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

Percentage Accurate: 73.8% → 81.4%

Time: 14.1s

Alternatives: 15

Speedup: 0.3×

• 57.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 81.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) + t\_1\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ t_3 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;t\_2 \leq 2 \cdot 10^{+296}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + \left(t\_3 + t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t\_3 + t \cdot \left(b \cdot i - x \cdot a\right)\right) + c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c))))
        (t_2 (+ (+ (* x (- (* y z) (* t a))) t_1) (* j (- (* a c) (* y i)))))
        (t_3 (* y (- (* x z) (* i j)))))
   (if (<= t_2 2e+296)
     t_2
     (if (<= t_2 INFINITY)
       (+ (* a (- (* c j) (* x t))) (+ t_3 t_1))
       (+ (+ t_3 (* t (- (* b i) (* x a)))) (* 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 t_1 = b * ((t * i) - (z * c));
	double t_2 = ((x * ((y * z) - (t * a))) + t_1) + (j * ((a * c) - (y * i)));
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (t_2 <= 2e+296) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = (a * ((c * j) - (x * t))) + (t_3 + t_1);
	} else {
		tmp = (t_3 + (t * ((b * i) - (x * a)))) + (c * ((a * j) - (z * b)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = ((x * ((y * z) - (t * a))) + t_1) + (j * ((a * c) - (y * i)));
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (t_2 <= 2e+296) {
		tmp = t_2;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = (a * ((c * j) - (x * t))) + (t_3 + t_1);
	} else {
		tmp = (t_3 + (t * ((b * i) - (x * a)))) + (c * ((a * j) - (z * b)));
	}
	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_1) + (j * ((a * c) - (y * i)))
	t_3 = y * ((x * z) - (i * j))
	tmp = 0
	if t_2 <= 2e+296:
		tmp = t_2
	elif t_2 <= math.inf:
		tmp = (a * ((c * j) - (x * t))) + (t_3 + t_1)
	else:
		tmp = (t_3 + (t * ((b * i) - (x * a)))) + (c * ((a * j) - (z * b)))
	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(x * Float64(Float64(y * z) - Float64(t * a))) + t_1) + Float64(j * Float64(Float64(a * c) - Float64(y * i))))
	t_3 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (t_2 <= 2e+296)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) + Float64(t_3 + t_1));
	else
		tmp = Float64(Float64(t_3 + Float64(t * Float64(Float64(b * i) - Float64(x * a)))) + 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)
	t_1 = b * ((t * i) - (z * c));
	t_2 = ((x * ((y * z) - (t * a))) + t_1) + (j * ((a * c) - (y * i)));
	t_3 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (t_2 <= 2e+296)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = (a * ((c * j) - (x * t))) + (t_3 + t_1);
	else
		tmp = (t_3 + (t * ((b * i) - (x * a)))) + (c * ((a * j) - (z * b)));
	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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, 2e+296], t$95$2, If[LessEqual[t$95$2, Infinity], N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$3 + t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$3 + N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 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)))) < 1.99999999999999996e296

   1. Initial program 92.7%

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

   if 1.99999999999999996e296 < (+.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 81.7%

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

   3. Taylor expanded in y around 0

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

   5. Simplified 91.3%

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

   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. Add Preprocessing

   3. Taylor expanded in y around 0

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

   5. Simplified 35.9%

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

   6. Taylor expanded in t around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. mul-1-neg N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

      12. distribute-lft-in N/A

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

      13. mul-1-neg N/A

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

      14. sub-neg N/A

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

   8. Simplified 64.1%

      \[\leadsto \color{blue}{\left(y \cdot \left(x \cdot z - i \cdot j\right) + \left(x \cdot a - i \cdot b\right) \cdot \left(0 - t\right)\right) + c \cdot \left(j \cdot a - z \cdot b\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right) \leq 2 \cdot 10^{+296}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right) \leq \infty:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + \left(y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x \cdot z - i \cdot j\right) + t \cdot \left(b \cdot i - x \cdot a\right)\right) + c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 81.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) + t\_1\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ t_3 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;t\_2 \leq 2 \cdot 10^{+296}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + \left(t\_3 + t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c))))
        (t_2 (+ (+ (* x (- (* y z) (* t a))) t_1) (* j (- (* a c) (* y i)))))
        (t_3 (* y (- (* x z) (* i j)))))
   (if (<= t_2 2e+296)
     t_2
     (if (<= t_2 INFINITY) (+ (* a (- (* c j) (* x t))) (+ t_3 t_1)) t_3))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = ((x * ((y * z) - (t * a))) + t_1) + (j * ((a * c) - (y * i)));
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (t_2 <= 2e+296) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = (a * ((c * j) - (x * t))) + (t_3 + t_1);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = ((x * ((y * z) - (t * a))) + t_1) + (j * ((a * c) - (y * i)));
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (t_2 <= 2e+296) {
		tmp = t_2;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = (a * ((c * j) - (x * t))) + (t_3 + t_1);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = ((x * ((y * z) - (t * a))) + t_1) + (j * ((a * c) - (y * i)))
	t_3 = y * ((x * z) - (i * j))
	tmp = 0
	if t_2 <= 2e+296:
		tmp = t_2
	elif t_2 <= math.inf:
		tmp = (a * ((c * j) - (x * t))) + (t_3 + t_1)
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_1) + Float64(j * Float64(Float64(a * c) - Float64(y * i))))
	t_3 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (t_2 <= 2e+296)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) + Float64(t_3 + t_1));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = ((x * ((y * z) - (t * a))) + t_1) + (j * ((a * c) - (y * i)));
	t_3 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (t_2 <= 2e+296)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = (a * ((c * j) - (x * t))) + (t_3 + t_1);
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, 2e+296], t$95$2, If[LessEqual[t$95$2, Infinity], N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$3 + t$95$1), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]

Derivation

1. Split input into 3 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)))) < 1.99999999999999996e296

   1. Initial program 92.7%

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

   if 1.99999999999999996e296 < (+.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 81.7%

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

   3. Taylor expanded in y around 0

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

   5. Simplified 91.3%

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

   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. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(x \cdot z + \color{blue}{-1 \cdot \left(i \cdot j\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(x \cdot z + \left(\mathsf{neg}\left(i \cdot j\right)\right)\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(x \cdot z - \color{blue}{i \cdot j}\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(x \cdot z\right), \color{blue}{\left(i \cdot j\right)}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(z \cdot x\right), \left(\color{blue}{i} \cdot j\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, x\right), \left(\color{blue}{i} \cdot j\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, x\right), \left(j \cdot \color{blue}{i}\right)\right)\right) \]

      9. *-lowering-*.f64 62.0%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, x\right), \mathsf{*.f64}\left(j, \color{blue}{i}\right)\right)\right) \]

   5. Simplified 62.0%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right) \leq 2 \cdot 10^{+296}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right) \leq \infty:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + \left(y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq 36000000000000:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + \left(y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j 36000000000000.0)
   (+
    (* a (- (* c j) (* x t)))
    (+ (* y (- (* x z) (* i j))) (* b (- (* t i) (* z c)))))
   (+ (* j (- (* a c) (* y i))) (* y (* x z)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= 36000000000000.0) {
		tmp = (a * ((c * j) - (x * t))) + ((y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c))));
	} else {
		tmp = (j * ((a * c) - (y * i))) + (y * (x * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (j <= 36000000000000.0d0) then
        tmp = (a * ((c * j) - (x * t))) + ((y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c))))
    else
        tmp = (j * ((a * c) - (y * i))) + (y * (x * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= 36000000000000.0) {
		tmp = (a * ((c * j) - (x * t))) + ((y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c))));
	} else {
		tmp = (j * ((a * c) - (y * i))) + (y * (x * z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= 36000000000000.0:
		tmp = (a * ((c * j) - (x * t))) + ((y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c))))
	else:
		tmp = (j * ((a * c) - (y * i))) + (y * (x * z))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= 36000000000000.0)
		tmp = Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) + Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(b * Float64(Float64(t * i) - Float64(z * c)))));
	else
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(y * Float64(x * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= 36000000000000.0)
		tmp = (a * ((c * j) - (x * t))) + ((y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c))));
	else
		tmp = (j * ((a * c) - (y * i))) + (y * (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, 36000000000000.0], N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < 3.6e13

   1. Initial program 75.4%

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

   3. Taylor expanded in y around 0

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

   5. Simplified 81.1%

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

   if 3.6e13 < j

   1. Initial program 79.2%

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

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(x \cdot \left(y \cdot z\right)\right)}, \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(y \cdot z\right) \cdot x\right), \mathsf{*.f64}\left(\color{blue}{j}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(y \cdot \left(z \cdot x\right)\right), \mathsf{*.f64}\left(\color{blue}{j}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(y \cdot \left(x \cdot z\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \left(x \cdot z\right)\right), \mathsf{*.f64}\left(\color{blue}{j}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \left(z \cdot x\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      6. *-lowering-*.f64 81.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, x\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

   5. Simplified 81.2%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq 36000000000000:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + \left(y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + y \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 59.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -2.5 \cdot 10^{+57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{-36}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right) + i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+74}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+171}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= x -2.5e+57)
     t_1
     (if (<= x 2.15e-36)
       (+ (* c (- (* a j) (* z b))) (* i (* t b)))
       (if (<= x 8e+74)
         (+ (* j (- (* a c) (* y i))) (* y (* x z)))
         (if (<= x 3.2e+171) (* t (- (* b i) (* x a))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -2.5e+57) {
		tmp = t_1;
	} else if (x <= 2.15e-36) {
		tmp = (c * ((a * j) - (z * b))) + (i * (t * b));
	} else if (x <= 8e+74) {
		tmp = (j * ((a * c) - (y * i))) + (y * (x * z));
	} else if (x <= 3.2e+171) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (x <= (-2.5d+57)) then
        tmp = t_1
    else if (x <= 2.15d-36) then
        tmp = (c * ((a * j) - (z * b))) + (i * (t * b))
    else if (x <= 8d+74) then
        tmp = (j * ((a * c) - (y * i))) + (y * (x * z))
    else if (x <= 3.2d+171) then
        tmp = t * ((b * i) - (x * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -2.5e+57) {
		tmp = t_1;
	} else if (x <= 2.15e-36) {
		tmp = (c * ((a * j) - (z * b))) + (i * (t * b));
	} else if (x <= 8e+74) {
		tmp = (j * ((a * c) - (y * i))) + (y * (x * z));
	} else if (x <= 3.2e+171) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -2.5e+57:
		tmp = t_1
	elif x <= 2.15e-36:
		tmp = (c * ((a * j) - (z * b))) + (i * (t * b))
	elif x <= 8e+74:
		tmp = (j * ((a * c) - (y * i))) + (y * (x * z))
	elif x <= 3.2e+171:
		tmp = t * ((b * i) - (x * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -2.5e+57)
		tmp = t_1;
	elseif (x <= 2.15e-36)
		tmp = Float64(Float64(c * Float64(Float64(a * j) - Float64(z * b))) + Float64(i * Float64(t * b)));
	elseif (x <= 8e+74)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(y * Float64(x * z)));
	elseif (x <= 3.2e+171)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -2.5e+57)
		tmp = t_1;
	elseif (x <= 2.15e-36)
		tmp = (c * ((a * j) - (z * b))) + (i * (t * b));
	elseif (x <= 8e+74)
		tmp = (j * ((a * c) - (y * i))) + (y * (x * z));
	elseif (x <= 3.2e+171)
		tmp = t * ((b * i) - (x * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.5e+57], t$95$1, If[LessEqual[x, 2.15e-36], N[(N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8e+74], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.2e+171], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.49999999999999986e57 or 3.20000000000000011e171 < x

   1. Initial program 85.0%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(y \cdot z - a \cdot t\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\left(y \cdot z\right), \color{blue}{\left(a \cdot t\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \left(\color{blue}{a} \cdot t\right)\right)\right) \]

      4. *-lowering-*.f64 81.4%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(a, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 81.4%

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

   if -2.49999999999999986e57 < x < 2.1500000000000001e-36

   1. Initial program 68.5%

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

   3. Taylor expanded in y around 0

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

   5. Simplified 78.3%

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

   6. Taylor expanded in t around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. mul-1-neg N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

      12. distribute-lft-in N/A

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

      13. mul-1-neg N/A

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

      14. sub-neg N/A

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

   8. Simplified 76.7%

      \[\leadsto \color{blue}{\left(y \cdot \left(x \cdot z - i \cdot j\right) + \left(x \cdot a - i \cdot b\right) \cdot \left(0 - t\right)\right) + c \cdot \left(j \cdot a - z \cdot b\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(b \cdot \left(i \cdot t\right)\right)}, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, a\right), \mathsf{*.f64}\left(z, b\right)\right)\right)\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\left(i \cdot t\right) \cdot b\right), \mathsf{*.f64}\left(\color{blue}{c}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, a\right), \mathsf{*.f64}\left(z, b\right)\right)\right)\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\left(i \cdot \left(t \cdot b\right)\right), \mathsf{*.f64}\left(\color{blue}{c}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, a\right), \mathsf{*.f64}\left(z, b\right)\right)\right)\right) \]

       3. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(i \cdot \left(b \cdot t\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, a\right), \mathsf{*.f64}\left(z, b\right)\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \left(b \cdot t\right)\right), \mathsf{*.f64}\left(\color{blue}{c}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, a\right), \mathsf{*.f64}\left(z, b\right)\right)\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \left(t \cdot b\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, a\right), \mathsf{*.f64}\left(z, b\right)\right)\right)\right) \]

       6. *-lowering-*.f64 62.4%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \mathsf{*.f64}\left(t, b\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, a\right), \mathsf{*.f64}\left(z, b\right)\right)\right)\right) \]

   11. Simplified 62.4%

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

   if 2.1500000000000001e-36 < x < 7.99999999999999961e74

   1. Initial program 81.9%

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

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(x \cdot \left(y \cdot z\right)\right)}, \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(y \cdot z\right) \cdot x\right), \mathsf{*.f64}\left(\color{blue}{j}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(y \cdot \left(z \cdot x\right)\right), \mathsf{*.f64}\left(\color{blue}{j}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(y \cdot \left(x \cdot z\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \left(x \cdot z\right)\right), \mathsf{*.f64}\left(\color{blue}{j}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \left(z \cdot x\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

      6. *-lowering-*.f64 72.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, x\right)\right), \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(c, a\right), \mathsf{*.f64}\left(y, i\right)\right)\right)\right) \]

   5. Simplified 72.4%

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

   if 7.99999999999999961e74 < x < 3.20000000000000011e171

   1. Initial program 79.2%

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

   3. Taylor expanded in t around inf

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

      1. distribute-lft-out-- N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(a \cdot x - b \cdot i\right), \color{blue}{\left(-1 \cdot t\right)}\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(a \cdot x\right), \left(b \cdot i\right)\right), \left(\color{blue}{-1} \cdot t\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(b \cdot i\right)\right), \left(-1 \cdot t\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(i \cdot b\right)\right), \left(-1 \cdot t\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(-1 \cdot t\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(\mathsf{neg}\left(t\right)\right)\right) \]

      11. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(0 - \color{blue}{t}\right)\right) \]

      12. --lowering--.f64 72.1%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \mathsf{\_.f64}\left(0, \color{blue}{t}\right)\right) \]

   5. Simplified 72.1%

      \[\leadsto \color{blue}{\left(a \cdot x - i \cdot b\right) \cdot \left(0 - t\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+57}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{-36}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right) + i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+74}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+171}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 58.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -6 \cdot 10^{+72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-9}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right) + i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{+74}:\\ \;\;\;\;j \cdot \left(a \cdot \left(c - \frac{y \cdot i}{a}\right)\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+171}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= x -6e+72)
     t_1
     (if (<= x 3.7e-9)
       (+ (* c (- (* a j) (* z b))) (* i (* t b)))
       (if (<= x 7.4e+74)
         (* j (* a (- c (/ (* y i) a))))
         (if (<= x 5.2e+171) (* t (- (* b i) (* x a))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -6e+72) {
		tmp = t_1;
	} else if (x <= 3.7e-9) {
		tmp = (c * ((a * j) - (z * b))) + (i * (t * b));
	} else if (x <= 7.4e+74) {
		tmp = j * (a * (c - ((y * i) / a)));
	} else if (x <= 5.2e+171) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (x <= (-6d+72)) then
        tmp = t_1
    else if (x <= 3.7d-9) then
        tmp = (c * ((a * j) - (z * b))) + (i * (t * b))
    else if (x <= 7.4d+74) then
        tmp = j * (a * (c - ((y * i) / a)))
    else if (x <= 5.2d+171) then
        tmp = t * ((b * i) - (x * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -6e+72) {
		tmp = t_1;
	} else if (x <= 3.7e-9) {
		tmp = (c * ((a * j) - (z * b))) + (i * (t * b));
	} else if (x <= 7.4e+74) {
		tmp = j * (a * (c - ((y * i) / a)));
	} else if (x <= 5.2e+171) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -6e+72:
		tmp = t_1
	elif x <= 3.7e-9:
		tmp = (c * ((a * j) - (z * b))) + (i * (t * b))
	elif x <= 7.4e+74:
		tmp = j * (a * (c - ((y * i) / a)))
	elif x <= 5.2e+171:
		tmp = t * ((b * i) - (x * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -6e+72)
		tmp = t_1;
	elseif (x <= 3.7e-9)
		tmp = Float64(Float64(c * Float64(Float64(a * j) - Float64(z * b))) + Float64(i * Float64(t * b)));
	elseif (x <= 7.4e+74)
		tmp = Float64(j * Float64(a * Float64(c - Float64(Float64(y * i) / a))));
	elseif (x <= 5.2e+171)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -6e+72)
		tmp = t_1;
	elseif (x <= 3.7e-9)
		tmp = (c * ((a * j) - (z * b))) + (i * (t * b));
	elseif (x <= 7.4e+74)
		tmp = j * (a * (c - ((y * i) / a)));
	elseif (x <= 5.2e+171)
		tmp = t * ((b * i) - (x * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6e+72], t$95$1, If[LessEqual[x, 3.7e-9], N[(N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.4e+74], N[(j * N[(a * N[(c - N[(N[(y * i), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.2e+171], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -6.00000000000000006e72 or 5.2e171 < x

   1. Initial program 85.0%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(y \cdot z - a \cdot t\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\left(y \cdot z\right), \color{blue}{\left(a \cdot t\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \left(\color{blue}{a} \cdot t\right)\right)\right) \]

      4. *-lowering-*.f64 81.4%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(a, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 81.4%

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

   if -6.00000000000000006e72 < x < 3.7e-9

   1. Initial program 68.6%

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

   3. Taylor expanded in y around 0

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

   5. Simplified 78.0%

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

   6. Taylor expanded in t around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. mul-1-neg N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

      12. distribute-lft-in N/A

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

      13. mul-1-neg N/A

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

      14. sub-neg N/A

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

   8. Simplified 76.5%

      \[\leadsto \color{blue}{\left(y \cdot \left(x \cdot z - i \cdot j\right) + \left(x \cdot a - i \cdot b\right) \cdot \left(0 - t\right)\right) + c \cdot \left(j \cdot a - z \cdot b\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(b \cdot \left(i \cdot t\right)\right)}, \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, a\right), \mathsf{*.f64}\left(z, b\right)\right)\right)\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\left(i \cdot t\right) \cdot b\right), \mathsf{*.f64}\left(\color{blue}{c}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, a\right), \mathsf{*.f64}\left(z, b\right)\right)\right)\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\left(i \cdot \left(t \cdot b\right)\right), \mathsf{*.f64}\left(\color{blue}{c}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, a\right), \mathsf{*.f64}\left(z, b\right)\right)\right)\right) \]

       3. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(i \cdot \left(b \cdot t\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, a\right), \mathsf{*.f64}\left(z, b\right)\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \left(b \cdot t\right)\right), \mathsf{*.f64}\left(\color{blue}{c}, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, a\right), \mathsf{*.f64}\left(z, b\right)\right)\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \left(t \cdot b\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, a\right), \mathsf{*.f64}\left(z, b\right)\right)\right)\right) \]

       6. *-lowering-*.f64 62.2%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(i, \mathsf{*.f64}\left(t, b\right)\right), \mathsf{*.f64}\left(c, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, a\right), \mathsf{*.f64}\left(z, b\right)\right)\right)\right) \]

   11. Simplified 62.2%

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

   if 3.7e-9 < x < 7.4000000000000002e74

   1. Initial program 85.4%

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

   3. Taylor expanded in j around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(a \cdot c - i \cdot y\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\left(a \cdot c\right), \color{blue}{\left(i \cdot y\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, c\right), \left(\color{blue}{i} \cdot y\right)\right)\right) \]

      4. *-lowering-*.f64 62.9%

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, c\right), \mathsf{*.f64}\left(i, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 62.9%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(a \cdot \left(c + -1 \cdot \frac{i \cdot y}{a}\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(a, \color{blue}{\left(c + -1 \cdot \frac{i \cdot y}{a}\right)}\right)\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(a, \left(c + \left(\mathsf{neg}\left(\frac{i \cdot y}{a}\right)\right)\right)\right)\right) \]

      3. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(a, \left(c - \color{blue}{\frac{i \cdot y}{a}}\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(c, \color{blue}{\left(\frac{i \cdot y}{a}\right)}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(c, \mathsf{/.f64}\left(\left(i \cdot y\right), \color{blue}{a}\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(c, \mathsf{/.f64}\left(\left(y \cdot i\right), a\right)\right)\right)\right) \]

      7. *-lowering-*.f64 67.4%

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(c, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, i\right), a\right)\right)\right)\right) \]

   8. Simplified 67.4%

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

   if 7.4000000000000002e74 < x < 5.2e171

   1. Initial program 79.2%

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

   3. Taylor expanded in t around inf

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

      1. distribute-lft-out-- N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(a \cdot x - b \cdot i\right), \color{blue}{\left(-1 \cdot t\right)}\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(a \cdot x\right), \left(b \cdot i\right)\right), \left(\color{blue}{-1} \cdot t\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(b \cdot i\right)\right), \left(-1 \cdot t\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \left(i \cdot b\right)\right), \left(-1 \cdot t\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(-1 \cdot t\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(\mathsf{neg}\left(t\right)\right)\right) \]

      11. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \left(0 - \color{blue}{t}\right)\right) \]

      12. --lowering--.f64 72.1%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, x\right), \mathsf{*.f64}\left(i, b\right)\right), \mathsf{\_.f64}\left(0, \color{blue}{t}\right)\right) \]

   5. Simplified 72.1%

      \[\leadsto \color{blue}{\left(a \cdot x - i \cdot b\right) \cdot \left(0 - t\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+72}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-9}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right) + i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{+74}:\\ \;\;\;\;j \cdot \left(a \cdot \left(c - \frac{y \cdot i}{a}\right)\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+171}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -3.2 \cdot 10^{+55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-46}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+57}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -3.2e+55)
     t_1
     (if (<= a 5.6e-46)
       (* y (- (* x z) (* i j)))
       (if (<= a 5.8e+57) (* i (- (* t b) (* y j))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -3.2e+55) {
		tmp = t_1;
	} else if (a <= 5.6e-46) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= 5.8e+57) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (a <= (-3.2d+55)) then
        tmp = t_1
    else if (a <= 5.6d-46) then
        tmp = y * ((x * z) - (i * j))
    else if (a <= 5.8d+57) then
        tmp = i * ((t * b) - (y * j))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -3.2e+55) {
		tmp = t_1;
	} else if (a <= 5.6e-46) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= 5.8e+57) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -3.2e+55:
		tmp = t_1
	elif a <= 5.6e-46:
		tmp = y * ((x * z) - (i * j))
	elif a <= 5.8e+57:
		tmp = i * ((t * b) - (y * j))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -3.2e+55)
		tmp = t_1;
	elseif (a <= 5.6e-46)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (a <= 5.8e+57)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * 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 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -3.2e+55)
		tmp = t_1;
	elseif (a <= 5.6e-46)
		tmp = y * ((x * z) - (i * j));
	elseif (a <= 5.8e+57)
		tmp = i * ((t * b) - (y * j));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.2e+55], t$95$1, If[LessEqual[a, 5.6e-46], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.8e+57], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.2000000000000003e55 or 5.8000000000000003e57 < a

   1. Initial program 74.8%

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

   3. Taylor expanded in a around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j + \color{blue}{-1 \cdot \left(t \cdot x\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j + \left(\mathsf{neg}\left(t \cdot x\right)\right)\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j - \color{blue}{t \cdot x}\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(c \cdot j\right), \color{blue}{\left(t \cdot x\right)}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(j \cdot c\right), \left(\color{blue}{t} \cdot x\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \left(\color{blue}{t} \cdot x\right)\right)\right) \]

      8. *-lowering-*.f64 70.0%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \mathsf{*.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 70.0%

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

   if -3.2000000000000003e55 < a < 5.5999999999999997e-46

   1. Initial program 77.2%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(x \cdot z + \color{blue}{-1 \cdot \left(i \cdot j\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(x \cdot z + \left(\mathsf{neg}\left(i \cdot j\right)\right)\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(x \cdot z - \color{blue}{i \cdot j}\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(x \cdot z\right), \color{blue}{\left(i \cdot j\right)}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(z \cdot x\right), \left(\color{blue}{i} \cdot j\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, x\right), \left(\color{blue}{i} \cdot j\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, x\right), \left(j \cdot \color{blue}{i}\right)\right)\right) \]

      9. *-lowering-*.f64 53.8%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(z, x\right), \mathsf{*.f64}\left(j, \color{blue}{i}\right)\right)\right) \]

   5. Simplified 53.8%

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

   if 5.5999999999999997e-46 < a < 5.8000000000000003e57

   1. Initial program 77.5%

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

   3. Taylor expanded in y around 0

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

   5. Simplified 77.8%

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

   6. Taylor expanded in t around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. mul-1-neg N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

      12. distribute-lft-in N/A

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

      13. mul-1-neg N/A

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

      14. sub-neg N/A

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

   8. Simplified 83.9%

      \[\leadsto \color{blue}{\left(y \cdot \left(x \cdot z - i \cdot j\right) + \left(x \cdot a - i \cdot b\right) \cdot \left(0 - t\right)\right) + c \cdot \left(j \cdot a - z \cdot b\right)} \]

   9. Taylor expanded in i around inf

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

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(i, \color{blue}{\left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)}\right) \]

       2. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(i, \left(b \cdot t + \color{blue}{-1 \cdot \left(j \cdot y\right)}\right)\right) \]

       3. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(i, \left(b \cdot t + \left(\mathsf{neg}\left(j \cdot y\right)\right)\right)\right) \]

       4. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(i, \left(b \cdot t - \color{blue}{j \cdot y}\right)\right) \]

       5. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\left(b \cdot t\right), \color{blue}{\left(j \cdot y\right)}\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\left(t \cdot b\right), \left(\color{blue}{j} \cdot y\right)\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, b\right), \left(\color{blue}{j} \cdot y\right)\right)\right) \]

       8. *-lowering-*.f64 69.7%

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, b\right), \mathsf{*.f64}\left(j, \color{blue}{y}\right)\right)\right) \]

   11. Simplified 69.7%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+55}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-46}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+57}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 29.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+129}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-109}:\\ \;\;\;\;a \cdot \left(0 - x \cdot t\right)\\ \mathbf{elif}\;z \leq 0.008:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -9.5e+129)
   (* x (* y z))
   (if (<= z -2.5e-109)
     (* a (- 0.0 (* x t)))
     (if (<= z 0.008) (* c (* a j)) (* y (* x z))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -9.5e+129) {
		tmp = x * (y * z);
	} else if (z <= -2.5e-109) {
		tmp = a * (0.0 - (x * t));
	} else if (z <= 0.008) {
		tmp = c * (a * j);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-9.5d+129)) then
        tmp = x * (y * z)
    else if (z <= (-2.5d-109)) then
        tmp = a * (0.0d0 - (x * t))
    else if (z <= 0.008d0) then
        tmp = c * (a * j)
    else
        tmp = y * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -9.5e+129) {
		tmp = x * (y * z);
	} else if (z <= -2.5e-109) {
		tmp = a * (0.0 - (x * t));
	} else if (z <= 0.008) {
		tmp = c * (a * j);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -9.5e+129:
		tmp = x * (y * z)
	elif z <= -2.5e-109:
		tmp = a * (0.0 - (x * t))
	elif z <= 0.008:
		tmp = c * (a * j)
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -9.5e+129)
		tmp = Float64(x * Float64(y * z));
	elseif (z <= -2.5e-109)
		tmp = Float64(a * Float64(0.0 - Float64(x * t)));
	elseif (z <= 0.008)
		tmp = Float64(c * Float64(a * j));
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -9.5e+129)
		tmp = x * (y * z);
	elseif (z <= -2.5e-109)
		tmp = a * (0.0 - (x * t));
	elseif (z <= 0.008)
		tmp = c * (a * j);
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -9.5e+129], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.5e-109], N[(a * N[(0.0 - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.008], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.5000000000000004e129

   1. Initial program 60.9%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(x \cdot y - b \cdot c\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(b \cdot c\right)}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(\color{blue}{b} \cdot c\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(\color{blue}{b} \cdot c\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(c \cdot \color{blue}{b}\right)\right)\right) \]

      6. *-lowering-*.f64 62.0%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(c, \color{blue}{b}\right)\right)\right) \]

   5. Simplified 62.0%

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

   6. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

         \[\leadsto \left(y \cdot x\right) \cdot z \]

      3. associate-*r* N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(x \cdot z\right)}\right) \]

      5. *-lowering-*.f64 48.5%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{z}\right)\right) \]

   8. Simplified 48.5%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y \cdot z\right), \color{blue}{x}\right) \]

      4. *-lowering-*.f64 55.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), x\right) \]

   10. Applied egg-rr 55.7%

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

   if -9.5000000000000004e129 < z < -2.5000000000000001e-109

   1. Initial program 73.1%

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

   3. Taylor expanded in a around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j + \color{blue}{-1 \cdot \left(t \cdot x\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j + \left(\mathsf{neg}\left(t \cdot x\right)\right)\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j - \color{blue}{t \cdot x}\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(c \cdot j\right), \color{blue}{\left(t \cdot x\right)}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(j \cdot c\right), \left(\color{blue}{t} \cdot x\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \left(\color{blue}{t} \cdot x\right)\right)\right) \]

      8. *-lowering-*.f64 49.9%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \mathsf{*.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 49.9%

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

   6. Taylor expanded in j around 0

      \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)}\right) \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(t \cdot x\right)\right)\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(0 - \color{blue}{t \cdot x}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(0, \color{blue}{\left(t \cdot x\right)}\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(0, \left(x \cdot \color{blue}{t}\right)\right)\right) \]

      5. *-lowering-*.f64 40.3%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(x, \color{blue}{t}\right)\right)\right) \]

   8. Simplified 40.3%

      \[\leadsto a \cdot \color{blue}{\left(0 - x \cdot t\right)} \]
   9. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(\mathsf{neg}\left(x \cdot t\right)\right)\right) \]

      2. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{neg.f64}\left(\left(x \cdot t\right)\right)\right) \]

      3. *-lowering-*.f64 40.3%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{neg.f64}\left(\mathsf{*.f64}\left(x, t\right)\right)\right) \]

   10. Applied egg-rr 40.3%

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

   if -2.5000000000000001e-109 < z < 0.0080000000000000002

   1. Initial program 82.9%

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

   3. Taylor expanded in a around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j + \color{blue}{-1 \cdot \left(t \cdot x\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j + \left(\mathsf{neg}\left(t \cdot x\right)\right)\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j - \color{blue}{t \cdot x}\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(c \cdot j\right), \color{blue}{\left(t \cdot x\right)}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(j \cdot c\right), \left(\color{blue}{t} \cdot x\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \left(\color{blue}{t} \cdot x\right)\right)\right) \]

      8. *-lowering-*.f64 54.6%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \mathsf{*.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 54.6%

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

   6. Taylor expanded in j around inf

      \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(c \cdot j\right)}\right) \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(j \cdot \color{blue}{c}\right)\right) \]

      2. *-lowering-*.f64 37.2%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(j, \color{blue}{c}\right)\right) \]

   8. Simplified 37.2%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

         \[\leadsto \left(j \cdot a\right) \cdot c \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(j \cdot a\right), \color{blue}{c}\right) \]

      4. *-lowering-*.f64 39.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, a\right), c\right) \]

   10. Applied egg-rr 39.9%

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

   if 0.0080000000000000002 < z

   1. Initial program 75.4%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(x \cdot y - b \cdot c\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(b \cdot c\right)}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(\color{blue}{b} \cdot c\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(\color{blue}{b} \cdot c\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(c \cdot \color{blue}{b}\right)\right)\right) \]

      6. *-lowering-*.f64 56.8%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(c, \color{blue}{b}\right)\right)\right) \]

   5. Simplified 56.8%

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

   6. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

         \[\leadsto \left(y \cdot x\right) \cdot z \]

      3. associate-*r* N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(x \cdot z\right)}\right) \]

      5. *-lowering-*.f64 46.7%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{z}\right)\right) \]

   8. Simplified 46.7%

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

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+129}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-109}:\\ \;\;\;\;a \cdot \left(0 - x \cdot t\right)\\ \mathbf{elif}\;z \leq 0.008:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 48.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -3 \cdot 10^{+112}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;i \leq 8.2 \cdot 10^{+89}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -3e+112)
   (* j (- (* a c) (* y i)))
   (if (<= i 8.2e+89) (* x (- (* y z) (* t a))) (* i (- (* t b) (* y j))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -3e+112) {
		tmp = j * ((a * c) - (y * i));
	} else if (i <= 8.2e+89) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = i * ((t * b) - (y * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (i <= (-3d+112)) then
        tmp = j * ((a * c) - (y * i))
    else if (i <= 8.2d+89) then
        tmp = x * ((y * z) - (t * a))
    else
        tmp = i * ((t * b) - (y * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -3e+112) {
		tmp = j * ((a * c) - (y * i));
	} else if (i <= 8.2e+89) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = i * ((t * b) - (y * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -3e+112:
		tmp = j * ((a * c) - (y * i))
	elif i <= 8.2e+89:
		tmp = x * ((y * z) - (t * a))
	else:
		tmp = i * ((t * b) - (y * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -3e+112)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (i <= 8.2e+89)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	else
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -3e+112)
		tmp = j * ((a * c) - (y * i));
	elseif (i <= 8.2e+89)
		tmp = x * ((y * z) - (t * a));
	else
		tmp = i * ((t * b) - (y * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -3e+112], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 8.2e+89], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if i < -2.99999999999999979e112

   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. Add Preprocessing

   3. Taylor expanded in j around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \color{blue}{\left(a \cdot c - i \cdot y\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\left(a \cdot c\right), \color{blue}{\left(i \cdot y\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, c\right), \left(\color{blue}{i} \cdot y\right)\right)\right) \]

      4. *-lowering-*.f64 69.8%

         \[\leadsto \mathsf{*.f64}\left(j, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, c\right), \mathsf{*.f64}\left(i, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 69.8%

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

   if -2.99999999999999979e112 < i < 8.1999999999999997e89

   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. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(y \cdot z - a \cdot t\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\left(y \cdot z\right), \color{blue}{\left(a \cdot t\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \left(\color{blue}{a} \cdot t\right)\right)\right) \]

      4. *-lowering-*.f64 54.3%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, z\right), \mathsf{*.f64}\left(a, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 54.3%

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

   if 8.1999999999999997e89 < i

   1. Initial program 57.6%

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

   3. Taylor expanded in y around 0

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

   5. Simplified 68.6%

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

   6. Taylor expanded in t around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. mul-1-neg N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

      12. distribute-lft-in N/A

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

      13. mul-1-neg N/A

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

      14. sub-neg N/A

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

   8. Simplified 84.1%

      \[\leadsto \color{blue}{\left(y \cdot \left(x \cdot z - i \cdot j\right) + \left(x \cdot a - i \cdot b\right) \cdot \left(0 - t\right)\right) + c \cdot \left(j \cdot a - z \cdot b\right)} \]

   9. Taylor expanded in i around inf

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

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(i, \color{blue}{\left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)}\right) \]

       2. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(i, \left(b \cdot t + \color{blue}{-1 \cdot \left(j \cdot y\right)}\right)\right) \]

       3. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(i, \left(b \cdot t + \left(\mathsf{neg}\left(j \cdot y\right)\right)\right)\right) \]

       4. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(i, \left(b \cdot t - \color{blue}{j \cdot y}\right)\right) \]

       5. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\left(b \cdot t\right), \color{blue}{\left(j \cdot y\right)}\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\left(t \cdot b\right), \left(\color{blue}{j} \cdot y\right)\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, b\right), \left(\color{blue}{j} \cdot y\right)\right)\right) \]

       8. *-lowering-*.f64 69.6%

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, b\right), \mathsf{*.f64}\left(j, \color{blue}{y}\right)\right)\right) \]

   11. Simplified 69.6%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3 \cdot 10^{+112}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;i \leq 8.2 \cdot 10^{+89}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 52.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -3.05 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 2.45 \cdot 10^{+92}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j)))))
   (if (<= i -3.05e+32)
     t_1
     (if (<= i 2.45e+92) (* a (- (* c j) (* x t))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -3.05e+32) {
		tmp = t_1;
	} else if (i <= 2.45e+92) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * ((t * b) - (y * j))
    if (i <= (-3.05d+32)) then
        tmp = t_1
    else if (i <= 2.45d+92) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -3.05e+32) {
		tmp = t_1;
	} else if (i <= 2.45e+92) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -3.05e+32:
		tmp = t_1
	elif i <= 2.45e+92:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -3.05e+32)
		tmp = t_1;
	elseif (i <= 2.45e+92)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -3.05e+32)
		tmp = t_1;
	elseif (i <= 2.45e+92)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -3.05e+32], t$95$1, If[LessEqual[i, 2.45e+92], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if i < -3.05000000000000014e32 or 2.4500000000000001e92 < i

   1. Initial program 63.4%

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

   3. Taylor expanded in y around 0

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

   5. Simplified 69.8%

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

   6. Taylor expanded in t around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. mul-1-neg N/A

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

      8. *-commutative N/A

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

      9. associate-*r* N/A

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

      10. associate-*l* N/A

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

      11. *-commutative N/A

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

      12. distribute-lft-in N/A

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

      13. mul-1-neg N/A

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

      14. sub-neg N/A

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

   8. Simplified 68.1%

      \[\leadsto \color{blue}{\left(y \cdot \left(x \cdot z - i \cdot j\right) + \left(x \cdot a - i \cdot b\right) \cdot \left(0 - t\right)\right) + c \cdot \left(j \cdot a - z \cdot b\right)} \]

   9. Taylor expanded in i around inf

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

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(i, \color{blue}{\left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)}\right) \]

       2. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(i, \left(b \cdot t + \color{blue}{-1 \cdot \left(j \cdot y\right)}\right)\right) \]

       3. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(i, \left(b \cdot t + \left(\mathsf{neg}\left(j \cdot y\right)\right)\right)\right) \]

       4. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(i, \left(b \cdot t - \color{blue}{j \cdot y}\right)\right) \]

       5. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\left(b \cdot t\right), \color{blue}{\left(j \cdot y\right)}\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\left(t \cdot b\right), \left(\color{blue}{j} \cdot y\right)\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, b\right), \left(\color{blue}{j} \cdot y\right)\right)\right) \]

       8. *-lowering-*.f64 66.2%

          \[\leadsto \mathsf{*.f64}\left(i, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, b\right), \mathsf{*.f64}\left(j, \color{blue}{y}\right)\right)\right) \]

   11. Simplified 66.2%

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

   if -3.05000000000000014e32 < i < 2.4500000000000001e92

   1. Initial program 85.0%

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

   3. Taylor expanded in a around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j + \color{blue}{-1 \cdot \left(t \cdot x\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j + \left(\mathsf{neg}\left(t \cdot x\right)\right)\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j - \color{blue}{t \cdot x}\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(c \cdot j\right), \color{blue}{\left(t \cdot x\right)}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(j \cdot c\right), \left(\color{blue}{t} \cdot x\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \left(\color{blue}{t} \cdot x\right)\right)\right) \]

      8. *-lowering-*.f64 50.3%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \mathsf{*.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 50.3%

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

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.05 \cdot 10^{+32}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq 2.45 \cdot 10^{+92}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -3.2 \cdot 10^{-104}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+39}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -3.2e-104)
     t_1
     (if (<= a 1.05e+39) (* 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 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -3.2e-104) {
		tmp = t_1;
	} else if (a <= 1.05e+39) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (a <= (-3.2d-104)) then
        tmp = t_1
    else if (a <= 1.05d+39) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -3.2e-104) {
		tmp = t_1;
	} else if (a <= 1.05e+39) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -3.2e-104:
		tmp = t_1
	elif a <= 1.05e+39:
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -3.2e-104)
		tmp = t_1;
	elseif (a <= 1.05e+39)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -3.2e-104)
		tmp = t_1;
	elseif (a <= 1.05e+39)
		tmp = b * ((t * i) - (z * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.2e-104], t$95$1, If[LessEqual[a, 1.05e+39], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -3.19999999999999989e-104 or 1.0499999999999999e39 < a

   1. Initial program 74.9%

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

   3. Taylor expanded in a around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j + \color{blue}{-1 \cdot \left(t \cdot x\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j + \left(\mathsf{neg}\left(t \cdot x\right)\right)\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j - \color{blue}{t \cdot x}\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(c \cdot j\right), \color{blue}{\left(t \cdot x\right)}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(j \cdot c\right), \left(\color{blue}{t} \cdot x\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \left(\color{blue}{t} \cdot x\right)\right)\right) \]

      8. *-lowering-*.f64 63.2%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \mathsf{*.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 63.2%

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

   if -3.19999999999999989e-104 < a < 1.0499999999999999e39

   1. Initial program 77.8%

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

   3. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \color{blue}{\left(i \cdot t - c \cdot z\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(i \cdot t\right), \color{blue}{\left(c \cdot z\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, t\right), \left(\color{blue}{c} \cdot z\right)\right)\right) \]

      4. *-lowering-*.f64 44.2%

         \[\leadsto \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(i, t\right), \mathsf{*.f64}\left(c, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 44.2%

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

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{-104}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+39}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 42.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+129}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+81}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -9.5e+129)
   (* x (* y z))
   (if (<= z 1.25e+81) (* a (- (* c j) (* x t))) (* y (* x z)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -9.5e+129) {
		tmp = x * (y * z);
	} else if (z <= 1.25e+81) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-9.5d+129)) then
        tmp = x * (y * z)
    else if (z <= 1.25d+81) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = y * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -9.5e+129) {
		tmp = x * (y * z);
	} else if (z <= 1.25e+81) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -9.5e+129:
		tmp = x * (y * z)
	elif z <= 1.25e+81:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -9.5e+129)
		tmp = Float64(x * Float64(y * z));
	elseif (z <= 1.25e+81)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -9.5e+129)
		tmp = x * (y * z);
	elseif (z <= 1.25e+81)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -9.5e+129], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e+81], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.5000000000000004e129

   1. Initial program 60.9%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(x \cdot y - b \cdot c\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(b \cdot c\right)}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(\color{blue}{b} \cdot c\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(\color{blue}{b} \cdot c\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(c \cdot \color{blue}{b}\right)\right)\right) \]

      6. *-lowering-*.f64 62.0%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(c, \color{blue}{b}\right)\right)\right) \]

   5. Simplified 62.0%

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

   6. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

         \[\leadsto \left(y \cdot x\right) \cdot z \]

      3. associate-*r* N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(x \cdot z\right)}\right) \]

      5. *-lowering-*.f64 48.5%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{z}\right)\right) \]

   8. Simplified 48.5%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y \cdot z\right), \color{blue}{x}\right) \]

      4. *-lowering-*.f64 55.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), x\right) \]

   10. Applied egg-rr 55.7%

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

   if -9.5000000000000004e129 < z < 1.25e81

   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. Add Preprocessing

   3. Taylor expanded in a around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j + \color{blue}{-1 \cdot \left(t \cdot x\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j + \left(\mathsf{neg}\left(t \cdot x\right)\right)\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j - \color{blue}{t \cdot x}\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(c \cdot j\right), \color{blue}{\left(t \cdot x\right)}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(j \cdot c\right), \left(\color{blue}{t} \cdot x\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \left(\color{blue}{t} \cdot x\right)\right)\right) \]

      8. *-lowering-*.f64 52.4%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \mathsf{*.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 52.4%

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

   if 1.25e81 < z

   1. Initial program 70.2%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(x \cdot y - b \cdot c\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(b \cdot c\right)}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(\color{blue}{b} \cdot c\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(\color{blue}{b} \cdot c\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(c \cdot \color{blue}{b}\right)\right)\right) \]

      6. *-lowering-*.f64 71.2%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(c, \color{blue}{b}\right)\right)\right) \]

   5. Simplified 71.2%

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

   6. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

         \[\leadsto \left(y \cdot x\right) \cdot z \]

      3. associate-*r* N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(x \cdot z\right)}\right) \]

      5. *-lowering-*.f64 55.3%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{z}\right)\right) \]

   8. Simplified 55.3%

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

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+129}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+81}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 29.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-88}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 0.045:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -3.9e-88)
   (* x (* y z))
   (if (<= z 0.045) (* c (* a j)) (* y (* x z)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -3.9e-88) {
		tmp = x * (y * z);
	} else if (z <= 0.045) {
		tmp = c * (a * j);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-3.9d-88)) then
        tmp = x * (y * z)
    else if (z <= 0.045d0) then
        tmp = c * (a * j)
    else
        tmp = y * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -3.9e-88) {
		tmp = x * (y * z);
	} else if (z <= 0.045) {
		tmp = c * (a * j);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -3.9e-88:
		tmp = x * (y * z)
	elif z <= 0.045:
		tmp = c * (a * j)
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -3.9e-88)
		tmp = Float64(x * Float64(y * z));
	elseif (z <= 0.045)
		tmp = Float64(c * Float64(a * j));
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -3.9e-88)
		tmp = x * (y * z);
	elseif (z <= 0.045)
		tmp = c * (a * j);
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -3.9e-88], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.045], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.89999999999999992e-88

   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. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(x \cdot y - b \cdot c\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(b \cdot c\right)}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(\color{blue}{b} \cdot c\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(\color{blue}{b} \cdot c\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(c \cdot \color{blue}{b}\right)\right)\right) \]

      6. *-lowering-*.f64 47.9%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(c, \color{blue}{b}\right)\right)\right) \]

   5. Simplified 47.9%

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

   6. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

         \[\leadsto \left(y \cdot x\right) \cdot z \]

      3. associate-*r* N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(x \cdot z\right)}\right) \]

      5. *-lowering-*.f64 38.8%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{z}\right)\right) \]

   8. Simplified 38.8%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y \cdot z\right), \color{blue}{x}\right) \]

      4. *-lowering-*.f64 39.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), x\right) \]

   10. Applied egg-rr 39.5%

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

   if -3.89999999999999992e-88 < z < 0.044999999999999998

   1. Initial program 83.4%

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

   3. Taylor expanded in a around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j + \color{blue}{-1 \cdot \left(t \cdot x\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j + \left(\mathsf{neg}\left(t \cdot x\right)\right)\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j - \color{blue}{t \cdot x}\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(c \cdot j\right), \color{blue}{\left(t \cdot x\right)}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(j \cdot c\right), \left(\color{blue}{t} \cdot x\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \left(\color{blue}{t} \cdot x\right)\right)\right) \]

      8. *-lowering-*.f64 55.9%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \mathsf{*.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 55.9%

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

   6. Taylor expanded in j around inf

      \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(c \cdot j\right)}\right) \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(j \cdot \color{blue}{c}\right)\right) \]

      2. *-lowering-*.f64 37.1%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(j, \color{blue}{c}\right)\right) \]

   8. Simplified 37.1%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

         \[\leadsto \left(j \cdot a\right) \cdot c \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(j \cdot a\right), \color{blue}{c}\right) \]

      4. *-lowering-*.f64 40.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, a\right), c\right) \]

   10. Applied egg-rr 40.7%

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

   if 0.044999999999999998 < z

   1. Initial program 75.4%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(x \cdot y - b \cdot c\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(b \cdot c\right)}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(\color{blue}{b} \cdot c\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(\color{blue}{b} \cdot c\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(c \cdot \color{blue}{b}\right)\right)\right) \]

      6. *-lowering-*.f64 56.8%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(c, \color{blue}{b}\right)\right)\right) \]

   5. Simplified 56.8%

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

   6. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

         \[\leadsto \left(y \cdot x\right) \cdot z \]

      3. associate-*r* N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(x \cdot z\right)}\right) \]

      5. *-lowering-*.f64 46.7%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{z}\right)\right) \]

   8. Simplified 46.7%

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

4. Final simplification 42.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-88}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 0.045:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 29.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{-88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.011:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* x z))))
   (if (<= z -2.5e-88) t_1 (if (<= z 0.011) (* c (* a 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 = y * (x * z);
	double tmp;
	if (z <= -2.5e-88) {
		tmp = t_1;
	} else if (z <= 0.011) {
		tmp = c * (a * 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 = y * (x * z)
    if (z <= (-2.5d-88)) then
        tmp = t_1
    else if (z <= 0.011d0) then
        tmp = c * (a * 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 = y * (x * z);
	double tmp;
	if (z <= -2.5e-88) {
		tmp = t_1;
	} else if (z <= 0.011) {
		tmp = c * (a * j);
	} 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 z <= -2.5e-88:
		tmp = t_1
	elif z <= 0.011:
		tmp = c * (a * j)
	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 (z <= -2.5e-88)
		tmp = t_1;
	elseif (z <= 0.011)
		tmp = Float64(c * Float64(a * 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 = y * (x * z);
	tmp = 0.0;
	if (z <= -2.5e-88)
		tmp = t_1;
	elseif (z <= 0.011)
		tmp = c * (a * 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[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.5e-88], t$95$1, If[LessEqual[z, 0.011], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.50000000000000004e-88 or 0.010999999999999999 < z

   1. Initial program 71.1%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(x \cdot y - b \cdot c\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(b \cdot c\right)}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(\color{blue}{b} \cdot c\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(\color{blue}{b} \cdot c\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(c \cdot \color{blue}{b}\right)\right)\right) \]

      6. *-lowering-*.f64 52.6%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(c, \color{blue}{b}\right)\right)\right) \]

   5. Simplified 52.6%

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

   6. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

         \[\leadsto \left(y \cdot x\right) \cdot z \]

      3. associate-*r* N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(x \cdot z\right)}\right) \]

      5. *-lowering-*.f64 43.0%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{z}\right)\right) \]

   8. Simplified 43.0%

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

   if -2.50000000000000004e-88 < z < 0.010999999999999999

   1. Initial program 83.4%

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

   3. Taylor expanded in a around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j + \color{blue}{-1 \cdot \left(t \cdot x\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j + \left(\mathsf{neg}\left(t \cdot x\right)\right)\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j - \color{blue}{t \cdot x}\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(c \cdot j\right), \color{blue}{\left(t \cdot x\right)}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(j \cdot c\right), \left(\color{blue}{t} \cdot x\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \left(\color{blue}{t} \cdot x\right)\right)\right) \]

      8. *-lowering-*.f64 55.9%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \mathsf{*.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 55.9%

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

   6. Taylor expanded in j around inf

      \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(c \cdot j\right)}\right) \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(j \cdot \color{blue}{c}\right)\right) \]

      2. *-lowering-*.f64 37.1%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(j, \color{blue}{c}\right)\right) \]

   8. Simplified 37.1%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

         \[\leadsto \left(j \cdot a\right) \cdot c \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(j \cdot a\right), \color{blue}{c}\right) \]

      4. *-lowering-*.f64 40.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(j, a\right), c\right) \]

   10. Applied egg-rr 40.7%

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

4. Final simplification 42.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-88}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 0.011:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 29.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{-46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.042:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* x z))))
   (if (<= z -1.7e-46) t_1 (if (<= z 0.042) (* 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 = y * (x * z);
	double tmp;
	if (z <= -1.7e-46) {
		tmp = t_1;
	} else if (z <= 0.042) {
		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 = y * (x * z)
    if (z <= (-1.7d-46)) then
        tmp = t_1
    else if (z <= 0.042d0) 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 = y * (x * z);
	double tmp;
	if (z <= -1.7e-46) {
		tmp = t_1;
	} else if (z <= 0.042) {
		tmp = a * (c * j);
	} 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 z <= -1.7e-46:
		tmp = t_1
	elif z <= 0.042:
		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(y * Float64(x * z))
	tmp = 0.0
	if (z <= -1.7e-46)
		tmp = t_1;
	elseif (z <= 0.042)
		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 = y * (x * z);
	tmp = 0.0;
	if (z <= -1.7e-46)
		tmp = t_1;
	elseif (z <= 0.042)
		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[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.7e-46], t$95$1, If[LessEqual[z, 0.042], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.69999999999999998e-46 or 0.0420000000000000026 < z

   1. Initial program 71.1%

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

   3. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(x \cdot y - b \cdot c\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(b \cdot c\right)}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\left(y \cdot x\right), \left(\color{blue}{b} \cdot c\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(\color{blue}{b} \cdot c\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \left(c \cdot \color{blue}{b}\right)\right)\right) \]

      6. *-lowering-*.f64 55.0%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, x\right), \mathsf{*.f64}\left(c, \color{blue}{b}\right)\right)\right) \]

   5. Simplified 55.0%

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

   6. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

         \[\leadsto \left(y \cdot x\right) \cdot z \]

      3. associate-*r* N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(x \cdot z\right)}\right) \]

      5. *-lowering-*.f64 45.1%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{z}\right)\right) \]

   8. Simplified 45.1%

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

   if -1.69999999999999998e-46 < z < 0.0420000000000000026

   1. Initial program 82.0%

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

   3. Taylor expanded in a around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j + \color{blue}{-1 \cdot \left(t \cdot x\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j + \left(\mathsf{neg}\left(t \cdot x\right)\right)\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j - \color{blue}{t \cdot x}\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(c \cdot j\right), \color{blue}{\left(t \cdot x\right)}\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(j \cdot c\right), \left(\color{blue}{t} \cdot x\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \left(\color{blue}{t} \cdot x\right)\right)\right) \]

      8. *-lowering-*.f64 56.1%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \mathsf{*.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 56.1%

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

   6. Taylor expanded in j around inf

      \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(c \cdot j\right)}\right) \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(j \cdot \color{blue}{c}\right)\right) \]

      2. *-lowering-*.f64 35.4%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(j, \color{blue}{c}\right)\right) \]

   8. Simplified 35.4%

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

4. Final simplification 40.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-46}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 0.042:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 21.7% 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 76.1%

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

3. Taylor expanded in a around inf

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

   1. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)}\right) \]

   2. +-commutative N/A

      \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j + \color{blue}{-1 \cdot \left(t \cdot x\right)}\right)\right) \]

   3. mul-1-neg N/A

      \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j + \left(\mathsf{neg}\left(t \cdot x\right)\right)\right)\right) \]

   4. unsub-neg N/A

      \[\leadsto \mathsf{*.f64}\left(a, \left(c \cdot j - \color{blue}{t \cdot x}\right)\right) \]

   5. --lowering--.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(c \cdot j\right), \color{blue}{\left(t \cdot x\right)}\right)\right) \]

   6. *-commutative N/A

      \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\left(j \cdot c\right), \left(\color{blue}{t} \cdot x\right)\right)\right) \]

   7. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \left(\color{blue}{t} \cdot x\right)\right)\right) \]

   8. *-lowering-*.f64 43.7%

      \[\leadsto \mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(j, c\right), \mathsf{*.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

5. Simplified 43.7%

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

6. Taylor expanded in j around inf

   \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(c \cdot j\right)}\right) \]
7. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \mathsf{*.f64}\left(a, \left(j \cdot \color{blue}{c}\right)\right) \]

   2. *-lowering-*.f64 23.4%

      \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(j, \color{blue}{c}\right)\right) \]

8. Simplified 23.4%

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

9. Final simplification 23.4%

   \[\leadsto a \cdot \left(c \cdot j\right) \]
10. Add Preprocessing

Developer Target 1: 59.4% 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 2024155 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< x -293938859355541/2000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2) (pow (* t i) 2))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 32113527362226803/10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2) (pow (* t i) 2))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i)))))