Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 72.9% → 82.5%

Time: 32.5s

Alternatives: 22

Speedup: 0.5×

• 57.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

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: 72.9% 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: 82.5% accurate, 0.1× speedup

Math

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

FPCore

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 91.6%

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

      1. +-commutative 91.6%

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

      2. fma-define 91.6%

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

      3. *-commutative 91.6%

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

      4. *-commutative 91.6%

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

      5. cancel-sign-sub-inv 91.6%

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

      6. cancel-sign-sub 91.6%

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

      7. sub-neg 91.6%

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

      8. sub-neg 91.6%

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

      9. *-commutative 91.6%

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

      10. fma-neg 91.6%

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

      11. *-commutative 91.6%

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

      12. distribute-rgt-neg-out 91.6%

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

      13. remove-double-neg 91.6%

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

      14. *-commutative 91.6%

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

      15. *-commutative 91.6%

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

   3. Simplified 91.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   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 y around inf 48.4%

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

      1. +-commutative 48.4%

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

      2. mul-1-neg 48.4%

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

      3. unsub-neg 48.4%

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

      4. *-commutative 48.4%

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

   5. Simplified 48.4%

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

   6. Taylor expanded in z around inf 53.2%

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

      1. mul-1-neg 53.2%

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

      2. unsub-neg 53.2%

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

      3. associate-/l* 54.4%

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

   8. Simplified 54.4%

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

4. Final simplification 83.0%

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

Alternative 2: 82.5% accurate, 0.5× speedup

Math

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

FPCore

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

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((t * c) - (y * i))) - ((b * ((z * c) - (a * i))) + (x * ((t * a) - (y * z))))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = y * (z * (x - (i * (j / z))))
	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(z * c) - Float64(a * i))) + Float64(x * Float64(Float64(t * a) - Float64(y * z)))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(z * Float64(x - Float64(i * Float64(j / z)))));
	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) - (a * i))) + (x * ((t * a) - (y * z))));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = y * (z * (x - (i * (j / z))));
	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[(z * c), $MachinePrecision] - N[(a * i), $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[(y * N[(z * N[(x - N[(i * N[(j / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 91.6%

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

   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 y around inf 48.4%

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

      1. +-commutative 48.4%

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

      2. mul-1-neg 48.4%

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

      3. unsub-neg 48.4%

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

      4. *-commutative 48.4%

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

   5. Simplified 48.4%

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

   6. Taylor expanded in z around inf 53.2%

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

      1. mul-1-neg 53.2%

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

      2. unsub-neg 53.2%

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

      3. associate-/l* 54.4%

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

   8. Simplified 54.4%

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

4. Final simplification 83.0%

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

Alternative 3: 48.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_3 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_4 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;b \leq -2.8 \cdot 10^{-52}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-175}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -5.4 \cdot 10^{-208}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-240}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-275}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-292}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.75 \cdot 10^{-32}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 10^{+109} \lor \neg \left(b \leq 1.6 \cdot 10^{+162}\right):\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* x y)))
        (t_2 (* j (- (* t c) (* y i))))
        (t_3 (* b (- (* a i) (* z c))))
        (t_4 (* t (- (* c j) (* x a)))))
   (if (<= b -2.8e-52)
     t_3
     (if (<= b -8e-175)
       t_1
       (if (<= b -5.4e-208)
         t_2
         (if (<= b -2.3e-240)
           (* y (* x z))
           (if (<= b -2.4e-275)
             t_4
             (if (<= b 3.2e-292)
               t_1
               (if (<= b 3.75e-32)
                 t_2
                 (if (or (<= b 1e+109) (not (<= b 1.6e+162))) 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 = z * (x * y);
	double t_2 = j * ((t * c) - (y * i));
	double t_3 = b * ((a * i) - (z * c));
	double t_4 = t * ((c * j) - (x * a));
	double tmp;
	if (b <= -2.8e-52) {
		tmp = t_3;
	} else if (b <= -8e-175) {
		tmp = t_1;
	} else if (b <= -5.4e-208) {
		tmp = t_2;
	} else if (b <= -2.3e-240) {
		tmp = y * (x * z);
	} else if (b <= -2.4e-275) {
		tmp = t_4;
	} else if (b <= 3.2e-292) {
		tmp = t_1;
	} else if (b <= 3.75e-32) {
		tmp = t_2;
	} else if ((b <= 1e+109) || !(b <= 1.6e+162)) {
		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 = z * (x * y)
    t_2 = j * ((t * c) - (y * i))
    t_3 = b * ((a * i) - (z * c))
    t_4 = t * ((c * j) - (x * a))
    if (b <= (-2.8d-52)) then
        tmp = t_3
    else if (b <= (-8d-175)) then
        tmp = t_1
    else if (b <= (-5.4d-208)) then
        tmp = t_2
    else if (b <= (-2.3d-240)) then
        tmp = y * (x * z)
    else if (b <= (-2.4d-275)) then
        tmp = t_4
    else if (b <= 3.2d-292) then
        tmp = t_1
    else if (b <= 3.75d-32) then
        tmp = t_2
    else if ((b <= 1d+109) .or. (.not. (b <= 1.6d+162))) 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 = z * (x * y);
	double t_2 = j * ((t * c) - (y * i));
	double t_3 = b * ((a * i) - (z * c));
	double t_4 = t * ((c * j) - (x * a));
	double tmp;
	if (b <= -2.8e-52) {
		tmp = t_3;
	} else if (b <= -8e-175) {
		tmp = t_1;
	} else if (b <= -5.4e-208) {
		tmp = t_2;
	} else if (b <= -2.3e-240) {
		tmp = y * (x * z);
	} else if (b <= -2.4e-275) {
		tmp = t_4;
	} else if (b <= 3.2e-292) {
		tmp = t_1;
	} else if (b <= 3.75e-32) {
		tmp = t_2;
	} else if ((b <= 1e+109) || !(b <= 1.6e+162)) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (x * y)
	t_2 = j * ((t * c) - (y * i))
	t_3 = b * ((a * i) - (z * c))
	t_4 = t * ((c * j) - (x * a))
	tmp = 0
	if b <= -2.8e-52:
		tmp = t_3
	elif b <= -8e-175:
		tmp = t_1
	elif b <= -5.4e-208:
		tmp = t_2
	elif b <= -2.3e-240:
		tmp = y * (x * z)
	elif b <= -2.4e-275:
		tmp = t_4
	elif b <= 3.2e-292:
		tmp = t_1
	elif b <= 3.75e-32:
		tmp = t_2
	elif (b <= 1e+109) or not (b <= 1.6e+162):
		tmp = t_3
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(x * y))
	t_2 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_3 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_4 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (b <= -2.8e-52)
		tmp = t_3;
	elseif (b <= -8e-175)
		tmp = t_1;
	elseif (b <= -5.4e-208)
		tmp = t_2;
	elseif (b <= -2.3e-240)
		tmp = Float64(y * Float64(x * z));
	elseif (b <= -2.4e-275)
		tmp = t_4;
	elseif (b <= 3.2e-292)
		tmp = t_1;
	elseif (b <= 3.75e-32)
		tmp = t_2;
	elseif ((b <= 1e+109) || !(b <= 1.6e+162))
		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 = z * (x * y);
	t_2 = j * ((t * c) - (y * i));
	t_3 = b * ((a * i) - (z * c));
	t_4 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (b <= -2.8e-52)
		tmp = t_3;
	elseif (b <= -8e-175)
		tmp = t_1;
	elseif (b <= -5.4e-208)
		tmp = t_2;
	elseif (b <= -2.3e-240)
		tmp = y * (x * z);
	elseif (b <= -2.4e-275)
		tmp = t_4;
	elseif (b <= 3.2e-292)
		tmp = t_1;
	elseif (b <= 3.75e-32)
		tmp = t_2;
	elseif ((b <= 1e+109) || ~((b <= 1.6e+162)))
		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[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.8e-52], t$95$3, If[LessEqual[b, -8e-175], t$95$1, If[LessEqual[b, -5.4e-208], t$95$2, If[LessEqual[b, -2.3e-240], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.4e-275], t$95$4, If[LessEqual[b, 3.2e-292], t$95$1, If[LessEqual[b, 3.75e-32], t$95$2, If[Or[LessEqual[b, 1e+109], N[Not[LessEqual[b, 1.6e+162]], $MachinePrecision]], t$95$3, t$95$4]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -2.79999999999999995e-52 or 3.74999999999999977e-32 < b < 9.99999999999999982e108 or 1.6000000000000001e162 < b

   1. Initial program 66.6%

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

   3. Taylor expanded in b around inf 60.5%

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

      1. *-commutative 60.5%

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

   5. Simplified 60.5%

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

   if -2.79999999999999995e-52 < b < -8e-175 or -2.39999999999999991e-275 < b < 3.2000000000000002e-292

   1. Initial program 82.4%

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

   3. Taylor expanded in t around 0 68.0%

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

      1. *-commutative 68.0%

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

      2. associate-*r* 63.2%

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

      3. associate-*r* 63.2%

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

      4. associate-*r* 63.2%

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

      5. distribute-rgt-in 63.2%

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

      6. +-commutative 63.2%

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

      7. mul-1-neg 63.2%

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

      8. unsub-neg 63.2%

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

      9. *-commutative 63.2%

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

      10. *-commutative 63.2%

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

   5. Simplified 63.2%

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

   6. Taylor expanded in x around inf 54.6%

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

      1. associate-*r* 54.7%

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

      2. *-commutative 54.7%

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

   8. Simplified 54.7%

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

   if -8e-175 < b < -5.4e-208 or 3.2000000000000002e-292 < b < 3.74999999999999977e-32

   1. Initial program 67.1%

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

   3. Taylor expanded in j around inf 62.0%

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

      1. sub-neg 62.0%

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

      2. *-commutative 62.0%

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

      3. *-commutative 62.0%

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

      4. sub-neg 62.0%

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

   5. Simplified 62.0%

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

   if -5.4e-208 < b < -2.29999999999999993e-240

   1. Initial program 63.8%

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

   3. Taylor expanded in y around inf 70.1%

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

      1. +-commutative 70.1%

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

      2. mul-1-neg 70.1%

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

      3. unsub-neg 70.1%

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

      4. *-commutative 70.1%

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

   5. Simplified 70.1%

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

   6. Taylor expanded in x around inf 60.9%

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

   if -2.29999999999999993e-240 < b < -2.39999999999999991e-275 or 9.99999999999999982e108 < b < 1.6000000000000001e162

   1. Initial program 88.3%

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

   3. Taylor expanded in t around inf 71.4%

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

      1. +-commutative 71.4%

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

      2. mul-1-neg 71.4%

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

      3. unsub-neg 71.4%

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

      4. *-commutative 71.4%

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

      5. *-commutative 71.4%

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

   5. Simplified 71.4%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.8 \cdot 10^{-52}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-175}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq -5.4 \cdot 10^{-208}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-240}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-275}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-292}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 3.75 \cdot 10^{-32}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 10^{+109} \lor \neg \left(b \leq 1.6 \cdot 10^{+162}\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 53.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_2 := x \cdot \left(y \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;y \leq -3 \cdot 10^{+54}:\\ \;\;\;\;y \cdot \left(z \cdot \left(x - i \cdot \frac{j}{z}\right)\right)\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-168}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-225}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-208}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-7}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+81}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+167}:\\ \;\;\;\;a \cdot \left(i \cdot \left(b - \frac{y \cdot j}{a}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b))))
        (t_2 (+ (* x (* y z)) (* b (- (* a i) (* z c)))))
        (t_3 (* a (- (* b i) (* x t)))))
   (if (<= y -3e+54)
     (* y (* z (- x (* i (/ j z)))))
     (if (<= y -3.9e-168)
       t_2
       (if (<= y -4.2e-225)
         t_1
         (if (<= y 5.5e-208)
           t_3
           (if (<= y 6.2e-92)
             t_1
             (if (<= y 1.7e-7)
               t_3
               (if (<= y 1.85e+81)
                 t_2
                 (if (<= y 7.8e+167)
                   (* a (* i (- b (/ (* y j) a))))
                   (* y (- (* x z) (* i j)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double t_2 = (x * (y * z)) + (b * ((a * i) - (z * c)));
	double t_3 = a * ((b * i) - (x * t));
	double tmp;
	if (y <= -3e+54) {
		tmp = y * (z * (x - (i * (j / z))));
	} else if (y <= -3.9e-168) {
		tmp = t_2;
	} else if (y <= -4.2e-225) {
		tmp = t_1;
	} else if (y <= 5.5e-208) {
		tmp = t_3;
	} else if (y <= 6.2e-92) {
		tmp = t_1;
	} else if (y <= 1.7e-7) {
		tmp = t_3;
	} else if (y <= 1.85e+81) {
		tmp = t_2;
	} else if (y <= 7.8e+167) {
		tmp = a * (i * (b - ((y * j) / a)));
	} else {
		tmp = y * ((x * z) - (i * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = c * ((t * j) - (z * b))
    t_2 = (x * (y * z)) + (b * ((a * i) - (z * c)))
    t_3 = a * ((b * i) - (x * t))
    if (y <= (-3d+54)) then
        tmp = y * (z * (x - (i * (j / z))))
    else if (y <= (-3.9d-168)) then
        tmp = t_2
    else if (y <= (-4.2d-225)) then
        tmp = t_1
    else if (y <= 5.5d-208) then
        tmp = t_3
    else if (y <= 6.2d-92) then
        tmp = t_1
    else if (y <= 1.7d-7) then
        tmp = t_3
    else if (y <= 1.85d+81) then
        tmp = t_2
    else if (y <= 7.8d+167) then
        tmp = a * (i * (b - ((y * j) / a)))
    else
        tmp = y * ((x * z) - (i * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double t_2 = (x * (y * z)) + (b * ((a * i) - (z * c)));
	double t_3 = a * ((b * i) - (x * t));
	double tmp;
	if (y <= -3e+54) {
		tmp = y * (z * (x - (i * (j / z))));
	} else if (y <= -3.9e-168) {
		tmp = t_2;
	} else if (y <= -4.2e-225) {
		tmp = t_1;
	} else if (y <= 5.5e-208) {
		tmp = t_3;
	} else if (y <= 6.2e-92) {
		tmp = t_1;
	} else if (y <= 1.7e-7) {
		tmp = t_3;
	} else if (y <= 1.85e+81) {
		tmp = t_2;
	} else if (y <= 7.8e+167) {
		tmp = a * (i * (b - ((y * j) / a)));
	} else {
		tmp = y * ((x * z) - (i * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	t_2 = (x * (y * z)) + (b * ((a * i) - (z * c)))
	t_3 = a * ((b * i) - (x * t))
	tmp = 0
	if y <= -3e+54:
		tmp = y * (z * (x - (i * (j / z))))
	elif y <= -3.9e-168:
		tmp = t_2
	elif y <= -4.2e-225:
		tmp = t_1
	elif y <= 5.5e-208:
		tmp = t_3
	elif y <= 6.2e-92:
		tmp = t_1
	elif y <= 1.7e-7:
		tmp = t_3
	elif y <= 1.85e+81:
		tmp = t_2
	elif y <= 7.8e+167:
		tmp = a * (i * (b - ((y * j) / a)))
	else:
		tmp = y * ((x * z) - (i * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	t_2 = Float64(Float64(x * Float64(y * z)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))))
	t_3 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (y <= -3e+54)
		tmp = Float64(y * Float64(z * Float64(x - Float64(i * Float64(j / z)))));
	elseif (y <= -3.9e-168)
		tmp = t_2;
	elseif (y <= -4.2e-225)
		tmp = t_1;
	elseif (y <= 5.5e-208)
		tmp = t_3;
	elseif (y <= 6.2e-92)
		tmp = t_1;
	elseif (y <= 1.7e-7)
		tmp = t_3;
	elseif (y <= 1.85e+81)
		tmp = t_2;
	elseif (y <= 7.8e+167)
		tmp = Float64(a * Float64(i * Float64(b - Float64(Float64(y * j) / a))));
	else
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((t * j) - (z * b));
	t_2 = (x * (y * z)) + (b * ((a * i) - (z * c)));
	t_3 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (y <= -3e+54)
		tmp = y * (z * (x - (i * (j / z))));
	elseif (y <= -3.9e-168)
		tmp = t_2;
	elseif (y <= -4.2e-225)
		tmp = t_1;
	elseif (y <= 5.5e-208)
		tmp = t_3;
	elseif (y <= 6.2e-92)
		tmp = t_1;
	elseif (y <= 1.7e-7)
		tmp = t_3;
	elseif (y <= 1.85e+81)
		tmp = t_2;
	elseif (y <= 7.8e+167)
		tmp = a * (i * (b - ((y * j) / a)));
	else
		tmp = y * ((x * z) - (i * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3e+54], N[(y * N[(z * N[(x - N[(i * N[(j / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.9e-168], t$95$2, If[LessEqual[y, -4.2e-225], t$95$1, If[LessEqual[y, 5.5e-208], t$95$3, If[LessEqual[y, 6.2e-92], t$95$1, If[LessEqual[y, 1.7e-7], t$95$3, If[LessEqual[y, 1.85e+81], t$95$2, If[LessEqual[y, 7.8e+167], N[(a * N[(i * N[(b - N[(N[(y * j), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -2.9999999999999999e54

   1. Initial program 68.0%

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

   3. Taylor expanded in y around inf 70.5%

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

      1. +-commutative 70.5%

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

      2. mul-1-neg 70.5%

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

      3. unsub-neg 70.5%

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

      4. *-commutative 70.5%

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

   5. Simplified 70.5%

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

   6. Taylor expanded in z around inf 70.5%

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

      1. mul-1-neg 70.5%

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

      2. unsub-neg 70.5%

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

      3. associate-/l* 72.5%

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

   8. Simplified 72.5%

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

   if -2.9999999999999999e54 < y < -3.90000000000000012e-168 or 1.69999999999999987e-7 < y < 1.85e81

   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 j around 0 67.9%

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

      1. *-commutative 67.9%

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

   5. Simplified 67.9%

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

   6. Taylor expanded in y around inf 63.4%

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

   if -3.90000000000000012e-168 < y < -4.20000000000000001e-225 or 5.4999999999999997e-208 < y < 6.2000000000000002e-92

   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 63.0%

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

      1. *-commutative 63.0%

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

      2. *-commutative 63.0%

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

   5. Simplified 63.0%

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

   if -4.20000000000000001e-225 < y < 5.4999999999999997e-208 or 6.2000000000000002e-92 < y < 1.69999999999999987e-7

   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 a around inf 70.1%

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

      1. distribute-lft-out-- 70.1%

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

      2. *-commutative 70.1%

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

      3. *-commutative 70.1%

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

   5. Simplified 70.1%

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

   if 1.85e81 < y < 7.7999999999999996e167

   1. Initial program 60.6%

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

   3. Taylor expanded in a around -inf 61.7%

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

   4. Taylor expanded in i around inf 65.0%

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

   if 7.7999999999999996e167 < y

   1. Initial program 58.5%

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

   3. Taylor expanded in y around inf 88.0%

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

      1. +-commutative 88.0%

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

      2. mul-1-neg 88.0%

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

      3. unsub-neg 88.0%

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

      4. *-commutative 88.0%

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

   5. Simplified 88.0%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+54}:\\ \;\;\;\;y \cdot \left(z \cdot \left(x - i \cdot \frac{j}{z}\right)\right)\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-168}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-225}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-208}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-92}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-7}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+81}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+167}:\\ \;\;\;\;a \cdot \left(i \cdot \left(b - \frac{y \cdot j}{a}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 53.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_3 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;y \leq -2.55 \cdot 10^{+54}:\\ \;\;\;\;y \cdot \left(z \cdot \left(x - i \cdot \frac{j}{z}\right)\right)\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-167}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-228}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-209}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+54}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 10^{+125}:\\ \;\;\;\;t\_2 - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;y \leq 7.9 \cdot 10^{+167}:\\ \;\;\;\;a \cdot \left(i \cdot \left(b - \frac{y \cdot j}{a}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b))))
        (t_2 (* y (- (* x z) (* i j))))
        (t_3 (* a (- (* b i) (* x t)))))
   (if (<= y -2.55e+54)
     (* y (* z (- x (* i (/ j z)))))
     (if (<= y -1.3e-167)
       (+ (* x (* y z)) (* b (- (* a i) (* z c))))
       (if (<= y -1.85e-228)
         t_1
         (if (<= y 4.1e-209)
           t_3
           (if (<= y 3.1e-92)
             t_1
             (if (<= y 2.15e+54)
               t_3
               (if (<= y 1e+125)
                 (- t_2 (* b (* z c)))
                 (if (<= y 7.9e+167)
                   (* a (* i (- b (/ (* y j) a))))
                   t_2))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = a * ((b * i) - (x * t));
	double tmp;
	if (y <= -2.55e+54) {
		tmp = y * (z * (x - (i * (j / z))));
	} else if (y <= -1.3e-167) {
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)));
	} else if (y <= -1.85e-228) {
		tmp = t_1;
	} else if (y <= 4.1e-209) {
		tmp = t_3;
	} else if (y <= 3.1e-92) {
		tmp = t_1;
	} else if (y <= 2.15e+54) {
		tmp = t_3;
	} else if (y <= 1e+125) {
		tmp = t_2 - (b * (z * c));
	} else if (y <= 7.9e+167) {
		tmp = a * (i * (b - ((y * j) / a)));
	} 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 = c * ((t * j) - (z * b))
    t_2 = y * ((x * z) - (i * j))
    t_3 = a * ((b * i) - (x * t))
    if (y <= (-2.55d+54)) then
        tmp = y * (z * (x - (i * (j / z))))
    else if (y <= (-1.3d-167)) then
        tmp = (x * (y * z)) + (b * ((a * i) - (z * c)))
    else if (y <= (-1.85d-228)) then
        tmp = t_1
    else if (y <= 4.1d-209) then
        tmp = t_3
    else if (y <= 3.1d-92) then
        tmp = t_1
    else if (y <= 2.15d+54) then
        tmp = t_3
    else if (y <= 1d+125) then
        tmp = t_2 - (b * (z * c))
    else if (y <= 7.9d+167) then
        tmp = a * (i * (b - ((y * j) / a)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = a * ((b * i) - (x * t));
	double tmp;
	if (y <= -2.55e+54) {
		tmp = y * (z * (x - (i * (j / z))));
	} else if (y <= -1.3e-167) {
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)));
	} else if (y <= -1.85e-228) {
		tmp = t_1;
	} else if (y <= 4.1e-209) {
		tmp = t_3;
	} else if (y <= 3.1e-92) {
		tmp = t_1;
	} else if (y <= 2.15e+54) {
		tmp = t_3;
	} else if (y <= 1e+125) {
		tmp = t_2 - (b * (z * c));
	} else if (y <= 7.9e+167) {
		tmp = a * (i * (b - ((y * j) / a)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	t_2 = y * ((x * z) - (i * j))
	t_3 = a * ((b * i) - (x * t))
	tmp = 0
	if y <= -2.55e+54:
		tmp = y * (z * (x - (i * (j / z))))
	elif y <= -1.3e-167:
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)))
	elif y <= -1.85e-228:
		tmp = t_1
	elif y <= 4.1e-209:
		tmp = t_3
	elif y <= 3.1e-92:
		tmp = t_1
	elif y <= 2.15e+54:
		tmp = t_3
	elif y <= 1e+125:
		tmp = t_2 - (b * (z * c))
	elif y <= 7.9e+167:
		tmp = a * (i * (b - ((y * j) / a)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_3 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (y <= -2.55e+54)
		tmp = Float64(y * Float64(z * Float64(x - Float64(i * Float64(j / z)))));
	elseif (y <= -1.3e-167)
		tmp = Float64(Float64(x * Float64(y * z)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (y <= -1.85e-228)
		tmp = t_1;
	elseif (y <= 4.1e-209)
		tmp = t_3;
	elseif (y <= 3.1e-92)
		tmp = t_1;
	elseif (y <= 2.15e+54)
		tmp = t_3;
	elseif (y <= 1e+125)
		tmp = Float64(t_2 - Float64(b * Float64(z * c)));
	elseif (y <= 7.9e+167)
		tmp = Float64(a * Float64(i * Float64(b - Float64(Float64(y * j) / a))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((t * j) - (z * b));
	t_2 = y * ((x * z) - (i * j));
	t_3 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (y <= -2.55e+54)
		tmp = y * (z * (x - (i * (j / z))));
	elseif (y <= -1.3e-167)
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)));
	elseif (y <= -1.85e-228)
		tmp = t_1;
	elseif (y <= 4.1e-209)
		tmp = t_3;
	elseif (y <= 3.1e-92)
		tmp = t_1;
	elseif (y <= 2.15e+54)
		tmp = t_3;
	elseif (y <= 1e+125)
		tmp = t_2 - (b * (z * c));
	elseif (y <= 7.9e+167)
		tmp = a * (i * (b - ((y * j) / a)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.55e+54], N[(y * N[(z * N[(x - N[(i * N[(j / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.3e-167], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.85e-228], t$95$1, If[LessEqual[y, 4.1e-209], t$95$3, If[LessEqual[y, 3.1e-92], t$95$1, If[LessEqual[y, 2.15e+54], t$95$3, If[LessEqual[y, 1e+125], N[(t$95$2 - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.9e+167], N[(a * N[(i * N[(b - N[(N[(y * j), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -2.55000000000000005e54

   1. Initial program 68.0%

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

   3. Taylor expanded in y around inf 70.5%

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

      1. +-commutative 70.5%

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

      2. mul-1-neg 70.5%

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

      3. unsub-neg 70.5%

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

      4. *-commutative 70.5%

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

   5. Simplified 70.5%

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

   6. Taylor expanded in z around inf 70.5%

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

      1. mul-1-neg 70.5%

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

      2. unsub-neg 70.5%

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

      3. associate-/l* 72.5%

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

   8. Simplified 72.5%

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

   if -2.55000000000000005e54 < y < -1.2999999999999999e-167

   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 j around 0 63.1%

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

      1. *-commutative 63.1%

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

   5. Simplified 63.1%

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

   6. Taylor expanded in y around inf 61.2%

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

   if -1.2999999999999999e-167 < y < -1.85e-228 or 4.09999999999999977e-209 < y < 3.1000000000000001e-92

   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 63.0%

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

      1. *-commutative 63.0%

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

      2. *-commutative 63.0%

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

   5. Simplified 63.0%

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

   if -1.85e-228 < y < 4.09999999999999977e-209 or 3.1000000000000001e-92 < y < 2.14999999999999988e54

   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 a around inf 66.9%

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

      1. distribute-lft-out-- 66.9%

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

      2. *-commutative 66.9%

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

      3. *-commutative 66.9%

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

   5. Simplified 66.9%

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

   if 2.14999999999999988e54 < y < 9.9999999999999992e124

   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 t around 0 59.6%

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

      1. *-commutative 59.6%

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

      2. associate-*r* 65.6%

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

      3. associate-*r* 70.7%

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

      4. associate-*r* 70.7%

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

      5. distribute-rgt-in 76.6%

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

      6. +-commutative 76.6%

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

      7. mul-1-neg 76.6%

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

      8. unsub-neg 76.6%

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

      9. *-commutative 76.6%

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

      10. *-commutative 76.6%

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

   5. Simplified 76.6%

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

   6. Taylor expanded in a around 0 76.6%

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

      1. *-commutative 76.6%

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

   8. Simplified 76.6%

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

   if 9.9999999999999992e124 < y < 7.89999999999999994e167

   1. Initial program 51.2%

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

   3. Taylor expanded in a around -inf 58.4%

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

   4. Taylor expanded in i around inf 78.9%

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

   if 7.89999999999999994e167 < y

   1. Initial program 58.5%

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

   3. Taylor expanded in y around inf 88.0%

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

      1. +-commutative 88.0%

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

      2. mul-1-neg 88.0%

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

      3. unsub-neg 88.0%

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

      4. *-commutative 88.0%

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

   5. Simplified 88.0%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{+54}:\\ \;\;\;\;y \cdot \left(z \cdot \left(x - i \cdot \frac{j}{z}\right)\right)\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-167}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-228}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-209}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-92}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+54}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq 10^{+125}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;y \leq 7.9 \cdot 10^{+167}:\\ \;\;\;\;a \cdot \left(i \cdot \left(b - \frac{y \cdot j}{a}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 53.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_3 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;y \leq -3.5 \cdot 10^{+54}:\\ \;\;\;\;y \cdot \left(z \cdot \left(x - i \cdot \frac{j}{z}\right)\right)\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-167}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) - b \cdot \left(z \cdot c - a \cdot i\right)\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-225}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-208}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+53}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+125}:\\ \;\;\;\;t\_2 - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+167}:\\ \;\;\;\;a \cdot \left(i \cdot \left(b - \frac{y \cdot j}{a}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b))))
        (t_2 (* y (- (* x z) (* i j))))
        (t_3 (* a (- (* b i) (* x t)))))
   (if (<= y -3.5e+54)
     (* y (* z (- x (* i (/ j z)))))
     (if (<= y -2.4e-167)
       (- (* z (* x y)) (* b (- (* z c) (* a i))))
       (if (<= y -3.5e-225)
         t_1
         (if (<= y 3.9e-208)
           t_3
           (if (<= y 3.2e-92)
             t_1
             (if (<= y 3.7e+53)
               t_3
               (if (<= y 5.8e+125)
                 (- t_2 (* b (* z c)))
                 (if (<= y 7.8e+167)
                   (* a (* i (- b (/ (* y j) a))))
                   t_2))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = a * ((b * i) - (x * t));
	double tmp;
	if (y <= -3.5e+54) {
		tmp = y * (z * (x - (i * (j / z))));
	} else if (y <= -2.4e-167) {
		tmp = (z * (x * y)) - (b * ((z * c) - (a * i)));
	} else if (y <= -3.5e-225) {
		tmp = t_1;
	} else if (y <= 3.9e-208) {
		tmp = t_3;
	} else if (y <= 3.2e-92) {
		tmp = t_1;
	} else if (y <= 3.7e+53) {
		tmp = t_3;
	} else if (y <= 5.8e+125) {
		tmp = t_2 - (b * (z * c));
	} else if (y <= 7.8e+167) {
		tmp = a * (i * (b - ((y * j) / a)));
	} 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 = c * ((t * j) - (z * b))
    t_2 = y * ((x * z) - (i * j))
    t_3 = a * ((b * i) - (x * t))
    if (y <= (-3.5d+54)) then
        tmp = y * (z * (x - (i * (j / z))))
    else if (y <= (-2.4d-167)) then
        tmp = (z * (x * y)) - (b * ((z * c) - (a * i)))
    else if (y <= (-3.5d-225)) then
        tmp = t_1
    else if (y <= 3.9d-208) then
        tmp = t_3
    else if (y <= 3.2d-92) then
        tmp = t_1
    else if (y <= 3.7d+53) then
        tmp = t_3
    else if (y <= 5.8d+125) then
        tmp = t_2 - (b * (z * c))
    else if (y <= 7.8d+167) then
        tmp = a * (i * (b - ((y * j) / a)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = a * ((b * i) - (x * t));
	double tmp;
	if (y <= -3.5e+54) {
		tmp = y * (z * (x - (i * (j / z))));
	} else if (y <= -2.4e-167) {
		tmp = (z * (x * y)) - (b * ((z * c) - (a * i)));
	} else if (y <= -3.5e-225) {
		tmp = t_1;
	} else if (y <= 3.9e-208) {
		tmp = t_3;
	} else if (y <= 3.2e-92) {
		tmp = t_1;
	} else if (y <= 3.7e+53) {
		tmp = t_3;
	} else if (y <= 5.8e+125) {
		tmp = t_2 - (b * (z * c));
	} else if (y <= 7.8e+167) {
		tmp = a * (i * (b - ((y * j) / a)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	t_2 = y * ((x * z) - (i * j))
	t_3 = a * ((b * i) - (x * t))
	tmp = 0
	if y <= -3.5e+54:
		tmp = y * (z * (x - (i * (j / z))))
	elif y <= -2.4e-167:
		tmp = (z * (x * y)) - (b * ((z * c) - (a * i)))
	elif y <= -3.5e-225:
		tmp = t_1
	elif y <= 3.9e-208:
		tmp = t_3
	elif y <= 3.2e-92:
		tmp = t_1
	elif y <= 3.7e+53:
		tmp = t_3
	elif y <= 5.8e+125:
		tmp = t_2 - (b * (z * c))
	elif y <= 7.8e+167:
		tmp = a * (i * (b - ((y * j) / a)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_3 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (y <= -3.5e+54)
		tmp = Float64(y * Float64(z * Float64(x - Float64(i * Float64(j / z)))));
	elseif (y <= -2.4e-167)
		tmp = Float64(Float64(z * Float64(x * y)) - Float64(b * Float64(Float64(z * c) - Float64(a * i))));
	elseif (y <= -3.5e-225)
		tmp = t_1;
	elseif (y <= 3.9e-208)
		tmp = t_3;
	elseif (y <= 3.2e-92)
		tmp = t_1;
	elseif (y <= 3.7e+53)
		tmp = t_3;
	elseif (y <= 5.8e+125)
		tmp = Float64(t_2 - Float64(b * Float64(z * c)));
	elseif (y <= 7.8e+167)
		tmp = Float64(a * Float64(i * Float64(b - Float64(Float64(y * j) / a))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((t * j) - (z * b));
	t_2 = y * ((x * z) - (i * j));
	t_3 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (y <= -3.5e+54)
		tmp = y * (z * (x - (i * (j / z))));
	elseif (y <= -2.4e-167)
		tmp = (z * (x * y)) - (b * ((z * c) - (a * i)));
	elseif (y <= -3.5e-225)
		tmp = t_1;
	elseif (y <= 3.9e-208)
		tmp = t_3;
	elseif (y <= 3.2e-92)
		tmp = t_1;
	elseif (y <= 3.7e+53)
		tmp = t_3;
	elseif (y <= 5.8e+125)
		tmp = t_2 - (b * (z * c));
	elseif (y <= 7.8e+167)
		tmp = a * (i * (b - ((y * j) / a)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.5e+54], N[(y * N[(z * N[(x - N[(i * N[(j / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.4e-167], N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.5e-225], t$95$1, If[LessEqual[y, 3.9e-208], t$95$3, If[LessEqual[y, 3.2e-92], t$95$1, If[LessEqual[y, 3.7e+53], t$95$3, If[LessEqual[y, 5.8e+125], N[(t$95$2 - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.8e+167], N[(a * N[(i * N[(b - N[(N[(y * j), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -3.5000000000000001e54

   1. Initial program 68.0%

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

   3. Taylor expanded in y around inf 70.5%

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

      1. +-commutative 70.5%

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

      2. mul-1-neg 70.5%

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

      3. unsub-neg 70.5%

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

      4. *-commutative 70.5%

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

   5. Simplified 70.5%

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

   6. Taylor expanded in z around inf 70.5%

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

      1. mul-1-neg 70.5%

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

      2. unsub-neg 70.5%

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

      3. associate-/l* 72.5%

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

   8. Simplified 72.5%

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

   if -3.5000000000000001e54 < y < -2.39999999999999993e-167

   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 t around 0 71.6%

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

      1. *-commutative 71.6%

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

      2. associate-*r* 68.4%

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

      3. associate-*r* 65.9%

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

      4. associate-*r* 65.9%

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

      5. distribute-rgt-in 65.9%

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

      6. +-commutative 65.9%

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

      7. mul-1-neg 65.9%

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

      8. unsub-neg 65.9%

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

      9. *-commutative 65.9%

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

      10. *-commutative 65.9%

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

   5. Simplified 65.9%

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

   6. Taylor expanded in j around 0 61.2%

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

      1. associate-*r* 63.7%

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

      2. *-commutative 63.7%

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

   8. Simplified 63.7%

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

   if -2.39999999999999993e-167 < y < -3.4999999999999997e-225 or 3.90000000000000004e-208 < y < 3.1999999999999997e-92

   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 63.0%

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

      1. *-commutative 63.0%

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

      2. *-commutative 63.0%

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

   5. Simplified 63.0%

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

   if -3.4999999999999997e-225 < y < 3.90000000000000004e-208 or 3.1999999999999997e-92 < y < 3.7e53

   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 a around inf 66.9%

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

      1. distribute-lft-out-- 66.9%

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

      2. *-commutative 66.9%

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

      3. *-commutative 66.9%

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

   5. Simplified 66.9%

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

   if 3.7e53 < y < 5.79999999999999986e125

   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 t around 0 59.6%

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

      1. *-commutative 59.6%

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

      2. associate-*r* 65.6%

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

      3. associate-*r* 70.7%

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

      4. associate-*r* 70.7%

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

      5. distribute-rgt-in 76.6%

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

      6. +-commutative 76.6%

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

      7. mul-1-neg 76.6%

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

      8. unsub-neg 76.6%

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

      9. *-commutative 76.6%

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

      10. *-commutative 76.6%

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

   5. Simplified 76.6%

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

   6. Taylor expanded in a around 0 76.6%

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

      1. *-commutative 76.6%

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

   8. Simplified 76.6%

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

   if 5.79999999999999986e125 < y < 7.7999999999999996e167

   1. Initial program 51.2%

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

   3. Taylor expanded in a around -inf 58.4%

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

   4. Taylor expanded in i around inf 78.9%

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

   if 7.7999999999999996e167 < y

   1. Initial program 58.5%

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

   3. Taylor expanded in y around inf 88.0%

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

      1. +-commutative 88.0%

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

      2. mul-1-neg 88.0%

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

      3. unsub-neg 88.0%

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

      4. *-commutative 88.0%

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

   5. Simplified 88.0%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+54}:\\ \;\;\;\;y \cdot \left(z \cdot \left(x - i \cdot \frac{j}{z}\right)\right)\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-167}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) - b \cdot \left(z \cdot c - a \cdot i\right)\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-225}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-208}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-92}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+53}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+125}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+167}:\\ \;\;\;\;a \cdot \left(i \cdot \left(b - \frac{y \cdot j}{a}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 48.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;b \leq -4.4 \cdot 10^{-52}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -7.4 \cdot 10^{-175}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{-207}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -1.32 \cdot 10^{-240}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-275}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-292}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-286}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-37}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* x y)))
        (t_2 (* b (- (* a i) (* z c))))
        (t_3 (* j (- (* t c) (* y i)))))
   (if (<= b -4.4e-52)
     t_2
     (if (<= b -7.4e-175)
       t_1
       (if (<= b -2.7e-207)
         t_3
         (if (<= b -1.32e-240)
           (* y (* x z))
           (if (<= b -3e-275)
             (* a (* t (- x)))
             (if (<= b 5.5e-292)
               t_1
               (if (<= b 4e-286)
                 (* c (- (* t j) (* z b)))
                 (if (<= b 1.7e-37) 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 = z * (x * y);
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = j * ((t * c) - (y * i));
	double tmp;
	if (b <= -4.4e-52) {
		tmp = t_2;
	} else if (b <= -7.4e-175) {
		tmp = t_1;
	} else if (b <= -2.7e-207) {
		tmp = t_3;
	} else if (b <= -1.32e-240) {
		tmp = y * (x * z);
	} else if (b <= -3e-275) {
		tmp = a * (t * -x);
	} else if (b <= 5.5e-292) {
		tmp = t_1;
	} else if (b <= 4e-286) {
		tmp = c * ((t * j) - (z * b));
	} else if (b <= 1.7e-37) {
		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 = z * (x * y)
    t_2 = b * ((a * i) - (z * c))
    t_3 = j * ((t * c) - (y * i))
    if (b <= (-4.4d-52)) then
        tmp = t_2
    else if (b <= (-7.4d-175)) then
        tmp = t_1
    else if (b <= (-2.7d-207)) then
        tmp = t_3
    else if (b <= (-1.32d-240)) then
        tmp = y * (x * z)
    else if (b <= (-3d-275)) then
        tmp = a * (t * -x)
    else if (b <= 5.5d-292) then
        tmp = t_1
    else if (b <= 4d-286) then
        tmp = c * ((t * j) - (z * b))
    else if (b <= 1.7d-37) 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 = z * (x * y);
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = j * ((t * c) - (y * i));
	double tmp;
	if (b <= -4.4e-52) {
		tmp = t_2;
	} else if (b <= -7.4e-175) {
		tmp = t_1;
	} else if (b <= -2.7e-207) {
		tmp = t_3;
	} else if (b <= -1.32e-240) {
		tmp = y * (x * z);
	} else if (b <= -3e-275) {
		tmp = a * (t * -x);
	} else if (b <= 5.5e-292) {
		tmp = t_1;
	} else if (b <= 4e-286) {
		tmp = c * ((t * j) - (z * b));
	} else if (b <= 1.7e-37) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (x * y)
	t_2 = b * ((a * i) - (z * c))
	t_3 = j * ((t * c) - (y * i))
	tmp = 0
	if b <= -4.4e-52:
		tmp = t_2
	elif b <= -7.4e-175:
		tmp = t_1
	elif b <= -2.7e-207:
		tmp = t_3
	elif b <= -1.32e-240:
		tmp = y * (x * z)
	elif b <= -3e-275:
		tmp = a * (t * -x)
	elif b <= 5.5e-292:
		tmp = t_1
	elif b <= 4e-286:
		tmp = c * ((t * j) - (z * b))
	elif b <= 1.7e-37:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(x * y))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_3 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (b <= -4.4e-52)
		tmp = t_2;
	elseif (b <= -7.4e-175)
		tmp = t_1;
	elseif (b <= -2.7e-207)
		tmp = t_3;
	elseif (b <= -1.32e-240)
		tmp = Float64(y * Float64(x * z));
	elseif (b <= -3e-275)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (b <= 5.5e-292)
		tmp = t_1;
	elseif (b <= 4e-286)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (b <= 1.7e-37)
		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 = z * (x * y);
	t_2 = b * ((a * i) - (z * c));
	t_3 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (b <= -4.4e-52)
		tmp = t_2;
	elseif (b <= -7.4e-175)
		tmp = t_1;
	elseif (b <= -2.7e-207)
		tmp = t_3;
	elseif (b <= -1.32e-240)
		tmp = y * (x * z);
	elseif (b <= -3e-275)
		tmp = a * (t * -x);
	elseif (b <= 5.5e-292)
		tmp = t_1;
	elseif (b <= 4e-286)
		tmp = c * ((t * j) - (z * b));
	elseif (b <= 1.7e-37)
		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[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.4e-52], t$95$2, If[LessEqual[b, -7.4e-175], t$95$1, If[LessEqual[b, -2.7e-207], t$95$3, If[LessEqual[b, -1.32e-240], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3e-275], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.5e-292], t$95$1, If[LessEqual[b, 4e-286], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.7e-37], t$95$3, t$95$2]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -4.40000000000000018e-52 or 1.70000000000000009e-37 < b

   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 b around inf 57.9%

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

      1. *-commutative 57.9%

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

   5. Simplified 57.9%

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

   if -4.40000000000000018e-52 < b < -7.39999999999999997e-175 or -3e-275 < b < 5.50000000000000006e-292

   1. Initial program 82.4%

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

   3. Taylor expanded in t around 0 68.0%

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

      1. *-commutative 68.0%

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

      2. associate-*r* 63.2%

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

      3. associate-*r* 63.2%

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

      4. associate-*r* 63.2%

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

      5. distribute-rgt-in 63.2%

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

      6. +-commutative 63.2%

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

      7. mul-1-neg 63.2%

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

      8. unsub-neg 63.2%

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

      9. *-commutative 63.2%

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

      10. *-commutative 63.2%

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

   5. Simplified 63.2%

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

   6. Taylor expanded in x around inf 54.6%

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

      1. associate-*r* 54.7%

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

      2. *-commutative 54.7%

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

   8. Simplified 54.7%

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

   if -7.39999999999999997e-175 < b < -2.7e-207 or 4.0000000000000002e-286 < b < 1.70000000000000009e-37

   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 j around inf 61.0%

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

      1. sub-neg 61.0%

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

      2. *-commutative 61.0%

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

      3. *-commutative 61.0%

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

      4. sub-neg 61.0%

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

   5. Simplified 61.0%

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

   if -2.7e-207 < b < -1.32e-240

   1. Initial program 63.8%

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

   3. Taylor expanded in y around inf 70.1%

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

      1. +-commutative 70.1%

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

      2. mul-1-neg 70.1%

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

      3. unsub-neg 70.1%

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

      4. *-commutative 70.1%

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

   5. Simplified 70.1%

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

   6. Taylor expanded in x around inf 60.9%

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

   if -1.32e-240 < b < -3e-275

   1. Initial program 87.8%

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

   3. Taylor expanded in z around inf 87.8%

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

      1. +-commutative 87.8%

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

      2. fma-define 87.8%

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

      3. mul-1-neg 87.8%

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

      4. associate-/l* 75.9%

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

      5. distribute-lft-neg-in 75.9%

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

      6. *-commutative 75.9%

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

   5. Simplified 75.9%

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

   6. Taylor expanded in x around inf 65.4%

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

      1. associate-*r* 65.6%

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

      2. mul-1-neg 65.6%

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

      3. unsub-neg 65.6%

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

      4. associate-/l* 63.4%

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

   8. Simplified 63.4%

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

   9. Taylor expanded in z around 0 64.9%

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

       1. associate-*r* 64.9%

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

       2. neg-mul-1 64.9%

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

       3. *-commutative 64.9%

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

   11. Simplified 64.9%

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

   if 5.50000000000000006e-292 < b < 4.0000000000000002e-286

   1. Initial program 26.2%

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

   3. Taylor expanded in c around inf 99.6%

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

      1. *-commutative 99.6%

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

      2. *-commutative 99.6%

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

   5. Simplified 99.6%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.4 \cdot 10^{-52}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -7.4 \cdot 10^{-175}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{-207}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq -1.32 \cdot 10^{-240}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-275}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-292}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-286}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-37}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;y \leq -9.8 \cdot 10^{+91}:\\ \;\;\;\;y \cdot \left(z \cdot \left(x - i \cdot \frac{j}{z}\right)\right)\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-45}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-98}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;y \leq -2.55 \cdot 10^{-167}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-224}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-209}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+49}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))) (t_2 (* a (- (* b i) (* x t)))))
   (if (<= y -9.8e+91)
     (* y (* z (- x (* i (/ j z)))))
     (if (<= y -6.6e-45)
       (* t (- (* c j) (* x a)))
       (if (<= y -1.7e-98)
         (* i (- (* a b) (* y j)))
         (if (<= y -2.55e-167)
           (* b (- (* a i) (* z c)))
           (if (<= y -9.5e-224)
             t_1
             (if (<= y 3.8e-209)
               t_2
               (if (<= y 3.4e-92)
                 t_1
                 (if (<= y 5e+49) t_2 (* y (- (* x z) (* i j)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (y <= -9.8e+91) {
		tmp = y * (z * (x - (i * (j / z))));
	} else if (y <= -6.6e-45) {
		tmp = t * ((c * j) - (x * a));
	} else if (y <= -1.7e-98) {
		tmp = i * ((a * b) - (y * j));
	} else if (y <= -2.55e-167) {
		tmp = b * ((a * i) - (z * c));
	} else if (y <= -9.5e-224) {
		tmp = t_1;
	} else if (y <= 3.8e-209) {
		tmp = t_2;
	} else if (y <= 3.4e-92) {
		tmp = t_1;
	} else if (y <= 5e+49) {
		tmp = t_2;
	} else {
		tmp = y * ((x * z) - (i * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * ((t * j) - (z * b))
    t_2 = a * ((b * i) - (x * t))
    if (y <= (-9.8d+91)) then
        tmp = y * (z * (x - (i * (j / z))))
    else if (y <= (-6.6d-45)) then
        tmp = t * ((c * j) - (x * a))
    else if (y <= (-1.7d-98)) then
        tmp = i * ((a * b) - (y * j))
    else if (y <= (-2.55d-167)) then
        tmp = b * ((a * i) - (z * c))
    else if (y <= (-9.5d-224)) then
        tmp = t_1
    else if (y <= 3.8d-209) then
        tmp = t_2
    else if (y <= 3.4d-92) then
        tmp = t_1
    else if (y <= 5d+49) then
        tmp = t_2
    else
        tmp = y * ((x * z) - (i * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (y <= -9.8e+91) {
		tmp = y * (z * (x - (i * (j / z))));
	} else if (y <= -6.6e-45) {
		tmp = t * ((c * j) - (x * a));
	} else if (y <= -1.7e-98) {
		tmp = i * ((a * b) - (y * j));
	} else if (y <= -2.55e-167) {
		tmp = b * ((a * i) - (z * c));
	} else if (y <= -9.5e-224) {
		tmp = t_1;
	} else if (y <= 3.8e-209) {
		tmp = t_2;
	} else if (y <= 3.4e-92) {
		tmp = t_1;
	} else if (y <= 5e+49) {
		tmp = t_2;
	} else {
		tmp = y * ((x * z) - (i * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	t_2 = a * ((b * i) - (x * t))
	tmp = 0
	if y <= -9.8e+91:
		tmp = y * (z * (x - (i * (j / z))))
	elif y <= -6.6e-45:
		tmp = t * ((c * j) - (x * a))
	elif y <= -1.7e-98:
		tmp = i * ((a * b) - (y * j))
	elif y <= -2.55e-167:
		tmp = b * ((a * i) - (z * c))
	elif y <= -9.5e-224:
		tmp = t_1
	elif y <= 3.8e-209:
		tmp = t_2
	elif y <= 3.4e-92:
		tmp = t_1
	elif y <= 5e+49:
		tmp = t_2
	else:
		tmp = y * ((x * z) - (i * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	t_2 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (y <= -9.8e+91)
		tmp = Float64(y * Float64(z * Float64(x - Float64(i * Float64(j / z)))));
	elseif (y <= -6.6e-45)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (y <= -1.7e-98)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (y <= -2.55e-167)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (y <= -9.5e-224)
		tmp = t_1;
	elseif (y <= 3.8e-209)
		tmp = t_2;
	elseif (y <= 3.4e-92)
		tmp = t_1;
	elseif (y <= 5e+49)
		tmp = t_2;
	else
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((t * j) - (z * b));
	t_2 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (y <= -9.8e+91)
		tmp = y * (z * (x - (i * (j / z))));
	elseif (y <= -6.6e-45)
		tmp = t * ((c * j) - (x * a));
	elseif (y <= -1.7e-98)
		tmp = i * ((a * b) - (y * j));
	elseif (y <= -2.55e-167)
		tmp = b * ((a * i) - (z * c));
	elseif (y <= -9.5e-224)
		tmp = t_1;
	elseif (y <= 3.8e-209)
		tmp = t_2;
	elseif (y <= 3.4e-92)
		tmp = t_1;
	elseif (y <= 5e+49)
		tmp = t_2;
	else
		tmp = y * ((x * z) - (i * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.8e+91], N[(y * N[(z * N[(x - N[(i * N[(j / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.6e-45], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.7e-98], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.55e-167], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -9.5e-224], t$95$1, If[LessEqual[y, 3.8e-209], t$95$2, If[LessEqual[y, 3.4e-92], t$95$1, If[LessEqual[y, 5e+49], t$95$2, N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -9.8000000000000006e91

   1. Initial program 70.4%

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

   3. Taylor expanded in y around inf 75.5%

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

      1. +-commutative 75.5%

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

      2. mul-1-neg 75.5%

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

      3. unsub-neg 75.5%

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

      4. *-commutative 75.5%

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

   5. Simplified 75.5%

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

   6. Taylor expanded in z around inf 75.5%

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

      1. mul-1-neg 75.5%

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

      2. unsub-neg 75.5%

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

      3. associate-/l* 75.5%

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

   8. Simplified 75.5%

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

   if -9.8000000000000006e91 < y < -6.6000000000000001e-45

   1. Initial program 63.6%

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

   3. Taylor expanded in t around inf 64.0%

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

      1. +-commutative 64.0%

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

      2. mul-1-neg 64.0%

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

      3. unsub-neg 64.0%

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

      4. *-commutative 64.0%

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

      5. *-commutative 64.0%

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

   5. Simplified 64.0%

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

   if -6.6000000000000001e-45 < y < -1.7000000000000001e-98

   1. Initial program 90.0%

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

   3. Taylor expanded in i around inf 60.6%

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

      1. distribute-lft-out-- 60.6%

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

      2. *-commutative 60.6%

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

   5. Simplified 60.6%

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

   6. Taylor expanded in i around 0 60.6%

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

      1. cancel-sign-sub-inv 60.6%

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

      2. fma-define 60.6%

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

      3. associate-*r* 60.6%

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

      4. mul-1-neg 60.6%

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

      5. fma-define 60.6%

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

      6. cancel-sign-sub-inv 60.6%

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

      7. *-commutative 60.6%

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

      8. *-commutative 60.6%

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

   8. Simplified 60.6%

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

   if -1.7000000000000001e-98 < y < -2.55000000000000019e-167

   1. Initial program 71.0%

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

   3. Taylor expanded in b around inf 65.4%

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

      1. *-commutative 65.4%

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

   5. Simplified 65.4%

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

   if -2.55000000000000019e-167 < y < -9.5000000000000003e-224 or 3.7999999999999999e-209 < y < 3.4000000000000003e-92

   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 63.0%

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

      1. *-commutative 63.0%

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

      2. *-commutative 63.0%

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

   5. Simplified 63.0%

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

   if -9.5000000000000003e-224 < y < 3.7999999999999999e-209 or 3.4000000000000003e-92 < y < 5.0000000000000004e49

   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 a around inf 67.8%

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

      1. distribute-lft-out-- 67.8%

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

      2. *-commutative 67.8%

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

      3. *-commutative 67.8%

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

   5. Simplified 67.8%

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

   if 5.0000000000000004e49 < y

   1. Initial program 59.4%

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

   3. Taylor expanded in y around inf 67.2%

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

      1. +-commutative 67.2%

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

      2. mul-1-neg 67.2%

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

      3. unsub-neg 67.2%

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

      4. *-commutative 67.2%

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

   5. Simplified 67.2%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{+91}:\\ \;\;\;\;y \cdot \left(z \cdot \left(x - i \cdot \frac{j}{z}\right)\right)\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-45}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-98}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;y \leq -2.55 \cdot 10^{-167}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-224}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-209}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-92}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+49}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -2.9 \cdot 10^{+138}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -5.5 \cdot 10^{+101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -2.8 \cdot 10^{+36}:\\ \;\;\;\;c \cdot \left(t \cdot \left(j - b \cdot \frac{z}{t}\right)\right)\\ \mathbf{elif}\;j \leq 5 \cdot 10^{-81}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 5.1 \cdot 10^{-25}:\\ \;\;\;\;z \cdot \left(c \cdot \left(x \cdot \frac{y}{c} - b\right)\right)\\ \mathbf{elif}\;j \leq 1.1 \cdot 10^{+162}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* x (- (* y z) (* t a))) (* b (- (* a i) (* z c)))))
        (t_2 (* j (- (* t c) (* y i)))))
   (if (<= j -2.9e+138)
     t_2
     (if (<= j -5.5e+101)
       t_1
       (if (<= j -2.8e+36)
         (* c (* t (- j (* b (/ z t)))))
         (if (<= j 5e-81)
           t_1
           (if (<= j 5.1e-25)
             (* z (* c (- (* x (/ y c)) b)))
             (if (<= j 1.1e+162) 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 * ((a * i) - (z * c)));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -2.9e+138) {
		tmp = t_2;
	} else if (j <= -5.5e+101) {
		tmp = t_1;
	} else if (j <= -2.8e+36) {
		tmp = c * (t * (j - (b * (z / t))));
	} else if (j <= 5e-81) {
		tmp = t_1;
	} else if (j <= 5.1e-25) {
		tmp = z * (c * ((x * (y / c)) - b));
	} else if (j <= 1.1e+162) {
		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 * ((a * i) - (z * c)))
    t_2 = j * ((t * c) - (y * i))
    if (j <= (-2.9d+138)) then
        tmp = t_2
    else if (j <= (-5.5d+101)) then
        tmp = t_1
    else if (j <= (-2.8d+36)) then
        tmp = c * (t * (j - (b * (z / t))))
    else if (j <= 5d-81) then
        tmp = t_1
    else if (j <= 5.1d-25) then
        tmp = z * (c * ((x * (y / c)) - b))
    else if (j <= 1.1d+162) 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 * ((a * i) - (z * c)));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -2.9e+138) {
		tmp = t_2;
	} else if (j <= -5.5e+101) {
		tmp = t_1;
	} else if (j <= -2.8e+36) {
		tmp = c * (t * (j - (b * (z / t))));
	} else if (j <= 5e-81) {
		tmp = t_1;
	} else if (j <= 5.1e-25) {
		tmp = z * (c * ((x * (y / c)) - b));
	} else if (j <= 1.1e+162) {
		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 * ((a * i) - (z * c)))
	t_2 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -2.9e+138:
		tmp = t_2
	elif j <= -5.5e+101:
		tmp = t_1
	elif j <= -2.8e+36:
		tmp = c * (t * (j - (b * (z / t))))
	elif j <= 5e-81:
		tmp = t_1
	elif j <= 5.1e-25:
		tmp = z * (c * ((x * (y / c)) - b))
	elif j <= 1.1e+162:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(a * i) - Float64(z * c))))
	t_2 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -2.9e+138)
		tmp = t_2;
	elseif (j <= -5.5e+101)
		tmp = t_1;
	elseif (j <= -2.8e+36)
		tmp = Float64(c * Float64(t * Float64(j - Float64(b * Float64(z / t)))));
	elseif (j <= 5e-81)
		tmp = t_1;
	elseif (j <= 5.1e-25)
		tmp = Float64(z * Float64(c * Float64(Float64(x * Float64(y / c)) - b)));
	elseif (j <= 1.1e+162)
		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 * ((a * i) - (z * c)));
	t_2 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -2.9e+138)
		tmp = t_2;
	elseif (j <= -5.5e+101)
		tmp = t_1;
	elseif (j <= -2.8e+36)
		tmp = c * (t * (j - (b * (z / t))));
	elseif (j <= 5e-81)
		tmp = t_1;
	elseif (j <= 5.1e-25)
		tmp = z * (c * ((x * (y / c)) - b));
	elseif (j <= 1.1e+162)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.9e+138], t$95$2, If[LessEqual[j, -5.5e+101], t$95$1, If[LessEqual[j, -2.8e+36], N[(c * N[(t * N[(j - N[(b * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5e-81], t$95$1, If[LessEqual[j, 5.1e-25], N[(z * N[(c * N[(N[(x * N[(y / c), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.1e+162], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -2.9000000000000001e138 or 1.1000000000000001e162 < j

   1. Initial program 69.2%

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

   3. Taylor expanded in j around inf 74.2%

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

      1. sub-neg 74.2%

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

      2. *-commutative 74.2%

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

      3. *-commutative 74.2%

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

      4. sub-neg 74.2%

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

   5. Simplified 74.2%

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

   if -2.9000000000000001e138 < j < -5.50000000000000018e101 or -2.8000000000000001e36 < j < 4.99999999999999981e-81 or 5.1000000000000003e-25 < j < 1.1000000000000001e162

   1. Initial program 75.5%

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

   3. Taylor expanded in j around 0 71.1%

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

      1. *-commutative 71.1%

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

   5. Simplified 71.1%

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

   if -5.50000000000000018e101 < j < -2.8000000000000001e36

   1. Initial program 30.7%

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

   3. Taylor expanded in c around inf 70.3%

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

      1. *-commutative 70.3%

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

      2. *-commutative 70.3%

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

   5. Simplified 70.3%

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

   6. Taylor expanded in t around inf 70.8%

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

      1. mul-1-neg 70.8%

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

      2. unsub-neg 70.8%

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

      3. associate-/l* 70.8%

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

   8. Simplified 70.8%

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

   if 4.99999999999999981e-81 < j < 5.1000000000000003e-25

   1. Initial program 41.9%

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

   3. Taylor expanded in z around inf 59.6%

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

      1. *-commutative 59.6%

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

   5. Simplified 59.6%

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

   6. Taylor expanded in c around inf 67.6%

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

      1. associate-/l* 75.8%

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

   8. Simplified 75.8%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.9 \cdot 10^{+138}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -5.5 \cdot 10^{+101}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -2.8 \cdot 10^{+36}:\\ \;\;\;\;c \cdot \left(t \cdot \left(j - b \cdot \frac{z}{t}\right)\right)\\ \mathbf{elif}\;j \leq 5 \cdot 10^{-81}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 5.1 \cdot 10^{-25}:\\ \;\;\;\;z \cdot \left(c \cdot \left(x \cdot \frac{y}{c} - b\right)\right)\\ \mathbf{elif}\;j \leq 1.1 \cdot 10^{+162}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_3 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_4 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;t \leq -6.2 \cdot 10^{+87}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -1.68 \cdot 10^{-140}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-243}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-279}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.52 \cdot 10^{-214}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+23}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c))))
        (t_2 (* y (- (* x z) (* i j))))
        (t_3 (* t (- (* c j) (* x a))))
        (t_4 (* i (- (* a b) (* y j)))))
   (if (<= t -6.2e+87)
     t_3
     (if (<= t -1.68e-140)
       t_2
       (if (<= t -4.4e-243)
         t_1
         (if (<= t 6.2e-279)
           t_2
           (if (<= t 1.52e-214)
             t_4
             (if (<= t 2.35e-119) t_1 (if (<= t 9.5e+23) t_4 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 = z * ((x * y) - (b * c));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = t * ((c * j) - (x * a));
	double t_4 = i * ((a * b) - (y * j));
	double tmp;
	if (t <= -6.2e+87) {
		tmp = t_3;
	} else if (t <= -1.68e-140) {
		tmp = t_2;
	} else if (t <= -4.4e-243) {
		tmp = t_1;
	} else if (t <= 6.2e-279) {
		tmp = t_2;
	} else if (t <= 1.52e-214) {
		tmp = t_4;
	} else if (t <= 2.35e-119) {
		tmp = t_1;
	} else if (t <= 9.5e+23) {
		tmp = t_4;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = z * ((x * y) - (b * c))
    t_2 = y * ((x * z) - (i * j))
    t_3 = t * ((c * j) - (x * a))
    t_4 = i * ((a * b) - (y * j))
    if (t <= (-6.2d+87)) then
        tmp = t_3
    else if (t <= (-1.68d-140)) then
        tmp = t_2
    else if (t <= (-4.4d-243)) then
        tmp = t_1
    else if (t <= 6.2d-279) then
        tmp = t_2
    else if (t <= 1.52d-214) then
        tmp = t_4
    else if (t <= 2.35d-119) then
        tmp = t_1
    else if (t <= 9.5d+23) then
        tmp = t_4
    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 = z * ((x * y) - (b * c));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = t * ((c * j) - (x * a));
	double t_4 = i * ((a * b) - (y * j));
	double tmp;
	if (t <= -6.2e+87) {
		tmp = t_3;
	} else if (t <= -1.68e-140) {
		tmp = t_2;
	} else if (t <= -4.4e-243) {
		tmp = t_1;
	} else if (t <= 6.2e-279) {
		tmp = t_2;
	} else if (t <= 1.52e-214) {
		tmp = t_4;
	} else if (t <= 2.35e-119) {
		tmp = t_1;
	} else if (t <= 9.5e+23) {
		tmp = t_4;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * ((x * y) - (b * c))
	t_2 = y * ((x * z) - (i * j))
	t_3 = t * ((c * j) - (x * a))
	t_4 = i * ((a * b) - (y * j))
	tmp = 0
	if t <= -6.2e+87:
		tmp = t_3
	elif t <= -1.68e-140:
		tmp = t_2
	elif t <= -4.4e-243:
		tmp = t_1
	elif t <= 6.2e-279:
		tmp = t_2
	elif t <= 1.52e-214:
		tmp = t_4
	elif t <= 2.35e-119:
		tmp = t_1
	elif t <= 9.5e+23:
		tmp = t_4
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_3 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_4 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	tmp = 0.0
	if (t <= -6.2e+87)
		tmp = t_3;
	elseif (t <= -1.68e-140)
		tmp = t_2;
	elseif (t <= -4.4e-243)
		tmp = t_1;
	elseif (t <= 6.2e-279)
		tmp = t_2;
	elseif (t <= 1.52e-214)
		tmp = t_4;
	elseif (t <= 2.35e-119)
		tmp = t_1;
	elseif (t <= 9.5e+23)
		tmp = t_4;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * ((x * y) - (b * c));
	t_2 = y * ((x * z) - (i * j));
	t_3 = t * ((c * j) - (x * a));
	t_4 = i * ((a * b) - (y * j));
	tmp = 0.0;
	if (t <= -6.2e+87)
		tmp = t_3;
	elseif (t <= -1.68e-140)
		tmp = t_2;
	elseif (t <= -4.4e-243)
		tmp = t_1;
	elseif (t <= 6.2e-279)
		tmp = t_2;
	elseif (t <= 1.52e-214)
		tmp = t_4;
	elseif (t <= 2.35e-119)
		tmp = t_1;
	elseif (t <= 9.5e+23)
		tmp = t_4;
	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[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.2e+87], t$95$3, If[LessEqual[t, -1.68e-140], t$95$2, If[LessEqual[t, -4.4e-243], t$95$1, If[LessEqual[t, 6.2e-279], t$95$2, If[LessEqual[t, 1.52e-214], t$95$4, If[LessEqual[t, 2.35e-119], t$95$1, If[LessEqual[t, 9.5e+23], t$95$4, t$95$3]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.1999999999999999e87 or 9.50000000000000038e23 < t

   1. Initial program 55.5%

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

   3. Taylor expanded in t around inf 66.1%

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

      1. +-commutative 66.1%

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

      2. mul-1-neg 66.1%

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

      3. unsub-neg 66.1%

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

      4. *-commutative 66.1%

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

      5. *-commutative 66.1%

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

   5. Simplified 66.1%

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

   if -6.1999999999999999e87 < t < -1.68e-140 or -4.3999999999999998e-243 < t < 6.1999999999999998e-279

   1. Initial program 77.2%

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

   3. Taylor expanded in y around inf 58.5%

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

      1. +-commutative 58.5%

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

      2. mul-1-neg 58.5%

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

      3. unsub-neg 58.5%

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

      4. *-commutative 58.5%

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

   5. Simplified 58.5%

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

   if -1.68e-140 < t < -4.3999999999999998e-243 or 1.51999999999999991e-214 < t < 2.35000000000000001e-119

   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 z around inf 67.8%

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

      1. *-commutative 67.8%

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

   5. Simplified 67.8%

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

   if 6.1999999999999998e-279 < t < 1.51999999999999991e-214 or 2.35000000000000001e-119 < t < 9.50000000000000038e23

   1. Initial program 79.3%

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

   3. Taylor expanded in i around inf 64.6%

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

      1. distribute-lft-out-- 64.6%

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

      2. *-commutative 64.6%

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

   5. Simplified 64.6%

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

   6. Taylor expanded in i around 0 64.6%

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

      1. cancel-sign-sub-inv 64.6%

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

      2. fma-define 64.6%

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

      3. associate-*r* 64.6%

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

      4. mul-1-neg 64.6%

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

      5. fma-define 64.6%

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

      6. cancel-sign-sub-inv 64.6%

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

      7. *-commutative 64.6%

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

      8. *-commutative 64.6%

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

   8. Simplified 64.6%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+87}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -1.68 \cdot 10^{-140}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-243}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-279}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 1.52 \cdot 10^{-214}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-119}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+23}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_3 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -7.2 \cdot 10^{+91}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-38}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-168}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-221}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-209}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-91}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+51}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t))))
        (t_2 (* c (- (* t j) (* z b))))
        (t_3 (* y (- (* x z) (* i j)))))
   (if (<= y -7.2e+91)
     t_3
     (if (<= y -4.1e-38)
       (* t (- (* c j) (* x a)))
       (if (<= y -2.8e-168)
         (* b (- (* a i) (* z c)))
         (if (<= y -1.5e-221)
           t_2
           (if (<= y 2e-209)
             t_1
             (if (<= y 1.8e-91) t_2 (if (<= y 3e+51) t_1 t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double t_2 = c * ((t * j) - (z * b));
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -7.2e+91) {
		tmp = t_3;
	} else if (y <= -4.1e-38) {
		tmp = t * ((c * j) - (x * a));
	} else if (y <= -2.8e-168) {
		tmp = b * ((a * i) - (z * c));
	} else if (y <= -1.5e-221) {
		tmp = t_2;
	} else if (y <= 2e-209) {
		tmp = t_1;
	} else if (y <= 1.8e-91) {
		tmp = t_2;
	} else if (y <= 3e+51) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a * ((b * i) - (x * t))
    t_2 = c * ((t * j) - (z * b))
    t_3 = y * ((x * z) - (i * j))
    if (y <= (-7.2d+91)) then
        tmp = t_3
    else if (y <= (-4.1d-38)) then
        tmp = t * ((c * j) - (x * a))
    else if (y <= (-2.8d-168)) then
        tmp = b * ((a * i) - (z * c))
    else if (y <= (-1.5d-221)) then
        tmp = t_2
    else if (y <= 2d-209) then
        tmp = t_1
    else if (y <= 1.8d-91) then
        tmp = t_2
    else if (y <= 3d+51) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double t_2 = c * ((t * j) - (z * b));
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -7.2e+91) {
		tmp = t_3;
	} else if (y <= -4.1e-38) {
		tmp = t * ((c * j) - (x * a));
	} else if (y <= -2.8e-168) {
		tmp = b * ((a * i) - (z * c));
	} else if (y <= -1.5e-221) {
		tmp = t_2;
	} else if (y <= 2e-209) {
		tmp = t_1;
	} else if (y <= 1.8e-91) {
		tmp = t_2;
	} else if (y <= 3e+51) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	t_2 = c * ((t * j) - (z * b))
	t_3 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -7.2e+91:
		tmp = t_3
	elif y <= -4.1e-38:
		tmp = t * ((c * j) - (x * a))
	elif y <= -2.8e-168:
		tmp = b * ((a * i) - (z * c))
	elif y <= -1.5e-221:
		tmp = t_2
	elif y <= 2e-209:
		tmp = t_1
	elif y <= 1.8e-91:
		tmp = t_2
	elif y <= 3e+51:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	t_3 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -7.2e+91)
		tmp = t_3;
	elseif (y <= -4.1e-38)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (y <= -2.8e-168)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (y <= -1.5e-221)
		tmp = t_2;
	elseif (y <= 2e-209)
		tmp = t_1;
	elseif (y <= 1.8e-91)
		tmp = t_2;
	elseif (y <= 3e+51)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((b * i) - (x * t));
	t_2 = c * ((t * j) - (z * b));
	t_3 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -7.2e+91)
		tmp = t_3;
	elseif (y <= -4.1e-38)
		tmp = t * ((c * j) - (x * a));
	elseif (y <= -2.8e-168)
		tmp = b * ((a * i) - (z * c));
	elseif (y <= -1.5e-221)
		tmp = t_2;
	elseif (y <= 2e-209)
		tmp = t_1;
	elseif (y <= 1.8e-91)
		tmp = t_2;
	elseif (y <= 3e+51)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.2e+91], t$95$3, If[LessEqual[y, -4.1e-38], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.8e-168], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.5e-221], t$95$2, If[LessEqual[y, 2e-209], t$95$1, If[LessEqual[y, 1.8e-91], t$95$2, If[LessEqual[y, 3e+51], t$95$1, t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -7.2e91 or 3e51 < y

   1. Initial program 64.0%

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

   3. Taylor expanded in y around inf 70.7%

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

      1. +-commutative 70.7%

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

      2. mul-1-neg 70.7%

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

      3. unsub-neg 70.7%

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

      4. *-commutative 70.7%

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

   5. Simplified 70.7%

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

   if -7.2e91 < y < -4.0999999999999998e-38

   1. Initial program 63.6%

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

   3. Taylor expanded in t around inf 64.0%

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

      1. +-commutative 64.0%

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

      2. mul-1-neg 64.0%

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

      3. unsub-neg 64.0%

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

      4. *-commutative 64.0%

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

      5. *-commutative 64.0%

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

   5. Simplified 64.0%

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

   if -4.0999999999999998e-38 < y < -2.8000000000000002e-168

   1. Initial program 78.9%

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

   3. Taylor expanded in b around inf 55.2%

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

      1. *-commutative 55.2%

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

   5. Simplified 55.2%

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

   if -2.8000000000000002e-168 < y < -1.5000000000000001e-221 or 2.0000000000000001e-209 < y < 1.8e-91

   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 63.0%

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

      1. *-commutative 63.0%

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

      2. *-commutative 63.0%

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

   5. Simplified 63.0%

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

   if -1.5000000000000001e-221 < y < 2.0000000000000001e-209 or 1.8e-91 < y < 3e51

   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 a around inf 67.8%

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

      1. distribute-lft-out-- 67.8%

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

      2. *-commutative 67.8%

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

      3. *-commutative 67.8%

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

   5. Simplified 67.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(x \cdot t - i \cdot b\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+91}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-38}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-168}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-221}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-209}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-91}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+51}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_3 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -1.12 \cdot 10^{+92}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{-39}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-167}:\\ \;\;\;\;b \cdot \left(i \cdot \left(a - c \cdot \frac{z}{i}\right)\right)\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-224}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-209}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-91}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t))))
        (t_2 (* c (- (* t j) (* z b))))
        (t_3 (* y (- (* x z) (* i j)))))
   (if (<= y -1.12e+92)
     t_3
     (if (<= y -9.2e-39)
       (* t (- (* c j) (* x a)))
       (if (<= y -2.2e-167)
         (* b (* i (- a (* c (/ z i)))))
         (if (<= y -2e-224)
           t_2
           (if (<= y 8.8e-209)
             t_1
             (if (<= y 1.8e-91) t_2 (if (<= y 7.5e+52) t_1 t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double t_2 = c * ((t * j) - (z * b));
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.12e+92) {
		tmp = t_3;
	} else if (y <= -9.2e-39) {
		tmp = t * ((c * j) - (x * a));
	} else if (y <= -2.2e-167) {
		tmp = b * (i * (a - (c * (z / i))));
	} else if (y <= -2e-224) {
		tmp = t_2;
	} else if (y <= 8.8e-209) {
		tmp = t_1;
	} else if (y <= 1.8e-91) {
		tmp = t_2;
	} else if (y <= 7.5e+52) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a * ((b * i) - (x * t))
    t_2 = c * ((t * j) - (z * b))
    t_3 = y * ((x * z) - (i * j))
    if (y <= (-1.12d+92)) then
        tmp = t_3
    else if (y <= (-9.2d-39)) then
        tmp = t * ((c * j) - (x * a))
    else if (y <= (-2.2d-167)) then
        tmp = b * (i * (a - (c * (z / i))))
    else if (y <= (-2d-224)) then
        tmp = t_2
    else if (y <= 8.8d-209) then
        tmp = t_1
    else if (y <= 1.8d-91) then
        tmp = t_2
    else if (y <= 7.5d+52) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double t_2 = c * ((t * j) - (z * b));
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.12e+92) {
		tmp = t_3;
	} else if (y <= -9.2e-39) {
		tmp = t * ((c * j) - (x * a));
	} else if (y <= -2.2e-167) {
		tmp = b * (i * (a - (c * (z / i))));
	} else if (y <= -2e-224) {
		tmp = t_2;
	} else if (y <= 8.8e-209) {
		tmp = t_1;
	} else if (y <= 1.8e-91) {
		tmp = t_2;
	} else if (y <= 7.5e+52) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	t_2 = c * ((t * j) - (z * b))
	t_3 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -1.12e+92:
		tmp = t_3
	elif y <= -9.2e-39:
		tmp = t * ((c * j) - (x * a))
	elif y <= -2.2e-167:
		tmp = b * (i * (a - (c * (z / i))))
	elif y <= -2e-224:
		tmp = t_2
	elif y <= 8.8e-209:
		tmp = t_1
	elif y <= 1.8e-91:
		tmp = t_2
	elif y <= 7.5e+52:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	t_3 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -1.12e+92)
		tmp = t_3;
	elseif (y <= -9.2e-39)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (y <= -2.2e-167)
		tmp = Float64(b * Float64(i * Float64(a - Float64(c * Float64(z / i)))));
	elseif (y <= -2e-224)
		tmp = t_2;
	elseif (y <= 8.8e-209)
		tmp = t_1;
	elseif (y <= 1.8e-91)
		tmp = t_2;
	elseif (y <= 7.5e+52)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((b * i) - (x * t));
	t_2 = c * ((t * j) - (z * b));
	t_3 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -1.12e+92)
		tmp = t_3;
	elseif (y <= -9.2e-39)
		tmp = t * ((c * j) - (x * a));
	elseif (y <= -2.2e-167)
		tmp = b * (i * (a - (c * (z / i))));
	elseif (y <= -2e-224)
		tmp = t_2;
	elseif (y <= 8.8e-209)
		tmp = t_1;
	elseif (y <= 1.8e-91)
		tmp = t_2;
	elseif (y <= 7.5e+52)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.12e+92], t$95$3, If[LessEqual[y, -9.2e-39], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.2e-167], N[(b * N[(i * N[(a - N[(c * N[(z / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2e-224], t$95$2, If[LessEqual[y, 8.8e-209], t$95$1, If[LessEqual[y, 1.8e-91], t$95$2, If[LessEqual[y, 7.5e+52], t$95$1, t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.1199999999999999e92 or 7.49999999999999995e52 < y

   1. Initial program 64.0%

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

   3. Taylor expanded in y around inf 70.7%

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

      1. +-commutative 70.7%

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

      2. mul-1-neg 70.7%

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

      3. unsub-neg 70.7%

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

      4. *-commutative 70.7%

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

   5. Simplified 70.7%

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

   if -1.1199999999999999e92 < y < -9.20000000000000033e-39

   1. Initial program 63.6%

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

   3. Taylor expanded in t around inf 64.0%

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

      1. +-commutative 64.0%

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

      2. mul-1-neg 64.0%

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

      3. unsub-neg 64.0%

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

      4. *-commutative 64.0%

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

      5. *-commutative 64.0%

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

   5. Simplified 64.0%

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

   if -9.20000000000000033e-39 < y < -2.2e-167

   1. Initial program 78.9%

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

   3. Taylor expanded in b around inf 55.2%

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

      1. *-commutative 55.2%

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

   5. Simplified 55.2%

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

   6. Taylor expanded in i around inf 55.2%

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

      1. mul-1-neg 55.2%

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

      2. unsub-neg 55.2%

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

      3. associate-/l* 55.3%

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

   8. Simplified 55.3%

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

   if -2.2e-167 < y < -2e-224 or 8.80000000000000039e-209 < y < 1.8e-91

   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 63.0%

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

      1. *-commutative 63.0%

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

      2. *-commutative 63.0%

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

   5. Simplified 63.0%

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

   if -2e-224 < y < 8.80000000000000039e-209 or 1.8e-91 < y < 7.49999999999999995e52

   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 a around inf 67.8%

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

      1. distribute-lft-out-- 67.8%

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

      2. *-commutative 67.8%

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

      3. *-commutative 67.8%

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

   5. Simplified 67.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(x \cdot t - i \cdot b\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+92}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{-39}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-167}:\\ \;\;\;\;b \cdot \left(i \cdot \left(a - c \cdot \frac{z}{i}\right)\right)\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-224}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-209}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-91}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+52}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 43.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.3 \cdot 10^{-52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -4.3 \cdot 10^{-241}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{-275}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-292}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{-221}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-35}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= b -1.3e-52)
     t_1
     (if (<= b -4.3e-241)
       (* x (* y z))
       (if (<= b -3.6e-275)
         (* a (* t (- x)))
         (if (<= b 9.5e-292)
           (* z (* x y))
           (if (<= b 8.2e-221)
             (* c (* t j))
             (if (<= b 2.7e-35) (* (* y j) (- i)) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.3e-52) {
		tmp = t_1;
	} else if (b <= -4.3e-241) {
		tmp = x * (y * z);
	} else if (b <= -3.6e-275) {
		tmp = a * (t * -x);
	} else if (b <= 9.5e-292) {
		tmp = z * (x * y);
	} else if (b <= 8.2e-221) {
		tmp = c * (t * j);
	} else if (b <= 2.7e-35) {
		tmp = (y * j) * -i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    if (b <= (-1.3d-52)) then
        tmp = t_1
    else if (b <= (-4.3d-241)) then
        tmp = x * (y * z)
    else if (b <= (-3.6d-275)) then
        tmp = a * (t * -x)
    else if (b <= 9.5d-292) then
        tmp = z * (x * y)
    else if (b <= 8.2d-221) then
        tmp = c * (t * j)
    else if (b <= 2.7d-35) then
        tmp = (y * j) * -i
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.3e-52) {
		tmp = t_1;
	} else if (b <= -4.3e-241) {
		tmp = x * (y * z);
	} else if (b <= -3.6e-275) {
		tmp = a * (t * -x);
	} else if (b <= 9.5e-292) {
		tmp = z * (x * y);
	} else if (b <= 8.2e-221) {
		tmp = c * (t * j);
	} else if (b <= 2.7e-35) {
		tmp = (y * j) * -i;
	} 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 <= -1.3e-52:
		tmp = t_1
	elif b <= -4.3e-241:
		tmp = x * (y * z)
	elif b <= -3.6e-275:
		tmp = a * (t * -x)
	elif b <= 9.5e-292:
		tmp = z * (x * y)
	elif b <= 8.2e-221:
		tmp = c * (t * j)
	elif b <= 2.7e-35:
		tmp = (y * j) * -i
	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 <= -1.3e-52)
		tmp = t_1;
	elseif (b <= -4.3e-241)
		tmp = Float64(x * Float64(y * z));
	elseif (b <= -3.6e-275)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (b <= 9.5e-292)
		tmp = Float64(z * Float64(x * y));
	elseif (b <= 8.2e-221)
		tmp = Float64(c * Float64(t * j));
	elseif (b <= 2.7e-35)
		tmp = Float64(Float64(y * j) * Float64(-i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -1.3e-52)
		tmp = t_1;
	elseif (b <= -4.3e-241)
		tmp = x * (y * z);
	elseif (b <= -3.6e-275)
		tmp = a * (t * -x);
	elseif (b <= 9.5e-292)
		tmp = z * (x * y);
	elseif (b <= 8.2e-221)
		tmp = c * (t * j);
	elseif (b <= 2.7e-35)
		tmp = (y * j) * -i;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.3e-52], t$95$1, If[LessEqual[b, -4.3e-241], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.6e-275], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.5e-292], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.2e-221], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.7e-35], N[(N[(y * j), $MachinePrecision] * (-i)), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -1.2999999999999999e-52 or 2.6999999999999997e-35 < b

   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 b around inf 57.9%

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

      1. *-commutative 57.9%

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

   5. Simplified 57.9%

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

   if -1.2999999999999999e-52 < b < -4.2999999999999999e-241

   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 y around inf 66.0%

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

      1. +-commutative 66.0%

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

      2. mul-1-neg 66.0%

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

      3. unsub-neg 66.0%

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

      4. *-commutative 66.0%

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

   5. Simplified 66.0%

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

   6. Taylor expanded in x around inf 63.1%

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

      1. +-commutative 63.1%

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

      2. *-commutative 63.1%

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

      3. mul-1-neg 63.1%

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

      4. unsub-neg 63.1%

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

      5. *-commutative 63.1%

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

      6. associate-*r* 64.9%

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

      7. *-commutative 64.9%

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

   8. Simplified 64.9%

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

   9. Taylor expanded in x around inf 48.3%

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

   if -4.2999999999999999e-241 < b < -3.5999999999999997e-275

   1. Initial program 87.8%

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

   3. Taylor expanded in z around inf 87.8%

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

      1. +-commutative 87.8%

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

      2. fma-define 87.8%

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

      3. mul-1-neg 87.8%

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

      4. associate-/l* 75.9%

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

      5. distribute-lft-neg-in 75.9%

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

      6. *-commutative 75.9%

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

   5. Simplified 75.9%

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

   6. Taylor expanded in x around inf 65.4%

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

      1. associate-*r* 65.6%

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

      2. mul-1-neg 65.6%

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

      3. unsub-neg 65.6%

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

      4. associate-/l* 63.4%

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

   8. Simplified 63.4%

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

   9. Taylor expanded in z around 0 64.9%

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

       1. associate-*r* 64.9%

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

       2. neg-mul-1 64.9%

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

       3. *-commutative 64.9%

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

   11. Simplified 64.9%

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

   if -3.5999999999999997e-275 < b < 9.4999999999999994e-292

   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 t around 0 67.1%

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

      1. *-commutative 67.1%

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

      2. associate-*r* 56.7%

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

      3. associate-*r* 56.9%

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

      4. associate-*r* 56.9%

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

      5. distribute-rgt-in 56.9%

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

      6. +-commutative 56.9%

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

      7. mul-1-neg 56.9%

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

      8. unsub-neg 56.9%

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

      9. *-commutative 56.9%

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

      10. *-commutative 56.9%

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

   5. Simplified 56.9%

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

   6. Taylor expanded in x around inf 67.7%

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

      1. associate-*r* 68.1%

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

      2. *-commutative 68.1%

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

   8. Simplified 68.1%

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

   if 9.4999999999999994e-292 < b < 8.19999999999999962e-221

   1. Initial program 70.6%

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

   3. Taylor expanded in c around inf 49.9%

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

      1. *-commutative 49.9%

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

      2. *-commutative 49.9%

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

   5. Simplified 49.9%

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

   6. Taylor expanded in t around inf 44.5%

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

   if 8.19999999999999962e-221 < b < 2.6999999999999997e-35

   1. Initial program 65.6%

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

   3. Taylor expanded in y around inf 43.1%

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

      1. +-commutative 43.1%

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

      2. mul-1-neg 43.1%

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

      3. unsub-neg 43.1%

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

      4. *-commutative 43.1%

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

   5. Simplified 43.1%

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

   6. Taylor expanded in x around 0 48.3%

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

      1. associate-*r* 48.3%

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

      2. neg-mul-1 48.3%

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

   8. Simplified 48.3%

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

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{-52}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -4.3 \cdot 10^{-241}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{-275}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-292}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{-221}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-35}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 43.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -7 \cdot 10^{-52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.05 \cdot 10^{-241}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-275}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-292}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-226}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{-38}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= b -7e-52)
     t_1
     (if (<= b -2.05e-241)
       (* x (* y z))
       (if (<= b -2.8e-275)
         (* a (* t (- x)))
         (if (<= b 8e-292)
           (* z (* x y))
           (if (<= b 1.9e-226)
             (* c (- (* t j) (* z b)))
             (if (<= b 5.8e-38) (* (* y j) (- i)) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -7e-52) {
		tmp = t_1;
	} else if (b <= -2.05e-241) {
		tmp = x * (y * z);
	} else if (b <= -2.8e-275) {
		tmp = a * (t * -x);
	} else if (b <= 8e-292) {
		tmp = z * (x * y);
	} else if (b <= 1.9e-226) {
		tmp = c * ((t * j) - (z * b));
	} else if (b <= 5.8e-38) {
		tmp = (y * j) * -i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    if (b <= (-7d-52)) then
        tmp = t_1
    else if (b <= (-2.05d-241)) then
        tmp = x * (y * z)
    else if (b <= (-2.8d-275)) then
        tmp = a * (t * -x)
    else if (b <= 8d-292) then
        tmp = z * (x * y)
    else if (b <= 1.9d-226) then
        tmp = c * ((t * j) - (z * b))
    else if (b <= 5.8d-38) then
        tmp = (y * j) * -i
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -7e-52) {
		tmp = t_1;
	} else if (b <= -2.05e-241) {
		tmp = x * (y * z);
	} else if (b <= -2.8e-275) {
		tmp = a * (t * -x);
	} else if (b <= 8e-292) {
		tmp = z * (x * y);
	} else if (b <= 1.9e-226) {
		tmp = c * ((t * j) - (z * b));
	} else if (b <= 5.8e-38) {
		tmp = (y * j) * -i;
	} 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 <= -7e-52:
		tmp = t_1
	elif b <= -2.05e-241:
		tmp = x * (y * z)
	elif b <= -2.8e-275:
		tmp = a * (t * -x)
	elif b <= 8e-292:
		tmp = z * (x * y)
	elif b <= 1.9e-226:
		tmp = c * ((t * j) - (z * b))
	elif b <= 5.8e-38:
		tmp = (y * j) * -i
	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 <= -7e-52)
		tmp = t_1;
	elseif (b <= -2.05e-241)
		tmp = Float64(x * Float64(y * z));
	elseif (b <= -2.8e-275)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (b <= 8e-292)
		tmp = Float64(z * Float64(x * y));
	elseif (b <= 1.9e-226)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (b <= 5.8e-38)
		tmp = Float64(Float64(y * j) * Float64(-i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -7e-52)
		tmp = t_1;
	elseif (b <= -2.05e-241)
		tmp = x * (y * z);
	elseif (b <= -2.8e-275)
		tmp = a * (t * -x);
	elseif (b <= 8e-292)
		tmp = z * (x * y);
	elseif (b <= 1.9e-226)
		tmp = c * ((t * j) - (z * b));
	elseif (b <= 5.8e-38)
		tmp = (y * j) * -i;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7e-52], t$95$1, If[LessEqual[b, -2.05e-241], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.8e-275], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8e-292], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.9e-226], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.8e-38], N[(N[(y * j), $MachinePrecision] * (-i)), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -7.0000000000000001e-52 or 5.79999999999999988e-38 < b

   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 b around inf 57.9%

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

      1. *-commutative 57.9%

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

   5. Simplified 57.9%

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

   if -7.0000000000000001e-52 < b < -2.0499999999999999e-241

   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 y around inf 66.0%

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

      1. +-commutative 66.0%

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

      2. mul-1-neg 66.0%

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

      3. unsub-neg 66.0%

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

      4. *-commutative 66.0%

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

   5. Simplified 66.0%

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

   6. Taylor expanded in x around inf 63.1%

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

      1. +-commutative 63.1%

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

      2. *-commutative 63.1%

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

      3. mul-1-neg 63.1%

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

      4. unsub-neg 63.1%

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

      5. *-commutative 63.1%

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

      6. associate-*r* 64.9%

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

      7. *-commutative 64.9%

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

   8. Simplified 64.9%

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

   9. Taylor expanded in x around inf 48.3%

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

   if -2.0499999999999999e-241 < b < -2.79999999999999994e-275

   1. Initial program 87.8%

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

   3. Taylor expanded in z around inf 87.8%

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

      1. +-commutative 87.8%

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

      2. fma-define 87.8%

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

      3. mul-1-neg 87.8%

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

      4. associate-/l* 75.9%

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

      5. distribute-lft-neg-in 75.9%

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

      6. *-commutative 75.9%

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

   5. Simplified 75.9%

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

   6. Taylor expanded in x around inf 65.4%

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

      1. associate-*r* 65.6%

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

      2. mul-1-neg 65.6%

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

      3. unsub-neg 65.6%

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

      4. associate-/l* 63.4%

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

   8. Simplified 63.4%

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

   9. Taylor expanded in z around 0 64.9%

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

       1. associate-*r* 64.9%

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

       2. neg-mul-1 64.9%

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

       3. *-commutative 64.9%

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

   11. Simplified 64.9%

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

   if -2.79999999999999994e-275 < b < 8.0000000000000004e-292

   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 t around 0 67.1%

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

      1. *-commutative 67.1%

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

      2. associate-*r* 56.7%

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

      3. associate-*r* 56.9%

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

      4. associate-*r* 56.9%

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

      5. distribute-rgt-in 56.9%

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

      6. +-commutative 56.9%

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

      7. mul-1-neg 56.9%

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

      8. unsub-neg 56.9%

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

      9. *-commutative 56.9%

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

      10. *-commutative 56.9%

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

   5. Simplified 56.9%

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

   6. Taylor expanded in x around inf 67.7%

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

      1. associate-*r* 68.1%

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

      2. *-commutative 68.1%

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

   8. Simplified 68.1%

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

   if 8.0000000000000004e-292 < b < 1.89999999999999991e-226

   1. Initial program 70.6%

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

   3. Taylor expanded in c around inf 49.9%

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

      1. *-commutative 49.9%

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

      2. *-commutative 49.9%

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

   5. Simplified 49.9%

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

   if 1.89999999999999991e-226 < b < 5.79999999999999988e-38

   1. Initial program 65.6%

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

   3. Taylor expanded in y around inf 43.1%

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

      1. +-commutative 43.1%

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

      2. mul-1-neg 43.1%

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

      3. unsub-neg 43.1%

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

      4. *-commutative 43.1%

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

   5. Simplified 43.1%

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

   6. Taylor expanded in x around 0 48.3%

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

      1. associate-*r* 48.3%

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

      2. neg-mul-1 48.3%

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

   8. Simplified 48.3%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{-52}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2.05 \cdot 10^{-241}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-275}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-292}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-226}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{-38}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 65.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right) + t\_1\\ t_3 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -1.35 \cdot 10^{+112}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -2.42 \cdot 10^{-60}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-170}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + t\_1\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+25}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c))))
        (t_2 (+ (* y (- (* x z) (* i j))) t_1))
        (t_3 (* t (- (* c j) (* x a)))))
   (if (<= t -1.35e+112)
     t_3
     (if (<= t -2.42e-60)
       t_2
       (if (<= t -1e-170)
         (+ (* x (- (* y z) (* t a))) t_1)
         (if (<= t 3.4e+25) 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 = b * ((a * i) - (z * c));
	double t_2 = (y * ((x * z) - (i * j))) + t_1;
	double t_3 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -1.35e+112) {
		tmp = t_3;
	} else if (t <= -2.42e-60) {
		tmp = t_2;
	} else if (t <= -1e-170) {
		tmp = (x * ((y * z) - (t * a))) + t_1;
	} else if (t <= 3.4e+25) {
		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 = b * ((a * i) - (z * c))
    t_2 = (y * ((x * z) - (i * j))) + t_1
    t_3 = t * ((c * j) - (x * a))
    if (t <= (-1.35d+112)) then
        tmp = t_3
    else if (t <= (-2.42d-60)) then
        tmp = t_2
    else if (t <= (-1d-170)) then
        tmp = (x * ((y * z) - (t * a))) + t_1
    else if (t <= 3.4d+25) 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 = b * ((a * i) - (z * c));
	double t_2 = (y * ((x * z) - (i * j))) + t_1;
	double t_3 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -1.35e+112) {
		tmp = t_3;
	} else if (t <= -2.42e-60) {
		tmp = t_2;
	} else if (t <= -1e-170) {
		tmp = (x * ((y * z) - (t * a))) + t_1;
	} else if (t <= 3.4e+25) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	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))) + t_1
	t_3 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -1.35e+112:
		tmp = t_3
	elif t <= -2.42e-60:
		tmp = t_2
	elif t <= -1e-170:
		tmp = (x * ((y * z) - (t * a))) + t_1
	elif t <= 3.4e+25:
		tmp = t_2
	else:
		tmp = t_3
	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(y * Float64(Float64(x * z) - Float64(i * j))) + t_1)
	t_3 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -1.35e+112)
		tmp = t_3;
	elseif (t <= -2.42e-60)
		tmp = t_2;
	elseif (t <= -1e-170)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_1);
	elseif (t <= 3.4e+25)
		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 = b * ((a * i) - (z * c));
	t_2 = (y * ((x * z) - (i * j))) + t_1;
	t_3 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -1.35e+112)
		tmp = t_3;
	elseif (t <= -2.42e-60)
		tmp = t_2;
	elseif (t <= -1e-170)
		tmp = (x * ((y * z) - (t * a))) + t_1;
	elseif (t <= 3.4e+25)
		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[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.35e+112], t$95$3, If[LessEqual[t, -2.42e-60], t$95$2, If[LessEqual[t, -1e-170], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t, 3.4e+25], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.3500000000000001e112 or 3.39999999999999984e25 < t

   1. Initial program 55.6%

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

   3. Taylor expanded in t around inf 66.5%

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

      1. +-commutative 66.5%

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

      2. mul-1-neg 66.5%

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

      3. unsub-neg 66.5%

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

      4. *-commutative 66.5%

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

      5. *-commutative 66.5%

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

   5. Simplified 66.5%

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

   if -1.3500000000000001e112 < t < -2.41999999999999992e-60 or -9.99999999999999983e-171 < t < 3.39999999999999984e25

   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 t around 0 70.3%

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

      1. *-commutative 70.3%

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

      2. associate-*r* 72.9%

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

      3. associate-*r* 72.2%

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

      4. associate-*r* 72.2%

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

      5. distribute-rgt-in 75.1%

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

      6. +-commutative 75.1%

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

      7. mul-1-neg 75.1%

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

      8. unsub-neg 75.1%

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

      9. *-commutative 75.1%

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

      10. *-commutative 75.1%

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

   5. Simplified 75.1%

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

   if -2.41999999999999992e-60 < t < -9.99999999999999983e-171

   1. Initial program 70.5%

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

   3. Taylor expanded in j around 0 67.3%

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

      1. *-commutative 67.3%

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

   5. Simplified 67.3%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+112}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -2.42 \cdot 10^{-60}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-170}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+25}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 30.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i\right)\\ \mathbf{if}\;b \leq -3.7 \cdot 10^{-46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.05 \cdot 10^{-241}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq -3.4 \cdot 10^{-275}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-292}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 3.05 \cdot 10^{-230}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{+44}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* b i))))
   (if (<= b -3.7e-46)
     t_1
     (if (<= b -2.05e-241)
       (* x (* y z))
       (if (<= b -3.4e-275)
         (* a (* t (- x)))
         (if (<= b 5.5e-292)
           (* z (* x y))
           (if (<= b 3.05e-230)
             (* c (* t j))
             (if (<= b 2.7e+44) (* (* y j) (- i)) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (b * i);
	double tmp;
	if (b <= -3.7e-46) {
		tmp = t_1;
	} else if (b <= -2.05e-241) {
		tmp = x * (y * z);
	} else if (b <= -3.4e-275) {
		tmp = a * (t * -x);
	} else if (b <= 5.5e-292) {
		tmp = z * (x * y);
	} else if (b <= 3.05e-230) {
		tmp = c * (t * j);
	} else if (b <= 2.7e+44) {
		tmp = (y * j) * -i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (b * i)
    if (b <= (-3.7d-46)) then
        tmp = t_1
    else if (b <= (-2.05d-241)) then
        tmp = x * (y * z)
    else if (b <= (-3.4d-275)) then
        tmp = a * (t * -x)
    else if (b <= 5.5d-292) then
        tmp = z * (x * y)
    else if (b <= 3.05d-230) then
        tmp = c * (t * j)
    else if (b <= 2.7d+44) then
        tmp = (y * j) * -i
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (b * i);
	double tmp;
	if (b <= -3.7e-46) {
		tmp = t_1;
	} else if (b <= -2.05e-241) {
		tmp = x * (y * z);
	} else if (b <= -3.4e-275) {
		tmp = a * (t * -x);
	} else if (b <= 5.5e-292) {
		tmp = z * (x * y);
	} else if (b <= 3.05e-230) {
		tmp = c * (t * j);
	} else if (b <= 2.7e+44) {
		tmp = (y * j) * -i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (b * i)
	tmp = 0
	if b <= -3.7e-46:
		tmp = t_1
	elif b <= -2.05e-241:
		tmp = x * (y * z)
	elif b <= -3.4e-275:
		tmp = a * (t * -x)
	elif b <= 5.5e-292:
		tmp = z * (x * y)
	elif b <= 3.05e-230:
		tmp = c * (t * j)
	elif b <= 2.7e+44:
		tmp = (y * j) * -i
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(b * i))
	tmp = 0.0
	if (b <= -3.7e-46)
		tmp = t_1;
	elseif (b <= -2.05e-241)
		tmp = Float64(x * Float64(y * z));
	elseif (b <= -3.4e-275)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (b <= 5.5e-292)
		tmp = Float64(z * Float64(x * y));
	elseif (b <= 3.05e-230)
		tmp = Float64(c * Float64(t * j));
	elseif (b <= 2.7e+44)
		tmp = Float64(Float64(y * j) * Float64(-i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (b * i);
	tmp = 0.0;
	if (b <= -3.7e-46)
		tmp = t_1;
	elseif (b <= -2.05e-241)
		tmp = x * (y * z);
	elseif (b <= -3.4e-275)
		tmp = a * (t * -x);
	elseif (b <= 5.5e-292)
		tmp = z * (x * y);
	elseif (b <= 3.05e-230)
		tmp = c * (t * j);
	elseif (b <= 2.7e+44)
		tmp = (y * j) * -i;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.7e-46], t$95$1, If[LessEqual[b, -2.05e-241], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.4e-275], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.5e-292], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.05e-230], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.7e+44], N[(N[(y * j), $MachinePrecision] * (-i)), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -3.69999999999999983e-46 or 2.7e44 < b

   1. Initial program 68.9%

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

   3. Taylor expanded in b around inf 60.1%

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

      1. *-commutative 60.1%

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

   5. Simplified 60.1%

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

   6. Taylor expanded in a around inf 42.4%

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

      1. *-commutative 42.4%

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

   8. Simplified 42.4%

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

   if -3.69999999999999983e-46 < b < -2.0499999999999999e-241

   1. Initial program 74.6%

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

   3. Taylor expanded in y around inf 64.8%

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

      1. +-commutative 64.8%

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

      2. mul-1-neg 64.8%

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

      3. unsub-neg 64.8%

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

      4. *-commutative 64.8%

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

   5. Simplified 64.8%

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

   6. Taylor expanded in x around inf 62.0%

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

      1. +-commutative 62.0%

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

      2. *-commutative 62.0%

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

      3. mul-1-neg 62.0%

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

      4. unsub-neg 62.0%

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

      5. *-commutative 62.0%

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

      6. associate-*r* 63.8%

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

      7. *-commutative 63.8%

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

   8. Simplified 63.8%

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

   9. Taylor expanded in x around inf 47.5%

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

   if -2.0499999999999999e-241 < b < -3.39999999999999968e-275

   1. Initial program 87.8%

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

   3. Taylor expanded in z around inf 87.8%

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

      1. +-commutative 87.8%

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

      2. fma-define 87.8%

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

      3. mul-1-neg 87.8%

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

      4. associate-/l* 75.9%

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

      5. distribute-lft-neg-in 75.9%

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

      6. *-commutative 75.9%

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

   5. Simplified 75.9%

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

   6. Taylor expanded in x around inf 65.4%

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

      1. associate-*r* 65.6%

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

      2. mul-1-neg 65.6%

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

      3. unsub-neg 65.6%

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

      4. associate-/l* 63.4%

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

   8. Simplified 63.4%

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

   9. Taylor expanded in z around 0 64.9%

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

       1. associate-*r* 64.9%

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

       2. neg-mul-1 64.9%

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

       3. *-commutative 64.9%

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

   11. Simplified 64.9%

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

   if -3.39999999999999968e-275 < b < 5.50000000000000006e-292

   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 t around 0 67.1%

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

      1. *-commutative 67.1%

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

      2. associate-*r* 56.7%

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

      3. associate-*r* 56.9%

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

      4. associate-*r* 56.9%

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

      5. distribute-rgt-in 56.9%

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

      6. +-commutative 56.9%

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

      7. mul-1-neg 56.9%

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

      8. unsub-neg 56.9%

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

      9. *-commutative 56.9%

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

      10. *-commutative 56.9%

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

   5. Simplified 56.9%

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

   6. Taylor expanded in x around inf 67.7%

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

      1. associate-*r* 68.1%

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

      2. *-commutative 68.1%

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

   8. Simplified 68.1%

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

   if 5.50000000000000006e-292 < b < 3.04999999999999978e-230

   1. Initial program 70.6%

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

   3. Taylor expanded in c around inf 49.9%

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

      1. *-commutative 49.9%

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

      2. *-commutative 49.9%

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

   5. Simplified 49.9%

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

   6. Taylor expanded in t around inf 44.5%

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

   if 3.04999999999999978e-230 < b < 2.7e44

   1. Initial program 65.6%

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

   3. Taylor expanded in y around inf 43.6%

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

      1. +-commutative 43.6%

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

      2. mul-1-neg 43.6%

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

      3. unsub-neg 43.6%

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

      4. *-commutative 43.6%

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

   5. Simplified 43.6%

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

   6. Taylor expanded in x around 0 41.3%

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

      1. associate-*r* 41.3%

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

      2. neg-mul-1 41.3%

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

   8. Simplified 41.3%

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

4. Final simplification 45.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.7 \cdot 10^{-46}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq -2.05 \cdot 10^{-241}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq -3.4 \cdot 10^{-275}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-292}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 3.05 \cdot 10^{-230}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{+44}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 62.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := t\_1 + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;y \leq -4 \cdot 10^{-112}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-7}:\\ \;\;\;\;z \cdot \left(\left(x \cdot y - a \cdot \left(x \cdot \frac{t}{z}\right)\right) + \left(a \cdot \frac{b \cdot i}{z} - b \cdot c\right)\right)\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+168}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j))))
        (t_2 (+ t_1 (* b (- (* a i) (* z c))))))
   (if (<= y -4e-112)
     t_2
     (if (<= y 1.7e-7)
       (*
        z
        (+ (- (* x y) (* a (* x (/ t z)))) (- (* a (/ (* b i) z)) (* b c))))
       (if (<= y 4.6e+168) t_2 t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double t_2 = t_1 + (b * ((a * i) - (z * c)));
	double tmp;
	if (y <= -4e-112) {
		tmp = t_2;
	} else if (y <= 1.7e-7) {
		tmp = z * (((x * y) - (a * (x * (t / z)))) + ((a * ((b * i) / z)) - (b * c)));
	} else if (y <= 4.6e+168) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((x * z) - (i * j))
    t_2 = t_1 + (b * ((a * i) - (z * c)))
    if (y <= (-4d-112)) then
        tmp = t_2
    else if (y <= 1.7d-7) then
        tmp = z * (((x * y) - (a * (x * (t / z)))) + ((a * ((b * i) / z)) - (b * c)))
    else if (y <= 4.6d+168) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double t_2 = t_1 + (b * ((a * i) - (z * c)));
	double tmp;
	if (y <= -4e-112) {
		tmp = t_2;
	} else if (y <= 1.7e-7) {
		tmp = z * (((x * y) - (a * (x * (t / z)))) + ((a * ((b * i) / z)) - (b * c)));
	} else if (y <= 4.6e+168) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	t_2 = t_1 + (b * ((a * i) - (z * c)))
	tmp = 0
	if y <= -4e-112:
		tmp = t_2
	elif y <= 1.7e-7:
		tmp = z * (((x * y) - (a * (x * (t / z)))) + ((a * ((b * i) / z)) - (b * c)))
	elif y <= 4.6e+168:
		tmp = t_2
	else:
		tmp = t_1
	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_1 + Float64(b * Float64(Float64(a * i) - Float64(z * c))))
	tmp = 0.0
	if (y <= -4e-112)
		tmp = t_2;
	elseif (y <= 1.7e-7)
		tmp = Float64(z * Float64(Float64(Float64(x * y) - Float64(a * Float64(x * Float64(t / z)))) + Float64(Float64(a * Float64(Float64(b * i) / z)) - Float64(b * c))));
	elseif (y <= 4.6e+168)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((x * z) - (i * j));
	t_2 = t_1 + (b * ((a * i) - (z * c)));
	tmp = 0.0;
	if (y <= -4e-112)
		tmp = t_2;
	elseif (y <= 1.7e-7)
		tmp = z * (((x * y) - (a * (x * (t / z)))) + ((a * ((b * i) / z)) - (b * c)));
	elseif (y <= 4.6e+168)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4e-112], t$95$2, If[LessEqual[y, 1.7e-7], N[(z * N[(N[(N[(x * y), $MachinePrecision] - N[(a * N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * N[(N[(b * i), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.6e+168], t$95$2, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.9999999999999998e-112 or 1.69999999999999987e-7 < y < 4.5999999999999999e168

   1. Initial program 69.5%

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

   3. Taylor expanded in t around 0 62.3%

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

      1. *-commutative 62.3%

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

      2. associate-*r* 65.2%

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

      3. associate-*r* 66.0%

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

      4. associate-*r* 66.0%

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

      5. distribute-rgt-in 69.2%

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

      6. +-commutative 69.2%

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

      7. mul-1-neg 69.2%

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

      8. unsub-neg 69.2%

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

      9. *-commutative 69.2%

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

      10. *-commutative 69.2%

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

   5. Simplified 69.2%

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

   if -3.9999999999999998e-112 < y < 1.69999999999999987e-7

   1. Initial program 75.5%

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

   3. Taylor expanded in j around 0 57.3%

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

      1. *-commutative 57.3%

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

   5. Simplified 57.3%

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

   6. Taylor expanded in z around inf 68.0%

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

      1. +-commutative 68.0%

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

      2. mul-1-neg 68.0%

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

      3. unsub-neg 68.0%

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

      4. associate-/l* 64.9%

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

      5. *-commutative 64.9%

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

      6. associate-*r/ 67.7%

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

      7. +-commutative 67.7%

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

      8. mul-1-neg 67.7%

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

      9. unsub-neg 67.7%

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

      10. *-commutative 67.7%

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

      11. associate-/l* 66.8%

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

      12. *-commutative 66.8%

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

   8. Simplified 66.8%

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

   if 4.5999999999999999e168 < y

   1. Initial program 57.0%

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

   3. Taylor expanded in y around inf 89.6%

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

      1. +-commutative 89.6%

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

      2. mul-1-neg 89.6%

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

      3. unsub-neg 89.6%

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

      4. *-commutative 89.6%

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

   5. Simplified 89.6%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-112}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-7}:\\ \;\;\;\;z \cdot \left(\left(x \cdot y - a \cdot \left(x \cdot \frac{t}{z}\right)\right) + \left(a \cdot \frac{b \cdot i}{z} - b \cdot c\right)\right)\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+168}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 51.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -4.4 \cdot 10^{-52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-252}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{-34}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{+114} \lor \neg \left(b \leq 2.8 \cdot 10^{+160}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= b -4.4e-52)
     t_1
     (if (<= b -2.8e-252)
       (* y (- (* x z) (* i j)))
       (if (<= b 9.2e-34)
         (* j (- (* t c) (* y i)))
         (if (or (<= b 1.8e+114) (not (<= b 2.8e+160)))
           t_1
           (* t (- (* c j) (* x 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 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -4.4e-52) {
		tmp = t_1;
	} else if (b <= -2.8e-252) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 9.2e-34) {
		tmp = j * ((t * c) - (y * i));
	} else if ((b <= 1.8e+114) || !(b <= 2.8e+160)) {
		tmp = t_1;
	} else {
		tmp = t * ((c * j) - (x * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    if (b <= (-4.4d-52)) then
        tmp = t_1
    else if (b <= (-2.8d-252)) then
        tmp = y * ((x * z) - (i * j))
    else if (b <= 9.2d-34) then
        tmp = j * ((t * c) - (y * i))
    else if ((b <= 1.8d+114) .or. (.not. (b <= 2.8d+160))) then
        tmp = t_1
    else
        tmp = t * ((c * j) - (x * 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 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -4.4e-52) {
		tmp = t_1;
	} else if (b <= -2.8e-252) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 9.2e-34) {
		tmp = j * ((t * c) - (y * i));
	} else if ((b <= 1.8e+114) || !(b <= 2.8e+160)) {
		tmp = t_1;
	} else {
		tmp = t * ((c * j) - (x * a));
	}
	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 <= -4.4e-52:
		tmp = t_1
	elif b <= -2.8e-252:
		tmp = y * ((x * z) - (i * j))
	elif b <= 9.2e-34:
		tmp = j * ((t * c) - (y * i))
	elif (b <= 1.8e+114) or not (b <= 2.8e+160):
		tmp = t_1
	else:
		tmp = t * ((c * j) - (x * a))
	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 <= -4.4e-52)
		tmp = t_1;
	elseif (b <= -2.8e-252)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (b <= 9.2e-34)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif ((b <= 1.8e+114) || !(b <= 2.8e+160))
		tmp = t_1;
	else
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	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 <= -4.4e-52)
		tmp = t_1;
	elseif (b <= -2.8e-252)
		tmp = y * ((x * z) - (i * j));
	elseif (b <= 9.2e-34)
		tmp = j * ((t * c) - (y * i));
	elseif ((b <= 1.8e+114) || ~((b <= 2.8e+160)))
		tmp = t_1;
	else
		tmp = t * ((c * j) - (x * a));
	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, -4.4e-52], t$95$1, If[LessEqual[b, -2.8e-252], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.2e-34], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, 1.8e+114], N[Not[LessEqual[b, 2.8e+160]], $MachinePrecision]], t$95$1, N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -4.40000000000000018e-52 or 9.20000000000000045e-34 < b < 1.8e114 or 2.8e160 < b

   1. Initial program 66.6%

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

   3. Taylor expanded in b around inf 60.5%

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

      1. *-commutative 60.5%

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

   5. Simplified 60.5%

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

   if -4.40000000000000018e-52 < b < -2.80000000000000018e-252

   1. Initial program 75.1%

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

   3. Taylor expanded in y around inf 63.8%

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

      1. +-commutative 63.8%

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

      2. mul-1-neg 63.8%

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

      3. unsub-neg 63.8%

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

      4. *-commutative 63.8%

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

   5. Simplified 63.8%

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

   if -2.80000000000000018e-252 < b < 9.20000000000000045e-34

   1. Initial program 71.5%

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

   3. Taylor expanded in j around inf 56.6%

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

      1. sub-neg 56.6%

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

      2. *-commutative 56.6%

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

      3. *-commutative 56.6%

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

      4. sub-neg 56.6%

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

   5. Simplified 56.6%

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

   if 1.8e114 < b < 2.8e160

   1. Initial program 88.7%

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

   3. Taylor expanded in t around inf 67.6%

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

      1. +-commutative 67.6%

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

      2. mul-1-neg 67.6%

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

      3. unsub-neg 67.6%

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

      4. *-commutative 67.6%

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

      5. *-commutative 67.6%

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

   5. Simplified 67.6%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.4 \cdot 10^{-52}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-252}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{-34}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{+114} \lor \neg \left(b \leq 2.8 \cdot 10^{+160}\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 29.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i\right)\\ \mathbf{if}\;b \leq -2.55 \cdot 10^{-45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -5.9 \cdot 10^{-241}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq -4.7 \cdot 10^{-275}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{-292}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{-105}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* b i))))
   (if (<= b -2.55e-45)
     t_1
     (if (<= b -5.9e-241)
       (* x (* y z))
       (if (<= b -4.7e-275)
         (* a (* t (- x)))
         (if (<= b 4.2e-292)
           (* z (* x y))
           (if (<= b 1.35e-105) (* c (* t j)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (b * i);
	double tmp;
	if (b <= -2.55e-45) {
		tmp = t_1;
	} else if (b <= -5.9e-241) {
		tmp = x * (y * z);
	} else if (b <= -4.7e-275) {
		tmp = a * (t * -x);
	} else if (b <= 4.2e-292) {
		tmp = z * (x * y);
	} else if (b <= 1.35e-105) {
		tmp = c * (t * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (b * i)
    if (b <= (-2.55d-45)) then
        tmp = t_1
    else if (b <= (-5.9d-241)) then
        tmp = x * (y * z)
    else if (b <= (-4.7d-275)) then
        tmp = a * (t * -x)
    else if (b <= 4.2d-292) then
        tmp = z * (x * y)
    else if (b <= 1.35d-105) then
        tmp = c * (t * j)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (b * i);
	double tmp;
	if (b <= -2.55e-45) {
		tmp = t_1;
	} else if (b <= -5.9e-241) {
		tmp = x * (y * z);
	} else if (b <= -4.7e-275) {
		tmp = a * (t * -x);
	} else if (b <= 4.2e-292) {
		tmp = z * (x * y);
	} else if (b <= 1.35e-105) {
		tmp = c * (t * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (b * i)
	tmp = 0
	if b <= -2.55e-45:
		tmp = t_1
	elif b <= -5.9e-241:
		tmp = x * (y * z)
	elif b <= -4.7e-275:
		tmp = a * (t * -x)
	elif b <= 4.2e-292:
		tmp = z * (x * y)
	elif b <= 1.35e-105:
		tmp = c * (t * j)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(b * i))
	tmp = 0.0
	if (b <= -2.55e-45)
		tmp = t_1;
	elseif (b <= -5.9e-241)
		tmp = Float64(x * Float64(y * z));
	elseif (b <= -4.7e-275)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (b <= 4.2e-292)
		tmp = Float64(z * Float64(x * y));
	elseif (b <= 1.35e-105)
		tmp = Float64(c * Float64(t * j));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (b * i);
	tmp = 0.0;
	if (b <= -2.55e-45)
		tmp = t_1;
	elseif (b <= -5.9e-241)
		tmp = x * (y * z);
	elseif (b <= -4.7e-275)
		tmp = a * (t * -x);
	elseif (b <= 4.2e-292)
		tmp = z * (x * y);
	elseif (b <= 1.35e-105)
		tmp = c * (t * j);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.55e-45], t$95$1, If[LessEqual[b, -5.9e-241], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.7e-275], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.2e-292], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.35e-105], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -2.5499999999999999e-45 or 1.34999999999999996e-105 < b

   1. Initial program 67.5%

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

   3. Taylor expanded in b around inf 53.4%

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

      1. *-commutative 53.4%

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

   5. Simplified 53.4%

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

   6. Taylor expanded in a around inf 38.9%

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

      1. *-commutative 38.9%

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

   8. Simplified 38.9%

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

   if -2.5499999999999999e-45 < b < -5.8999999999999998e-241

   1. Initial program 74.6%

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

   3. Taylor expanded in y around inf 64.8%

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

      1. +-commutative 64.8%

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

      2. mul-1-neg 64.8%

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

      3. unsub-neg 64.8%

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

      4. *-commutative 64.8%

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

   5. Simplified 64.8%

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

   6. Taylor expanded in x around inf 62.0%

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

      1. +-commutative 62.0%

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

      2. *-commutative 62.0%

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

      3. mul-1-neg 62.0%

         \[\leadsto x \cdot \left(z \cdot y + \color{blue}{\left(-\frac{i \cdot \left(j \cdot y\right)}{x}\right)}\right) \]

      4. unsub-neg 62.0%

         \[\leadsto x \cdot \color{blue}{\left(z \cdot y - \frac{i \cdot \left(j \cdot y\right)}{x}\right)} \]

      5. *-commutative 62.0%

         \[\leadsto x \cdot \left(\color{blue}{y \cdot z} - \frac{i \cdot \left(j \cdot y\right)}{x}\right) \]

      6. associate-*r* 63.8%

         \[\leadsto x \cdot \left(y \cdot z - \frac{\color{blue}{\left(i \cdot j\right) \cdot y}}{x}\right) \]

      7. *-commutative 63.8%

         \[\leadsto x \cdot \left(y \cdot z - \frac{\color{blue}{\left(j \cdot i\right)} \cdot y}{x}\right) \]

   8. Simplified 63.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - \frac{\left(j \cdot i\right) \cdot y}{x}\right)} \]

   9. Taylor expanded in x around inf 47.5%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   if -5.8999999999999998e-241 < b < -4.6999999999999998e-275

   1. Initial program 87.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 87.8%

      \[\leadsto \left(\color{blue}{z \cdot \left(-1 \cdot \frac{a \cdot \left(t \cdot x\right)}{z} + x \cdot y\right)} - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. +-commutative 87.8%

         \[\leadsto \left(z \cdot \color{blue}{\left(x \cdot y + -1 \cdot \frac{a \cdot \left(t \cdot x\right)}{z}\right)} - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. fma-define 87.8%

         \[\leadsto \left(z \cdot \color{blue}{\mathsf{fma}\left(x, y, -1 \cdot \frac{a \cdot \left(t \cdot x\right)}{z}\right)} - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      3. mul-1-neg 87.8%

         \[\leadsto \left(z \cdot \mathsf{fma}\left(x, y, \color{blue}{-\frac{a \cdot \left(t \cdot x\right)}{z}}\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      4. associate-/l* 75.9%

         \[\leadsto \left(z \cdot \mathsf{fma}\left(x, y, -\color{blue}{a \cdot \frac{t \cdot x}{z}}\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      5. distribute-lft-neg-in 75.9%

         \[\leadsto \left(z \cdot \mathsf{fma}\left(x, y, \color{blue}{\left(-a\right) \cdot \frac{t \cdot x}{z}}\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 75.9%

         \[\leadsto \left(z \cdot \mathsf{fma}\left(x, y, \left(-a\right) \cdot \frac{\color{blue}{x \cdot t}}{z}\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 75.9%

      \[\leadsto \left(\color{blue}{z \cdot \mathsf{fma}\left(x, y, \left(-a\right) \cdot \frac{x \cdot t}{z}\right)} - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   6. Taylor expanded in x around inf 65.4%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot \left(y + -1 \cdot \frac{a \cdot t}{z}\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 65.6%

         \[\leadsto \color{blue}{\left(x \cdot z\right) \cdot \left(y + -1 \cdot \frac{a \cdot t}{z}\right)} \]

      2. mul-1-neg 65.6%

         \[\leadsto \left(x \cdot z\right) \cdot \left(y + \color{blue}{\left(-\frac{a \cdot t}{z}\right)}\right) \]

      3. unsub-neg 65.6%

         \[\leadsto \left(x \cdot z\right) \cdot \color{blue}{\left(y - \frac{a \cdot t}{z}\right)} \]

      4. associate-/l* 63.4%

         \[\leadsto \left(x \cdot z\right) \cdot \left(y - \color{blue}{a \cdot \frac{t}{z}}\right) \]

   8. Simplified 63.4%

      \[\leadsto \color{blue}{\left(x \cdot z\right) \cdot \left(y - a \cdot \frac{t}{z}\right)} \]

   9. Taylor expanded in z around 0 64.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 64.9%

          \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x\right)} \]

       2. neg-mul-1 64.9%

          \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(t \cdot x\right) \]

       3. *-commutative 64.9%

          \[\leadsto \left(-a\right) \cdot \color{blue}{\left(x \cdot t\right)} \]

   11. Simplified 64.9%

       \[\leadsto \color{blue}{\left(-a\right) \cdot \left(x \cdot t\right)} \]

   if -4.6999999999999998e-275 < b < 4.19999999999999977e-292

   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 t around 0 67.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. *-commutative 67.1%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 56.7%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. associate-*r* 56.9%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 56.9%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 56.9%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 56.9%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 56.9%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 56.9%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 56.9%

         \[\leadsto y \cdot \left(x \cdot z - \color{blue}{j \cdot i}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      10. *-commutative 56.9%

          \[\leadsto y \cdot \left(x \cdot z - j \cdot i\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right) \]

   5. Simplified 56.9%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z - j \cdot i\right) - b \cdot \left(z \cdot c - a \cdot i\right)} \]

   6. Taylor expanded in x around inf 67.7%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 68.1%

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot z} \]

      2. *-commutative 68.1%

         \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]

   8. Simplified 68.1%

      \[\leadsto \color{blue}{\left(y \cdot x\right) \cdot z} \]

   if 4.19999999999999977e-292 < b < 1.34999999999999996e-105

   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 c around inf 46.8%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 46.8%

         \[\leadsto c \cdot \left(\color{blue}{t \cdot j} - b \cdot z\right) \]

      2. *-commutative 46.8%

         \[\leadsto c \cdot \left(t \cdot j - \color{blue}{z \cdot b}\right) \]

   5. Simplified 46.8%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   6. Taylor expanded in t around inf 41.6%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.55 \cdot 10^{-45}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq -5.9 \cdot 10^{-241}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq -4.7 \cdot 10^{-275}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{-292}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{-105}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 28.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i\right)\\ \mathbf{if}\;b \leq -1.35 \cdot 10^{-49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-292}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{-105}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* b i))))
   (if (<= b -1.35e-49)
     t_1
     (if (<= b 8.5e-292)
       (* x (* y z))
       (if (<= b 1.35e-105) (* c (* t j)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (b * i);
	double tmp;
	if (b <= -1.35e-49) {
		tmp = t_1;
	} else if (b <= 8.5e-292) {
		tmp = x * (y * z);
	} else if (b <= 1.35e-105) {
		tmp = c * (t * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (b * i)
    if (b <= (-1.35d-49)) then
        tmp = t_1
    else if (b <= 8.5d-292) then
        tmp = x * (y * z)
    else if (b <= 1.35d-105) then
        tmp = c * (t * j)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (b * i);
	double tmp;
	if (b <= -1.35e-49) {
		tmp = t_1;
	} else if (b <= 8.5e-292) {
		tmp = x * (y * z);
	} else if (b <= 1.35e-105) {
		tmp = c * (t * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (b * i)
	tmp = 0
	if b <= -1.35e-49:
		tmp = t_1
	elif b <= 8.5e-292:
		tmp = x * (y * z)
	elif b <= 1.35e-105:
		tmp = c * (t * j)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(b * i))
	tmp = 0.0
	if (b <= -1.35e-49)
		tmp = t_1;
	elseif (b <= 8.5e-292)
		tmp = Float64(x * Float64(y * z));
	elseif (b <= 1.35e-105)
		tmp = Float64(c * Float64(t * j));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (b * i);
	tmp = 0.0;
	if (b <= -1.35e-49)
		tmp = t_1;
	elseif (b <= 8.5e-292)
		tmp = x * (y * z);
	elseif (b <= 1.35e-105)
		tmp = c * (t * j);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.35e-49], t$95$1, If[LessEqual[b, 8.5e-292], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.35e-105], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.35e-49 or 1.34999999999999996e-105 < b

   1. Initial program 67.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 53.4%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 53.4%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   5. Simplified 53.4%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   6. Taylor expanded in a around inf 38.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   7. Step-by-step derivation

      1. *-commutative 38.9%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b\right)} \]

   8. Simplified 38.9%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]

   if -1.35e-49 < b < 8.50000000000000066e-292

   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 y around inf 59.7%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 59.7%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 59.7%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 59.7%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 59.7%

         \[\leadsto y \cdot \left(x \cdot z - \color{blue}{j \cdot i}\right) \]

   5. Simplified 59.7%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z - j \cdot i\right)} \]

   6. Taylor expanded in x around inf 60.1%

      \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \frac{i \cdot \left(j \cdot y\right)}{x} + y \cdot z\right)} \]
   7. Step-by-step derivation

      1. +-commutative 60.1%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z + -1 \cdot \frac{i \cdot \left(j \cdot y\right)}{x}\right)} \]

      2. *-commutative 60.1%

         \[\leadsto x \cdot \left(\color{blue}{z \cdot y} + -1 \cdot \frac{i \cdot \left(j \cdot y\right)}{x}\right) \]

      3. mul-1-neg 60.1%

         \[\leadsto x \cdot \left(z \cdot y + \color{blue}{\left(-\frac{i \cdot \left(j \cdot y\right)}{x}\right)}\right) \]

      4. unsub-neg 60.1%

         \[\leadsto x \cdot \color{blue}{\left(z \cdot y - \frac{i \cdot \left(j \cdot y\right)}{x}\right)} \]

      5. *-commutative 60.1%

         \[\leadsto x \cdot \left(\color{blue}{y \cdot z} - \frac{i \cdot \left(j \cdot y\right)}{x}\right) \]

      6. associate-*r* 61.5%

         \[\leadsto x \cdot \left(y \cdot z - \frac{\color{blue}{\left(i \cdot j\right) \cdot y}}{x}\right) \]

      7. *-commutative 61.5%

         \[\leadsto x \cdot \left(y \cdot z - \frac{\color{blue}{\left(j \cdot i\right)} \cdot y}{x}\right) \]

   8. Simplified 61.5%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - \frac{\left(j \cdot i\right) \cdot y}{x}\right)} \]

   9. Taylor expanded in x around inf 46.4%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   if 8.50000000000000066e-292 < b < 1.34999999999999996e-105

   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 c around inf 46.8%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 46.8%

         \[\leadsto c \cdot \left(\color{blue}{t \cdot j} - b \cdot z\right) \]

      2. *-commutative 46.8%

         \[\leadsto c \cdot \left(t \cdot j - \color{blue}{z \cdot b}\right) \]

   5. Simplified 46.8%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   6. Taylor expanded in t around inf 41.6%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 41.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.35 \cdot 10^{-49}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-292}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{-105}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 29.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.3 \cdot 10^{-53} \lor \neg \left(b \leq 1.35 \cdot 10^{-105}\right):\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -6.3e-53) (not (<= b 1.35e-105))) (* a (* b i)) (* c (* t j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -6.3e-53) || !(b <= 1.35e-105)) {
		tmp = a * (b * i);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-6.3d-53)) .or. (.not. (b <= 1.35d-105))) then
        tmp = a * (b * i)
    else
        tmp = c * (t * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -6.3e-53) || !(b <= 1.35e-105)) {
		tmp = a * (b * i);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -6.3e-53) or not (b <= 1.35e-105):
		tmp = a * (b * i)
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -6.3e-53) || !(b <= 1.35e-105))
		tmp = Float64(a * Float64(b * i));
	else
		tmp = Float64(c * Float64(t * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -6.3e-53) || ~((b <= 1.35e-105)))
		tmp = a * (b * i);
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -6.3e-53], N[Not[LessEqual[b, 1.35e-105]], $MachinePrecision]], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.29999999999999979e-53 or 1.34999999999999996e-105 < b

   1. Initial program 67.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 53.4%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 53.4%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   5. Simplified 53.4%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   6. Taylor expanded in a around inf 38.4%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   7. Step-by-step derivation

      1. *-commutative 38.4%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b\right)} \]

   8. Simplified 38.4%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]

   if -6.29999999999999979e-53 < b < 1.34999999999999996e-105

   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 c around inf 30.9%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 30.9%

         \[\leadsto c \cdot \left(\color{blue}{t \cdot j} - b \cdot z\right) \]

      2. *-commutative 30.9%

         \[\leadsto c \cdot \left(t \cdot j - \color{blue}{z \cdot b}\right) \]

   5. Simplified 30.9%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   6. Taylor expanded in t around inf 26.3%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 33.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.3 \cdot 10^{-53} \lor \neg \left(b \leq 1.35 \cdot 10^{-105}\right):\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 22.1% 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 70.5%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
2. Add Preprocessing

3. Taylor expanded in b around inf 35.8%

   \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
4. Step-by-step derivation

   1. *-commutative 35.8%

      \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

5. Simplified 35.8%

   \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

6. Taylor expanded in a around inf 24.1%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
7. Step-by-step derivation

   1. *-commutative 24.1%

      \[\leadsto a \cdot \color{blue}{\left(i \cdot b\right)} \]

8. Simplified 24.1%

   \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]

9. Final simplification 24.1%

   \[\leadsto a \cdot \left(b \cdot i\right) \]
10. Add Preprocessing

Developer target: 68.2% 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 2024059 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :alt
  (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)))))