 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 c * (a * j);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return c * (a * j)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(c * Float64(a * j))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = c * (a * j);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 70.7%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
2. Step-by-step derivation

   1. associate-+l- 70.7%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

   2. *-commutative 70.7%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

   3. sub-neg 70.7%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

   4. sub-neg 70.7%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

   5. *-commutative 70.7%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

3. Simplified 70.7%

   \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]
4. Step-by-step derivation

   1. add-cube-cbrt 70.6%

      \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)} \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right) \cdot \sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   2. pow3 70.6%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(y \cdot z - t \cdot a\right)}\right)}^{3}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   3. *-commutative 70.6%

      \[\leadsto {\left(\sqrt[3]{x \cdot \left(\color{blue}{z \cdot y} - t \cdot a\right)}\right)}^{3} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

5. Applied egg-rr 70.6%

   \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(z \cdot y - t \cdot a\right)}\right)}^{3}} - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

6. Taylor expanded in a around inf 24.3%

   \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]

7. Final simplification 24.3%

   \[\leadsto c \cdot \left(a \cdot j\right) \]

Developer target: 60.0% 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 2023309 
(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)))))