Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 74.2% → 82.3%

Time: 33.8s

Alternatives: 25

Speedup: 0.5×

• 58.0% 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: 74.2% accurate, 1.0× speedup

Math

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

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: 82.3% accurate, 0.1× speedup

Math

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

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))) (t_2 (- (* t c) (* y i))))
   (if (<= (+ (* j t_2) (- t_1 (* x (- (* t a) (* y z))))) INFINITY)
     (fma j t_2 (+ (* x (fma y z (* t (- a)))) t_1))
     (* 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 = b * ((a * i) - (z * c));
	double t_2 = (t * c) - (y * i);
	double tmp;
	if (((j * t_2) + (t_1 - (x * ((t * a) - (y * z))))) <= ((double) INFINITY)) {
		tmp = fma(j, t_2, ((x * fma(y, z, (t * -a))) + t_1));
	} else {
		tmp = a * ((b * i) - (x * t));
	}
	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(Float64(t * c) - Float64(y * i))
	tmp = 0.0
	if (Float64(Float64(j * t_2) + Float64(t_1 - Float64(x * Float64(Float64(t * a) - Float64(y * z))))) <= Inf)
		tmp = fma(j, t_2, Float64(Float64(x * fma(y, z, Float64(t * Float64(-a)))) + t_1));
	else
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	end
	return 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[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(j * t$95$2), $MachinePrecision] + N[(t$95$1 - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(j * t$95$2 + N[(N[(x * N[(y * z + N[(t * (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 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. Step-by-step derivation

      1. +-commutative 91.8%

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

      2. fma-def 91.8%

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

      3. *-commutative 91.8%

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

      4. *-commutative 91.8%

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

      5. cancel-sign-sub-inv 91.8%

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

      6. cancel-sign-sub 91.8%

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

      7. fma-neg 91.8%

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

      8. distribute-rgt-neg-out 91.8%

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

      9. remove-double-neg 91.8%

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

      10. *-commutative 91.8%

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

      11. *-commutative 91.8%

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

   3. Simplified 91.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. 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 a around -inf 59.7%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.3%

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

Alternative 2: 82.3% accurate, 0.5× speedup

Math

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

FPCore

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

Java

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

Python

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

Julia

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 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 a around -inf 59.7%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.3%

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

Alternative 3: 55.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(z \cdot c\right)\\ t_3 := t\_1 - t\_2\\ t_4 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -8.1 \cdot 10^{+65}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;a \leq -1.08 \cdot 10^{-47}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-133}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-188}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - t\_2\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-230}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-264}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-211}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq 7.4 \cdot 10^{+74}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+105}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i))))
        (t_2 (* b (* z c)))
        (t_3 (- t_1 t_2))
        (t_4 (* a (- (* b i) (* x t)))))
   (if (<= a -8.1e+65)
     t_4
     (if (<= a -1.08e-47)
       (+ (* x (* y z)) (* i (* a b)))
       (if (<= a -1e-133)
         t_3
         (if (<= a -1.05e-188)
           (- (* x (- (* y z) (* t a))) t_2)
           (if (<= a -1.2e-230)
             t_1
             (if (<= a 1.45e-264)
               (* z (- (* x y) (* b c)))
               (if (<= a 8e-211)
                 t_3
                 (if (<= a 7.4e+74)
                   (- (* b (- (* a i) (* z c))) (* i (* y j)))
                   (if (<= a 1.6e+105) (* c (- (* t j) (* z b))) t_4)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * (z * c);
	double t_3 = t_1 - t_2;
	double t_4 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -8.1e+65) {
		tmp = t_4;
	} else if (a <= -1.08e-47) {
		tmp = (x * (y * z)) + (i * (a * b));
	} else if (a <= -1e-133) {
		tmp = t_3;
	} else if (a <= -1.05e-188) {
		tmp = (x * ((y * z) - (t * a))) - t_2;
	} else if (a <= -1.2e-230) {
		tmp = t_1;
	} else if (a <= 1.45e-264) {
		tmp = z * ((x * y) - (b * c));
	} else if (a <= 8e-211) {
		tmp = t_3;
	} else if (a <= 7.4e+74) {
		tmp = (b * ((a * i) - (z * c))) - (i * (y * j));
	} else if (a <= 1.6e+105) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = b * (z * c)
    t_3 = t_1 - t_2
    t_4 = a * ((b * i) - (x * t))
    if (a <= (-8.1d+65)) then
        tmp = t_4
    else if (a <= (-1.08d-47)) then
        tmp = (x * (y * z)) + (i * (a * b))
    else if (a <= (-1d-133)) then
        tmp = t_3
    else if (a <= (-1.05d-188)) then
        tmp = (x * ((y * z) - (t * a))) - t_2
    else if (a <= (-1.2d-230)) then
        tmp = t_1
    else if (a <= 1.45d-264) then
        tmp = z * ((x * y) - (b * c))
    else if (a <= 8d-211) then
        tmp = t_3
    else if (a <= 7.4d+74) then
        tmp = (b * ((a * i) - (z * c))) - (i * (y * j))
    else if (a <= 1.6d+105) then
        tmp = c * ((t * j) - (z * b))
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * (z * c);
	double t_3 = t_1 - t_2;
	double t_4 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -8.1e+65) {
		tmp = t_4;
	} else if (a <= -1.08e-47) {
		tmp = (x * (y * z)) + (i * (a * b));
	} else if (a <= -1e-133) {
		tmp = t_3;
	} else if (a <= -1.05e-188) {
		tmp = (x * ((y * z) - (t * a))) - t_2;
	} else if (a <= -1.2e-230) {
		tmp = t_1;
	} else if (a <= 1.45e-264) {
		tmp = z * ((x * y) - (b * c));
	} else if (a <= 8e-211) {
		tmp = t_3;
	} else if (a <= 7.4e+74) {
		tmp = (b * ((a * i) - (z * c))) - (i * (y * j));
	} else if (a <= 1.6e+105) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = b * (z * c)
	t_3 = t_1 - t_2
	t_4 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -8.1e+65:
		tmp = t_4
	elif a <= -1.08e-47:
		tmp = (x * (y * z)) + (i * (a * b))
	elif a <= -1e-133:
		tmp = t_3
	elif a <= -1.05e-188:
		tmp = (x * ((y * z) - (t * a))) - t_2
	elif a <= -1.2e-230:
		tmp = t_1
	elif a <= 1.45e-264:
		tmp = z * ((x * y) - (b * c))
	elif a <= 8e-211:
		tmp = t_3
	elif a <= 7.4e+74:
		tmp = (b * ((a * i) - (z * c))) - (i * (y * j))
	elif a <= 1.6e+105:
		tmp = c * ((t * j) - (z * b))
	else:
		tmp = t_4
	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)))
	t_2 = Float64(b * Float64(z * c))
	t_3 = Float64(t_1 - t_2)
	t_4 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -8.1e+65)
		tmp = t_4;
	elseif (a <= -1.08e-47)
		tmp = Float64(Float64(x * Float64(y * z)) + Float64(i * Float64(a * b)));
	elseif (a <= -1e-133)
		tmp = t_3;
	elseif (a <= -1.05e-188)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - t_2);
	elseif (a <= -1.2e-230)
		tmp = t_1;
	elseif (a <= 1.45e-264)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (a <= 8e-211)
		tmp = t_3;
	elseif (a <= 7.4e+74)
		tmp = Float64(Float64(b * Float64(Float64(a * i) - Float64(z * c))) - Float64(i * Float64(y * j)));
	elseif (a <= 1.6e+105)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	else
		tmp = t_4;
	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));
	t_2 = b * (z * c);
	t_3 = t_1 - t_2;
	t_4 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -8.1e+65)
		tmp = t_4;
	elseif (a <= -1.08e-47)
		tmp = (x * (y * z)) + (i * (a * b));
	elseif (a <= -1e-133)
		tmp = t_3;
	elseif (a <= -1.05e-188)
		tmp = (x * ((y * z) - (t * a))) - t_2;
	elseif (a <= -1.2e-230)
		tmp = t_1;
	elseif (a <= 1.45e-264)
		tmp = z * ((x * y) - (b * c));
	elseif (a <= 8e-211)
		tmp = t_3;
	elseif (a <= 7.4e+74)
		tmp = (b * ((a * i) - (z * c))) - (i * (y * j));
	elseif (a <= 1.6e+105)
		tmp = c * ((t * j) - (z * b));
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 - t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.1e+65], t$95$4, If[LessEqual[a, -1.08e-47], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1e-133], t$95$3, If[LessEqual[a, -1.05e-188], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[a, -1.2e-230], t$95$1, If[LessEqual[a, 1.45e-264], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8e-211], t$95$3, If[LessEqual[a, 7.4e+74], N[(N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.6e+105], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if a < -8.1000000000000001e65 or 1.6e105 < a

   1. Initial program 56.8%

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

   3. Taylor expanded in a around -inf 74.8%

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

   if -8.1000000000000001e65 < a < -1.08000000000000005e-47

   1. Initial program 70.9%

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

   3. Taylor expanded in j around 0 67.0%

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

      1. *-commutative 67.0%

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

   5. Simplified 67.0%

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

   6. Taylor expanded in t around 0 59.3%

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

      1. *-commutative 59.3%

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

   8. Simplified 59.3%

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

   9. Taylor expanded in z around 0 67.5%

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

       1. associate-*r* 67.6%

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

       2. *-commutative 67.6%

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

       3. neg-mul-1 67.6%

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

       4. distribute-lft-neg-in 67.6%

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

       5. *-commutative 67.6%

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

   11. Simplified 67.6%

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

   if -1.08000000000000005e-47 < a < -1.0000000000000001e-133 or 1.4499999999999999e-264 < a < 8.00000000000000069e-211

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 96.9%

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

   4. Taylor expanded in c around inf 90.6%

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

   if -1.0000000000000001e-133 < a < -1.05e-188

   1. Initial program 86.4%

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

   3. Taylor expanded in j around 0 86.4%

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

      1. *-commutative 86.4%

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

   5. Simplified 86.4%

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

   6. Taylor expanded in c around inf 73.6%

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

   if -1.05e-188 < a < -1.2000000000000001e-230

   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 x around 0 81.1%

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

   4. Taylor expanded in j around inf 81.1%

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

   if -1.2000000000000001e-230 < a < 1.4499999999999999e-264

   1. Initial program 73.5%

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

   3. Taylor expanded in z around inf 64.7%

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

   if 8.00000000000000069e-211 < a < 7.4000000000000002e74

   1. Initial program 88.2%

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

   3. Taylor expanded in x around 0 76.3%

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

   4. Taylor expanded in c around 0 65.0%

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

      1. associate-*r* 65.0%

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

      2. neg-mul-1 65.0%

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

      3. *-commutative 65.0%

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

   6. Simplified 65.0%

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

   if 7.4000000000000002e74 < a < 1.6e105

   1. Initial program 71.4%

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

   3. Taylor expanded in c around inf 85.8%

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

      1. *-commutative 85.8%

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

   5. Simplified 85.8%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - b \cdot z\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.1 \cdot 10^{+65}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.08 \cdot 10^{-47}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-133}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-188}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-230}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-264}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-211}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;a \leq 7.4 \cdot 10^{+74}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+105}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 29.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-a\right) \cdot \left(x \cdot t\right)\\ t_2 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{+107}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2150000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-222}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-303}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-254}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+94}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+123}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+131}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+155}:\\ \;\;\;\;z \cdot \left(-b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (- a) (* x t))) (t_2 (* x (* y z))))
   (if (<= z -5.5e+107)
     t_2
     (if (<= z -2150000000.0)
       t_1
       (if (<= z -7e-222)
         (* i (* y (- j)))
         (if (<= z -1.25e-303)
           (* b (* a i))
           (if (<= z 5e-254)
             (* j (* t c))
             (if (<= z 2.4e+94)
               (* a (* b i))
               (if (<= z 2.35e+123)
                 (* c (* t j))
                 (if (<= z 1.1e+131)
                   t_1
                   (if (<= z 1.05e+155) (* z (- (* b c))) t_2)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = -a * (x * t);
	double t_2 = x * (y * z);
	double tmp;
	if (z <= -5.5e+107) {
		tmp = t_2;
	} else if (z <= -2150000000.0) {
		tmp = t_1;
	} else if (z <= -7e-222) {
		tmp = i * (y * -j);
	} else if (z <= -1.25e-303) {
		tmp = b * (a * i);
	} else if (z <= 5e-254) {
		tmp = j * (t * c);
	} else if (z <= 2.4e+94) {
		tmp = a * (b * i);
	} else if (z <= 2.35e+123) {
		tmp = c * (t * j);
	} else if (z <= 1.1e+131) {
		tmp = t_1;
	} else if (z <= 1.05e+155) {
		tmp = z * -(b * c);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = -a * (x * t)
    t_2 = x * (y * z)
    if (z <= (-5.5d+107)) then
        tmp = t_2
    else if (z <= (-2150000000.0d0)) then
        tmp = t_1
    else if (z <= (-7d-222)) then
        tmp = i * (y * -j)
    else if (z <= (-1.25d-303)) then
        tmp = b * (a * i)
    else if (z <= 5d-254) then
        tmp = j * (t * c)
    else if (z <= 2.4d+94) then
        tmp = a * (b * i)
    else if (z <= 2.35d+123) then
        tmp = c * (t * j)
    else if (z <= 1.1d+131) then
        tmp = t_1
    else if (z <= 1.05d+155) then
        tmp = z * -(b * c)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = -a * (x * t);
	double t_2 = x * (y * z);
	double tmp;
	if (z <= -5.5e+107) {
		tmp = t_2;
	} else if (z <= -2150000000.0) {
		tmp = t_1;
	} else if (z <= -7e-222) {
		tmp = i * (y * -j);
	} else if (z <= -1.25e-303) {
		tmp = b * (a * i);
	} else if (z <= 5e-254) {
		tmp = j * (t * c);
	} else if (z <= 2.4e+94) {
		tmp = a * (b * i);
	} else if (z <= 2.35e+123) {
		tmp = c * (t * j);
	} else if (z <= 1.1e+131) {
		tmp = t_1;
	} else if (z <= 1.05e+155) {
		tmp = z * -(b * c);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = -a * (x * t)
	t_2 = x * (y * z)
	tmp = 0
	if z <= -5.5e+107:
		tmp = t_2
	elif z <= -2150000000.0:
		tmp = t_1
	elif z <= -7e-222:
		tmp = i * (y * -j)
	elif z <= -1.25e-303:
		tmp = b * (a * i)
	elif z <= 5e-254:
		tmp = j * (t * c)
	elif z <= 2.4e+94:
		tmp = a * (b * i)
	elif z <= 2.35e+123:
		tmp = c * (t * j)
	elif z <= 1.1e+131:
		tmp = t_1
	elif z <= 1.05e+155:
		tmp = z * -(b * c)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(-a) * Float64(x * t))
	t_2 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (z <= -5.5e+107)
		tmp = t_2;
	elseif (z <= -2150000000.0)
		tmp = t_1;
	elseif (z <= -7e-222)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (z <= -1.25e-303)
		tmp = Float64(b * Float64(a * i));
	elseif (z <= 5e-254)
		tmp = Float64(j * Float64(t * c));
	elseif (z <= 2.4e+94)
		tmp = Float64(a * Float64(b * i));
	elseif (z <= 2.35e+123)
		tmp = Float64(c * Float64(t * j));
	elseif (z <= 1.1e+131)
		tmp = t_1;
	elseif (z <= 1.05e+155)
		tmp = Float64(z * Float64(-Float64(b * c)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = -a * (x * t);
	t_2 = x * (y * z);
	tmp = 0.0;
	if (z <= -5.5e+107)
		tmp = t_2;
	elseif (z <= -2150000000.0)
		tmp = t_1;
	elseif (z <= -7e-222)
		tmp = i * (y * -j);
	elseif (z <= -1.25e-303)
		tmp = b * (a * i);
	elseif (z <= 5e-254)
		tmp = j * (t * c);
	elseif (z <= 2.4e+94)
		tmp = a * (b * i);
	elseif (z <= 2.35e+123)
		tmp = c * (t * j);
	elseif (z <= 1.1e+131)
		tmp = t_1;
	elseif (z <= 1.05e+155)
		tmp = z * -(b * c);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[((-a) * N[(x * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.5e+107], t$95$2, If[LessEqual[z, -2150000000.0], t$95$1, If[LessEqual[z, -7e-222], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.25e-303], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e-254], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4e+94], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.35e+123], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1e+131], t$95$1, If[LessEqual[z, 1.05e+155], N[(z * (-N[(b * c), $MachinePrecision])), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if z < -5.5000000000000003e107 or 1.05e155 < z

   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 z around inf 78.2%

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

   4. Taylor expanded in x around inf 61.1%

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

   if -5.5000000000000003e107 < z < -2.15e9 or 2.3499999999999999e123 < z < 1.0999999999999999e131

   1. Initial program 62.3%

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

   3. Taylor expanded in a around -inf 62.2%

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

   4. Taylor expanded in t around inf 46.9%

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

   if -2.15e9 < z < -7.00000000000000049e-222

   1. Initial program 84.0%

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

   3. Taylor expanded in x around 0 64.5%

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

   4. Taylor expanded in y around inf 29.9%

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

      1. mul-1-neg 29.9%

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

      2. *-commutative 29.9%

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

      3. distribute-rgt-neg-in 29.9%

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

   6. Simplified 29.9%

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

   if -7.00000000000000049e-222 < z < -1.25e-303

   1. Initial program 90.7%

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

   3. Taylor expanded in x around 0 67.6%

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

   4. Taylor expanded in a around inf 35.5%

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

      1. *-commutative 35.5%

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

      2. associate-*l* 39.9%

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

      3. *-commutative 39.9%

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

   6. Simplified 39.9%

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

   if -1.25e-303 < z < 5.0000000000000003e-254

   1. Initial program 86.6%

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

   3. Taylor expanded in x around 0 93.2%

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

   4. Taylor expanded in j around inf 80.4%

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

   5. Taylor expanded in c around inf 55.5%

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

      1. *-commutative 55.5%

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

   7. Simplified 55.5%

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

   if 5.0000000000000003e-254 < z < 2.39999999999999983e94

   1. Initial program 72.9%

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

   3. Taylor expanded in x around 0 64.8%

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

   4. Taylor expanded in a around inf 47.3%

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

   if 2.39999999999999983e94 < z < 2.3499999999999999e123

   1. Initial program 75.9%

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

   3. Taylor expanded in x around 0 75.8%

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

   4. Taylor expanded in t around inf 63.3%

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

   if 1.0999999999999999e131 < z < 1.05e155

   1. Initial program 61.0%

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

   3. Taylor expanded in z around inf 86.1%

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

   4. Taylor expanded in x around 0 86.1%

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

      1. neg-mul-1 86.1%

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

      2. distribute-rgt-neg-in 86.1%

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

   6. Simplified 86.1%

      \[\leadsto z \cdot \color{blue}{\left(b \cdot \left(-c\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+107}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -2150000000:\\ \;\;\;\;\left(-a\right) \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-222}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-303}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-254}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+94}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+123}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+131}:\\ \;\;\;\;\left(-a\right) \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+155}:\\ \;\;\;\;z \cdot \left(-b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 56.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := t\_1 - b \cdot \left(z \cdot c\right)\\ t_3 := x \cdot \left(y \cdot z\right)\\ t_4 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -3.5 \cdot 10^{+64}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;a \leq -9.8 \cdot 10^{-48}:\\ \;\;\;\;t\_3 + i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq -1.22 \cdot 10^{-133}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -4.3 \cdot 10^{-191}:\\ \;\;\;\;t\_3 + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq -2.55 \cdot 10^{-228}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-265}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+104}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i))))
        (t_2 (- t_1 (* b (* z c))))
        (t_3 (* x (* y z)))
        (t_4 (* a (- (* b i) (* x t)))))
   (if (<= a -3.5e+64)
     t_4
     (if (<= a -9.8e-48)
       (+ t_3 (* i (* a b)))
       (if (<= a -1.22e-133)
         t_2
         (if (<= a -4.3e-191)
           (+ t_3 (* b (- (* a i) (* z c))))
           (if (<= a -2.55e-228)
             t_1
             (if (<= a 9.2e-265)
               (* z (- (* x y) (* b c)))
               (if (<= a 7.2e+104) t_2 t_4)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = t_1 - (b * (z * c));
	double t_3 = x * (y * z);
	double t_4 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -3.5e+64) {
		tmp = t_4;
	} else if (a <= -9.8e-48) {
		tmp = t_3 + (i * (a * b));
	} else if (a <= -1.22e-133) {
		tmp = t_2;
	} else if (a <= -4.3e-191) {
		tmp = t_3 + (b * ((a * i) - (z * c)));
	} else if (a <= -2.55e-228) {
		tmp = t_1;
	} else if (a <= 9.2e-265) {
		tmp = z * ((x * y) - (b * c));
	} else if (a <= 7.2e+104) {
		tmp = t_2;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = t_1 - (b * (z * c))
    t_3 = x * (y * z)
    t_4 = a * ((b * i) - (x * t))
    if (a <= (-3.5d+64)) then
        tmp = t_4
    else if (a <= (-9.8d-48)) then
        tmp = t_3 + (i * (a * b))
    else if (a <= (-1.22d-133)) then
        tmp = t_2
    else if (a <= (-4.3d-191)) then
        tmp = t_3 + (b * ((a * i) - (z * c)))
    else if (a <= (-2.55d-228)) then
        tmp = t_1
    else if (a <= 9.2d-265) then
        tmp = z * ((x * y) - (b * c))
    else if (a <= 7.2d+104) then
        tmp = t_2
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = t_1 - (b * (z * c));
	double t_3 = x * (y * z);
	double t_4 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -3.5e+64) {
		tmp = t_4;
	} else if (a <= -9.8e-48) {
		tmp = t_3 + (i * (a * b));
	} else if (a <= -1.22e-133) {
		tmp = t_2;
	} else if (a <= -4.3e-191) {
		tmp = t_3 + (b * ((a * i) - (z * c)));
	} else if (a <= -2.55e-228) {
		tmp = t_1;
	} else if (a <= 9.2e-265) {
		tmp = z * ((x * y) - (b * c));
	} else if (a <= 7.2e+104) {
		tmp = t_2;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = t_1 - (b * (z * c))
	t_3 = x * (y * z)
	t_4 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -3.5e+64:
		tmp = t_4
	elif a <= -9.8e-48:
		tmp = t_3 + (i * (a * b))
	elif a <= -1.22e-133:
		tmp = t_2
	elif a <= -4.3e-191:
		tmp = t_3 + (b * ((a * i) - (z * c)))
	elif a <= -2.55e-228:
		tmp = t_1
	elif a <= 9.2e-265:
		tmp = z * ((x * y) - (b * c))
	elif a <= 7.2e+104:
		tmp = t_2
	else:
		tmp = t_4
	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)))
	t_2 = Float64(t_1 - Float64(b * Float64(z * c)))
	t_3 = Float64(x * Float64(y * z))
	t_4 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -3.5e+64)
		tmp = t_4;
	elseif (a <= -9.8e-48)
		tmp = Float64(t_3 + Float64(i * Float64(a * b)));
	elseif (a <= -1.22e-133)
		tmp = t_2;
	elseif (a <= -4.3e-191)
		tmp = Float64(t_3 + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (a <= -2.55e-228)
		tmp = t_1;
	elseif (a <= 9.2e-265)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (a <= 7.2e+104)
		tmp = t_2;
	else
		tmp = t_4;
	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));
	t_2 = t_1 - (b * (z * c));
	t_3 = x * (y * z);
	t_4 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -3.5e+64)
		tmp = t_4;
	elseif (a <= -9.8e-48)
		tmp = t_3 + (i * (a * b));
	elseif (a <= -1.22e-133)
		tmp = t_2;
	elseif (a <= -4.3e-191)
		tmp = t_3 + (b * ((a * i) - (z * c)));
	elseif (a <= -2.55e-228)
		tmp = t_1;
	elseif (a <= 9.2e-265)
		tmp = z * ((x * y) - (b * c));
	elseif (a <= 7.2e+104)
		tmp = t_2;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.5e+64], t$95$4, If[LessEqual[a, -9.8e-48], N[(t$95$3 + N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.22e-133], t$95$2, If[LessEqual[a, -4.3e-191], N[(t$95$3 + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.55e-228], t$95$1, If[LessEqual[a, 9.2e-265], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.2e+104], t$95$2, t$95$4]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -3.4999999999999999e64 or 7.20000000000000001e104 < a

   1. Initial program 56.2%

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

   3. Taylor expanded in a around -inf 73.9%

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

   if -3.4999999999999999e64 < a < -9.8000000000000005e-48

   1. Initial program 70.9%

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

   3. Taylor expanded in j around 0 67.0%

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

      1. *-commutative 67.0%

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

   5. Simplified 67.0%

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

   6. Taylor expanded in t around 0 59.3%

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

      1. *-commutative 59.3%

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

   8. Simplified 59.3%

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

   9. Taylor expanded in z around 0 67.5%

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

       1. associate-*r* 67.6%

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

       2. *-commutative 67.6%

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

       3. neg-mul-1 67.6%

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

       4. distribute-lft-neg-in 67.6%

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

       5. *-commutative 67.6%

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

   11. Simplified 67.6%

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

   if -9.8000000000000005e-48 < a < -1.2199999999999999e-133 or 9.1999999999999996e-265 < a < 7.20000000000000001e104

   1. Initial program 91.5%

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

   3. Taylor expanded in x around 0 83.1%

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

   4. Taylor expanded in c around inf 69.1%

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

   if -1.2199999999999999e-133 < a < -4.29999999999999983e-191

   1. Initial program 86.4%

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

   3. Taylor expanded in j around 0 86.4%

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

      1. *-commutative 86.4%

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

   5. Simplified 86.4%

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

   6. Taylor expanded in t around 0 61.3%

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

      1. *-commutative 61.3%

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

   8. Simplified 61.3%

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

   if -4.29999999999999983e-191 < a < -2.5500000000000001e-228

   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 x around 0 81.1%

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

   4. Taylor expanded in j around inf 81.1%

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

   if -2.5500000000000001e-228 < a < 9.1999999999999996e-265

   1. Initial program 73.5%

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

   3. Taylor expanded in z around inf 64.7%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+64}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -9.8 \cdot 10^{-48}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq -1.22 \cdot 10^{-133}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;a \leq -4.3 \cdot 10^{-191}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq -2.55 \cdot 10^{-228}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-265}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+104}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 56.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(z \cdot c\right)\\ t_3 := t\_1 - t\_2\\ t_4 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -2.7 \cdot 10^{+64}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;a \leq -4.7 \cdot 10^{-49}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq -1.58 \cdot 10^{-133}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq -2.05 \cdot 10^{-190}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - t\_2\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-231}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-265}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+104}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i))))
        (t_2 (* b (* z c)))
        (t_3 (- t_1 t_2))
        (t_4 (* a (- (* b i) (* x t)))))
   (if (<= a -2.7e+64)
     t_4
     (if (<= a -4.7e-49)
       (+ (* x (* y z)) (* i (* a b)))
       (if (<= a -1.58e-133)
         t_3
         (if (<= a -2.05e-190)
           (- (* x (- (* y z) (* t a))) t_2)
           (if (<= a -4.5e-231)
             t_1
             (if (<= a 1.6e-265)
               (* z (- (* x y) (* b c)))
               (if (<= a 9.5e+104) t_3 t_4)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * (z * c);
	double t_3 = t_1 - t_2;
	double t_4 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -2.7e+64) {
		tmp = t_4;
	} else if (a <= -4.7e-49) {
		tmp = (x * (y * z)) + (i * (a * b));
	} else if (a <= -1.58e-133) {
		tmp = t_3;
	} else if (a <= -2.05e-190) {
		tmp = (x * ((y * z) - (t * a))) - t_2;
	} else if (a <= -4.5e-231) {
		tmp = t_1;
	} else if (a <= 1.6e-265) {
		tmp = z * ((x * y) - (b * c));
	} else if (a <= 9.5e+104) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = b * (z * c)
    t_3 = t_1 - t_2
    t_4 = a * ((b * i) - (x * t))
    if (a <= (-2.7d+64)) then
        tmp = t_4
    else if (a <= (-4.7d-49)) then
        tmp = (x * (y * z)) + (i * (a * b))
    else if (a <= (-1.58d-133)) then
        tmp = t_3
    else if (a <= (-2.05d-190)) then
        tmp = (x * ((y * z) - (t * a))) - t_2
    else if (a <= (-4.5d-231)) then
        tmp = t_1
    else if (a <= 1.6d-265) then
        tmp = z * ((x * y) - (b * c))
    else if (a <= 9.5d+104) then
        tmp = t_3
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * (z * c);
	double t_3 = t_1 - t_2;
	double t_4 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -2.7e+64) {
		tmp = t_4;
	} else if (a <= -4.7e-49) {
		tmp = (x * (y * z)) + (i * (a * b));
	} else if (a <= -1.58e-133) {
		tmp = t_3;
	} else if (a <= -2.05e-190) {
		tmp = (x * ((y * z) - (t * a))) - t_2;
	} else if (a <= -4.5e-231) {
		tmp = t_1;
	} else if (a <= 1.6e-265) {
		tmp = z * ((x * y) - (b * c));
	} else if (a <= 9.5e+104) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = b * (z * c)
	t_3 = t_1 - t_2
	t_4 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -2.7e+64:
		tmp = t_4
	elif a <= -4.7e-49:
		tmp = (x * (y * z)) + (i * (a * b))
	elif a <= -1.58e-133:
		tmp = t_3
	elif a <= -2.05e-190:
		tmp = (x * ((y * z) - (t * a))) - t_2
	elif a <= -4.5e-231:
		tmp = t_1
	elif a <= 1.6e-265:
		tmp = z * ((x * y) - (b * c))
	elif a <= 9.5e+104:
		tmp = t_3
	else:
		tmp = t_4
	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)))
	t_2 = Float64(b * Float64(z * c))
	t_3 = Float64(t_1 - t_2)
	t_4 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -2.7e+64)
		tmp = t_4;
	elseif (a <= -4.7e-49)
		tmp = Float64(Float64(x * Float64(y * z)) + Float64(i * Float64(a * b)));
	elseif (a <= -1.58e-133)
		tmp = t_3;
	elseif (a <= -2.05e-190)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - t_2);
	elseif (a <= -4.5e-231)
		tmp = t_1;
	elseif (a <= 1.6e-265)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (a <= 9.5e+104)
		tmp = t_3;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = b * (z * c);
	t_3 = t_1 - t_2;
	t_4 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -2.7e+64)
		tmp = t_4;
	elseif (a <= -4.7e-49)
		tmp = (x * (y * z)) + (i * (a * b));
	elseif (a <= -1.58e-133)
		tmp = t_3;
	elseif (a <= -2.05e-190)
		tmp = (x * ((y * z) - (t * a))) - t_2;
	elseif (a <= -4.5e-231)
		tmp = t_1;
	elseif (a <= 1.6e-265)
		tmp = z * ((x * y) - (b * c));
	elseif (a <= 9.5e+104)
		tmp = t_3;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 - t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.7e+64], t$95$4, If[LessEqual[a, -4.7e-49], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.58e-133], t$95$3, If[LessEqual[a, -2.05e-190], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[a, -4.5e-231], t$95$1, If[LessEqual[a, 1.6e-265], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.5e+104], t$95$3, t$95$4]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -2.7e64 or 9.5e104 < a

   1. Initial program 56.2%

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

   3. Taylor expanded in a around -inf 73.9%

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

   if -2.7e64 < a < -4.70000000000000021e-49

   1. Initial program 70.9%

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

   3. Taylor expanded in j around 0 67.0%

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

      1. *-commutative 67.0%

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

   5. Simplified 67.0%

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

   6. Taylor expanded in t around 0 59.3%

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

      1. *-commutative 59.3%

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

   8. Simplified 59.3%

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

   9. Taylor expanded in z around 0 67.5%

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

       1. associate-*r* 67.6%

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

       2. *-commutative 67.6%

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

       3. neg-mul-1 67.6%

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

       4. distribute-lft-neg-in 67.6%

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

       5. *-commutative 67.6%

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

   11. Simplified 67.6%

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

   if -4.70000000000000021e-49 < a < -1.58e-133 or 1.6e-265 < a < 9.5e104

   1. Initial program 91.5%

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

   3. Taylor expanded in x around 0 83.1%

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

   4. Taylor expanded in c around inf 69.1%

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

   if -1.58e-133 < a < -2.0500000000000001e-190

   1. Initial program 86.4%

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

   3. Taylor expanded in j around 0 86.4%

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

      1. *-commutative 86.4%

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

   5. Simplified 86.4%

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

   6. Taylor expanded in c around inf 73.6%

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

   if -2.0500000000000001e-190 < a < -4.4999999999999998e-231

   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 x around 0 81.1%

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

   4. Taylor expanded in j around inf 81.1%

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

   if -4.4999999999999998e-231 < a < 1.6e-265

   1. Initial program 73.5%

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

   3. Taylor expanded in z around inf 64.7%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{+64}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -4.7 \cdot 10^{-49}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq -1.58 \cdot 10^{-133}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;a \leq -2.05 \cdot 10^{-190}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-231}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-265}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+104}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := t\_1 - b \cdot \left(z \cdot c\right)\\ t_3 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_4 := t\_3 + t\_1\\ t_5 := t\_3 + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;x \leq -1.1 \cdot 10^{+113}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-47}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-124}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{+83}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+204} \lor \neg \left(x \leq 2.4 \cdot 10^{+258}\right):\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (- t_1 (* b (* z c))))
        (t_3 (* j (- (* t c) (* y i))))
        (t_4 (+ t_3 t_1))
        (t_5 (+ t_3 (* b (- (* a i) (* z c))))))
   (if (<= x -1.1e+113)
     t_2
     (if (<= x -3.8e-47)
       t_5
       (if (<= x -1.6e-124)
         t_4
         (if (<= x 4.3e+83)
           t_5
           (if (or (<= x 1.15e+204) (not (<= x 2.4e+258))) t_4 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = t_1 - (b * (z * c));
	double t_3 = j * ((t * c) - (y * i));
	double t_4 = t_3 + t_1;
	double t_5 = t_3 + (b * ((a * i) - (z * c)));
	double tmp;
	if (x <= -1.1e+113) {
		tmp = t_2;
	} else if (x <= -3.8e-47) {
		tmp = t_5;
	} else if (x <= -1.6e-124) {
		tmp = t_4;
	} else if (x <= 4.3e+83) {
		tmp = t_5;
	} else if ((x <= 1.15e+204) || !(x <= 2.4e+258)) {
		tmp = t_4;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = t_1 - (b * (z * c))
    t_3 = j * ((t * c) - (y * i))
    t_4 = t_3 + t_1
    t_5 = t_3 + (b * ((a * i) - (z * c)))
    if (x <= (-1.1d+113)) then
        tmp = t_2
    else if (x <= (-3.8d-47)) then
        tmp = t_5
    else if (x <= (-1.6d-124)) then
        tmp = t_4
    else if (x <= 4.3d+83) then
        tmp = t_5
    else if ((x <= 1.15d+204) .or. (.not. (x <= 2.4d+258))) then
        tmp = t_4
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = t_1 - (b * (z * c));
	double t_3 = j * ((t * c) - (y * i));
	double t_4 = t_3 + t_1;
	double t_5 = t_3 + (b * ((a * i) - (z * c)));
	double tmp;
	if (x <= -1.1e+113) {
		tmp = t_2;
	} else if (x <= -3.8e-47) {
		tmp = t_5;
	} else if (x <= -1.6e-124) {
		tmp = t_4;
	} else if (x <= 4.3e+83) {
		tmp = t_5;
	} else if ((x <= 1.15e+204) || !(x <= 2.4e+258)) {
		tmp = t_4;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = t_1 - (b * (z * c))
	t_3 = j * ((t * c) - (y * i))
	t_4 = t_3 + t_1
	t_5 = t_3 + (b * ((a * i) - (z * c)))
	tmp = 0
	if x <= -1.1e+113:
		tmp = t_2
	elif x <= -3.8e-47:
		tmp = t_5
	elif x <= -1.6e-124:
		tmp = t_4
	elif x <= 4.3e+83:
		tmp = t_5
	elif (x <= 1.15e+204) or not (x <= 2.4e+258):
		tmp = t_4
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(t_1 - Float64(b * Float64(z * c)))
	t_3 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_4 = Float64(t_3 + t_1)
	t_5 = Float64(t_3 + Float64(b * Float64(Float64(a * i) - Float64(z * c))))
	tmp = 0.0
	if (x <= -1.1e+113)
		tmp = t_2;
	elseif (x <= -3.8e-47)
		tmp = t_5;
	elseif (x <= -1.6e-124)
		tmp = t_4;
	elseif (x <= 4.3e+83)
		tmp = t_5;
	elseif ((x <= 1.15e+204) || !(x <= 2.4e+258))
		tmp = t_4;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = t_1 - (b * (z * c));
	t_3 = j * ((t * c) - (y * i));
	t_4 = t_3 + t_1;
	t_5 = t_3 + (b * ((a * i) - (z * c)));
	tmp = 0.0;
	if (x <= -1.1e+113)
		tmp = t_2;
	elseif (x <= -3.8e-47)
		tmp = t_5;
	elseif (x <= -1.6e-124)
		tmp = t_4;
	elseif (x <= 4.3e+83)
		tmp = t_5;
	elseif ((x <= 1.15e+204) || ~((x <= 2.4e+258)))
		tmp = t_4;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 + t$95$1), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$3 + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.1e+113], t$95$2, If[LessEqual[x, -3.8e-47], t$95$5, If[LessEqual[x, -1.6e-124], t$95$4, If[LessEqual[x, 4.3e+83], t$95$5, If[Or[LessEqual[x, 1.15e+204], N[Not[LessEqual[x, 2.4e+258]], $MachinePrecision]], t$95$4, t$95$2]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.10000000000000005e113 or 1.14999999999999995e204 < x < 2.4e258

   1. Initial program 60.7%

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

   3. Taylor expanded in j around 0 76.6%

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

      1. *-commutative 76.6%

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

   5. Simplified 76.6%

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

   6. Taylor expanded in c around inf 73.0%

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

   if -1.10000000000000005e113 < x < -3.80000000000000015e-47 or -1.60000000000000002e-124 < x < 4.3e83

   1. Initial program 81.2%

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

   3. Taylor expanded in x around 0 75.5%

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

   if -3.80000000000000015e-47 < x < -1.60000000000000002e-124 or 4.3e83 < x < 1.14999999999999995e204 or 2.4e258 < x

   1. Initial program 76.4%

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

   3. Taylor expanded in b around 0 88.1%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+113}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-47}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-124}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{+83}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+204} \lor \neg \left(x \leq 2.4 \cdot 10^{+258}\right):\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 52.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -9.2 \cdot 10^{+49}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-36}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq -1.26 \cdot 10^{-106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{-153}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 5.3 \cdot 10^{-90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.72 \cdot 10^{-46}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{+36}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j)))) (t_2 (* b (- (* a i) (* z c)))))
   (if (<= b -9.2e+49)
     t_2
     (if (<= b -2.3e-36)
       (* t (- (* c j) (* x a)))
       (if (<= b -1.26e-106)
         t_1
         (if (<= b 4.6e-153)
           (* j (- (* t c) (* y i)))
           (if (<= b 5.3e-90)
             t_1
             (if (<= b 1.72e-46)
               (* c (- (* t j) (* z b)))
               (if (<= b 1.8e+36) (* a (- (* b i) (* x t))) 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 = y * ((x * z) - (i * j));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -9.2e+49) {
		tmp = t_2;
	} else if (b <= -2.3e-36) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= -1.26e-106) {
		tmp = t_1;
	} else if (b <= 4.6e-153) {
		tmp = j * ((t * c) - (y * i));
	} else if (b <= 5.3e-90) {
		tmp = t_1;
	} else if (b <= 1.72e-46) {
		tmp = c * ((t * j) - (z * b));
	} else if (b <= 1.8e+36) {
		tmp = a * ((b * i) - (x * t));
	} 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 = y * ((x * z) - (i * j))
    t_2 = b * ((a * i) - (z * c))
    if (b <= (-9.2d+49)) then
        tmp = t_2
    else if (b <= (-2.3d-36)) then
        tmp = t * ((c * j) - (x * a))
    else if (b <= (-1.26d-106)) then
        tmp = t_1
    else if (b <= 4.6d-153) then
        tmp = j * ((t * c) - (y * i))
    else if (b <= 5.3d-90) then
        tmp = t_1
    else if (b <= 1.72d-46) then
        tmp = c * ((t * j) - (z * b))
    else if (b <= 1.8d+36) then
        tmp = a * ((b * i) - (x * t))
    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 = y * ((x * z) - (i * j));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -9.2e+49) {
		tmp = t_2;
	} else if (b <= -2.3e-36) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= -1.26e-106) {
		tmp = t_1;
	} else if (b <= 4.6e-153) {
		tmp = j * ((t * c) - (y * i));
	} else if (b <= 5.3e-90) {
		tmp = t_1;
	} else if (b <= 1.72e-46) {
		tmp = c * ((t * j) - (z * b));
	} else if (b <= 1.8e+36) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -9.2e+49:
		tmp = t_2
	elif b <= -2.3e-36:
		tmp = t * ((c * j) - (x * a))
	elif b <= -1.26e-106:
		tmp = t_1
	elif b <= 4.6e-153:
		tmp = j * ((t * c) - (y * i))
	elif b <= 5.3e-90:
		tmp = t_1
	elif b <= 1.72e-46:
		tmp = c * ((t * j) - (z * b))
	elif b <= 1.8e+36:
		tmp = a * ((b * i) - (x * t))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -9.2e+49)
		tmp = t_2;
	elseif (b <= -2.3e-36)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (b <= -1.26e-106)
		tmp = t_1;
	elseif (b <= 4.6e-153)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (b <= 5.3e-90)
		tmp = t_1;
	elseif (b <= 1.72e-46)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (b <= 1.8e+36)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((x * z) - (i * j));
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -9.2e+49)
		tmp = t_2;
	elseif (b <= -2.3e-36)
		tmp = t * ((c * j) - (x * a));
	elseif (b <= -1.26e-106)
		tmp = t_1;
	elseif (b <= 4.6e-153)
		tmp = j * ((t * c) - (y * i));
	elseif (b <= 5.3e-90)
		tmp = t_1;
	elseif (b <= 1.72e-46)
		tmp = c * ((t * j) - (z * b));
	elseif (b <= 1.8e+36)
		tmp = a * ((b * i) - (x * t));
	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[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9.2e+49], t$95$2, If[LessEqual[b, -2.3e-36], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.26e-106], t$95$1, If[LessEqual[b, 4.6e-153], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.3e-90], t$95$1, If[LessEqual[b, 1.72e-46], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.8e+36], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -9.20000000000000008e49 or 1.7999999999999999e36 < b

   1. Initial program 77.5%

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

   3. Taylor expanded in b around inf 67.8%

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

   if -9.20000000000000008e49 < b < -2.29999999999999996e-36

   1. Initial program 83.9%

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

   3. Taylor expanded in t around -inf 64.1%

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

      1. mul-1-neg 64.1%

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

      2. distribute-rgt-neg-in 64.1%

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

      3. +-commutative 64.1%

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

      4. mul-1-neg 64.1%

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

      5. unsub-neg 64.1%

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

   5. Simplified 64.1%

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

   if -2.29999999999999996e-36 < b < -1.2600000000000001e-106 or 4.59999999999999994e-153 < b < 5.3000000000000004e-90

   1. Initial program 79.5%

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

   3. Taylor expanded in y around inf 66.1%

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

   4. Taylor expanded in i around 0 65.9%

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

      1. +-commutative 65.9%

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

      2. mul-1-neg 65.9%

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

      3. *-commutative 65.9%

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

      4. associate-*r* 62.6%

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

      5. associate-*r* 66.1%

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

      6. distribute-lft-neg-out 66.1%

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

      7. *-commutative 66.1%

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

      8. distribute-lft-in 66.1%

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

      9. unsub-neg 66.1%

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

   6. Simplified 66.1%

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

   if -1.2600000000000001e-106 < b < 4.59999999999999994e-153

   1. Initial program 71.2%

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

   3. Taylor expanded in x around 0 59.9%

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

   4. Taylor expanded in j around inf 60.3%

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

   if 5.3000000000000004e-90 < b < 1.7199999999999999e-46

   1. Initial program 99.6%

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

   3. Taylor expanded in c around inf 64.2%

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

      1. *-commutative 64.2%

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

   5. Simplified 64.2%

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

   if 1.7199999999999999e-46 < b < 1.7999999999999999e36

   1. Initial program 62.9%

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

   3. Taylor expanded in a around -inf 59.2%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.2 \cdot 10^{+49}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-36}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq -1.26 \cdot 10^{-106}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{-153}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 5.3 \cdot 10^{-90}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 1.72 \cdot 10^{-46}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{+36}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 52.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.25 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.02 \cdot 10^{-36}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq -3.8 \cdot 10^{-166}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;b \leq 1.32 \cdot 10^{-151}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 8.6 \cdot 10^{-89}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-44}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+36}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= b -1.25e+50)
     t_1
     (if (<= b -1.02e-36)
       (* t (- (* c j) (* x a)))
       (if (<= b -3.8e-166)
         (- (* y (* x z)) (* y (* i j)))
         (if (<= b 1.32e-151)
           (* j (- (* t c) (* y i)))
           (if (<= b 8.6e-89)
             (* y (- (* x z) (* i j)))
             (if (<= b 2.4e-44)
               (* c (- (* t j) (* z b)))
               (if (<= b 2e+36) (* a (- (* b i) (* x t))) t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.25e+50) {
		tmp = t_1;
	} else if (b <= -1.02e-36) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= -3.8e-166) {
		tmp = (y * (x * z)) - (y * (i * j));
	} else if (b <= 1.32e-151) {
		tmp = j * ((t * c) - (y * i));
	} else if (b <= 8.6e-89) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 2.4e-44) {
		tmp = c * ((t * j) - (z * b));
	} else if (b <= 2e+36) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    if (b <= (-1.25d+50)) then
        tmp = t_1
    else if (b <= (-1.02d-36)) then
        tmp = t * ((c * j) - (x * a))
    else if (b <= (-3.8d-166)) then
        tmp = (y * (x * z)) - (y * (i * j))
    else if (b <= 1.32d-151) then
        tmp = j * ((t * c) - (y * i))
    else if (b <= 8.6d-89) then
        tmp = y * ((x * z) - (i * j))
    else if (b <= 2.4d-44) then
        tmp = c * ((t * j) - (z * b))
    else if (b <= 2d+36) then
        tmp = a * ((b * i) - (x * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.25e+50) {
		tmp = t_1;
	} else if (b <= -1.02e-36) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= -3.8e-166) {
		tmp = (y * (x * z)) - (y * (i * j));
	} else if (b <= 1.32e-151) {
		tmp = j * ((t * c) - (y * i));
	} else if (b <= 8.6e-89) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 2.4e-44) {
		tmp = c * ((t * j) - (z * b));
	} else if (b <= 2e+36) {
		tmp = a * ((b * i) - (x * t));
	} 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))
	tmp = 0
	if b <= -1.25e+50:
		tmp = t_1
	elif b <= -1.02e-36:
		tmp = t * ((c * j) - (x * a))
	elif b <= -3.8e-166:
		tmp = (y * (x * z)) - (y * (i * j))
	elif b <= 1.32e-151:
		tmp = j * ((t * c) - (y * i))
	elif b <= 8.6e-89:
		tmp = y * ((x * z) - (i * j))
	elif b <= 2.4e-44:
		tmp = c * ((t * j) - (z * b))
	elif b <= 2e+36:
		tmp = a * ((b * i) - (x * t))
	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)))
	tmp = 0.0
	if (b <= -1.25e+50)
		tmp = t_1;
	elseif (b <= -1.02e-36)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (b <= -3.8e-166)
		tmp = Float64(Float64(y * Float64(x * z)) - Float64(y * Float64(i * j)));
	elseif (b <= 1.32e-151)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (b <= 8.6e-89)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (b <= 2.4e-44)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (b <= 2e+36)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -1.25e+50)
		tmp = t_1;
	elseif (b <= -1.02e-36)
		tmp = t * ((c * j) - (x * a));
	elseif (b <= -3.8e-166)
		tmp = (y * (x * z)) - (y * (i * j));
	elseif (b <= 1.32e-151)
		tmp = j * ((t * c) - (y * i));
	elseif (b <= 8.6e-89)
		tmp = y * ((x * z) - (i * j));
	elseif (b <= 2.4e-44)
		tmp = c * ((t * j) - (z * b));
	elseif (b <= 2e+36)
		tmp = a * ((b * i) - (x * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.25e+50], t$95$1, If[LessEqual[b, -1.02e-36], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.8e-166], N[(N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision] - N[(y * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.32e-151], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.6e-89], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.4e-44], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2e+36], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -1.25e50 or 2.00000000000000008e36 < b

   1. Initial program 77.5%

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

   3. Taylor expanded in b around inf 67.8%

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

   if -1.25e50 < b < -1.02e-36

   1. Initial program 83.9%

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

   3. Taylor expanded in t around -inf 64.1%

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

      1. mul-1-neg 64.1%

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

      2. distribute-rgt-neg-in 64.1%

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

      3. +-commutative 64.1%

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

      4. mul-1-neg 64.1%

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

      5. unsub-neg 64.1%

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

   5. Simplified 64.1%

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

   if -1.02e-36 < b < -3.79999999999999982e-166

   1. Initial program 73.4%

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

   3. Taylor expanded in y around inf 56.1%

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

      1. distribute-rgt-in 56.2%

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

      2. mul-1-neg 56.2%

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

      3. *-commutative 56.2%

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

   5. Applied egg-rr 56.2%

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

   if -3.79999999999999982e-166 < b < 1.31999999999999999e-151

   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 x around 0 64.4%

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

   4. Taylor expanded in j around inf 62.9%

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

   if 1.31999999999999999e-151 < b < 8.59999999999999974e-89

   1. Initial program 74.9%

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

   3. Taylor expanded in y around inf 74.6%

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

   4. Taylor expanded in i around 0 66.3%

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

      1. +-commutative 66.3%

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

      2. mul-1-neg 66.3%

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

      3. *-commutative 66.3%

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

      4. associate-*r* 66.3%

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

      5. associate-*r* 74.6%

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

      6. distribute-lft-neg-out 74.6%

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

      7. *-commutative 74.6%

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

      8. distribute-lft-in 74.6%

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

      9. unsub-neg 74.6%

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

   6. Simplified 74.6%

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

   if 8.59999999999999974e-89 < b < 2.40000000000000009e-44

   1. Initial program 99.6%

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

   3. Taylor expanded in c around inf 64.2%

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

      1. *-commutative 64.2%

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

   5. Simplified 64.2%

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

   if 2.40000000000000009e-44 < b < 2.00000000000000008e36

   1. Initial program 62.9%

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

   3. Taylor expanded in a around -inf 59.2%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+50}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.02 \cdot 10^{-36}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq -3.8 \cdot 10^{-166}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;b \leq 1.32 \cdot 10^{-151}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 8.6 \cdot 10^{-89}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-44}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+36}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -8.2 \cdot 10^{+49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-36}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq -3.8 \cdot 10^{-166}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{-148}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-83}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-46}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{+36}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= b -8.2e+49)
     t_1
     (if (<= b -2.8e-36)
       (* t (- (* c j) (* x a)))
       (if (<= b -3.8e-166)
         (- (* y (* x z)) (* y (* i j)))
         (if (<= b 4.3e-148)
           (* j (- (* t c) (* y i)))
           (if (<= b 1.2e-83)
             (+ (* x (* y z)) (* i (* a b)))
             (if (<= b 1.6e-46)
               (* c (- (* t j) (* z b)))
               (if (<= b 1.85e+36) (* a (- (* b i) (* x t))) t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -8.2e+49) {
		tmp = t_1;
	} else if (b <= -2.8e-36) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= -3.8e-166) {
		tmp = (y * (x * z)) - (y * (i * j));
	} else if (b <= 4.3e-148) {
		tmp = j * ((t * c) - (y * i));
	} else if (b <= 1.2e-83) {
		tmp = (x * (y * z)) + (i * (a * b));
	} else if (b <= 1.6e-46) {
		tmp = c * ((t * j) - (z * b));
	} else if (b <= 1.85e+36) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    if (b <= (-8.2d+49)) then
        tmp = t_1
    else if (b <= (-2.8d-36)) then
        tmp = t * ((c * j) - (x * a))
    else if (b <= (-3.8d-166)) then
        tmp = (y * (x * z)) - (y * (i * j))
    else if (b <= 4.3d-148) then
        tmp = j * ((t * c) - (y * i))
    else if (b <= 1.2d-83) then
        tmp = (x * (y * z)) + (i * (a * b))
    else if (b <= 1.6d-46) then
        tmp = c * ((t * j) - (z * b))
    else if (b <= 1.85d+36) then
        tmp = a * ((b * i) - (x * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -8.2e+49) {
		tmp = t_1;
	} else if (b <= -2.8e-36) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= -3.8e-166) {
		tmp = (y * (x * z)) - (y * (i * j));
	} else if (b <= 4.3e-148) {
		tmp = j * ((t * c) - (y * i));
	} else if (b <= 1.2e-83) {
		tmp = (x * (y * z)) + (i * (a * b));
	} else if (b <= 1.6e-46) {
		tmp = c * ((t * j) - (z * b));
	} else if (b <= 1.85e+36) {
		tmp = a * ((b * i) - (x * t));
	} 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))
	tmp = 0
	if b <= -8.2e+49:
		tmp = t_1
	elif b <= -2.8e-36:
		tmp = t * ((c * j) - (x * a))
	elif b <= -3.8e-166:
		tmp = (y * (x * z)) - (y * (i * j))
	elif b <= 4.3e-148:
		tmp = j * ((t * c) - (y * i))
	elif b <= 1.2e-83:
		tmp = (x * (y * z)) + (i * (a * b))
	elif b <= 1.6e-46:
		tmp = c * ((t * j) - (z * b))
	elif b <= 1.85e+36:
		tmp = a * ((b * i) - (x * t))
	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)))
	tmp = 0.0
	if (b <= -8.2e+49)
		tmp = t_1;
	elseif (b <= -2.8e-36)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (b <= -3.8e-166)
		tmp = Float64(Float64(y * Float64(x * z)) - Float64(y * Float64(i * j)));
	elseif (b <= 4.3e-148)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (b <= 1.2e-83)
		tmp = Float64(Float64(x * Float64(y * z)) + Float64(i * Float64(a * b)));
	elseif (b <= 1.6e-46)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (b <= 1.85e+36)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -8.2e+49)
		tmp = t_1;
	elseif (b <= -2.8e-36)
		tmp = t * ((c * j) - (x * a));
	elseif (b <= -3.8e-166)
		tmp = (y * (x * z)) - (y * (i * j));
	elseif (b <= 4.3e-148)
		tmp = j * ((t * c) - (y * i));
	elseif (b <= 1.2e-83)
		tmp = (x * (y * z)) + (i * (a * b));
	elseif (b <= 1.6e-46)
		tmp = c * ((t * j) - (z * b));
	elseif (b <= 1.85e+36)
		tmp = a * ((b * i) - (x * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8.2e+49], t$95$1, If[LessEqual[b, -2.8e-36], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.8e-166], N[(N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision] - N[(y * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.3e-148], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.2e-83], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.6e-46], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.85e+36], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -8.2e49 or 1.85000000000000014e36 < b

   1. Initial program 77.5%

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

   3. Taylor expanded in b around inf 67.8%

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

   if -8.2e49 < b < -2.8000000000000001e-36

   1. Initial program 83.9%

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

   3. Taylor expanded in t around -inf 64.1%

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

      1. mul-1-neg 64.1%

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

      2. distribute-rgt-neg-in 64.1%

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

      3. +-commutative 64.1%

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

      4. mul-1-neg 64.1%

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

      5. unsub-neg 64.1%

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

   5. Simplified 64.1%

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

   if -2.8000000000000001e-36 < b < -3.79999999999999982e-166

   1. Initial program 73.4%

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

   3. Taylor expanded in y around inf 56.1%

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

      1. distribute-rgt-in 56.2%

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

      2. mul-1-neg 56.2%

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

      3. *-commutative 56.2%

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

   5. Applied egg-rr 56.2%

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

   if -3.79999999999999982e-166 < b < 4.2999999999999998e-148

   1. Initial program 73.2%

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

   3. Taylor expanded in x around 0 61.0%

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

   4. Taylor expanded in j around inf 61.4%

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

   if 4.2999999999999998e-148 < b < 1.2e-83

   1. Initial program 79.8%

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

   3. Taylor expanded in j around 0 70.5%

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

      1. *-commutative 70.5%

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

   5. Simplified 70.5%

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

   6. Taylor expanded in t around 0 70.6%

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

      1. *-commutative 70.6%

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

   8. Simplified 70.6%

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

   9. Taylor expanded in z around 0 79.4%

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

       1. associate-*r* 79.4%

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

       2. *-commutative 79.4%

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

       3. neg-mul-1 79.4%

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

       4. distribute-lft-neg-in 79.4%

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

       5. *-commutative 79.4%

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

   11. Simplified 79.4%

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

   if 1.2e-83 < b < 1.6e-46

   1. Initial program 99.6%

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

   3. Taylor expanded in c around inf 73.0%

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

      1. *-commutative 73.0%

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

   5. Simplified 73.0%

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

   if 1.6e-46 < b < 1.85000000000000014e36

   1. Initial program 62.9%

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

   3. Taylor expanded in a around -inf 59.2%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{+49}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-36}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq -3.8 \cdot 10^{-166}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{-148}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-83}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-46}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{+36}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 28.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c\right)\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+107}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-222}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-304}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-253}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+95}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+145}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+249}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (* t c))))
   (if (<= z -8.5e+107)
     (* x (* y z))
     (if (<= z -3.6e-222)
       t_1
       (if (<= z -6.8e-304)
         (* b (* a i))
         (if (<= z 6.6e-253)
           t_1
           (if (<= z 1.25e+95)
             (* a (* b i))
             (if (<= z 6.5e+145)
               (* c (* t j))
               (if (<= z 4.5e+249) (* z (* x y)) (* y (* x z)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (t * c);
	double tmp;
	if (z <= -8.5e+107) {
		tmp = x * (y * z);
	} else if (z <= -3.6e-222) {
		tmp = t_1;
	} else if (z <= -6.8e-304) {
		tmp = b * (a * i);
	} else if (z <= 6.6e-253) {
		tmp = t_1;
	} else if (z <= 1.25e+95) {
		tmp = a * (b * i);
	} else if (z <= 6.5e+145) {
		tmp = c * (t * j);
	} else if (z <= 4.5e+249) {
		tmp = z * (x * y);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (t * c)
    if (z <= (-8.5d+107)) then
        tmp = x * (y * z)
    else if (z <= (-3.6d-222)) then
        tmp = t_1
    else if (z <= (-6.8d-304)) then
        tmp = b * (a * i)
    else if (z <= 6.6d-253) then
        tmp = t_1
    else if (z <= 1.25d+95) then
        tmp = a * (b * i)
    else if (z <= 6.5d+145) then
        tmp = c * (t * j)
    else if (z <= 4.5d+249) then
        tmp = z * (x * y)
    else
        tmp = y * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (t * c);
	double tmp;
	if (z <= -8.5e+107) {
		tmp = x * (y * z);
	} else if (z <= -3.6e-222) {
		tmp = t_1;
	} else if (z <= -6.8e-304) {
		tmp = b * (a * i);
	} else if (z <= 6.6e-253) {
		tmp = t_1;
	} else if (z <= 1.25e+95) {
		tmp = a * (b * i);
	} else if (z <= 6.5e+145) {
		tmp = c * (t * j);
	} else if (z <= 4.5e+249) {
		tmp = z * (x * y);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * (t * c)
	tmp = 0
	if z <= -8.5e+107:
		tmp = x * (y * z)
	elif z <= -3.6e-222:
		tmp = t_1
	elif z <= -6.8e-304:
		tmp = b * (a * i)
	elif z <= 6.6e-253:
		tmp = t_1
	elif z <= 1.25e+95:
		tmp = a * (b * i)
	elif z <= 6.5e+145:
		tmp = c * (t * j)
	elif z <= 4.5e+249:
		tmp = z * (x * y)
	else:
		tmp = y * (x * z)
	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 (z <= -8.5e+107)
		tmp = Float64(x * Float64(y * z));
	elseif (z <= -3.6e-222)
		tmp = t_1;
	elseif (z <= -6.8e-304)
		tmp = Float64(b * Float64(a * i));
	elseif (z <= 6.6e-253)
		tmp = t_1;
	elseif (z <= 1.25e+95)
		tmp = Float64(a * Float64(b * i));
	elseif (z <= 6.5e+145)
		tmp = Float64(c * Float64(t * j));
	elseif (z <= 4.5e+249)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * (t * c);
	tmp = 0.0;
	if (z <= -8.5e+107)
		tmp = x * (y * z);
	elseif (z <= -3.6e-222)
		tmp = t_1;
	elseif (z <= -6.8e-304)
		tmp = b * (a * i);
	elseif (z <= 6.6e-253)
		tmp = t_1;
	elseif (z <= 1.25e+95)
		tmp = a * (b * i);
	elseif (z <= 6.5e+145)
		tmp = c * (t * j);
	elseif (z <= 4.5e+249)
		tmp = z * (x * y);
	else
		tmp = y * (x * z);
	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[z, -8.5e+107], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.6e-222], t$95$1, If[LessEqual[z, -6.8e-304], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.6e-253], t$95$1, If[LessEqual[z, 1.25e+95], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e+145], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e+249], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if z < -8.4999999999999999e107

   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 z around inf 77.0%

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

   4. Taylor expanded in x around inf 60.3%

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

   if -8.4999999999999999e107 < z < -3.59999999999999974e-222 or -6.7999999999999997e-304 < z < 6.6000000000000002e-253

   1. Initial program 80.2%

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

   3. Taylor expanded in x around 0 65.0%

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

   4. Taylor expanded in j around inf 51.2%

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

   5. Taylor expanded in c around inf 30.6%

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

      1. *-commutative 30.6%

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

   7. Simplified 30.6%

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

   if -3.59999999999999974e-222 < z < -6.7999999999999997e-304

   1. Initial program 90.7%

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

   3. Taylor expanded in x around 0 67.6%

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

   4. Taylor expanded in a around inf 35.5%

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

      1. *-commutative 35.5%

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

      2. associate-*l* 39.9%

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

      3. *-commutative 39.9%

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

   6. Simplified 39.9%

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

   if 6.6000000000000002e-253 < z < 1.25000000000000006e95

   1. Initial program 72.9%

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

   3. Taylor expanded in x around 0 64.8%

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

   4. Taylor expanded in a around inf 47.3%

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

   if 1.25000000000000006e95 < z < 6.50000000000000034e145

   1. Initial program 62.5%

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

   3. Taylor expanded in x around 0 62.4%

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

   4. Taylor expanded in t around inf 47.2%

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

   if 6.50000000000000034e145 < z < 4.4999999999999996e249

   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 z around inf 88.2%

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

   4. Taylor expanded in x around inf 58.1%

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

      1. associate-*r* 63.9%

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

      2. *-commutative 63.9%

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

      3. *-commutative 63.9%

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

   6. Simplified 63.9%

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

   if 4.4999999999999996e249 < z

   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 y around inf 69.6%

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

   4. Taylor expanded in i around 0 62.6%

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

      1. *-commutative 62.6%

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

   6. Simplified 62.6%

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

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+107}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-222}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-304}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-253}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+95}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+145}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+249}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 58.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.18 \cdot 10^{+64}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-49}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-240}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-261}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+104}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* j (- (* t c) (* y i))) (* b (* z c))))
        (t_2 (* a (- (* b i) (* x t)))))
   (if (<= a -1.18e+64)
     t_2
     (if (<= a -4.4e-49)
       (+ (* x (* y z)) (* i (* a b)))
       (if (<= a -2.6e-240)
         t_1
         (if (<= a 2.4e-261)
           (* z (- (* x y) (* b c)))
           (if (<= a 9e+104) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((t * c) - (y * i))) - (b * (z * c));
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -1.18e+64) {
		tmp = t_2;
	} else if (a <= -4.4e-49) {
		tmp = (x * (y * z)) + (i * (a * b));
	} else if (a <= -2.6e-240) {
		tmp = t_1;
	} else if (a <= 2.4e-261) {
		tmp = z * ((x * y) - (b * c));
	} else if (a <= 9e+104) {
		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 = (j * ((t * c) - (y * i))) - (b * (z * c))
    t_2 = a * ((b * i) - (x * t))
    if (a <= (-1.18d+64)) then
        tmp = t_2
    else if (a <= (-4.4d-49)) then
        tmp = (x * (y * z)) + (i * (a * b))
    else if (a <= (-2.6d-240)) then
        tmp = t_1
    else if (a <= 2.4d-261) then
        tmp = z * ((x * y) - (b * c))
    else if (a <= 9d+104) 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 = (j * ((t * c) - (y * i))) - (b * (z * c));
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -1.18e+64) {
		tmp = t_2;
	} else if (a <= -4.4e-49) {
		tmp = (x * (y * z)) + (i * (a * b));
	} else if (a <= -2.6e-240) {
		tmp = t_1;
	} else if (a <= 2.4e-261) {
		tmp = z * ((x * y) - (b * c));
	} else if (a <= 9e+104) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((t * c) - (y * i))) - (b * (z * c))
	t_2 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -1.18e+64:
		tmp = t_2
	elif a <= -4.4e-49:
		tmp = (x * (y * z)) + (i * (a * b))
	elif a <= -2.6e-240:
		tmp = t_1
	elif a <= 2.4e-261:
		tmp = z * ((x * y) - (b * c))
	elif a <= 9e+104:
		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(j * Float64(Float64(t * c) - Float64(y * i))) - Float64(b * Float64(z * c)))
	t_2 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -1.18e+64)
		tmp = t_2;
	elseif (a <= -4.4e-49)
		tmp = Float64(Float64(x * Float64(y * z)) + Float64(i * Float64(a * b)));
	elseif (a <= -2.6e-240)
		tmp = t_1;
	elseif (a <= 2.4e-261)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (a <= 9e+104)
		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 = (j * ((t * c) - (y * i))) - (b * (z * c));
	t_2 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -1.18e+64)
		tmp = t_2;
	elseif (a <= -4.4e-49)
		tmp = (x * (y * z)) + (i * (a * b));
	elseif (a <= -2.6e-240)
		tmp = t_1;
	elseif (a <= 2.4e-261)
		tmp = z * ((x * y) - (b * c));
	elseif (a <= 9e+104)
		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[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.18e+64], t$95$2, If[LessEqual[a, -4.4e-49], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.6e-240], t$95$1, If[LessEqual[a, 2.4e-261], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9e+104], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.18000000000000006e64 or 8.9999999999999997e104 < a

   1. Initial program 56.2%

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

   3. Taylor expanded in a around -inf 73.9%

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

   if -1.18000000000000006e64 < a < -4.3999999999999998e-49

   1. Initial program 70.9%

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

   3. Taylor expanded in j around 0 67.0%

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

      1. *-commutative 67.0%

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

   5. Simplified 67.0%

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

   6. Taylor expanded in t around 0 59.3%

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

      1. *-commutative 59.3%

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

   8. Simplified 59.3%

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

   9. Taylor expanded in z around 0 67.5%

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

       1. associate-*r* 67.6%

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

       2. *-commutative 67.6%

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

       3. neg-mul-1 67.6%

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

       4. distribute-lft-neg-in 67.6%

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

       5. *-commutative 67.6%

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

   11. Simplified 67.6%

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

   if -4.3999999999999998e-49 < a < -2.59999999999999992e-240 or 2.40000000000000014e-261 < a < 8.9999999999999997e104

   1. Initial program 91.5%

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

   3. Taylor expanded in x around 0 77.7%

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

   4. Taylor expanded in c around inf 65.0%

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

   if -2.59999999999999992e-240 < a < 2.40000000000000014e-261

   1. Initial program 73.5%

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

   3. Taylor expanded in z around inf 64.7%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.18 \cdot 10^{+64}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-49}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-240}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-261}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+104}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 42.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;b \leq -1.55 \cdot 10^{+50}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{-36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{-107}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{-248}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{-161}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-90}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (* t c)))
        (t_2 (* b (- (* a i) (* z c))))
        (t_3 (* x (* y z))))
   (if (<= b -1.55e+50)
     t_2
     (if (<= b -1.45e-36)
       t_1
       (if (<= b -4.6e-107)
         t_3
         (if (<= b -1.6e-248)
           t_1
           (if (<= b 1.1e-161)
             (* (* y i) (- j))
             (if (<= b 2.2e-90) t_3 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (t * c);
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = x * (y * z);
	double tmp;
	if (b <= -1.55e+50) {
		tmp = t_2;
	} else if (b <= -1.45e-36) {
		tmp = t_1;
	} else if (b <= -4.6e-107) {
		tmp = t_3;
	} else if (b <= -1.6e-248) {
		tmp = t_1;
	} else if (b <= 1.1e-161) {
		tmp = (y * i) * -j;
	} else if (b <= 2.2e-90) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * (t * c)
    t_2 = b * ((a * i) - (z * c))
    t_3 = x * (y * z)
    if (b <= (-1.55d+50)) then
        tmp = t_2
    else if (b <= (-1.45d-36)) then
        tmp = t_1
    else if (b <= (-4.6d-107)) then
        tmp = t_3
    else if (b <= (-1.6d-248)) then
        tmp = t_1
    else if (b <= 1.1d-161) then
        tmp = (y * i) * -j
    else if (b <= 2.2d-90) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (t * c);
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = x * (y * z);
	double tmp;
	if (b <= -1.55e+50) {
		tmp = t_2;
	} else if (b <= -1.45e-36) {
		tmp = t_1;
	} else if (b <= -4.6e-107) {
		tmp = t_3;
	} else if (b <= -1.6e-248) {
		tmp = t_1;
	} else if (b <= 1.1e-161) {
		tmp = (y * i) * -j;
	} else if (b <= 2.2e-90) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * (t * c)
	t_2 = b * ((a * i) - (z * c))
	t_3 = x * (y * z)
	tmp = 0
	if b <= -1.55e+50:
		tmp = t_2
	elif b <= -1.45e-36:
		tmp = t_1
	elif b <= -4.6e-107:
		tmp = t_3
	elif b <= -1.6e-248:
		tmp = t_1
	elif b <= 1.1e-161:
		tmp = (y * i) * -j
	elif b <= 2.2e-90:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(t * c))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_3 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (b <= -1.55e+50)
		tmp = t_2;
	elseif (b <= -1.45e-36)
		tmp = t_1;
	elseif (b <= -4.6e-107)
		tmp = t_3;
	elseif (b <= -1.6e-248)
		tmp = t_1;
	elseif (b <= 1.1e-161)
		tmp = Float64(Float64(y * i) * Float64(-j));
	elseif (b <= 2.2e-90)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * (t * c);
	t_2 = b * ((a * i) - (z * c));
	t_3 = x * (y * z);
	tmp = 0.0;
	if (b <= -1.55e+50)
		tmp = t_2;
	elseif (b <= -1.45e-36)
		tmp = t_1;
	elseif (b <= -4.6e-107)
		tmp = t_3;
	elseif (b <= -1.6e-248)
		tmp = t_1;
	elseif (b <= 1.1e-161)
		tmp = (y * i) * -j;
	elseif (b <= 2.2e-90)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.55e+50], t$95$2, If[LessEqual[b, -1.45e-36], t$95$1, If[LessEqual[b, -4.6e-107], t$95$3, If[LessEqual[b, -1.6e-248], t$95$1, If[LessEqual[b, 1.1e-161], N[(N[(y * i), $MachinePrecision] * (-j)), $MachinePrecision], If[LessEqual[b, 2.2e-90], t$95$3, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.55000000000000001e50 or 2.19999999999999986e-90 < b

   1. Initial program 77.1%

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

   3. Taylor expanded in b around inf 61.0%

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

   if -1.55000000000000001e50 < b < -1.45000000000000006e-36 or -4.60000000000000007e-107 < b < -1.60000000000000009e-248

   1. Initial program 76.6%

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

   3. Taylor expanded in x around 0 62.8%

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

   4. Taylor expanded in j around inf 59.4%

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

   5. Taylor expanded in c around inf 46.8%

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

      1. *-commutative 46.8%

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

   7. Simplified 46.8%

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

   if -1.45000000000000006e-36 < b < -4.60000000000000007e-107 or 1.10000000000000001e-161 < b < 2.19999999999999986e-90

   1. Initial program 77.6%

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

   3. Taylor expanded in z around inf 47.7%

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

   4. Taylor expanded in x around inf 52.6%

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

   if -1.60000000000000009e-248 < b < 1.10000000000000001e-161

   1. Initial program 68.4%

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

   3. Taylor expanded in x around 0 62.3%

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

   4. Taylor expanded in j around inf 59.5%

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

   5. Taylor expanded in c around 0 43.3%

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

      1. mul-1-neg 43.3%

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

      2. distribute-rgt-neg-in 43.3%

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

      3. *-commutative 43.3%

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

   7. Simplified 43.3%

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

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{+50}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{-36}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{-107}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{-248}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{-161}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-90}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 50.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;b \leq -2.3 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.55 \cdot 10^{-35}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;b \leq -3.85 \cdot 10^{-106}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{-151}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 1.18 \cdot 10^{-88}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{-51}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))) (t_2 (* y (- (* x z) (* i j)))))
   (if (<= b -2.3e+50)
     t_1
     (if (<= b -1.55e-35)
       (* j (* t c))
       (if (<= b -3.85e-106)
         t_2
         (if (<= b 1.65e-151)
           (* j (- (* t c) (* y i)))
           (if (<= b 1.18e-88)
             t_2
             (if (<= b 9.2e-51) (* c (- (* t j) (* z b))) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (b <= -2.3e+50) {
		tmp = t_1;
	} else if (b <= -1.55e-35) {
		tmp = j * (t * c);
	} else if (b <= -3.85e-106) {
		tmp = t_2;
	} else if (b <= 1.65e-151) {
		tmp = j * ((t * c) - (y * i));
	} else if (b <= 1.18e-88) {
		tmp = t_2;
	} else if (b <= 9.2e-51) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = y * ((x * z) - (i * j))
    if (b <= (-2.3d+50)) then
        tmp = t_1
    else if (b <= (-1.55d-35)) then
        tmp = j * (t * c)
    else if (b <= (-3.85d-106)) then
        tmp = t_2
    else if (b <= 1.65d-151) then
        tmp = j * ((t * c) - (y * i))
    else if (b <= 1.18d-88) then
        tmp = t_2
    else if (b <= 9.2d-51) then
        tmp = c * ((t * j) - (z * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (b <= -2.3e+50) {
		tmp = t_1;
	} else if (b <= -1.55e-35) {
		tmp = j * (t * c);
	} else if (b <= -3.85e-106) {
		tmp = t_2;
	} else if (b <= 1.65e-151) {
		tmp = j * ((t * c) - (y * i));
	} else if (b <= 1.18e-88) {
		tmp = t_2;
	} else if (b <= 9.2e-51) {
		tmp = c * ((t * j) - (z * b));
	} 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 = y * ((x * z) - (i * j))
	tmp = 0
	if b <= -2.3e+50:
		tmp = t_1
	elif b <= -1.55e-35:
		tmp = j * (t * c)
	elif b <= -3.85e-106:
		tmp = t_2
	elif b <= 1.65e-151:
		tmp = j * ((t * c) - (y * i))
	elif b <= 1.18e-88:
		tmp = t_2
	elif b <= 9.2e-51:
		tmp = c * ((t * j) - (z * b))
	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(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (b <= -2.3e+50)
		tmp = t_1;
	elseif (b <= -1.55e-35)
		tmp = Float64(j * Float64(t * c));
	elseif (b <= -3.85e-106)
		tmp = t_2;
	elseif (b <= 1.65e-151)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (b <= 1.18e-88)
		tmp = t_2;
	elseif (b <= 9.2e-51)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (b <= -2.3e+50)
		tmp = t_1;
	elseif (b <= -1.55e-35)
		tmp = j * (t * c);
	elseif (b <= -3.85e-106)
		tmp = t_2;
	elseif (b <= 1.65e-151)
		tmp = j * ((t * c) - (y * i));
	elseif (b <= 1.18e-88)
		tmp = t_2;
	elseif (b <= 9.2e-51)
		tmp = c * ((t * j) - (z * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.3e+50], t$95$1, If[LessEqual[b, -1.55e-35], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.85e-106], t$95$2, If[LessEqual[b, 1.65e-151], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.18e-88], t$95$2, If[LessEqual[b, 9.2e-51], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -2.29999999999999997e50 or 9.20000000000000007e-51 < b

   1. Initial program 76.0%

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

   3. Taylor expanded in b around inf 62.7%

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

   if -2.29999999999999997e50 < b < -1.55000000000000006e-35

   1. Initial program 79.7%

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

   3. Taylor expanded in x around 0 70.5%

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

   4. Taylor expanded in j around inf 55.9%

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

   5. Taylor expanded in c around inf 56.0%

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

      1. *-commutative 56.0%

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

   7. Simplified 56.0%

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

   if -1.55000000000000006e-35 < b < -3.8499999999999998e-106 or 1.6499999999999999e-151 < b < 1.18000000000000004e-88

   1. Initial program 79.5%

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

   3. Taylor expanded in y around inf 66.1%

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

   4. Taylor expanded in i around 0 65.9%

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

      1. +-commutative 65.9%

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

      2. mul-1-neg 65.9%

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

      3. *-commutative 65.9%

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

      4. associate-*r* 62.6%

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

      5. associate-*r* 66.1%

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

      6. distribute-lft-neg-out 66.1%

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

      7. *-commutative 66.1%

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

      8. distribute-lft-in 66.1%

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

      9. unsub-neg 66.1%

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

   6. Simplified 66.1%

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

   if -3.8499999999999998e-106 < b < 1.6499999999999999e-151

   1. Initial program 71.2%

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

   3. Taylor expanded in x around 0 59.9%

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

   4. Taylor expanded in j around inf 60.3%

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

   if 1.18000000000000004e-88 < b < 9.20000000000000007e-51

   1. Initial program 99.6%

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

   3. Taylor expanded in c around inf 72.1%

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

      1. *-commutative 72.1%

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

   5. Simplified 72.1%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{+50}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.55 \cdot 10^{-35}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;b \leq -3.85 \cdot 10^{-106}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{-151}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 1.18 \cdot 10^{-88}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{-51}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 53.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_3 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.25 \cdot 10^{+50}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -2.2 \cdot 10^{-36}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -2.2 \cdot 10^{-106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-152}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 2.55 \cdot 10^{-83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{+36}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j))))
        (t_2 (* t (- (* c j) (* x a))))
        (t_3 (* b (- (* a i) (* z c)))))
   (if (<= b -1.25e+50)
     t_3
     (if (<= b -2.2e-36)
       t_2
       (if (<= b -2.2e-106)
         t_1
         (if (<= b 6.2e-152)
           (* j (- (* t c) (* y i)))
           (if (<= b 2.55e-83) t_1 (if (<= b 2.05e+36) t_2 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double t_2 = t * ((c * j) - (x * a));
	double t_3 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.25e+50) {
		tmp = t_3;
	} else if (b <= -2.2e-36) {
		tmp = t_2;
	} else if (b <= -2.2e-106) {
		tmp = t_1;
	} else if (b <= 6.2e-152) {
		tmp = j * ((t * c) - (y * i));
	} else if (b <= 2.55e-83) {
		tmp = t_1;
	} else if (b <= 2.05e+36) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y * ((x * z) - (i * j))
    t_2 = t * ((c * j) - (x * a))
    t_3 = b * ((a * i) - (z * c))
    if (b <= (-1.25d+50)) then
        tmp = t_3
    else if (b <= (-2.2d-36)) then
        tmp = t_2
    else if (b <= (-2.2d-106)) then
        tmp = t_1
    else if (b <= 6.2d-152) then
        tmp = j * ((t * c) - (y * i))
    else if (b <= 2.55d-83) then
        tmp = t_1
    else if (b <= 2.05d+36) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double t_2 = t * ((c * j) - (x * a));
	double t_3 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.25e+50) {
		tmp = t_3;
	} else if (b <= -2.2e-36) {
		tmp = t_2;
	} else if (b <= -2.2e-106) {
		tmp = t_1;
	} else if (b <= 6.2e-152) {
		tmp = j * ((t * c) - (y * i));
	} else if (b <= 2.55e-83) {
		tmp = t_1;
	} else if (b <= 2.05e+36) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	t_2 = t * ((c * j) - (x * a))
	t_3 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -1.25e+50:
		tmp = t_3
	elif b <= -2.2e-36:
		tmp = t_2
	elif b <= -2.2e-106:
		tmp = t_1
	elif b <= 6.2e-152:
		tmp = j * ((t * c) - (y * i))
	elif b <= 2.55e-83:
		tmp = t_1
	elif b <= 2.05e+36:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_2 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_3 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -1.25e+50)
		tmp = t_3;
	elseif (b <= -2.2e-36)
		tmp = t_2;
	elseif (b <= -2.2e-106)
		tmp = t_1;
	elseif (b <= 6.2e-152)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (b <= 2.55e-83)
		tmp = t_1;
	elseif (b <= 2.05e+36)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((x * z) - (i * j));
	t_2 = t * ((c * j) - (x * a));
	t_3 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -1.25e+50)
		tmp = t_3;
	elseif (b <= -2.2e-36)
		tmp = t_2;
	elseif (b <= -2.2e-106)
		tmp = t_1;
	elseif (b <= 6.2e-152)
		tmp = j * ((t * c) - (y * i));
	elseif (b <= 2.55e-83)
		tmp = t_1;
	elseif (b <= 2.05e+36)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.25e+50], t$95$3, If[LessEqual[b, -2.2e-36], t$95$2, If[LessEqual[b, -2.2e-106], t$95$1, If[LessEqual[b, 6.2e-152], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.55e-83], t$95$1, If[LessEqual[b, 2.05e+36], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.25e50 or 2.05000000000000006e36 < b

   1. Initial program 77.5%

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

   3. Taylor expanded in b around inf 67.8%

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

   if -1.25e50 < b < -2.1999999999999999e-36 or 2.55000000000000018e-83 < b < 2.05000000000000006e36

   1. Initial program 76.8%

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

   3. Taylor expanded in t around -inf 52.6%

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

      1. mul-1-neg 52.6%

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

      2. distribute-rgt-neg-in 52.6%

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

      3. +-commutative 52.6%

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

      4. mul-1-neg 52.6%

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

      5. unsub-neg 52.6%

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

   5. Simplified 52.6%

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

   if -2.1999999999999999e-36 < b < -2.19999999999999994e-106 or 6.1999999999999997e-152 < b < 2.55000000000000018e-83

   1. Initial program 80.2%

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

   3. Taylor expanded in y around inf 64.0%

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

   4. Taylor expanded in i around 0 63.8%

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

      1. +-commutative 63.8%

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

      2. mul-1-neg 63.8%

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

      3. *-commutative 63.8%

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

      4. associate-*r* 60.7%

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

      5. associate-*r* 64.0%

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

      6. distribute-lft-neg-out 64.0%

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

      7. *-commutative 64.0%

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

      8. distribute-lft-in 64.0%

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

      9. unsub-neg 64.0%

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

   6. Simplified 64.0%

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

   if -2.19999999999999994e-106 < b < 6.1999999999999997e-152

   1. Initial program 71.2%

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

   3. Taylor expanded in x around 0 59.9%

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

   4. Taylor expanded in j around inf 60.3%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+50}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2.2 \cdot 10^{-36}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq -2.2 \cdot 10^{-106}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-152}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 2.55 \cdot 10^{-83}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{+36}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 70.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := t\_2 - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{if}\;b \leq -7 \cdot 10^{+221}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -1.25 \cdot 10^{+131}:\\ \;\;\;\;t\_1 + t\_2\\ \mathbf{elif}\;b \leq -86000000000000 \lor \neg \left(b \leq 2.55 \cdot 10^{-52}\right):\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1 + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i))))
        (t_2 (* b (- (* a i) (* z c))))
        (t_3 (- t_2 (* x (- (* t a) (* y z))))))
   (if (<= b -7e+221)
     t_3
     (if (<= b -1.25e+131)
       (+ t_1 t_2)
       (if (or (<= b -86000000000000.0) (not (<= b 2.55e-52)))
         t_3
         (+ t_1 (* x (- (* y z) (* t a)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = t_2 - (x * ((t * a) - (y * z)));
	double tmp;
	if (b <= -7e+221) {
		tmp = t_3;
	} else if (b <= -1.25e+131) {
		tmp = t_1 + t_2;
	} else if ((b <= -86000000000000.0) || !(b <= 2.55e-52)) {
		tmp = t_3;
	} else {
		tmp = t_1 + (x * ((y * z) - (t * a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = b * ((a * i) - (z * c))
    t_3 = t_2 - (x * ((t * a) - (y * z)))
    if (b <= (-7d+221)) then
        tmp = t_3
    else if (b <= (-1.25d+131)) then
        tmp = t_1 + t_2
    else if ((b <= (-86000000000000.0d0)) .or. (.not. (b <= 2.55d-52))) then
        tmp = t_3
    else
        tmp = t_1 + (x * ((y * z) - (t * a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = t_2 - (x * ((t * a) - (y * z)));
	double tmp;
	if (b <= -7e+221) {
		tmp = t_3;
	} else if (b <= -1.25e+131) {
		tmp = t_1 + t_2;
	} else if ((b <= -86000000000000.0) || !(b <= 2.55e-52)) {
		tmp = t_3;
	} else {
		tmp = t_1 + (x * ((y * z) - (t * a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = b * ((a * i) - (z * c))
	t_3 = t_2 - (x * ((t * a) - (y * z)))
	tmp = 0
	if b <= -7e+221:
		tmp = t_3
	elif b <= -1.25e+131:
		tmp = t_1 + t_2
	elif (b <= -86000000000000.0) or not (b <= 2.55e-52):
		tmp = t_3
	else:
		tmp = t_1 + (x * ((y * z) - (t * a)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_3 = Float64(t_2 - Float64(x * Float64(Float64(t * a) - Float64(y * z))))
	tmp = 0.0
	if (b <= -7e+221)
		tmp = t_3;
	elseif (b <= -1.25e+131)
		tmp = Float64(t_1 + t_2);
	elseif ((b <= -86000000000000.0) || !(b <= 2.55e-52))
		tmp = t_3;
	else
		tmp = Float64(t_1 + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = b * ((a * i) - (z * c));
	t_3 = t_2 - (x * ((t * a) - (y * z)));
	tmp = 0.0;
	if (b <= -7e+221)
		tmp = t_3;
	elseif (b <= -1.25e+131)
		tmp = t_1 + t_2;
	elseif ((b <= -86000000000000.0) || ~((b <= 2.55e-52)))
		tmp = t_3;
	else
		tmp = t_1 + (x * ((y * z) - (t * a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7e+221], t$95$3, If[LessEqual[b, -1.25e+131], N[(t$95$1 + t$95$2), $MachinePrecision], If[Or[LessEqual[b, -86000000000000.0], N[Not[LessEqual[b, 2.55e-52]], $MachinePrecision]], t$95$3, N[(t$95$1 + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.0000000000000003e221 or -1.24999999999999999e131 < b < -8.6e13 or 2.54999999999999995e-52 < b

   1. Initial program 74.8%

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

   3. Taylor expanded in j around 0 75.5%

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

      1. *-commutative 75.5%

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

   5. Simplified 75.5%

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

   if -7.0000000000000003e221 < b < -1.24999999999999999e131

   1. Initial program 80.9%

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

   3. Taylor expanded in x around 0 80.9%

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

   if -8.6e13 < b < 2.54999999999999995e-52

   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 b around 0 76.9%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+221}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;b \leq -1.25 \cdot 10^{+131}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -86000000000000 \lor \neg \left(b \leq 2.55 \cdot 10^{-52}\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 29.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;b \leq -6.5 \cdot 10^{+50}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{elif}\;b \leq -1.08 \cdot 10^{-35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{-106}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -3.7 \cdot 10^{-246}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{-162}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-94}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (* t c))) (t_2 (* x (* y z))))
   (if (<= b -6.5e+50)
     (* (* z b) (- c))
     (if (<= b -1.08e-35)
       t_1
       (if (<= b -1.45e-106)
         t_2
         (if (<= b -3.7e-246)
           t_1
           (if (<= b 7.5e-162)
             (* (* y i) (- j))
             (if (<= b 1.15e-94) t_2 (* b (* a 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 = j * (t * c);
	double t_2 = x * (y * z);
	double tmp;
	if (b <= -6.5e+50) {
		tmp = (z * b) * -c;
	} else if (b <= -1.08e-35) {
		tmp = t_1;
	} else if (b <= -1.45e-106) {
		tmp = t_2;
	} else if (b <= -3.7e-246) {
		tmp = t_1;
	} else if (b <= 7.5e-162) {
		tmp = (y * i) * -j;
	} else if (b <= 1.15e-94) {
		tmp = t_2;
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (t * c)
    t_2 = x * (y * z)
    if (b <= (-6.5d+50)) then
        tmp = (z * b) * -c
    else if (b <= (-1.08d-35)) then
        tmp = t_1
    else if (b <= (-1.45d-106)) then
        tmp = t_2
    else if (b <= (-3.7d-246)) then
        tmp = t_1
    else if (b <= 7.5d-162) then
        tmp = (y * i) * -j
    else if (b <= 1.15d-94) then
        tmp = t_2
    else
        tmp = b * (a * 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 = j * (t * c);
	double t_2 = x * (y * z);
	double tmp;
	if (b <= -6.5e+50) {
		tmp = (z * b) * -c;
	} else if (b <= -1.08e-35) {
		tmp = t_1;
	} else if (b <= -1.45e-106) {
		tmp = t_2;
	} else if (b <= -3.7e-246) {
		tmp = t_1;
	} else if (b <= 7.5e-162) {
		tmp = (y * i) * -j;
	} else if (b <= 1.15e-94) {
		tmp = t_2;
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * (t * c)
	t_2 = x * (y * z)
	tmp = 0
	if b <= -6.5e+50:
		tmp = (z * b) * -c
	elif b <= -1.08e-35:
		tmp = t_1
	elif b <= -1.45e-106:
		tmp = t_2
	elif b <= -3.7e-246:
		tmp = t_1
	elif b <= 7.5e-162:
		tmp = (y * i) * -j
	elif b <= 1.15e-94:
		tmp = t_2
	else:
		tmp = b * (a * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(t * c))
	t_2 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (b <= -6.5e+50)
		tmp = Float64(Float64(z * b) * Float64(-c));
	elseif (b <= -1.08e-35)
		tmp = t_1;
	elseif (b <= -1.45e-106)
		tmp = t_2;
	elseif (b <= -3.7e-246)
		tmp = t_1;
	elseif (b <= 7.5e-162)
		tmp = Float64(Float64(y * i) * Float64(-j));
	elseif (b <= 1.15e-94)
		tmp = t_2;
	else
		tmp = Float64(b * Float64(a * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * (t * c);
	t_2 = x * (y * z);
	tmp = 0.0;
	if (b <= -6.5e+50)
		tmp = (z * b) * -c;
	elseif (b <= -1.08e-35)
		tmp = t_1;
	elseif (b <= -1.45e-106)
		tmp = t_2;
	elseif (b <= -3.7e-246)
		tmp = t_1;
	elseif (b <= 7.5e-162)
		tmp = (y * i) * -j;
	elseif (b <= 1.15e-94)
		tmp = t_2;
	else
		tmp = b * (a * i);
	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]}, Block[{t$95$2 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.5e+50], N[(N[(z * b), $MachinePrecision] * (-c)), $MachinePrecision], If[LessEqual[b, -1.08e-35], t$95$1, If[LessEqual[b, -1.45e-106], t$95$2, If[LessEqual[b, -3.7e-246], t$95$1, If[LessEqual[b, 7.5e-162], N[(N[(y * i), $MachinePrecision] * (-j)), $MachinePrecision], If[LessEqual[b, 1.15e-94], t$95$2, N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -6.5000000000000003e50

   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 44.9%

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

      1. *-commutative 44.9%

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

   5. Simplified 44.9%

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

   6. Taylor expanded in t around 0 38.2%

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

      1. mul-1-neg 38.2%

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

      2. distribute-rgt-neg-out 38.2%

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

   8. Simplified 38.2%

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

   if -6.5000000000000003e50 < b < -1.08000000000000003e-35 or -1.45e-106 < b < -3.7e-246

   1. Initial program 76.6%

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

   3. Taylor expanded in x around 0 62.8%

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

   4. Taylor expanded in j around inf 59.4%

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

   5. Taylor expanded in c around inf 46.8%

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

      1. *-commutative 46.8%

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

   7. Simplified 46.8%

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

   if -1.08000000000000003e-35 < b < -1.45e-106 or 7.49999999999999972e-162 < b < 1.15e-94

   1. Initial program 77.6%

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

   3. Taylor expanded in z around inf 47.7%

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

   4. Taylor expanded in x around inf 52.6%

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

   if -3.7e-246 < b < 7.49999999999999972e-162

   1. Initial program 68.4%

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

   3. Taylor expanded in x around 0 62.3%

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

   4. Taylor expanded in j around inf 59.5%

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

   5. Taylor expanded in c around 0 43.3%

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

      1. mul-1-neg 43.3%

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

      2. distribute-rgt-neg-in 43.3%

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

      3. *-commutative 43.3%

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

   7. Simplified 43.3%

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

   if 1.15e-94 < b

   1. Initial program 77.5%

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

   3. Taylor expanded in x around 0 70.4%

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

   4. Taylor expanded in a around inf 38.9%

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

      1. *-commutative 38.9%

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

      2. associate-*l* 40.0%

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

      3. *-commutative 40.0%

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

   6. Simplified 40.0%

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

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.5 \cdot 10^{+50}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{elif}\;b \leq -1.08 \cdot 10^{-35}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{-106}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq -3.7 \cdot 10^{-246}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{-162}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-94}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 29.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -9 \cdot 10^{+107}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-223}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-303}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-255}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+105}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (* t c))) (t_2 (* x (* y z))))
   (if (<= z -9e+107)
     t_2
     (if (<= z -4.7e-223)
       t_1
       (if (<= z -1.7e-303)
         (* b (* a i))
         (if (<= z 3.3e-255) t_1 (if (<= z 5e+105) (* a (* b i)) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (t * c);
	double t_2 = x * (y * z);
	double tmp;
	if (z <= -9e+107) {
		tmp = t_2;
	} else if (z <= -4.7e-223) {
		tmp = t_1;
	} else if (z <= -1.7e-303) {
		tmp = b * (a * i);
	} else if (z <= 3.3e-255) {
		tmp = t_1;
	} else if (z <= 5e+105) {
		tmp = a * (b * i);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (t * c)
    t_2 = x * (y * z)
    if (z <= (-9d+107)) then
        tmp = t_2
    else if (z <= (-4.7d-223)) then
        tmp = t_1
    else if (z <= (-1.7d-303)) then
        tmp = b * (a * i)
    else if (z <= 3.3d-255) then
        tmp = t_1
    else if (z <= 5d+105) then
        tmp = a * (b * i)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (t * c);
	double t_2 = x * (y * z);
	double tmp;
	if (z <= -9e+107) {
		tmp = t_2;
	} else if (z <= -4.7e-223) {
		tmp = t_1;
	} else if (z <= -1.7e-303) {
		tmp = b * (a * i);
	} else if (z <= 3.3e-255) {
		tmp = t_1;
	} else if (z <= 5e+105) {
		tmp = a * (b * i);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * (t * c)
	t_2 = x * (y * z)
	tmp = 0
	if z <= -9e+107:
		tmp = t_2
	elif z <= -4.7e-223:
		tmp = t_1
	elif z <= -1.7e-303:
		tmp = b * (a * i)
	elif z <= 3.3e-255:
		tmp = t_1
	elif z <= 5e+105:
		tmp = a * (b * i)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(t * c))
	t_2 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (z <= -9e+107)
		tmp = t_2;
	elseif (z <= -4.7e-223)
		tmp = t_1;
	elseif (z <= -1.7e-303)
		tmp = Float64(b * Float64(a * i));
	elseif (z <= 3.3e-255)
		tmp = t_1;
	elseif (z <= 5e+105)
		tmp = Float64(a * Float64(b * i));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * (t * c);
	t_2 = x * (y * z);
	tmp = 0.0;
	if (z <= -9e+107)
		tmp = t_2;
	elseif (z <= -4.7e-223)
		tmp = t_1;
	elseif (z <= -1.7e-303)
		tmp = b * (a * i);
	elseif (z <= 3.3e-255)
		tmp = t_1;
	elseif (z <= 5e+105)
		tmp = a * (b * i);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9e+107], t$95$2, If[LessEqual[z, -4.7e-223], t$95$1, If[LessEqual[z, -1.7e-303], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.3e-255], t$95$1, If[LessEqual[z, 5e+105], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9e107 or 5.00000000000000046e105 < z

   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 z around inf 76.4%

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

   4. Taylor expanded in x around inf 54.5%

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

   if -9e107 < z < -4.70000000000000021e-223 or -1.7e-303 < z < 3.29999999999999988e-255

   1. Initial program 80.2%

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

   3. Taylor expanded in x around 0 65.0%

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

   4. Taylor expanded in j around inf 51.2%

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

   5. Taylor expanded in c around inf 30.6%

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

      1. *-commutative 30.6%

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

   7. Simplified 30.6%

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

   if -4.70000000000000021e-223 < z < -1.7e-303

   1. Initial program 90.7%

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

   3. Taylor expanded in x around 0 67.6%

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

   4. Taylor expanded in a around inf 35.5%

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

      1. *-commutative 35.5%

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

      2. associate-*l* 39.9%

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

      3. *-commutative 39.9%

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

   6. Simplified 39.9%

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

   if 3.29999999999999988e-255 < z < 5.00000000000000046e105

   1. Initial program 72.8%

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

   3. Taylor expanded in x around 0 65.0%

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

   4. Taylor expanded in a around inf 45.6%

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

4. Final simplification 42.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+107}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-223}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-303}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-255}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+105}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 68.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z\right) + t\_1\\ \mathbf{if}\;b \leq -8.4 \cdot 10^{+49}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-32}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+122}:\\ \;\;\;\;t\_1 - i \cdot \left(y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))) (t_2 (+ (* x (* y z)) t_1)))
   (if (<= b -8.4e+49)
     t_2
     (if (<= b 3.4e-32)
       (+ (* j (- (* t c) (* y i))) (* x (- (* y z) (* t a))))
       (if (<= b 4e+122) (- t_1 (* 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 = b * ((a * i) - (z * c));
	double t_2 = (x * (y * z)) + t_1;
	double tmp;
	if (b <= -8.4e+49) {
		tmp = t_2;
	} else if (b <= 3.4e-32) {
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else if (b <= 4e+122) {
		tmp = t_1 - (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 = b * ((a * i) - (z * c))
    t_2 = (x * (y * z)) + t_1
    if (b <= (-8.4d+49)) then
        tmp = t_2
    else if (b <= 3.4d-32) then
        tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)))
    else if (b <= 4d+122) then
        tmp = t_1 - (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 = b * ((a * i) - (z * c));
	double t_2 = (x * (y * z)) + t_1;
	double tmp;
	if (b <= -8.4e+49) {
		tmp = t_2;
	} else if (b <= 3.4e-32) {
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else if (b <= 4e+122) {
		tmp = t_1 - (i * (y * j));
	} 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))
	t_2 = (x * (y * z)) + t_1
	tmp = 0
	if b <= -8.4e+49:
		tmp = t_2
	elif b <= 3.4e-32:
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)))
	elif b <= 4e+122:
		tmp = t_1 - (i * (y * j))
	else:
		tmp = t_2
	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(Float64(x * Float64(y * z)) + t_1)
	tmp = 0.0
	if (b <= -8.4e+49)
		tmp = t_2;
	elseif (b <= 3.4e-32)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	elseif (b <= 4e+122)
		tmp = Float64(t_1 - Float64(i * Float64(y * 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 = b * ((a * i) - (z * c));
	t_2 = (x * (y * z)) + t_1;
	tmp = 0.0;
	if (b <= -8.4e+49)
		tmp = t_2;
	elseif (b <= 3.4e-32)
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	elseif (b <= 4e+122)
		tmp = t_1 - (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[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[b, -8.4e+49], t$95$2, If[LessEqual[b, 3.4e-32], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4e+122], N[(t$95$1 - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.40000000000000043e49 or 4.00000000000000006e122 < b

   1. Initial program 77.8%

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

   3. Taylor expanded in j around 0 80.3%

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

      1. *-commutative 80.3%

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

   5. Simplified 80.3%

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

   6. Taylor expanded in t around 0 76.2%

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

      1. *-commutative 76.2%

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

   8. Simplified 76.2%

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

   if -8.40000000000000043e49 < b < 3.39999999999999978e-32

   1. Initial program 77.3%

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

   3. Taylor expanded in b around 0 74.7%

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

   if 3.39999999999999978e-32 < b < 4.00000000000000006e122

   1. Initial program 68.1%

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

   3. Taylor expanded in x around 0 63.7%

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

   4. Taylor expanded in c around 0 59.7%

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

      1. associate-*r* 59.7%

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

      2. neg-mul-1 59.7%

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

      3. *-commutative 59.7%

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

   6. Simplified 59.7%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.4 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-32}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+122}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 44.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -1 \cdot 10^{+103}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -4.4 \cdot 10^{-126}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{-248}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))) (t_2 (* c (- (* t j) (* z b)))))
   (if (<= c -1e+103)
     t_2
     (if (<= c -4.4e-126)
       t_1
       (if (<= c 1.1e-248) (* i (* y (- j))) (if (<= c 1.3e+62) 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));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -1e+103) {
		tmp = t_2;
	} else if (c <= -4.4e-126) {
		tmp = t_1;
	} else if (c <= 1.1e-248) {
		tmp = i * (y * -j);
	} else if (c <= 1.3e+62) {
		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))
    t_2 = c * ((t * j) - (z * b))
    if (c <= (-1d+103)) then
        tmp = t_2
    else if (c <= (-4.4d-126)) then
        tmp = t_1
    else if (c <= 1.1d-248) then
        tmp = i * (y * -j)
    else if (c <= 1.3d+62) 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));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -1e+103) {
		tmp = t_2;
	} else if (c <= -4.4e-126) {
		tmp = t_1;
	} else if (c <= 1.1e-248) {
		tmp = i * (y * -j);
	} else if (c <= 1.3e+62) {
		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))
	t_2 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -1e+103:
		tmp = t_2
	elif c <= -4.4e-126:
		tmp = t_1
	elif c <= 1.1e-248:
		tmp = i * (y * -j)
	elif c <= 1.3e+62:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -1e+103)
		tmp = t_2;
	elseif (c <= -4.4e-126)
		tmp = t_1;
	elseif (c <= 1.1e-248)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (c <= 1.3e+62)
		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));
	t_2 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -1e+103)
		tmp = t_2;
	elseif (c <= -4.4e-126)
		tmp = t_1;
	elseif (c <= 1.1e-248)
		tmp = i * (y * -j);
	elseif (c <= 1.3e+62)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1e+103], t$95$2, If[LessEqual[c, -4.4e-126], t$95$1, If[LessEqual[c, 1.1e-248], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.3e+62], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1e103 or 1.29999999999999992e62 < c

   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 c around inf 66.6%

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

      1. *-commutative 66.6%

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

   5. Simplified 66.6%

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

   if -1e103 < c < -4.40000000000000029e-126 or 1.1e-248 < c < 1.29999999999999992e62

   1. Initial program 82.7%

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

   3. Taylor expanded in b around inf 46.8%

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

   if -4.40000000000000029e-126 < c < 1.1e-248

   1. Initial program 85.2%

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

   3. Taylor expanded in x around 0 48.9%

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

   4. Taylor expanded in y around inf 36.6%

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

      1. mul-1-neg 36.6%

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

      2. *-commutative 36.6%

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

      3. distribute-rgt-neg-in 36.6%

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

   6. Simplified 36.6%

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

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1 \cdot 10^{+103}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -4.4 \cdot 10^{-126}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{-248}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{+62}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 52.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -9.2 \cdot 10^{+50}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{-153}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-117}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 9.1 \cdot 10^{-51}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))) (t_2 (* b (- (* a i) (* z c)))))
   (if (<= b -9.2e+50)
     t_2
     (if (<= b 8.2e-153)
       t_1
       (if (<= b 6e-117) (* x (* y z)) (if (<= b 9.1e-51) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -9.2e+50) {
		tmp = t_2;
	} else if (b <= 8.2e-153) {
		tmp = t_1;
	} else if (b <= 6e-117) {
		tmp = x * (y * z);
	} else if (b <= 9.1e-51) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = b * ((a * i) - (z * c))
    if (b <= (-9.2d+50)) then
        tmp = t_2
    else if (b <= 8.2d-153) then
        tmp = t_1
    else if (b <= 6d-117) then
        tmp = x * (y * z)
    else if (b <= 9.1d-51) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -9.2e+50) {
		tmp = t_2;
	} else if (b <= 8.2e-153) {
		tmp = t_1;
	} else if (b <= 6e-117) {
		tmp = x * (y * z);
	} else if (b <= 9.1e-51) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -9.2e+50:
		tmp = t_2
	elif b <= 8.2e-153:
		tmp = t_1
	elif b <= 6e-117:
		tmp = x * (y * z)
	elif b <= 9.1e-51:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -9.2e+50)
		tmp = t_2;
	elseif (b <= 8.2e-153)
		tmp = t_1;
	elseif (b <= 6e-117)
		tmp = Float64(x * Float64(y * z));
	elseif (b <= 9.1e-51)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -9.2e+50)
		tmp = t_2;
	elseif (b <= 8.2e-153)
		tmp = t_1;
	elseif (b <= 6e-117)
		tmp = x * (y * z);
	elseif (b <= 9.1e-51)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9.2e+50], t$95$2, If[LessEqual[b, 8.2e-153], t$95$1, If[LessEqual[b, 6e-117], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.1e-51], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.19999999999999987e50 or 9.09999999999999977e-51 < b

   1. Initial program 76.0%

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

   3. Taylor expanded in b around inf 62.7%

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

   if -9.19999999999999987e50 < b < 8.2e-153 or 5.99999999999999982e-117 < b < 9.09999999999999977e-51

   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 60.2%

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

   4. Taylor expanded in j around inf 55.7%

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

   if 8.2e-153 < b < 5.99999999999999982e-117

   1. Initial program 72.6%

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

   3. Taylor expanded in z around inf 56.0%

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

   4. Taylor expanded in x around inf 72.3%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.2 \cdot 10^{+50}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{-153}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-117}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 9.1 \cdot 10^{-51}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 28.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{+116}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-254}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+97}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+158}:\\ \;\;\;\;z \cdot \left(-b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))))
   (if (<= z -2.5e+116)
     t_1
     (if (<= z 1.4e-254)
       (* j (* t c))
       (if (<= z 1.45e+97)
         (* a (* b i))
         (if (<= z 1.25e+158) (* z (- (* b c))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double tmp;
	if (z <= -2.5e+116) {
		tmp = t_1;
	} else if (z <= 1.4e-254) {
		tmp = j * (t * c);
	} else if (z <= 1.45e+97) {
		tmp = a * (b * i);
	} else if (z <= 1.25e+158) {
		tmp = z * -(b * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y * z)
    if (z <= (-2.5d+116)) then
        tmp = t_1
    else if (z <= 1.4d-254) then
        tmp = j * (t * c)
    else if (z <= 1.45d+97) then
        tmp = a * (b * i)
    else if (z <= 1.25d+158) then
        tmp = z * -(b * c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double tmp;
	if (z <= -2.5e+116) {
		tmp = t_1;
	} else if (z <= 1.4e-254) {
		tmp = j * (t * c);
	} else if (z <= 1.45e+97) {
		tmp = a * (b * i);
	} else if (z <= 1.25e+158) {
		tmp = z * -(b * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	tmp = 0
	if z <= -2.5e+116:
		tmp = t_1
	elif z <= 1.4e-254:
		tmp = j * (t * c)
	elif z <= 1.45e+97:
		tmp = a * (b * i)
	elif z <= 1.25e+158:
		tmp = z * -(b * c)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (z <= -2.5e+116)
		tmp = t_1;
	elseif (z <= 1.4e-254)
		tmp = Float64(j * Float64(t * c));
	elseif (z <= 1.45e+97)
		tmp = Float64(a * Float64(b * i));
	elseif (z <= 1.25e+158)
		tmp = Float64(z * Float64(-Float64(b * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (y * z);
	tmp = 0.0;
	if (z <= -2.5e+116)
		tmp = t_1;
	elseif (z <= 1.4e-254)
		tmp = j * (t * c);
	elseif (z <= 1.45e+97)
		tmp = a * (b * i);
	elseif (z <= 1.25e+158)
		tmp = z * -(b * c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.5e+116], t$95$1, If[LessEqual[z, 1.4e-254], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e+97], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e+158], N[(z * (-N[(b * c), $MachinePrecision])), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.50000000000000013e116 or 1.2499999999999999e158 < z

   1. Initial program 71.9%

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

   3. Taylor expanded in z around inf 79.5%

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

   4. Taylor expanded in x around inf 62.1%

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

   if -2.50000000000000013e116 < z < 1.39999999999999992e-254

   1. Initial program 82.2%

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

   3. Taylor expanded in x around 0 65.5%

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

   4. Taylor expanded in j around inf 47.5%

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

   5. Taylor expanded in c around inf 27.1%

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

      1. *-commutative 27.1%

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

   7. Simplified 27.1%

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

   if 1.39999999999999992e-254 < z < 1.44999999999999994e97

   1. Initial program 72.1%

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

   3. Taylor expanded in x around 0 64.1%

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

   4. Taylor expanded in a around inf 46.8%

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

   if 1.44999999999999994e97 < z < 1.2499999999999999e158

   1. Initial program 64.5%

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

   3. Taylor expanded in z around inf 53.8%

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

   4. Taylor expanded in x around 0 46.7%

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

      1. neg-mul-1 46.7%

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

      2. distribute-rgt-neg-in 46.7%

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

   6. Simplified 46.7%

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

4. Final simplification 41.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+116}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-254}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+97}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+158}:\\ \;\;\;\;z \cdot \left(-b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 30.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{+64}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{-51}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -4.2e+64)
   (* a (* b i))
   (if (<= b 2.15e-51) (* c (* t j)) (* b (* a 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 (b <= -4.2e+64) {
		tmp = a * (b * i);
	} else if (b <= 2.15e-51) {
		tmp = c * (t * j);
	} else {
		tmp = b * (a * 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 (b <= (-4.2d+64)) then
        tmp = a * (b * i)
    else if (b <= 2.15d-51) then
        tmp = c * (t * j)
    else
        tmp = b * (a * 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 (b <= -4.2e+64) {
		tmp = a * (b * i);
	} else if (b <= 2.15e-51) {
		tmp = c * (t * j);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -4.2e+64:
		tmp = a * (b * i)
	elif b <= 2.15e-51:
		tmp = c * (t * j)
	else:
		tmp = b * (a * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -4.2e+64)
		tmp = Float64(a * Float64(b * i));
	elseif (b <= 2.15e-51)
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(b * Float64(a * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -4.2e+64)
		tmp = a * (b * i);
	elseif (b <= 2.15e-51)
		tmp = c * (t * j);
	else
		tmp = b * (a * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -4.2e+64], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.15e-51], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.2000000000000001e64

   1. Initial program 77.6%

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

   3. Taylor expanded in x around 0 62.5%

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

   4. Taylor expanded in a around inf 35.1%

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

   if -4.2000000000000001e64 < b < 2.1499999999999999e-51

   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 55.8%

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

   4. Taylor expanded in t around inf 30.4%

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

   if 2.1499999999999999e-51 < b

   1. Initial program 75.4%

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

   3. Taylor expanded in x around 0 67.6%

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

   4. Taylor expanded in a around inf 41.2%

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

      1. *-commutative 41.2%

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

      2. associate-*l* 42.4%

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

      3. *-commutative 42.4%

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

   6. Simplified 42.4%

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

4. Final simplification 34.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{+64}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{-51}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 29.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.6 \cdot 10^{+50}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq 9.1 \cdot 10^{-51}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -2.6e+50)
   (* a (* b i))
   (if (<= b 9.1e-51) (* j (* t c)) (* b (* a 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 (b <= -2.6e+50) {
		tmp = a * (b * i);
	} else if (b <= 9.1e-51) {
		tmp = j * (t * c);
	} else {
		tmp = b * (a * 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 (b <= (-2.6d+50)) then
        tmp = a * (b * i)
    else if (b <= 9.1d-51) then
        tmp = j * (t * c)
    else
        tmp = b * (a * 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 (b <= -2.6e+50) {
		tmp = a * (b * i);
	} else if (b <= 9.1e-51) {
		tmp = j * (t * c);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -2.6e+50:
		tmp = a * (b * i)
	elif b <= 9.1e-51:
		tmp = j * (t * c)
	else:
		tmp = b * (a * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -2.6e+50)
		tmp = Float64(a * Float64(b * i));
	elseif (b <= 9.1e-51)
		tmp = Float64(j * Float64(t * c));
	else
		tmp = Float64(b * Float64(a * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -2.6e+50)
		tmp = a * (b * i);
	elseif (b <= 9.1e-51)
		tmp = j * (t * c);
	else
		tmp = b * (a * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -2.6e+50], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.1e-51], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.6000000000000002e50

   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 x around 0 62.1%

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

   4. Taylor expanded in a around inf 34.0%

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

   if -2.6000000000000002e50 < b < 9.09999999999999977e-51

   1. Initial program 76.1%

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

   3. Taylor expanded in x around 0 55.9%

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

   4. Taylor expanded in j around inf 52.5%

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

   5. Taylor expanded in c around inf 30.9%

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

      1. *-commutative 30.9%

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

   7. Simplified 30.9%

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

   if 9.09999999999999977e-51 < b

   1. Initial program 75.4%

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

   3. Taylor expanded in x around 0 67.6%

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

   4. Taylor expanded in a around inf 41.2%

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

      1. *-commutative 41.2%

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

      2. associate-*l* 42.4%

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

      3. *-commutative 42.4%

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

   6. Simplified 42.4%

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

4. Final simplification 34.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.6 \cdot 10^{+50}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq 9.1 \cdot 10^{-51}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 22.5% 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 76.0%

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

3. Taylor expanded in x around 0 60.6%

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

4. Taylor expanded in a around inf 24.8%

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

5. Final simplification 24.8%

   \[\leadsto a \cdot \left(b \cdot i\right) \]
6. Add Preprocessing

Developer target: 69.6% 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 2024031 
(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)))))