Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.1% → 81.9%

Time: 30.9s

Alternatives: 18

Speedup: 0.5×

• 58.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

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) - (i * a)))) + (j * ((c * t) - (i * y)));
}

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) - (i * a)))) + (j * ((c * t) - (i * y)))
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) - (i * a)))) + (j * ((c * t) - (i * y)));
}

Python

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

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(i * a)))) + Float64(j * Float64(Float64(c * t) - Float64(i * y))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
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[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 73.1% accurate, 1.0× speedup

Math

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

FPCore

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

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) - (i * a)))) + (j * ((c * t) - (i * y)));
}

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) - (i * a)))) + (j * ((c * t) - (i * y)))
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) - (i * a)))) + (j * ((c * t) - (i * y)));
}

Python

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

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(i * a)))) + Float64(j * Float64(Float64(c * t) - Float64(i * y))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
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[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 81.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 91.8%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x around 0 24.1%

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

      1. *-commutative 24.1%

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

   5. Simplified 24.1%

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

   6. Taylor expanded in c around 0 37.1%

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

      1. associate-*r* 37.1%

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

      2. neg-mul-1 37.1%

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

      3. cancel-sign-sub 37.1%

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

      4. *-commutative 37.1%

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

      5. associate-*r* 37.1%

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

      6. associate-*r* 40.3%

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

      7. *-commutative 40.3%

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

      8. distribute-rgt-in 50.7%

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

      9. cancel-sign-sub 50.7%

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

      10. distribute-lft-neg-in 50.7%

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

      11. *-commutative 50.7%

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

      12. mul-1-neg 50.7%

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

      13. mul-1-neg 50.7%

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

      14. *-commutative 50.7%

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

      15. mul-1-neg 50.7%

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

      16. neg-sub0 50.7%

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

      17. associate--r+ 50.7%

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

      18. +-commutative 50.7%

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

      19. associate--r+ 50.7%

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

   8. Simplified 50.7%

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

4. Final simplification 82.5%

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

Alternative 2: 63.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := t\_1 - y \cdot \left(i \cdot j\right)\\ t_3 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_4 := x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;b \leq -2.95 \cdot 10^{+284}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{+215}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -1.92 \cdot 10^{+80}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -3800000000000:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-42}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{+35}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{+119}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{+178}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c))))
        (t_2 (- t_1 (* y (* i j))))
        (t_3 (* i (- (* a b) (* y j))))
        (t_4 (+ (* x (- (* y z) (* t a))) (* j (- (* t c) (* y i))))))
   (if (<= b -2.95e+284)
     (* z (- (* x y) (* b c)))
     (if (<= b -2.5e+215)
       t_3
       (if (<= b -1.92e+80)
         t_2
         (if (<= b -3800000000000.0)
           t_4
           (if (<= b -2.6e-42)
             t_3
             (if (<= b 6.2e+35)
               t_4
               (if (<= b 1.55e+119) t_2 (if (<= b 1.75e+178) t_4 t_1))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = t_1 - (y * (i * j));
	double t_3 = i * ((a * b) - (y * j));
	double t_4 = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	double tmp;
	if (b <= -2.95e+284) {
		tmp = z * ((x * y) - (b * c));
	} else if (b <= -2.5e+215) {
		tmp = t_3;
	} else if (b <= -1.92e+80) {
		tmp = t_2;
	} else if (b <= -3800000000000.0) {
		tmp = t_4;
	} else if (b <= -2.6e-42) {
		tmp = t_3;
	} else if (b <= 6.2e+35) {
		tmp = t_4;
	} else if (b <= 1.55e+119) {
		tmp = t_2;
	} else if (b <= 1.75e+178) {
		tmp = t_4;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = t_1 - (y * (i * j))
    t_3 = i * ((a * b) - (y * j))
    t_4 = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)))
    if (b <= (-2.95d+284)) then
        tmp = z * ((x * y) - (b * c))
    else if (b <= (-2.5d+215)) then
        tmp = t_3
    else if (b <= (-1.92d+80)) then
        tmp = t_2
    else if (b <= (-3800000000000.0d0)) then
        tmp = t_4
    else if (b <= (-2.6d-42)) then
        tmp = t_3
    else if (b <= 6.2d+35) then
        tmp = t_4
    else if (b <= 1.55d+119) then
        tmp = t_2
    else if (b <= 1.75d+178) then
        tmp = t_4
    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 = b * ((a * i) - (z * c));
	double t_2 = t_1 - (y * (i * j));
	double t_3 = i * ((a * b) - (y * j));
	double t_4 = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	double tmp;
	if (b <= -2.95e+284) {
		tmp = z * ((x * y) - (b * c));
	} else if (b <= -2.5e+215) {
		tmp = t_3;
	} else if (b <= -1.92e+80) {
		tmp = t_2;
	} else if (b <= -3800000000000.0) {
		tmp = t_4;
	} else if (b <= -2.6e-42) {
		tmp = t_3;
	} else if (b <= 6.2e+35) {
		tmp = t_4;
	} else if (b <= 1.55e+119) {
		tmp = t_2;
	} else if (b <= 1.75e+178) {
		tmp = t_4;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = t_1 - (y * (i * j))
	t_3 = i * ((a * b) - (y * j))
	t_4 = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)))
	tmp = 0
	if b <= -2.95e+284:
		tmp = z * ((x * y) - (b * c))
	elif b <= -2.5e+215:
		tmp = t_3
	elif b <= -1.92e+80:
		tmp = t_2
	elif b <= -3800000000000.0:
		tmp = t_4
	elif b <= -2.6e-42:
		tmp = t_3
	elif b <= 6.2e+35:
		tmp = t_4
	elif b <= 1.55e+119:
		tmp = t_2
	elif b <= 1.75e+178:
		tmp = t_4
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(t_1 - Float64(y * Float64(i * j)))
	t_3 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	t_4 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))))
	tmp = 0.0
	if (b <= -2.95e+284)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (b <= -2.5e+215)
		tmp = t_3;
	elseif (b <= -1.92e+80)
		tmp = t_2;
	elseif (b <= -3800000000000.0)
		tmp = t_4;
	elseif (b <= -2.6e-42)
		tmp = t_3;
	elseif (b <= 6.2e+35)
		tmp = t_4;
	elseif (b <= 1.55e+119)
		tmp = t_2;
	elseif (b <= 1.75e+178)
		tmp = t_4;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = t_1 - (y * (i * j));
	t_3 = i * ((a * b) - (y * j));
	t_4 = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	tmp = 0.0;
	if (b <= -2.95e+284)
		tmp = z * ((x * y) - (b * c));
	elseif (b <= -2.5e+215)
		tmp = t_3;
	elseif (b <= -1.92e+80)
		tmp = t_2;
	elseif (b <= -3800000000000.0)
		tmp = t_4;
	elseif (b <= -2.6e-42)
		tmp = t_3;
	elseif (b <= 6.2e+35)
		tmp = t_4;
	elseif (b <= 1.55e+119)
		tmp = t_2;
	elseif (b <= 1.75e+178)
		tmp = t_4;
	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[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - N[(y * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.95e+284], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.5e+215], t$95$3, If[LessEqual[b, -1.92e+80], t$95$2, If[LessEqual[b, -3800000000000.0], t$95$4, If[LessEqual[b, -2.6e-42], t$95$3, If[LessEqual[b, 6.2e+35], t$95$4, If[LessEqual[b, 1.55e+119], t$95$2, If[LessEqual[b, 1.75e+178], t$95$4, t$95$1]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -2.95000000000000013e284

   1. Initial program 66.7%

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

   3. Taylor expanded in z around inf 84.5%

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

      1. *-commutative 84.5%

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

      2. *-commutative 84.5%

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

   5. Simplified 84.5%

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

   if -2.95000000000000013e284 < b < -2.5000000000000001e215 or -3.8e12 < b < -2.6e-42

   1. Initial program 51.1%

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

   3. Taylor expanded in x around 0 54.1%

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

      1. *-commutative 54.1%

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

   5. Simplified 54.1%

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

   6. Taylor expanded in c around 0 60.5%

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

      1. associate-*r* 60.5%

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

      2. neg-mul-1 60.5%

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

      3. cancel-sign-sub 60.5%

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

      4. *-commutative 60.5%

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

      5. associate-*r* 60.5%

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

      6. associate-*r* 66.4%

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

      7. *-commutative 66.4%

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

      8. distribute-rgt-in 75.8%

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

      9. cancel-sign-sub 75.8%

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

      10. distribute-lft-neg-in 75.8%

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

      11. *-commutative 75.8%

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

      12. mul-1-neg 75.8%

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

      13. mul-1-neg 75.8%

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

      14. *-commutative 75.8%

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

      15. mul-1-neg 75.8%

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

      16. neg-sub0 75.8%

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

      17. associate--r+ 75.8%

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

      18. +-commutative 75.8%

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

      19. associate--r+ 75.8%

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

   8. Simplified 75.8%

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

   if -2.5000000000000001e215 < b < -1.91999999999999988e80 or 6.19999999999999973e35 < b < 1.54999999999999998e119

   1. Initial program 75.7%

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

   3. Taylor expanded in x around 0 76.0%

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

      1. *-commutative 76.0%

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

   5. Simplified 76.0%

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

   6. Taylor expanded in c around 0 77.4%

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

      1. associate-*r* 79.2%

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

      2. associate-*r* 79.2%

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

      3. *-commutative 79.2%

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

      4. mul-1-neg 79.2%

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

      5. *-commutative 79.2%

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

      6. distribute-rgt-neg-in 79.2%

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

   8. Simplified 79.2%

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

   9. Taylor expanded in y around 0 77.4%

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

       1. *-commutative 77.4%

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

       2. *-commutative 77.4%

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

       3. associate-*r* 77.4%

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

       4. neg-mul-1 77.4%

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

       5. *-commutative 77.4%

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

       6. *-commutative 77.4%

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

       7. fma-def 77.4%

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

       8. distribute-rgt-neg-out 77.4%

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

       9. associate-*r* 79.2%

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

       10. fma-neg 79.2%

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

   11. Simplified 79.2%

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

   if -1.91999999999999988e80 < b < -3.8e12 or -2.6e-42 < b < 6.19999999999999973e35 or 1.54999999999999998e119 < b < 1.75e178

   1. Initial program 73.9%

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

   3. Taylor expanded in b around 0 73.7%

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

   if 1.75e178 < b

   1. Initial program 71.7%

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

   3. Taylor expanded in b around inf 72.6%

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

      1. *-commutative 72.6%

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

   5. Simplified 72.6%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.95 \cdot 10^{+284}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{+215}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq -1.92 \cdot 10^{+80}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;b \leq -3800000000000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-42}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{+35}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{+119}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{+178}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -7 \cdot 10^{-6}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{-210}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 0.0035:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+109}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+169} \lor \neg \left(x \leq 2.2 \cdot 10^{+294}\right):\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* a b) (* y j)))) (t_2 (* x (- (* y z) (* t a)))))
   (if (<= x -7e-6)
     t_2
     (if (<= x 5.6e-210)
       t_1
       (if (<= x 0.0035)
         (* c (- (* t j) (* z b)))
         (if (<= x 3.8e+59)
           t_1
           (if (<= x 2.6e+109)
             (* t (- (* c j) (* x a)))
             (if (or (<= x 4.2e+169) (not (<= x 2.2e+294)))
               (* y (- (* x z) (* i j)))
               t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -7e-6) {
		tmp = t_2;
	} else if (x <= 5.6e-210) {
		tmp = t_1;
	} else if (x <= 0.0035) {
		tmp = c * ((t * j) - (z * b));
	} else if (x <= 3.8e+59) {
		tmp = t_1;
	} else if (x <= 2.6e+109) {
		tmp = t * ((c * j) - (x * a));
	} else if ((x <= 4.2e+169) || !(x <= 2.2e+294)) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i * ((a * b) - (y * j))
    t_2 = x * ((y * z) - (t * a))
    if (x <= (-7d-6)) then
        tmp = t_2
    else if (x <= 5.6d-210) then
        tmp = t_1
    else if (x <= 0.0035d0) then
        tmp = c * ((t * j) - (z * b))
    else if (x <= 3.8d+59) then
        tmp = t_1
    else if (x <= 2.6d+109) then
        tmp = t * ((c * j) - (x * a))
    else if ((x <= 4.2d+169) .or. (.not. (x <= 2.2d+294))) then
        tmp = y * ((x * z) - (i * j))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -7e-6) {
		tmp = t_2;
	} else if (x <= 5.6e-210) {
		tmp = t_1;
	} else if (x <= 0.0035) {
		tmp = c * ((t * j) - (z * b));
	} else if (x <= 3.8e+59) {
		tmp = t_1;
	} else if (x <= 2.6e+109) {
		tmp = t * ((c * j) - (x * a));
	} else if ((x <= 4.2e+169) || !(x <= 2.2e+294)) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((a * b) - (y * j))
	t_2 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -7e-6:
		tmp = t_2
	elif x <= 5.6e-210:
		tmp = t_1
	elif x <= 0.0035:
		tmp = c * ((t * j) - (z * b))
	elif x <= 3.8e+59:
		tmp = t_1
	elif x <= 2.6e+109:
		tmp = t * ((c * j) - (x * a))
	elif (x <= 4.2e+169) or not (x <= 2.2e+294):
		tmp = y * ((x * z) - (i * j))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -7e-6)
		tmp = t_2;
	elseif (x <= 5.6e-210)
		tmp = t_1;
	elseif (x <= 0.0035)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (x <= 3.8e+59)
		tmp = t_1;
	elseif (x <= 2.6e+109)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif ((x <= 4.2e+169) || !(x <= 2.2e+294))
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((a * b) - (y * j));
	t_2 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -7e-6)
		tmp = t_2;
	elseif (x <= 5.6e-210)
		tmp = t_1;
	elseif (x <= 0.0035)
		tmp = c * ((t * j) - (z * b));
	elseif (x <= 3.8e+59)
		tmp = t_1;
	elseif (x <= 2.6e+109)
		tmp = t * ((c * j) - (x * a));
	elseif ((x <= 4.2e+169) || ~((x <= 2.2e+294)))
		tmp = y * ((x * z) - (i * j));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7e-6], t$95$2, If[LessEqual[x, 5.6e-210], t$95$1, If[LessEqual[x, 0.0035], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.8e+59], t$95$1, If[LessEqual[x, 2.6e+109], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 4.2e+169], N[Not[LessEqual[x, 2.2e+294]], $MachinePrecision]], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -6.99999999999999989e-6 or 4.2000000000000002e169 < x < 2.2000000000000001e294

   1. Initial program 71.1%

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

   3. Taylor expanded in x around inf 67.4%

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

      1. *-commutative 67.4%

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

   5. Simplified 67.4%

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

   if -6.99999999999999989e-6 < x < 5.6e-210 or 0.00350000000000000007 < x < 3.8000000000000001e59

   1. Initial program 72.4%

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

   3. Taylor expanded in x around 0 68.3%

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

      1. *-commutative 68.3%

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

   5. Simplified 68.3%

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

   6. Taylor expanded in c around 0 52.2%

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

      1. associate-*r* 52.2%

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

      2. neg-mul-1 52.2%

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

      3. cancel-sign-sub 52.2%

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

      4. *-commutative 52.2%

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

      5. associate-*r* 52.2%

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

      6. associate-*r* 56.6%

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

      7. *-commutative 56.6%

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

      8. distribute-rgt-in 62.4%

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

      9. cancel-sign-sub 62.4%

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

      10. distribute-lft-neg-in 62.4%

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

      11. *-commutative 62.4%

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

      12. mul-1-neg 62.4%

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

      13. mul-1-neg 62.4%

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

      14. *-commutative 62.4%

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

      15. mul-1-neg 62.4%

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

      16. neg-sub0 62.4%

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

      17. associate--r+ 62.4%

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

      18. +-commutative 62.4%

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

      19. associate--r+ 62.4%

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

   8. Simplified 62.4%

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

   if 5.6e-210 < x < 0.00350000000000000007

   1. Initial program 69.6%

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

   3. Taylor expanded in c around inf 65.7%

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

   if 3.8000000000000001e59 < x < 2.5999999999999998e109

   1. Initial program 65.4%

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

   3. Taylor expanded in b around 0 65.7%

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

   4. Taylor expanded in t around -inf 72.7%

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

      1. mul-1-neg 72.7%

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

      2. distribute-rgt-neg-in 72.7%

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

      3. +-commutative 72.7%

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

      4. mul-1-neg 72.7%

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

      5. unsub-neg 72.7%

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

      6. *-commutative 72.7%

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

   6. Simplified 72.7%

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

   if 2.5999999999999998e109 < x < 4.2000000000000002e169 or 2.2000000000000001e294 < x

   1. Initial program 71.5%

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

   3. Taylor expanded in b around 0 62.6%

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

   4. Taylor expanded in t around 0 58.3%

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

      1. +-commutative 58.3%

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

      2. associate-*r* 58.3%

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

      3. neg-mul-1 58.3%

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

      4. *-commutative 58.3%

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

      5. *-commutative 58.3%

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

      6. *-commutative 58.3%

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

      7. associate-*r* 62.9%

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

      8. *-commutative 62.9%

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

      9. associate-*l* 67.3%

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

      10. distribute-lft-in 72.1%

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

      11. distribute-rgt-neg-out 72.1%

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

      12. unsub-neg 72.1%

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

   6. Simplified 72.1%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{-210}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 0.0035:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+59}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+109}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+169} \lor \neg \left(x \leq 2.2 \cdot 10^{+294}\right):\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 48.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;x \leq -5.8 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-212}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 0.0072:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+109}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+218} \lor \neg \left(x \leq 6.2 \cdot 10^{+293}\right):\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* a b) (* y j)))))
   (if (<= x -5.8e-6)
     (* x (- (* y z) (* t a)))
     (if (<= x 2.4e-212)
       t_1
       (if (<= x 0.0072)
         (* c (- (* t j) (* z b)))
         (if (<= x 1.12e+60)
           t_1
           (if (<= x 1.6e+109)
             (* t (- (* c j) (* x a)))
             (if (or (<= x 3.3e+218) (not (<= x 6.2e+293)))
               (* y (- (* x z) (* i j)))
               (* a (- (* b i) (* x t)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double tmp;
	if (x <= -5.8e-6) {
		tmp = x * ((y * z) - (t * a));
	} else if (x <= 2.4e-212) {
		tmp = t_1;
	} else if (x <= 0.0072) {
		tmp = c * ((t * j) - (z * b));
	} else if (x <= 1.12e+60) {
		tmp = t_1;
	} else if (x <= 1.6e+109) {
		tmp = t * ((c * j) - (x * a));
	} else if ((x <= 3.3e+218) || !(x <= 6.2e+293)) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = a * ((b * i) - (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * ((a * b) - (y * j))
    if (x <= (-5.8d-6)) then
        tmp = x * ((y * z) - (t * a))
    else if (x <= 2.4d-212) then
        tmp = t_1
    else if (x <= 0.0072d0) then
        tmp = c * ((t * j) - (z * b))
    else if (x <= 1.12d+60) then
        tmp = t_1
    else if (x <= 1.6d+109) then
        tmp = t * ((c * j) - (x * a))
    else if ((x <= 3.3d+218) .or. (.not. (x <= 6.2d+293))) then
        tmp = y * ((x * z) - (i * j))
    else
        tmp = a * ((b * i) - (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double tmp;
	if (x <= -5.8e-6) {
		tmp = x * ((y * z) - (t * a));
	} else if (x <= 2.4e-212) {
		tmp = t_1;
	} else if (x <= 0.0072) {
		tmp = c * ((t * j) - (z * b));
	} else if (x <= 1.12e+60) {
		tmp = t_1;
	} else if (x <= 1.6e+109) {
		tmp = t * ((c * j) - (x * a));
	} else if ((x <= 3.3e+218) || !(x <= 6.2e+293)) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = a * ((b * i) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((a * b) - (y * j))
	tmp = 0
	if x <= -5.8e-6:
		tmp = x * ((y * z) - (t * a))
	elif x <= 2.4e-212:
		tmp = t_1
	elif x <= 0.0072:
		tmp = c * ((t * j) - (z * b))
	elif x <= 1.12e+60:
		tmp = t_1
	elif x <= 1.6e+109:
		tmp = t * ((c * j) - (x * a))
	elif (x <= 3.3e+218) or not (x <= 6.2e+293):
		tmp = y * ((x * z) - (i * j))
	else:
		tmp = a * ((b * i) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	tmp = 0.0
	if (x <= -5.8e-6)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (x <= 2.4e-212)
		tmp = t_1;
	elseif (x <= 0.0072)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (x <= 1.12e+60)
		tmp = t_1;
	elseif (x <= 1.6e+109)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif ((x <= 3.3e+218) || !(x <= 6.2e+293))
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	else
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((a * b) - (y * j));
	tmp = 0.0;
	if (x <= -5.8e-6)
		tmp = x * ((y * z) - (t * a));
	elseif (x <= 2.4e-212)
		tmp = t_1;
	elseif (x <= 0.0072)
		tmp = c * ((t * j) - (z * b));
	elseif (x <= 1.12e+60)
		tmp = t_1;
	elseif (x <= 1.6e+109)
		tmp = t * ((c * j) - (x * a));
	elseif ((x <= 3.3e+218) || ~((x <= 6.2e+293)))
		tmp = y * ((x * z) - (i * j));
	else
		tmp = a * ((b * i) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.8e-6], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.4e-212], t$95$1, If[LessEqual[x, 0.0072], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.12e+60], t$95$1, If[LessEqual[x, 1.6e+109], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 3.3e+218], N[Not[LessEqual[x, 6.2e+293]], $MachinePrecision]], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -5.8000000000000004e-6

   1. Initial program 77.4%

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

   3. Taylor expanded in x around inf 66.6%

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

      1. *-commutative 66.6%

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

   5. Simplified 66.6%

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

   if -5.8000000000000004e-6 < x < 2.39999999999999989e-212 or 0.0071999999999999998 < x < 1.1199999999999999e60

   1. Initial program 72.4%

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

   3. Taylor expanded in x around 0 68.3%

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

      1. *-commutative 68.3%

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

   5. Simplified 68.3%

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

   6. Taylor expanded in c around 0 52.2%

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

      1. associate-*r* 52.2%

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

      2. neg-mul-1 52.2%

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

      3. cancel-sign-sub 52.2%

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

      4. *-commutative 52.2%

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

      5. associate-*r* 52.2%

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

      6. associate-*r* 56.6%

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

      7. *-commutative 56.6%

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

      8. distribute-rgt-in 62.4%

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

      9. cancel-sign-sub 62.4%

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

      10. distribute-lft-neg-in 62.4%

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

      11. *-commutative 62.4%

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

      12. mul-1-neg 62.4%

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

      13. mul-1-neg 62.4%

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

      14. *-commutative 62.4%

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

      15. mul-1-neg 62.4%

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

      16. neg-sub0 62.4%

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

      17. associate--r+ 62.4%

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

      18. +-commutative 62.4%

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

      19. associate--r+ 62.4%

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

   8. Simplified 62.4%

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

   if 2.39999999999999989e-212 < x < 0.0071999999999999998

   1. Initial program 69.6%

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

   3. Taylor expanded in c around inf 65.7%

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

   if 1.1199999999999999e60 < x < 1.6000000000000001e109

   1. Initial program 65.4%

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

   3. Taylor expanded in b around 0 65.7%

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

   4. Taylor expanded in t around -inf 72.7%

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

      1. mul-1-neg 72.7%

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

      2. distribute-rgt-neg-in 72.7%

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

      3. +-commutative 72.7%

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

      4. mul-1-neg 72.7%

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

      5. unsub-neg 72.7%

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

      6. *-commutative 72.7%

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

   6. Simplified 72.7%

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

   if 1.6000000000000001e109 < x < 3.29999999999999998e218 or 6.1999999999999998e293 < x

   1. Initial program 65.5%

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

   3. Taylor expanded in b around 0 59.1%

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

   4. Taylor expanded in t around 0 54.9%

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

      1. +-commutative 54.9%

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

      2. associate-*r* 54.9%

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

      3. neg-mul-1 54.9%

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

      4. *-commutative 54.9%

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

      5. *-commutative 54.9%

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

      6. *-commutative 54.9%

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

      7. associate-*r* 56.6%

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

      8. *-commutative 56.6%

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

      9. associate-*l* 66.6%

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

      10. distribute-lft-in 70.0%

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

      11. distribute-rgt-neg-out 70.0%

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

      12. unsub-neg 70.0%

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

   6. Simplified 70.0%

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

   if 3.29999999999999998e218 < x < 6.1999999999999998e293

   1. Initial program 50.0%

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

   3. Taylor expanded in a around inf 75.4%

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

      1. distribute-lft-out-- 75.4%

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

      2. *-commutative 75.4%

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

   5. Simplified 75.4%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-212}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 0.0072:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{+60}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+109}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+218} \lor \neg \left(x \leq 6.2 \cdot 10^{+293}\right):\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 42.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.75 \cdot 10^{+289}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{elif}\;b \leq -1.32 \cdot 10^{+249}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{-104}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{-263}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-254}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{-163}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 10^{-65}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j))) (t_2 (* b (- (* a i) (* z c)))))
   (if (<= b -1.75e+289)
     (* (* z b) (- c))
     (if (<= b -1.32e+249)
       (* a (* b i))
       (if (<= b -4.5e-104)
         t_2
         (if (<= b -4.6e-263)
           t_1
           (if (<= b 1.8e-254)
             (* j (* y (- i)))
             (if (<= b 1.1e-163)
               t_1
               (if (<= b 1e-65) (* i (* y (- j))) t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.75e+289) {
		tmp = (z * b) * -c;
	} else if (b <= -1.32e+249) {
		tmp = a * (b * i);
	} else if (b <= -4.5e-104) {
		tmp = t_2;
	} else if (b <= -4.6e-263) {
		tmp = t_1;
	} else if (b <= 1.8e-254) {
		tmp = j * (y * -i);
	} else if (b <= 1.1e-163) {
		tmp = t_1;
	} else if (b <= 1e-65) {
		tmp = i * (y * -j);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * (t * j)
    t_2 = b * ((a * i) - (z * c))
    if (b <= (-1.75d+289)) then
        tmp = (z * b) * -c
    else if (b <= (-1.32d+249)) then
        tmp = a * (b * i)
    else if (b <= (-4.5d-104)) then
        tmp = t_2
    else if (b <= (-4.6d-263)) then
        tmp = t_1
    else if (b <= 1.8d-254) then
        tmp = j * (y * -i)
    else if (b <= 1.1d-163) then
        tmp = t_1
    else if (b <= 1d-65) then
        tmp = i * (y * -j)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.75e+289) {
		tmp = (z * b) * -c;
	} else if (b <= -1.32e+249) {
		tmp = a * (b * i);
	} else if (b <= -4.5e-104) {
		tmp = t_2;
	} else if (b <= -4.6e-263) {
		tmp = t_1;
	} else if (b <= 1.8e-254) {
		tmp = j * (y * -i);
	} else if (b <= 1.1e-163) {
		tmp = t_1;
	} else if (b <= 1e-65) {
		tmp = i * (y * -j);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (t * j)
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -1.75e+289:
		tmp = (z * b) * -c
	elif b <= -1.32e+249:
		tmp = a * (b * i)
	elif b <= -4.5e-104:
		tmp = t_2
	elif b <= -4.6e-263:
		tmp = t_1
	elif b <= 1.8e-254:
		tmp = j * (y * -i)
	elif b <= 1.1e-163:
		tmp = t_1
	elif b <= 1e-65:
		tmp = i * (y * -j)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(t * j))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -1.75e+289)
		tmp = Float64(Float64(z * b) * Float64(-c));
	elseif (b <= -1.32e+249)
		tmp = Float64(a * Float64(b * i));
	elseif (b <= -4.5e-104)
		tmp = t_2;
	elseif (b <= -4.6e-263)
		tmp = t_1;
	elseif (b <= 1.8e-254)
		tmp = Float64(j * Float64(y * Float64(-i)));
	elseif (b <= 1.1e-163)
		tmp = t_1;
	elseif (b <= 1e-65)
		tmp = Float64(i * Float64(y * Float64(-j)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (t * j);
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -1.75e+289)
		tmp = (z * b) * -c;
	elseif (b <= -1.32e+249)
		tmp = a * (b * i);
	elseif (b <= -4.5e-104)
		tmp = t_2;
	elseif (b <= -4.6e-263)
		tmp = t_1;
	elseif (b <= 1.8e-254)
		tmp = j * (y * -i);
	elseif (b <= 1.1e-163)
		tmp = t_1;
	elseif (b <= 1e-65)
		tmp = i * (y * -j);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.75e+289], N[(N[(z * b), $MachinePrecision] * (-c)), $MachinePrecision], If[LessEqual[b, -1.32e+249], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.5e-104], t$95$2, If[LessEqual[b, -4.6e-263], t$95$1, If[LessEqual[b, 1.8e-254], N[(j * N[(y * (-i)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.1e-163], t$95$1, If[LessEqual[b, 1e-65], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -1.75000000000000011e289

   1. Initial program 60.0%

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

   3. Taylor expanded in c around inf 100.0%

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

   4. Taylor expanded in j around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-lft-neg-out 100.0%

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

      3. *-commutative 100.0%

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

   6. Simplified 100.0%

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

   if -1.75000000000000011e289 < b < -1.3200000000000001e249

   1. Initial program 58.9%

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

   3. Taylor expanded in x around 0 58.4%

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

      1. *-commutative 58.4%

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

   5. Simplified 58.4%

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

   6. Taylor expanded in a around inf 67.4%

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

   if -1.3200000000000001e249 < b < -4.4999999999999997e-104 or 9.99999999999999923e-66 < b

   1. Initial program 70.3%

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

   3. Taylor expanded in b around inf 52.1%

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

      1. *-commutative 52.1%

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

   5. Simplified 52.1%

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

   if -4.4999999999999997e-104 < b < -4.60000000000000006e-263 or 1.79999999999999992e-254 < b < 1.10000000000000005e-163

   1. Initial program 79.3%

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

   3. Taylor expanded in x around 0 56.6%

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

      1. *-commutative 56.6%

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

   5. Simplified 56.6%

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

   6. Taylor expanded in t around inf 49.2%

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

   if -4.60000000000000006e-263 < b < 1.79999999999999992e-254

   1. Initial program 72.2%

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

   3. Taylor expanded in j around inf 67.0%

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

   4. Taylor expanded in c around 0 51.1%

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

      1. neg-mul-1 51.1%

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

      2. distribute-rgt-neg-in 51.1%

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

   6. Simplified 51.1%

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

   if 1.10000000000000005e-163 < b < 9.99999999999999923e-66

   1. Initial program 59.7%

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

   3. Taylor expanded in x around 0 35.5%

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

      1. *-commutative 35.5%

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

   5. Simplified 35.5%

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

   6. Taylor expanded in y around inf 51.6%

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

      1. associate-*r* 51.6%

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

      2. neg-mul-1 51.6%

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

   8. Simplified 51.6%

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

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.75 \cdot 10^{+289}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{elif}\;b \leq -1.32 \cdot 10^{+249}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{-104}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{-263}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-254}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{-163}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;b \leq 10^{-65}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 29.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c\right)\\ \mathbf{if}\;c \leq -5.4 \cdot 10^{+200}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq -2.55 \cdot 10^{+87}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{-277}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;c \leq 2.1 \cdot 10^{-78}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;c \leq 140000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 7 \cdot 10^{+36}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 2.6 \cdot 10^{+220}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (* t c))))
   (if (<= c -5.4e+200)
     (* b (* z (- c)))
     (if (<= c -2.55e+87)
       (* t (* c j))
       (if (<= c 1.3e-277)
         (* i (* a b))
         (if (<= c 2.1e-78)
           (* j (* y (- i)))
           (if (<= c 140000.0)
             t_1
             (if (<= c 7e+36)
               (* z (* x y))
               (if (<= c 2.6e+220) t_1 (* (* z b) (- c)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (t * c);
	double tmp;
	if (c <= -5.4e+200) {
		tmp = b * (z * -c);
	} else if (c <= -2.55e+87) {
		tmp = t * (c * j);
	} else if (c <= 1.3e-277) {
		tmp = i * (a * b);
	} else if (c <= 2.1e-78) {
		tmp = j * (y * -i);
	} else if (c <= 140000.0) {
		tmp = t_1;
	} else if (c <= 7e+36) {
		tmp = z * (x * y);
	} else if (c <= 2.6e+220) {
		tmp = t_1;
	} else {
		tmp = (z * b) * -c;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (t * c)
    if (c <= (-5.4d+200)) then
        tmp = b * (z * -c)
    else if (c <= (-2.55d+87)) then
        tmp = t * (c * j)
    else if (c <= 1.3d-277) then
        tmp = i * (a * b)
    else if (c <= 2.1d-78) then
        tmp = j * (y * -i)
    else if (c <= 140000.0d0) then
        tmp = t_1
    else if (c <= 7d+36) then
        tmp = z * (x * y)
    else if (c <= 2.6d+220) then
        tmp = t_1
    else
        tmp = (z * b) * -c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (t * c);
	double tmp;
	if (c <= -5.4e+200) {
		tmp = b * (z * -c);
	} else if (c <= -2.55e+87) {
		tmp = t * (c * j);
	} else if (c <= 1.3e-277) {
		tmp = i * (a * b);
	} else if (c <= 2.1e-78) {
		tmp = j * (y * -i);
	} else if (c <= 140000.0) {
		tmp = t_1;
	} else if (c <= 7e+36) {
		tmp = z * (x * y);
	} else if (c <= 2.6e+220) {
		tmp = t_1;
	} else {
		tmp = (z * b) * -c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * (t * c)
	tmp = 0
	if c <= -5.4e+200:
		tmp = b * (z * -c)
	elif c <= -2.55e+87:
		tmp = t * (c * j)
	elif c <= 1.3e-277:
		tmp = i * (a * b)
	elif c <= 2.1e-78:
		tmp = j * (y * -i)
	elif c <= 140000.0:
		tmp = t_1
	elif c <= 7e+36:
		tmp = z * (x * y)
	elif c <= 2.6e+220:
		tmp = t_1
	else:
		tmp = (z * b) * -c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(t * c))
	tmp = 0.0
	if (c <= -5.4e+200)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (c <= -2.55e+87)
		tmp = Float64(t * Float64(c * j));
	elseif (c <= 1.3e-277)
		tmp = Float64(i * Float64(a * b));
	elseif (c <= 2.1e-78)
		tmp = Float64(j * Float64(y * Float64(-i)));
	elseif (c <= 140000.0)
		tmp = t_1;
	elseif (c <= 7e+36)
		tmp = Float64(z * Float64(x * y));
	elseif (c <= 2.6e+220)
		tmp = t_1;
	else
		tmp = Float64(Float64(z * b) * Float64(-c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * (t * c);
	tmp = 0.0;
	if (c <= -5.4e+200)
		tmp = b * (z * -c);
	elseif (c <= -2.55e+87)
		tmp = t * (c * j);
	elseif (c <= 1.3e-277)
		tmp = i * (a * b);
	elseif (c <= 2.1e-78)
		tmp = j * (y * -i);
	elseif (c <= 140000.0)
		tmp = t_1;
	elseif (c <= 7e+36)
		tmp = z * (x * y);
	elseif (c <= 2.6e+220)
		tmp = t_1;
	else
		tmp = (z * b) * -c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -5.4e+200], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.55e+87], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.3e-277], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.1e-78], N[(j * N[(y * (-i)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 140000.0], t$95$1, If[LessEqual[c, 7e+36], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.6e+220], t$95$1, N[(N[(z * b), $MachinePrecision] * (-c)), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if c < -5.40000000000000031e200

   1. Initial program 63.8%

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

   3. Taylor expanded in x around 0 60.3%

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

      1. *-commutative 60.3%

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

   5. Simplified 60.3%

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

   6. Taylor expanded in z around inf 47.5%

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

      1. associate-*r* 47.5%

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

      2. neg-mul-1 47.5%

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

   8. Simplified 47.5%

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

   if -5.40000000000000031e200 < c < -2.54999999999999994e87

   1. Initial program 54.3%

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

   3. Taylor expanded in b around 0 66.5%

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

   4. Taylor expanded in c around inf 44.0%

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

      1. *-commutative 44.0%

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

      2. *-commutative 44.0%

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

      3. associate-*r* 47.8%

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

   6. Simplified 47.8%

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

   if -2.54999999999999994e87 < c < 1.3e-277

   1. Initial program 74.4%

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

   3. Taylor expanded in x around 0 51.7%

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

      1. *-commutative 51.7%

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

   5. Simplified 51.7%

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

   6. Taylor expanded in c around 0 43.2%

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

      1. associate-*r* 43.2%

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

      2. neg-mul-1 43.2%

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

      3. cancel-sign-sub 43.2%

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

      4. *-commutative 43.2%

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

      5. associate-*r* 43.2%

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

      6. associate-*r* 48.1%

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

      7. *-commutative 48.1%

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

      8. distribute-rgt-in 50.7%

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

      9. cancel-sign-sub 50.7%

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

      10. distribute-lft-neg-in 50.7%

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

      11. *-commutative 50.7%

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

      12. mul-1-neg 50.7%

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

      13. mul-1-neg 50.7%

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

      14. *-commutative 50.7%

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

      15. mul-1-neg 50.7%

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

      16. neg-sub0 50.7%

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

      17. associate--r+ 50.7%

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

      18. +-commutative 50.7%

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

      19. associate--r+ 50.7%

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

   8. Simplified 50.7%

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

   9. Taylor expanded in b around inf 33.3%

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

       1. *-commutative 33.3%

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

   11. Simplified 33.3%

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

   if 1.3e-277 < c < 2.1000000000000001e-78

   1. Initial program 82.3%

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

   3. Taylor expanded in j around inf 60.2%

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

   4. Taylor expanded in c around 0 52.5%

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

      1. neg-mul-1 52.5%

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

      2. distribute-rgt-neg-in 52.5%

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

   6. Simplified 52.5%

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

   if 2.1000000000000001e-78 < c < 1.4e5 or 6.9999999999999996e36 < c < 2.59999999999999994e220

   1. Initial program 73.6%

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

   3. Taylor expanded in j around inf 50.1%

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

   4. Taylor expanded in c around inf 44.3%

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

   if 1.4e5 < c < 6.9999999999999996e36

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 86.3%

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

      1. *-commutative 86.3%

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

      2. *-commutative 86.3%

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

   5. Simplified 86.3%

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

   6. Taylor expanded in y around inf 45.4%

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

      1. *-commutative 45.4%

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

      2. *-commutative 45.4%

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

      3. associate-*l* 72.2%

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

   8. Simplified 72.2%

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

   if 2.59999999999999994e220 < c

   1. Initial program 45.5%

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

   3. Taylor expanded in c around inf 70.3%

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

   4. Taylor expanded in j around 0 55.4%

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

      1. mul-1-neg 55.4%

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

      2. distribute-lft-neg-out 55.4%

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

      3. *-commutative 55.4%

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

   6. Simplified 55.4%

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

4. Final simplification 44.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.4 \cdot 10^{+200}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq -2.55 \cdot 10^{+87}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{-277}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;c \leq 2.1 \cdot 10^{-78}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;c \leq 140000:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq 7 \cdot 10^{+36}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 2.6 \cdot 10^{+220}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 29.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c\right)\\ \mathbf{if}\;c \leq -1.58 \cdot 10^{+91}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{-277}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;c \leq 4.6 \cdot 10^{-79}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;c \leq 1800000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{+34}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{+220}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (* t c))))
   (if (<= c -1.58e+91)
     (* t (* c j))
     (if (<= c 1.3e-277)
       (* i (* a b))
       (if (<= c 4.6e-79)
         (* j (* y (- i)))
         (if (<= c 1800000.0)
           t_1
           (if (<= c 5.8e+34)
             (* z (* x y))
             (if (<= c 2.5e+220) t_1 (* (* z b) (- c))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (t * c);
	double tmp;
	if (c <= -1.58e+91) {
		tmp = t * (c * j);
	} else if (c <= 1.3e-277) {
		tmp = i * (a * b);
	} else if (c <= 4.6e-79) {
		tmp = j * (y * -i);
	} else if (c <= 1800000.0) {
		tmp = t_1;
	} else if (c <= 5.8e+34) {
		tmp = z * (x * y);
	} else if (c <= 2.5e+220) {
		tmp = t_1;
	} else {
		tmp = (z * b) * -c;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (t * c)
    if (c <= (-1.58d+91)) then
        tmp = t * (c * j)
    else if (c <= 1.3d-277) then
        tmp = i * (a * b)
    else if (c <= 4.6d-79) then
        tmp = j * (y * -i)
    else if (c <= 1800000.0d0) then
        tmp = t_1
    else if (c <= 5.8d+34) then
        tmp = z * (x * y)
    else if (c <= 2.5d+220) then
        tmp = t_1
    else
        tmp = (z * b) * -c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (t * c);
	double tmp;
	if (c <= -1.58e+91) {
		tmp = t * (c * j);
	} else if (c <= 1.3e-277) {
		tmp = i * (a * b);
	} else if (c <= 4.6e-79) {
		tmp = j * (y * -i);
	} else if (c <= 1800000.0) {
		tmp = t_1;
	} else if (c <= 5.8e+34) {
		tmp = z * (x * y);
	} else if (c <= 2.5e+220) {
		tmp = t_1;
	} else {
		tmp = (z * b) * -c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * (t * c)
	tmp = 0
	if c <= -1.58e+91:
		tmp = t * (c * j)
	elif c <= 1.3e-277:
		tmp = i * (a * b)
	elif c <= 4.6e-79:
		tmp = j * (y * -i)
	elif c <= 1800000.0:
		tmp = t_1
	elif c <= 5.8e+34:
		tmp = z * (x * y)
	elif c <= 2.5e+220:
		tmp = t_1
	else:
		tmp = (z * b) * -c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(t * c))
	tmp = 0.0
	if (c <= -1.58e+91)
		tmp = Float64(t * Float64(c * j));
	elseif (c <= 1.3e-277)
		tmp = Float64(i * Float64(a * b));
	elseif (c <= 4.6e-79)
		tmp = Float64(j * Float64(y * Float64(-i)));
	elseif (c <= 1800000.0)
		tmp = t_1;
	elseif (c <= 5.8e+34)
		tmp = Float64(z * Float64(x * y));
	elseif (c <= 2.5e+220)
		tmp = t_1;
	else
		tmp = Float64(Float64(z * b) * Float64(-c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * (t * c);
	tmp = 0.0;
	if (c <= -1.58e+91)
		tmp = t * (c * j);
	elseif (c <= 1.3e-277)
		tmp = i * (a * b);
	elseif (c <= 4.6e-79)
		tmp = j * (y * -i);
	elseif (c <= 1800000.0)
		tmp = t_1;
	elseif (c <= 5.8e+34)
		tmp = z * (x * y);
	elseif (c <= 2.5e+220)
		tmp = t_1;
	else
		tmp = (z * b) * -c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.58e+91], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.3e-277], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.6e-79], N[(j * N[(y * (-i)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1800000.0], t$95$1, If[LessEqual[c, 5.8e+34], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.5e+220], t$95$1, N[(N[(z * b), $MachinePrecision] * (-c)), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -1.5799999999999999e91

   1. Initial program 58.3%

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

   3. Taylor expanded in b around 0 54.7%

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

   4. Taylor expanded in c around inf 37.6%

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

      1. *-commutative 37.6%

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

      2. *-commutative 37.6%

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

      3. associate-*r* 37.8%

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

   6. Simplified 37.8%

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

   if -1.5799999999999999e91 < c < 1.3e-277

   1. Initial program 74.4%

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

   3. Taylor expanded in x around 0 51.7%

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

      1. *-commutative 51.7%

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

   5. Simplified 51.7%

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

   6. Taylor expanded in c around 0 43.2%

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

      1. associate-*r* 43.2%

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

      2. neg-mul-1 43.2%

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

      3. cancel-sign-sub 43.2%

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

      4. *-commutative 43.2%

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

      5. associate-*r* 43.2%

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

      6. associate-*r* 48.1%

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

      7. *-commutative 48.1%

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

      8. distribute-rgt-in 50.7%

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

      9. cancel-sign-sub 50.7%

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

      10. distribute-lft-neg-in 50.7%

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

      11. *-commutative 50.7%

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

      12. mul-1-neg 50.7%

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

      13. mul-1-neg 50.7%

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

      14. *-commutative 50.7%

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

      15. mul-1-neg 50.7%

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

      16. neg-sub0 50.7%

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

      17. associate--r+ 50.7%

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

      18. +-commutative 50.7%

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

      19. associate--r+ 50.7%

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

   8. Simplified 50.7%

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

   9. Taylor expanded in b around inf 33.3%

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

       1. *-commutative 33.3%

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

   11. Simplified 33.3%

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

   if 1.3e-277 < c < 4.60000000000000023e-79

   1. Initial program 82.3%

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

   3. Taylor expanded in j around inf 60.2%

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

   4. Taylor expanded in c around 0 52.5%

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

      1. neg-mul-1 52.5%

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

      2. distribute-rgt-neg-in 52.5%

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

   6. Simplified 52.5%

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

   if 4.60000000000000023e-79 < c < 1.8e6 or 5.8000000000000003e34 < c < 2.5000000000000001e220

   1. Initial program 73.6%

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

   3. Taylor expanded in j around inf 50.1%

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

   4. Taylor expanded in c around inf 44.3%

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

   if 1.8e6 < c < 5.8000000000000003e34

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 86.3%

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

      1. *-commutative 86.3%

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

      2. *-commutative 86.3%

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

   5. Simplified 86.3%

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

   6. Taylor expanded in y around inf 45.4%

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

      1. *-commutative 45.4%

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

      2. *-commutative 45.4%

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

      3. associate-*l* 72.2%

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

   8. Simplified 72.2%

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

   if 2.5000000000000001e220 < c

   1. Initial program 45.5%

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

   3. Taylor expanded in c around inf 70.3%

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

   4. Taylor expanded in j around 0 55.4%

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

      1. mul-1-neg 55.4%

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

      2. distribute-lft-neg-out 55.4%

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

      3. *-commutative 55.4%

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

   6. Simplified 55.4%

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

4. Final simplification 42.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.58 \cdot 10^{+91}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{-277}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;c \leq 4.6 \cdot 10^{-79}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \mathbf{elif}\;c \leq 1800000:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{+34}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{+220}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 58.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right) - y \cdot \left(i \cdot j\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -3.9 \cdot 10^{+76}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-95}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+46}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* b (- (* a i) (* z c))) (* y (* i j))))
        (t_2 (* t (- (* c j) (* x a)))))
   (if (<= t -3.9e+76)
     t_2
     (if (<= t -7.5e-55)
       t_1
       (if (<= t -2.1e-95)
         (* c (- (* t j) (* z b)))
         (if (<= t 5.6e+46) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (b * ((a * i) - (z * c))) - (y * (i * j));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -3.9e+76) {
		tmp = t_2;
	} else if (t <= -7.5e-55) {
		tmp = t_1;
	} else if (t <= -2.1e-95) {
		tmp = c * ((t * j) - (z * b));
	} else if (t <= 5.6e+46) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * ((a * i) - (z * c))) - (y * (i * j))
    t_2 = t * ((c * j) - (x * a))
    if (t <= (-3.9d+76)) then
        tmp = t_2
    else if (t <= (-7.5d-55)) then
        tmp = t_1
    else if (t <= (-2.1d-95)) then
        tmp = c * ((t * j) - (z * b))
    else if (t <= 5.6d+46) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (b * ((a * i) - (z * c))) - (y * (i * j));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -3.9e+76) {
		tmp = t_2;
	} else if (t <= -7.5e-55) {
		tmp = t_1;
	} else if (t <= -2.1e-95) {
		tmp = c * ((t * j) - (z * b));
	} else if (t <= 5.6e+46) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (b * ((a * i) - (z * c))) - (y * (i * j))
	t_2 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -3.9e+76:
		tmp = t_2
	elif t <= -7.5e-55:
		tmp = t_1
	elif t <= -2.1e-95:
		tmp = c * ((t * j) - (z * b))
	elif t <= 5.6e+46:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(b * Float64(Float64(a * i) - Float64(z * c))) - Float64(y * Float64(i * j)))
	t_2 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -3.9e+76)
		tmp = t_2;
	elseif (t <= -7.5e-55)
		tmp = t_1;
	elseif (t <= -2.1e-95)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (t <= 5.6e+46)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (b * ((a * i) - (z * c))) - (y * (i * j));
	t_2 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -3.9e+76)
		tmp = t_2;
	elseif (t <= -7.5e-55)
		tmp = t_1;
	elseif (t <= -2.1e-95)
		tmp = c * ((t * j) - (z * b));
	elseif (t <= 5.6e+46)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.9e+76], t$95$2, If[LessEqual[t, -7.5e-55], t$95$1, If[LessEqual[t, -2.1e-95], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.6e+46], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.89999999999999989e76 or 5.60000000000000037e46 < t

   1. Initial program 62.4%

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

   3. Taylor expanded in b around 0 62.9%

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

   4. Taylor expanded in t around -inf 69.9%

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

      1. mul-1-neg 69.9%

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

      2. distribute-rgt-neg-in 69.9%

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

      3. +-commutative 69.9%

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

      4. mul-1-neg 69.9%

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

      5. unsub-neg 69.9%

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

      6. *-commutative 69.9%

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

   6. Simplified 69.9%

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

   if -3.89999999999999989e76 < t < -7.50000000000000023e-55 or -2.1e-95 < t < 5.60000000000000037e46

   1. Initial program 76.5%

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

   3. Taylor expanded in x around 0 66.4%

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

      1. *-commutative 66.4%

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

   5. Simplified 66.4%

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

   6. Taylor expanded in c around 0 61.4%

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

      1. associate-*r* 62.7%

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

      2. associate-*r* 62.7%

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

      3. *-commutative 62.7%

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

      4. mul-1-neg 62.7%

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

      5. *-commutative 62.7%

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

      6. distribute-rgt-neg-in 62.7%

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

   8. Simplified 62.7%

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

   9. Taylor expanded in y around 0 61.4%

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

       1. *-commutative 61.4%

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

       2. *-commutative 61.4%

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

       3. associate-*r* 61.4%

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

       4. neg-mul-1 61.4%

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

       5. *-commutative 61.4%

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

       6. *-commutative 61.4%

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

       7. fma-def 61.4%

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

       8. distribute-rgt-neg-out 61.4%

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

       9. associate-*r* 62.7%

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

       10. fma-neg 62.7%

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

   11. Simplified 62.7%

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

   if -7.50000000000000023e-55 < t < -2.1e-95

   1. Initial program 76.7%

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

   3. Taylor expanded in c around inf 69.5%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{+76}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-55}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-95}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+46}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 50.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -1.4 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{-208}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+36}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+127} \lor \neg \left(x \leq 7 \cdot 10^{+174}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= x -1.4e-10)
     t_1
     (if (<= x 2.35e-208)
       (* i (- (* a b) (* y j)))
       (if (<= x 1.2e+36)
         (* c (- (* t j) (* z b)))
         (if (or (<= x 8e+127) (not (<= x 7e+174)))
           t_1
           (* j (- (* t c) (* y i)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.4e-10) {
		tmp = t_1;
	} else if (x <= 2.35e-208) {
		tmp = i * ((a * b) - (y * j));
	} else if (x <= 1.2e+36) {
		tmp = c * ((t * j) - (z * b));
	} else if ((x <= 8e+127) || !(x <= 7e+174)) {
		tmp = t_1;
	} else {
		tmp = j * ((t * c) - (y * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (x <= (-1.4d-10)) then
        tmp = t_1
    else if (x <= 2.35d-208) then
        tmp = i * ((a * b) - (y * j))
    else if (x <= 1.2d+36) then
        tmp = c * ((t * j) - (z * b))
    else if ((x <= 8d+127) .or. (.not. (x <= 7d+174))) then
        tmp = t_1
    else
        tmp = j * ((t * c) - (y * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.4e-10) {
		tmp = t_1;
	} else if (x <= 2.35e-208) {
		tmp = i * ((a * b) - (y * j));
	} else if (x <= 1.2e+36) {
		tmp = c * ((t * j) - (z * b));
	} else if ((x <= 8e+127) || !(x <= 7e+174)) {
		tmp = t_1;
	} else {
		tmp = j * ((t * c) - (y * i));
	}
	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 <= -1.4e-10:
		tmp = t_1
	elif x <= 2.35e-208:
		tmp = i * ((a * b) - (y * j))
	elif x <= 1.2e+36:
		tmp = c * ((t * j) - (z * b))
	elif (x <= 8e+127) or not (x <= 7e+174):
		tmp = t_1
	else:
		tmp = j * ((t * c) - (y * i))
	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 <= -1.4e-10)
		tmp = t_1;
	elseif (x <= 2.35e-208)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (x <= 1.2e+36)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif ((x <= 8e+127) || !(x <= 7e+174))
		tmp = t_1;
	else
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	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 <= -1.4e-10)
		tmp = t_1;
	elseif (x <= 2.35e-208)
		tmp = i * ((a * b) - (y * j));
	elseif (x <= 1.2e+36)
		tmp = c * ((t * j) - (z * b));
	elseif ((x <= 8e+127) || ~((x <= 7e+174)))
		tmp = t_1;
	else
		tmp = j * ((t * c) - (y * i));
	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, -1.4e-10], t$95$1, If[LessEqual[x, 2.35e-208], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.2e+36], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 8e+127], N[Not[LessEqual[x, 7e+174]], $MachinePrecision]], t$95$1, N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.40000000000000008e-10 or 1.19999999999999996e36 < x < 7.99999999999999964e127 or 7.0000000000000003e174 < x

   1. Initial program 70.4%

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

   3. Taylor expanded in x around inf 65.3%

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

      1. *-commutative 65.3%

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

   5. Simplified 65.3%

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

   if -1.40000000000000008e-10 < x < 2.3500000000000001e-208

   1. Initial program 69.5%

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

   3. Taylor expanded in x around 0 68.1%

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

      1. *-commutative 68.1%

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

   5. Simplified 68.1%

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

   6. Taylor expanded in c around 0 53.3%

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

      1. associate-*r* 53.3%

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

      2. neg-mul-1 53.3%

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

      3. cancel-sign-sub 53.3%

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

      4. *-commutative 53.3%

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

      5. associate-*r* 53.3%

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

      6. associate-*r* 55.8%

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

      7. *-commutative 55.8%

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

      8. distribute-rgt-in 61.5%

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

      9. cancel-sign-sub 61.5%

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

      10. distribute-lft-neg-in 61.5%

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

      11. *-commutative 61.5%

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

      12. mul-1-neg 61.5%

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

      13. mul-1-neg 61.5%

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

      14. *-commutative 61.5%

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

      15. mul-1-neg 61.5%

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

      16. neg-sub0 61.5%

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

      17. associate--r+ 61.5%

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

      18. +-commutative 61.5%

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

      19. associate--r+ 61.5%

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

   8. Simplified 61.5%

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

   if 2.3500000000000001e-208 < x < 1.19999999999999996e36

   1. Initial program 69.9%

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

   3. Taylor expanded in c around inf 62.9%

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

   if 7.99999999999999964e127 < x < 7.0000000000000003e174

   1. Initial program 91.4%

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

   3. Taylor expanded in j around inf 59.0%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{-208}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+36}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+127} \lor \neg \left(x \leq 7 \cdot 10^{+174}\right):\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -6.9 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-208}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+36}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{+119} \lor \neg \left(x \leq 3.5 \cdot 10^{+173}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= x -6.9e-9)
     t_1
     (if (<= x 7.6e-208)
       (* i (- (* a b) (* y j)))
       (if (<= x 3.4e+36)
         (* c (- (* t j) (* z b)))
         (if (or (<= x 6.6e+119) (not (<= x 3.5e+173)))
           t_1
           (* y (- (* x z) (* i j)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -6.9e-9) {
		tmp = t_1;
	} else if (x <= 7.6e-208) {
		tmp = i * ((a * b) - (y * j));
	} else if (x <= 3.4e+36) {
		tmp = c * ((t * j) - (z * b));
	} else if ((x <= 6.6e+119) || !(x <= 3.5e+173)) {
		tmp = t_1;
	} else {
		tmp = y * ((x * z) - (i * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (x <= (-6.9d-9)) then
        tmp = t_1
    else if (x <= 7.6d-208) then
        tmp = i * ((a * b) - (y * j))
    else if (x <= 3.4d+36) then
        tmp = c * ((t * j) - (z * b))
    else if ((x <= 6.6d+119) .or. (.not. (x <= 3.5d+173))) then
        tmp = t_1
    else
        tmp = y * ((x * z) - (i * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -6.9e-9) {
		tmp = t_1;
	} else if (x <= 7.6e-208) {
		tmp = i * ((a * b) - (y * j));
	} else if (x <= 3.4e+36) {
		tmp = c * ((t * j) - (z * b));
	} else if ((x <= 6.6e+119) || !(x <= 3.5e+173)) {
		tmp = t_1;
	} else {
		tmp = y * ((x * z) - (i * j));
	}
	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 <= -6.9e-9:
		tmp = t_1
	elif x <= 7.6e-208:
		tmp = i * ((a * b) - (y * j))
	elif x <= 3.4e+36:
		tmp = c * ((t * j) - (z * b))
	elif (x <= 6.6e+119) or not (x <= 3.5e+173):
		tmp = t_1
	else:
		tmp = y * ((x * z) - (i * j))
	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 <= -6.9e-9)
		tmp = t_1;
	elseif (x <= 7.6e-208)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (x <= 3.4e+36)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif ((x <= 6.6e+119) || !(x <= 3.5e+173))
		tmp = t_1;
	else
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	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 <= -6.9e-9)
		tmp = t_1;
	elseif (x <= 7.6e-208)
		tmp = i * ((a * b) - (y * j));
	elseif (x <= 3.4e+36)
		tmp = c * ((t * j) - (z * b));
	elseif ((x <= 6.6e+119) || ~((x <= 3.5e+173)))
		tmp = t_1;
	else
		tmp = y * ((x * z) - (i * j));
	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, -6.9e-9], t$95$1, If[LessEqual[x, 7.6e-208], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.4e+36], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 6.6e+119], N[Not[LessEqual[x, 3.5e+173]], $MachinePrecision]], t$95$1, N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -6.89999999999999975e-9 or 3.3999999999999998e36 < x < 6.6000000000000004e119 or 3.4999999999999999e173 < x

   1. Initial program 71.0%

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

   3. Taylor expanded in x around inf 64.1%

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

      1. *-commutative 64.1%

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

   5. Simplified 64.1%

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

   if -6.89999999999999975e-9 < x < 7.60000000000000023e-208

   1. Initial program 69.5%

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

   3. Taylor expanded in x around 0 68.1%

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

      1. *-commutative 68.1%

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

   5. Simplified 68.1%

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

   6. Taylor expanded in c around 0 53.3%

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

      1. associate-*r* 53.3%

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

      2. neg-mul-1 53.3%

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

      3. cancel-sign-sub 53.3%

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

      4. *-commutative 53.3%

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

      5. associate-*r* 53.3%

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

      6. associate-*r* 55.8%

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

      7. *-commutative 55.8%

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

      8. distribute-rgt-in 61.5%

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

      9. cancel-sign-sub 61.5%

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

      10. distribute-lft-neg-in 61.5%

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

      11. *-commutative 61.5%

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

      12. mul-1-neg 61.5%

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

      13. mul-1-neg 61.5%

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

      14. *-commutative 61.5%

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

      15. mul-1-neg 61.5%

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

      16. neg-sub0 61.5%

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

      17. associate--r+ 61.5%

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

      18. +-commutative 61.5%

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

      19. associate--r+ 61.5%

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

   8. Simplified 61.5%

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

   if 7.60000000000000023e-208 < x < 3.3999999999999998e36

   1. Initial program 69.9%

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

   3. Taylor expanded in c around inf 62.9%

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

   if 6.6000000000000004e119 < x < 3.4999999999999999e173

   1. Initial program 84.5%

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

   3. Taylor expanded in b around 0 77.4%

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

   4. Taylor expanded in t around 0 77.4%

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

      1. +-commutative 77.4%

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

      2. associate-*r* 77.4%

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

      3. neg-mul-1 77.4%

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

      4. *-commutative 77.4%

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

      5. *-commutative 77.4%

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

      6. *-commutative 77.4%

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

      7. associate-*r* 77.4%

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

      8. *-commutative 77.4%

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

      9. associate-*l* 77.3%

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

      10. distribute-lft-in 77.3%

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

      11. distribute-rgt-neg-out 77.3%

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

      12. unsub-neg 77.3%

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

   6. Simplified 77.3%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.9 \cdot 10^{-9}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-208}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+36}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{+119} \lor \neg \left(x \leq 3.5 \cdot 10^{+173}\right):\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 52.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_2 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -2.5 \cdot 10^{-51}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq 3.7 \cdot 10^{-87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 1000000000:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;i \leq 3.7 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))) (t_2 (* i (- (* a b) (* y j)))))
   (if (<= i -2.5e-51)
     t_2
     (if (<= i 3.7e-87)
       t_1
       (if (<= i 1000000000.0)
         (* j (- (* t c) (* y i)))
         (if (<= i 3.7e+33) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double t_2 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -2.5e-51) {
		tmp = t_2;
	} else if (i <= 3.7e-87) {
		tmp = t_1;
	} else if (i <= 1000000000.0) {
		tmp = j * ((t * c) - (y * i));
	} else if (i <= 3.7e+33) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * ((t * j) - (z * b))
    t_2 = i * ((a * b) - (y * j))
    if (i <= (-2.5d-51)) then
        tmp = t_2
    else if (i <= 3.7d-87) then
        tmp = t_1
    else if (i <= 1000000000.0d0) then
        tmp = j * ((t * c) - (y * i))
    else if (i <= 3.7d+33) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double t_2 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -2.5e-51) {
		tmp = t_2;
	} else if (i <= 3.7e-87) {
		tmp = t_1;
	} else if (i <= 1000000000.0) {
		tmp = j * ((t * c) - (y * i));
	} else if (i <= 3.7e+33) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	t_2 = i * ((a * b) - (y * j))
	tmp = 0
	if i <= -2.5e-51:
		tmp = t_2
	elif i <= 3.7e-87:
		tmp = t_1
	elif i <= 1000000000.0:
		tmp = j * ((t * c) - (y * i))
	elif i <= 3.7e+33:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	t_2 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -2.5e-51)
		tmp = t_2;
	elseif (i <= 3.7e-87)
		tmp = t_1;
	elseif (i <= 1000000000.0)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (i <= 3.7e+33)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((t * j) - (z * b));
	t_2 = i * ((a * b) - (y * j));
	tmp = 0.0;
	if (i <= -2.5e-51)
		tmp = t_2;
	elseif (i <= 3.7e-87)
		tmp = t_1;
	elseif (i <= 1000000000.0)
		tmp = j * ((t * c) - (y * i));
	elseif (i <= 3.7e+33)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.5e-51], t$95$2, If[LessEqual[i, 3.7e-87], t$95$1, If[LessEqual[i, 1000000000.0], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.7e+33], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -2.50000000000000002e-51 or 3.6999999999999999e33 < i

   1. Initial program 62.8%

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

   3. Taylor expanded in x around 0 64.2%

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

      1. *-commutative 64.2%

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

   5. Simplified 64.2%

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

   6. Taylor expanded in c around 0 52.1%

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

      1. associate-*r* 52.1%

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

      2. neg-mul-1 52.1%

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

      3. cancel-sign-sub 52.1%

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

      4. *-commutative 52.1%

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

      5. associate-*r* 52.1%

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

      6. associate-*r* 56.9%

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

      7. *-commutative 56.9%

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

      8. distribute-rgt-in 61.2%

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

      9. cancel-sign-sub 61.2%

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

      10. distribute-lft-neg-in 61.2%

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

      11. *-commutative 61.2%

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

      12. mul-1-neg 61.2%

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

      13. mul-1-neg 61.2%

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

      14. *-commutative 61.2%

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

      15. mul-1-neg 61.2%

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

      16. neg-sub0 61.2%

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

      17. associate--r+ 61.2%

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

      18. +-commutative 61.2%

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

      19. associate--r+ 61.2%

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

   8. Simplified 61.2%

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

   if -2.50000000000000002e-51 < i < 3.7000000000000002e-87 or 1e9 < i < 3.6999999999999999e33

   1. Initial program 80.1%

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

   3. Taylor expanded in c around inf 54.0%

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

   if 3.7000000000000002e-87 < i < 1e9

   1. Initial program 85.5%

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

   3. Taylor expanded in j around inf 51.4%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.5 \cdot 10^{-51}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq 3.7 \cdot 10^{-87}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 1000000000:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;i \leq 3.7 \cdot 10^{+33}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 67.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;x \leq -2.5 \cdot 10^{-173} \lor \neg \left(x \leq 1.5 \cdot 10^{+26}\right):\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_1 + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))))
   (if (or (<= x -2.5e-173) (not (<= x 1.5e+26)))
     (+ (* x (- (* y z) (* t a))) t_1)
     (+ t_1 (* b (- (* a i) (* z c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double tmp;
	if ((x <= -2.5e-173) || !(x <= 1.5e+26)) {
		tmp = (x * ((y * z) - (t * a))) + t_1;
	} else {
		tmp = t_1 + (b * ((a * i) - (z * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    if ((x <= (-2.5d-173)) .or. (.not. (x <= 1.5d+26))) then
        tmp = (x * ((y * z) - (t * a))) + t_1
    else
        tmp = t_1 + (b * ((a * i) - (z * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double tmp;
	if ((x <= -2.5e-173) || !(x <= 1.5e+26)) {
		tmp = (x * ((y * z) - (t * a))) + t_1;
	} else {
		tmp = t_1 + (b * ((a * i) - (z * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	tmp = 0
	if (x <= -2.5e-173) or not (x <= 1.5e+26):
		tmp = (x * ((y * z) - (t * a))) + t_1
	else:
		tmp = t_1 + (b * ((a * i) - (z * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if ((x <= -2.5e-173) || !(x <= 1.5e+26))
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_1);
	else
		tmp = Float64(t_1 + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if ((x <= -2.5e-173) || ~((x <= 1.5e+26)))
		tmp = (x * ((y * z) - (t * a))) + t_1;
	else
		tmp = t_1 + (b * ((a * i) - (z * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -2.5e-173], N[Not[LessEqual[x, 1.5e+26]], $MachinePrecision]], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(t$95$1 + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.5000000000000001e-173 or 1.49999999999999999e26 < x

   1. Initial program 71.8%

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

   3. Taylor expanded in b around 0 66.0%

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

   if -2.5000000000000001e-173 < x < 1.49999999999999999e26

   1. Initial program 69.7%

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

   3. Taylor expanded in x around 0 78.6%

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

      1. *-commutative 78.6%

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

   5. Simplified 78.6%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{-173} \lor \neg \left(x \leq 1.5 \cdot 10^{+26}\right):\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 52.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.75 \cdot 10^{-50} \lor \neg \left(i \leq 9.6 \cdot 10^{+33}\right):\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -1.75e-50) (not (<= i 9.6e+33)))
   (* i (- (* a b) (* y j)))
   (* c (- (* t j) (* z b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -1.75e-50) || !(i <= 9.6e+33)) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = c * ((t * j) - (z * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((i <= (-1.75d-50)) .or. (.not. (i <= 9.6d+33))) then
        tmp = i * ((a * b) - (y * j))
    else
        tmp = c * ((t * j) - (z * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -1.75e-50) || !(i <= 9.6e+33)) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = c * ((t * j) - (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (i <= -1.75e-50) or not (i <= 9.6e+33):
		tmp = i * ((a * b) - (y * j))
	else:
		tmp = c * ((t * j) - (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((i <= -1.75e-50) || !(i <= 9.6e+33))
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	else
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((i <= -1.75e-50) || ~((i <= 9.6e+33)))
		tmp = i * ((a * b) - (y * j));
	else
		tmp = c * ((t * j) - (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[i, -1.75e-50], N[Not[LessEqual[i, 9.6e+33]], $MachinePrecision]], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -1.74999999999999998e-50 or 9.5999999999999999e33 < i

   1. Initial program 62.8%

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

   3. Taylor expanded in x around 0 64.2%

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

      1. *-commutative 64.2%

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

   5. Simplified 64.2%

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

   6. Taylor expanded in c around 0 52.1%

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

      1. associate-*r* 52.1%

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

      2. neg-mul-1 52.1%

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

      3. cancel-sign-sub 52.1%

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

      4. *-commutative 52.1%

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

      5. associate-*r* 52.1%

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

      6. associate-*r* 56.9%

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

      7. *-commutative 56.9%

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

      8. distribute-rgt-in 61.2%

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

      9. cancel-sign-sub 61.2%

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

      10. distribute-lft-neg-in 61.2%

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

      11. *-commutative 61.2%

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

      12. mul-1-neg 61.2%

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

      13. mul-1-neg 61.2%

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

      14. *-commutative 61.2%

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

      15. mul-1-neg 61.2%

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

      16. neg-sub0 61.2%

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

      17. associate--r+ 61.2%

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

      18. +-commutative 61.2%

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

      19. associate--r+ 61.2%

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

   8. Simplified 61.2%

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

   if -1.74999999999999998e-50 < i < 9.5999999999999999e33

   1. Initial program 80.7%

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

   3. Taylor expanded in c around inf 49.5%

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

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.75 \cdot 10^{-50} \lor \neg \left(i \leq 9.6 \cdot 10^{+33}\right):\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 43.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -4.8 \cdot 10^{-49}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq 4.4 \cdot 10^{+195}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -4.8e-49)
   (* b (- (* a i) (* z c)))
   (if (<= i 4.4e+195) (* c (- (* t j) (* z b))) (* j (* y (- i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -4.8e-49) {
		tmp = b * ((a * i) - (z * c));
	} else if (i <= 4.4e+195) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = j * (y * -i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (i <= (-4.8d-49)) then
        tmp = b * ((a * i) - (z * c))
    else if (i <= 4.4d+195) then
        tmp = c * ((t * j) - (z * b))
    else
        tmp = j * (y * -i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -4.8e-49) {
		tmp = b * ((a * i) - (z * c));
	} else if (i <= 4.4e+195) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = j * (y * -i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -4.8e-49:
		tmp = b * ((a * i) - (z * c))
	elif i <= 4.4e+195:
		tmp = c * ((t * j) - (z * b))
	else:
		tmp = j * (y * -i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -4.8e-49)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (i <= 4.4e+195)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	else
		tmp = Float64(j * Float64(y * Float64(-i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -4.8e-49)
		tmp = b * ((a * i) - (z * c));
	elseif (i <= 4.4e+195)
		tmp = c * ((t * j) - (z * b));
	else
		tmp = j * (y * -i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -4.8e-49], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4.4e+195], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(y * (-i)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if i < -4.79999999999999985e-49

   1. Initial program 64.7%

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

   3. Taylor expanded in b around inf 55.5%

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

      1. *-commutative 55.5%

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

   5. Simplified 55.5%

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

   if -4.79999999999999985e-49 < i < 4.4e195

   1. Initial program 78.6%

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

   3. Taylor expanded in c around inf 48.3%

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

   if 4.4e195 < i

   1. Initial program 51.9%

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

   3. Taylor expanded in j around inf 56.3%

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

   4. Taylor expanded in c around 0 53.1%

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

      1. neg-mul-1 53.1%

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

      2. distribute-rgt-neg-in 53.1%

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

   6. Simplified 53.1%

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

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4.8 \cdot 10^{-49}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq 4.4 \cdot 10^{+195}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 30.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{+85} \lor \neg \left(a \leq 2.22 \cdot 10^{+86}\right):\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -8.2e+85) (not (<= a 2.22e+86))) (* b (* a i)) (* c (* t 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 ((a <= -8.2e+85) || !(a <= 2.22e+86)) {
		tmp = b * (a * i);
	} else {
		tmp = c * (t * 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 ((a <= (-8.2d+85)) .or. (.not. (a <= 2.22d+86))) then
        tmp = b * (a * i)
    else
        tmp = c * (t * 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 ((a <= -8.2e+85) || !(a <= 2.22e+86)) {
		tmp = b * (a * i);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (a <= -8.2e+85) or not (a <= 2.22e+86):
		tmp = b * (a * i)
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -8.2e+85) || !(a <= 2.22e+86))
		tmp = Float64(b * Float64(a * i));
	else
		tmp = Float64(c * Float64(t * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((a <= -8.2e+85) || ~((a <= 2.22e+86)))
		tmp = b * (a * i);
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -8.2e+85], N[Not[LessEqual[a, 2.22e+86]], $MachinePrecision]], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -8.19999999999999957e85 or 2.22000000000000012e86 < a

   1. Initial program 59.3%

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

   3. Taylor expanded in x around 0 50.4%

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

      1. *-commutative 50.4%

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

   5. Simplified 50.4%

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

   6. Taylor expanded in c around 0 45.6%

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

      1. associate-*r* 45.6%

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

      2. neg-mul-1 45.6%

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

      3. cancel-sign-sub 45.6%

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

      4. *-commutative 45.6%

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

      5. associate-*r* 45.6%

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

      6. associate-*r* 50.0%

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

      7. *-commutative 50.0%

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

      8. distribute-rgt-in 53.8%

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

      9. cancel-sign-sub 53.8%

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

      10. distribute-lft-neg-in 53.8%

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

      11. *-commutative 53.8%

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

      12. mul-1-neg 53.8%

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

      13. mul-1-neg 53.8%

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

      14. *-commutative 53.8%

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

      15. mul-1-neg 53.8%

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

      16. neg-sub0 53.8%

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

      17. associate--r+ 53.8%

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

      18. +-commutative 53.8%

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

      19. associate--r+ 53.8%

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

   8. Simplified 53.8%

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

   9. Taylor expanded in b around inf 40.1%

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

       1. associate-*r* 44.5%

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

       2. *-commutative 44.5%

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

       3. associate-*l* 43.2%

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

   11. Simplified 43.2%

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

   if -8.19999999999999957e85 < a < 2.22000000000000012e86

   1. Initial program 79.1%

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

   3. Taylor expanded in x around 0 65.8%

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

      1. *-commutative 65.8%

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

   5. Simplified 65.8%

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

   6. Taylor expanded in t around inf 31.9%

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

4. Final simplification 36.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{+85} \lor \neg \left(a \leq 2.22 \cdot 10^{+86}\right):\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 30.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.6 \cdot 10^{+85}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+85}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -9.6e+85)
   (* b (* a i))
   (if (<= a 5.2e+85) (* c (* t j)) (* i (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -9.6e+85) {
		tmp = b * (a * i);
	} else if (a <= 5.2e+85) {
		tmp = c * (t * j);
	} else {
		tmp = i * (a * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (a <= (-9.6d+85)) then
        tmp = b * (a * i)
    else if (a <= 5.2d+85) then
        tmp = c * (t * j)
    else
        tmp = i * (a * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -9.6e+85) {
		tmp = b * (a * i);
	} else if (a <= 5.2e+85) {
		tmp = c * (t * j);
	} else {
		tmp = i * (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -9.6e+85:
		tmp = b * (a * i)
	elif a <= 5.2e+85:
		tmp = c * (t * j)
	else:
		tmp = i * (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -9.6e+85)
		tmp = Float64(b * Float64(a * i));
	elseif (a <= 5.2e+85)
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(i * Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -9.6e+85)
		tmp = b * (a * i);
	elseif (a <= 5.2e+85)
		tmp = c * (t * j);
	else
		tmp = i * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -9.6e+85], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.2e+85], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.59999999999999986e85

   1. Initial program 59.8%

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

   3. Taylor expanded in x around 0 56.5%

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

      1. *-commutative 56.5%

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

   5. Simplified 56.5%

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

   6. Taylor expanded in c around 0 50.5%

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

      1. associate-*r* 50.5%

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

      2. neg-mul-1 50.5%

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

      3. cancel-sign-sub 50.5%

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

      4. *-commutative 50.5%

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

      5. associate-*r* 50.5%

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

      6. associate-*r* 55.7%

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

      7. *-commutative 55.7%

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

      8. distribute-rgt-in 55.7%

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

      9. cancel-sign-sub 55.7%

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

      10. distribute-lft-neg-in 55.7%

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

      11. *-commutative 55.7%

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

      12. mul-1-neg 55.7%

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

      13. mul-1-neg 55.7%

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

      14. *-commutative 55.7%

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

      15. mul-1-neg 55.7%

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

      16. neg-sub0 55.7%

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

      17. associate--r+ 55.7%

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

      18. +-commutative 55.7%

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

      19. associate--r+ 55.7%

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

   8. Simplified 55.7%

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

   9. Taylor expanded in b around inf 41.7%

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

       1. associate-*r* 46.9%

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

       2. *-commutative 46.9%

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

       3. associate-*l* 47.7%

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

   11. Simplified 47.7%

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

   if -9.59999999999999986e85 < a < 5.20000000000000021e85

   1. Initial program 79.1%

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

   3. Taylor expanded in x around 0 65.8%

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

      1. *-commutative 65.8%

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

   5. Simplified 65.8%

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

   6. Taylor expanded in t around inf 31.9%

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

   if 5.20000000000000021e85 < a

   1. Initial program 58.8%

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

   3. Taylor expanded in x around 0 44.0%

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

      1. *-commutative 44.0%

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

   5. Simplified 44.0%

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

   6. Taylor expanded in c around 0 40.4%

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

      1. associate-*r* 40.4%

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

      2. neg-mul-1 40.4%

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

      3. cancel-sign-sub 40.4%

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

      4. *-commutative 40.4%

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

      5. associate-*r* 40.4%

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

      6. associate-*r* 44.0%

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

      7. *-commutative 44.0%

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

      8. distribute-rgt-in 51.8%

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

      9. cancel-sign-sub 51.8%

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

      10. distribute-lft-neg-in 51.8%

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

      11. *-commutative 51.8%

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

      12. mul-1-neg 51.8%

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

      13. mul-1-neg 51.8%

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

      14. *-commutative 51.8%

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

      15. mul-1-neg 51.8%

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

      16. neg-sub0 51.8%

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

      17. associate--r+ 51.8%

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

      18. +-commutative 51.8%

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

      19. associate--r+ 51.8%

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

   8. Simplified 51.8%

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

   9. Taylor expanded in b around inf 42.1%

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

       1. *-commutative 42.1%

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

   11. Simplified 42.1%

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

4. Final simplification 37.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.6 \cdot 10^{+85}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+85}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 22.7% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq 4.4 \cdot 10^{-77}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j 4.4e-77) (* b (* a i)) (* a (* b i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= 4.4e-77) {
		tmp = b * (a * i);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (j <= 4.4d-77) then
        tmp = b * (a * i)
    else
        tmp = a * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= 4.4e-77) {
		tmp = b * (a * i);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= 4.4e-77:
		tmp = b * (a * i)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= 4.4e-77)
		tmp = Float64(b * Float64(a * i));
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= 4.4e-77)
		tmp = b * (a * i);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, 4.4e-77], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < 4.40000000000000014e-77

   1. Initial program 71.3%

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

   3. Taylor expanded in x around 0 54.3%

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

      1. *-commutative 54.3%

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

   5. Simplified 54.3%

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

   6. Taylor expanded in c around 0 32.6%

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

      1. associate-*r* 32.6%

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

      2. neg-mul-1 32.6%

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

      3. cancel-sign-sub 32.6%

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

      4. *-commutative 32.6%

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

      5. associate-*r* 32.6%

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

      6. associate-*r* 38.1%

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

      7. *-commutative 38.1%

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

      8. distribute-rgt-in 40.3%

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

      9. cancel-sign-sub 40.3%

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

      10. distribute-lft-neg-in 40.3%

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

      11. *-commutative 40.3%

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

      12. mul-1-neg 40.3%

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

      13. mul-1-neg 40.3%

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

      14. *-commutative 40.3%

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

      15. mul-1-neg 40.3%

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

      16. neg-sub0 40.3%

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

      17. associate--r+ 40.3%

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

      18. +-commutative 40.3%

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

      19. associate--r+ 40.3%

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

   8. Simplified 40.3%

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

   9. Taylor expanded in b around inf 21.4%

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

       1. associate-*r* 25.8%

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

       2. *-commutative 25.8%

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

       3. associate-*l* 25.9%

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

   11. Simplified 25.9%

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

   if 4.40000000000000014e-77 < j

   1. Initial program 70.2%

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

   3. Taylor expanded in x around 0 73.1%

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

      1. *-commutative 73.1%

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

   5. Simplified 73.1%

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

   6. Taylor expanded in a around inf 29.3%

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

4. Final simplification 26.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq 4.4 \cdot 10^{-77}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 22.8% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(b \cdot i\right) \end{array} \]

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 71.0%

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

3. Taylor expanded in x around 0 59.5%

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

   1. *-commutative 59.5%

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

5. Simplified 59.5%

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

6. Taylor expanded in a around inf 23.5%

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

7. Final simplification 23.5%

   \[\leadsto a \cdot \left(b \cdot i\right) \]
8. Add Preprocessing

Developer target: 68.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ t_2 := x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{if}\;t < -8.120978919195912 \cdot 10^{-33}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < -4.712553818218485 \cdot 10^{-169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t < -7.633533346031584 \cdot 10^{-308}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 1.0535888557455487 \cdot 10^{-139}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
          (/
           (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0)))
           (+ (* c t) (* i y)))))
        (t_2
         (-
          (* x (- (* z y) (* a t)))
          (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))
   (if (< t -8.120978919195912e-33)
     t_2
     (if (< t -4.712553818218485e-169)
       t_1
       (if (< t -7.633533346031584e-308)
         t_2
         (if (< t 1.0535888557455487e-139) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (pow((c * t), 2.0) - pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ** 2.0d0) - ((i * y) ** 2.0d0))) / ((c * t) + (i * y)))
    t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
    if (t < (-8.120978919195912d-33)) then
        tmp = t_2
    else if (t < (-4.712553818218485d-169)) then
        tmp = t_1
    else if (t < (-7.633533346031584d-308)) then
        tmp = t_2
    else if (t < 1.0535888557455487d-139) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (Math.pow((c * t), 2.0) - Math.pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (math.pow((c * t), 2.0) - math.pow((i * y), 2.0))) / ((c * t) + (i * y)))
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
	tmp = 0
	if t < -8.120978919195912e-33:
		tmp = t_2
	elif t < -4.712553818218485e-169:
		tmp = t_1
	elif t < -7.633533346031584e-308:
		tmp = t_2
	elif t < 1.0535888557455487e-139:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(Float64(j * Float64((Float64(c * t) ^ 2.0) - (Float64(i * y) ^ 2.0))) / Float64(Float64(c * t) + Float64(i * y))))
	t_2 = Float64(Float64(x * Float64(Float64(z * y) - Float64(a * t))) - Float64(Float64(b * Float64(Float64(z * c) - Float64(a * i))) - Float64(Float64(Float64(c * t) - Float64(y * i)) * j)))
	tmp = 0.0
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ^ 2.0) - ((i * y) ^ 2.0))) / ((c * t) + (i * y)));
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	tmp = 0.0;
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[Power[N[(c * t), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(i * y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * t), $MachinePrecision] + N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(c * t), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -8.120978919195912e-33], t$95$2, If[Less[t, -4.712553818218485e-169], t$95$1, If[Less[t, -7.633533346031584e-308], t$95$2, If[Less[t, 1.0535888557455487e-139], t$95$1, t$95$2]]]]]]

Reproduce

herbie shell --seed 2024036 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< t -8.120978919195912e-33) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -4.712553818218485e-169) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (if (< t -7.633533346031584e-308) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 1.0535888557455487e-139) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))