Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.8% → 84.5%

Time: 18.4s

Alternatives: 22

Speedup: 0.5×

• 58.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.8% accurate, 1.0× speedup

Math

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

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: 84.5% accurate, 0.2× speedup

Math

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

FPCore

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(t * N[(N[(z * N[(N[(y * x + N[(N[(N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] - N[(x * a), $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 91.5%

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

   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 c around 0 28.1%

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

   5. Simplified 36.9%

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

   6. Taylor expanded in t around 0 36.9%

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

      1. associate-*r* 36.9%

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

      2. neg-mul-1 36.9%

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

      3. *-commutative 36.9%

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

   8. Simplified 36.9%

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

   9. Taylor expanded in z around -inf 45.6%

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

   11. Simplified 51.5%

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

   12. Taylor expanded in t around -inf 45.7%

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

   14. Simplified 57.5%

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

4. Final simplification 82.5%

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

Alternative 2: 82.0% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $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 91.5%

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

   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 z around inf 52.0%

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

      1. *-commutative 52.0%

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

   5. Simplified 52.0%

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

4. Final simplification 81.0%

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

Alternative 3: 69.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - \left(b \cdot c - \frac{a \cdot \left(b \cdot i - x \cdot t\right) - j \cdot \left(y \cdot i\right)}{z}\right)\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -6.4 \cdot 10^{+81}:\\ \;\;\;\;t\_3 + t\_2\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-157}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7.1 \cdot 10^{-118}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + t\_2\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+126}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (*
          z
          (-
           (* x y)
           (- (* b c) (/ (- (* a (- (* b i) (* x t))) (* j (* y i))) z)))))
        (t_2 (* b (- (* a i) (* z c))))
        (t_3 (* y (- (* x z) (* i j)))))
   (if (<= y -6.4e+81)
     (+ t_3 t_2)
     (if (<= y -6.5e-157)
       t_1
       (if (<= y 7.1e-118)
         (+ (* t (- (* c j) (* x a))) t_2)
         (if (<= y 7.6e+126) 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 = z * ((x * y) - ((b * c) - (((a * ((b * i) - (x * t))) - (j * (y * i))) / z)));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -6.4e+81) {
		tmp = t_3 + t_2;
	} else if (y <= -6.5e-157) {
		tmp = t_1;
	} else if (y <= 7.1e-118) {
		tmp = (t * ((c * j) - (x * a))) + t_2;
	} else if (y <= 7.6e+126) {
		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 = z * ((x * y) - ((b * c) - (((a * ((b * i) - (x * t))) - (j * (y * i))) / z)))
    t_2 = b * ((a * i) - (z * c))
    t_3 = y * ((x * z) - (i * j))
    if (y <= (-6.4d+81)) then
        tmp = t_3 + t_2
    else if (y <= (-6.5d-157)) then
        tmp = t_1
    else if (y <= 7.1d-118) then
        tmp = (t * ((c * j) - (x * a))) + t_2
    else if (y <= 7.6d+126) 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 = z * ((x * y) - ((b * c) - (((a * ((b * i) - (x * t))) - (j * (y * i))) / z)));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -6.4e+81) {
		tmp = t_3 + t_2;
	} else if (y <= -6.5e-157) {
		tmp = t_1;
	} else if (y <= 7.1e-118) {
		tmp = (t * ((c * j) - (x * a))) + t_2;
	} else if (y <= 7.6e+126) {
		tmp = t_1;
	} 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) - (((a * ((b * i) - (x * t))) - (j * (y * i))) / z)))
	t_2 = b * ((a * i) - (z * c))
	t_3 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -6.4e+81:
		tmp = t_3 + t_2
	elif y <= -6.5e-157:
		tmp = t_1
	elif y <= 7.1e-118:
		tmp = (t * ((c * j) - (x * a))) + t_2
	elif y <= 7.6e+126:
		tmp = t_1
	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(Float64(b * c) - Float64(Float64(Float64(a * Float64(Float64(b * i) - Float64(x * t))) - Float64(j * Float64(y * i))) / z))))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_3 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -6.4e+81)
		tmp = Float64(t_3 + t_2);
	elseif (y <= -6.5e-157)
		tmp = t_1;
	elseif (y <= 7.1e-118)
		tmp = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) + t_2);
	elseif (y <= 7.6e+126)
		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 = z * ((x * y) - ((b * c) - (((a * ((b * i) - (x * t))) - (j * (y * i))) / z)));
	t_2 = b * ((a * i) - (z * c));
	t_3 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -6.4e+81)
		tmp = t_3 + t_2;
	elseif (y <= -6.5e-157)
		tmp = t_1;
	elseif (y <= 7.1e-118)
		tmp = (t * ((c * j) - (x * a))) + t_2;
	elseif (y <= 7.6e+126)
		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[(z * N[(N[(x * y), $MachinePrecision] - N[(N[(b * c), $MachinePrecision] - N[(N[(N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.4e+81], N[(t$95$3 + t$95$2), $MachinePrecision], If[LessEqual[y, -6.5e-157], t$95$1, If[LessEqual[y, 7.1e-118], N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[y, 7.6e+126], t$95$1, t$95$3]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.4e81

   1. Initial program 56.0%

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

   3. Taylor expanded in t around 0 69.4%

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

      1. mul-1-neg 69.4%

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

      2. *-commutative 69.4%

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

      3. distribute-rgt-neg-in 69.4%

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

      4. associate-*r* 60.2%

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

      5. *-commutative 60.2%

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

      6. associate-*l* 66.4%

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

      7. neg-mul-1 66.4%

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

      8. associate-*r* 66.4%

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

      9. *-commutative 66.4%

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

      10. associate-*l* 74.0%

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

      11. *-commutative 74.0%

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

      12. distribute-lft-in 79.7%

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

      13. +-commutative 79.7%

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

      14. mul-1-neg 79.7%

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

      15. unsub-neg 79.7%

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

      16. *-commutative 79.7%

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

   5. Simplified 79.7%

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

   if -6.4e81 < y < -6.5000000000000002e-157 or 7.10000000000000005e-118 < y < 7.60000000000000033e126

   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 c around 0 71.6%

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

   5. Simplified 73.6%

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

   6. Taylor expanded in t around 0 65.7%

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

      1. associate-*r* 65.7%

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

      2. neg-mul-1 65.7%

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

      3. *-commutative 65.7%

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

   8. Simplified 65.7%

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

   9. Taylor expanded in z around -inf 73.7%

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

   11. Simplified 77.8%

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

   if -6.5000000000000002e-157 < y < 7.10000000000000005e-118

   1. Initial program 84.8%

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

   3. Taylor expanded in y around 0 80.7%

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

      1. +-commutative 80.7%

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

      2. mul-1-neg 80.7%

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

      3. *-commutative 80.7%

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

      4. associate-*r* 82.1%

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

      5. *-commutative 82.1%

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

      6. associate-*l* 80.8%

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

      7. associate-*r* 77.9%

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

      8. *-commutative 77.9%

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

      9. associate-*l* 78.1%

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

      10. distribute-rgt-neg-in 78.1%

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

      11. mul-1-neg 78.1%

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

      12. distribute-lft-in 79.5%

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

      13. mul-1-neg 79.5%

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

      14. unsub-neg 79.5%

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

      15. *-commutative 79.5%

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

      16. *-commutative 79.5%

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

   5. Simplified 79.5%

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

   if 7.60000000000000033e126 < y

   1. Initial program 39.6%

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

   3. Taylor expanded in y around inf 79.0%

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

      1. +-commutative 79.0%

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

      2. mul-1-neg 79.0%

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

      3. unsub-neg 79.0%

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

   5. Simplified 79.0%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+81}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-157}:\\ \;\;\;\;z \cdot \left(x \cdot y - \left(b \cdot c - \frac{a \cdot \left(b \cdot i - x \cdot t\right) - j \cdot \left(y \cdot i\right)}{z}\right)\right)\\ \mathbf{elif}\;y \leq 7.1 \cdot 10^{-118}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+126}:\\ \;\;\;\;z \cdot \left(x \cdot y - \left(b \cdot c - \frac{a \cdot \left(b \cdot i - x \cdot t\right) - j \cdot \left(y \cdot i\right)}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 30.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i\right)\\ \mathbf{if}\;y \leq -6 \cdot 10^{+234}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{+60}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-174}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-221}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+82}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(-y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* a i))))
   (if (<= y -6e+234)
     (* x (* y z))
     (if (<= y -7.2e+60)
       (* i (* y (- j)))
       (if (<= y -1.4e-174)
         t_1
         (if (<= y 1.15e-221)
           (* (* t a) (- x))
           (if (<= y 4.4e-46)
             t_1
             (if (<= y 2.7e+82) (* (* z b) (- c)) (* j (- (* y i)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (a * i);
	double tmp;
	if (y <= -6e+234) {
		tmp = x * (y * z);
	} else if (y <= -7.2e+60) {
		tmp = i * (y * -j);
	} else if (y <= -1.4e-174) {
		tmp = t_1;
	} else if (y <= 1.15e-221) {
		tmp = (t * a) * -x;
	} else if (y <= 4.4e-46) {
		tmp = t_1;
	} else if (y <= 2.7e+82) {
		tmp = (z * b) * -c;
	} else {
		tmp = j * -(y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a * i)
    if (y <= (-6d+234)) then
        tmp = x * (y * z)
    else if (y <= (-7.2d+60)) then
        tmp = i * (y * -j)
    else if (y <= (-1.4d-174)) then
        tmp = t_1
    else if (y <= 1.15d-221) then
        tmp = (t * a) * -x
    else if (y <= 4.4d-46) then
        tmp = t_1
    else if (y <= 2.7d+82) then
        tmp = (z * b) * -c
    else
        tmp = j * -(y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (a * i);
	double tmp;
	if (y <= -6e+234) {
		tmp = x * (y * z);
	} else if (y <= -7.2e+60) {
		tmp = i * (y * -j);
	} else if (y <= -1.4e-174) {
		tmp = t_1;
	} else if (y <= 1.15e-221) {
		tmp = (t * a) * -x;
	} else if (y <= 4.4e-46) {
		tmp = t_1;
	} else if (y <= 2.7e+82) {
		tmp = (z * b) * -c;
	} else {
		tmp = j * -(y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (a * i)
	tmp = 0
	if y <= -6e+234:
		tmp = x * (y * z)
	elif y <= -7.2e+60:
		tmp = i * (y * -j)
	elif y <= -1.4e-174:
		tmp = t_1
	elif y <= 1.15e-221:
		tmp = (t * a) * -x
	elif y <= 4.4e-46:
		tmp = t_1
	elif y <= 2.7e+82:
		tmp = (z * b) * -c
	else:
		tmp = j * -(y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(a * i))
	tmp = 0.0
	if (y <= -6e+234)
		tmp = Float64(x * Float64(y * z));
	elseif (y <= -7.2e+60)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (y <= -1.4e-174)
		tmp = t_1;
	elseif (y <= 1.15e-221)
		tmp = Float64(Float64(t * a) * Float64(-x));
	elseif (y <= 4.4e-46)
		tmp = t_1;
	elseif (y <= 2.7e+82)
		tmp = Float64(Float64(z * b) * Float64(-c));
	else
		tmp = Float64(j * Float64(-Float64(y * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (a * i);
	tmp = 0.0;
	if (y <= -6e+234)
		tmp = x * (y * z);
	elseif (y <= -7.2e+60)
		tmp = i * (y * -j);
	elseif (y <= -1.4e-174)
		tmp = t_1;
	elseif (y <= 1.15e-221)
		tmp = (t * a) * -x;
	elseif (y <= 4.4e-46)
		tmp = t_1;
	elseif (y <= 2.7e+82)
		tmp = (z * b) * -c;
	else
		tmp = j * -(y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6e+234], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.2e+60], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.4e-174], t$95$1, If[LessEqual[y, 1.15e-221], N[(N[(t * a), $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[y, 4.4e-46], t$95$1, If[LessEqual[y, 2.7e+82], N[(N[(z * b), $MachinePrecision] * (-c)), $MachinePrecision], N[(j * (-N[(y * i), $MachinePrecision])), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -5.9999999999999998e234

   1. Initial program 55.4%

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

   3. Taylor expanded in c around 0 55.6%

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

   5. Simplified 66.7%

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

   6. Taylor expanded in x around inf 61.6%

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

   7. Taylor expanded in y around inf 61.7%

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

   if -5.9999999999999998e234 < y < -7.19999999999999935e60

   1. Initial program 56.8%

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

   3. Taylor expanded in c around 0 59.4%

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

   5. Simplified 62.5%

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

   6. Taylor expanded in t around 0 57.7%

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

      1. associate-*r* 57.7%

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

      2. neg-mul-1 57.7%

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

      3. *-commutative 57.7%

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

   8. Simplified 57.7%

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

   9. Taylor expanded in j around inf 52.5%

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

       1. neg-mul-1 52.5%

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

       2. associate-*r* 45.9%

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

       3. distribute-lft-neg-out 45.9%

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

       4. *-commutative 45.9%

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

       5. distribute-lft-neg-in 45.9%

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

   11. Simplified 45.9%

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

   12. Taylor expanded in y around 0 52.5%

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

       1. mul-1-neg 52.5%

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

       2. *-commutative 52.5%

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

       3. distribute-rgt-neg-in 52.5%

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

       4. distribute-lft-neg-in 52.5%

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

       5. *-commutative 52.5%

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

   14. Simplified 52.5%

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

   if -7.19999999999999935e60 < y < -1.39999999999999999e-174 or 1.15e-221 < y < 4.4000000000000002e-46

   1. Initial program 77.5%

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

   3. Taylor expanded in b around inf 59.9%

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

      1. *-commutative 59.9%

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

   5. Simplified 59.9%

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

   6. Taylor expanded in a around inf 44.5%

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

   if -1.39999999999999999e-174 < y < 1.15e-221

   1. Initial program 81.6%

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

   3. Taylor expanded in c around 0 82.7%

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

   5. Simplified 82.8%

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

   6. Taylor expanded in x around inf 42.5%

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

   7. Taylor expanded in y around 0 40.5%

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

      1. neg-mul-1 40.5%

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

      2. distribute-rgt-neg-in 40.5%

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

   9. Simplified 40.5%

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

   if 4.4000000000000002e-46 < y < 2.6999999999999999e82

   1. Initial program 79.0%

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

   3. Taylor expanded in c around 0 78.7%

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

   5. Simplified 78.7%

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

   6. Taylor expanded in t around 0 73.5%

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

      1. associate-*r* 73.5%

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

      2. neg-mul-1 73.5%

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

      3. *-commutative 73.5%

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

   8. Simplified 73.5%

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

   9. Taylor expanded in c around inf 42.5%

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

       1. mul-1-neg 42.5%

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

       2. *-commutative 42.5%

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

       3. associate-*r* 47.2%

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

       4. distribute-rgt-neg-in 47.2%

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

       5. *-commutative 47.2%

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

       6. distribute-rgt-neg-in 47.2%

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

   11. Simplified 47.2%

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

   if 2.6999999999999999e82 < y

   1. Initial program 41.6%

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

   3. Taylor expanded in c around 0 55.0%

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

   5. Simplified 63.5%

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

   6. Taylor expanded in t around 0 65.6%

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

      1. associate-*r* 65.6%

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

      2. neg-mul-1 65.6%

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

      3. *-commutative 65.6%

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

   8. Simplified 65.6%

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

   9. Taylor expanded in j around inf 43.2%

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

       1. neg-mul-1 43.2%

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

       2. associate-*r* 45.2%

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

       3. distribute-lft-neg-out 45.2%

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

       4. *-commutative 45.2%

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

       5. distribute-lft-neg-in 45.2%

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

   11. Simplified 45.2%

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

   12. Taylor expanded in y around 0 43.2%

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

       1. mul-1-neg 43.2%

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

       2. associate-*r* 45.2%

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

       3. *-commutative 45.2%

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

       4. associate-*r* 51.2%

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

       5. distribute-rgt-neg-in 51.2%

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

   14. Simplified 51.2%

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

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+234}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{+60}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-174}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-221}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-46}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+82}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(-y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 53.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.6 \cdot 10^{+60}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-177}:\\ \;\;\;\;z \cdot \left(\frac{i \cdot \left(a \cdot b - y \cdot j\right)}{z} - b \cdot c\right)\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-165}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-46}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - j \cdot \left(y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -9.6e+60)
   (* y (- (* x z) (* i j)))
   (if (<= y -9e-177)
     (* z (- (/ (* i (- (* a b) (* y j))) z) (* b c)))
     (if (<= y 1.7e-165)
       (* t (- (* c j) (* x a)))
       (if (<= y 6.8e-46)
         (* b (- (* a i) (* z c)))
         (- (* z (- (* x y) (* b c))) (* j (* y i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -9.6e+60) {
		tmp = y * ((x * z) - (i * j));
	} else if (y <= -9e-177) {
		tmp = z * (((i * ((a * b) - (y * j))) / z) - (b * c));
	} else if (y <= 1.7e-165) {
		tmp = t * ((c * j) - (x * a));
	} else if (y <= 6.8e-46) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = (z * ((x * y) - (b * c))) - (j * (y * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-9.6d+60)) then
        tmp = y * ((x * z) - (i * j))
    else if (y <= (-9d-177)) then
        tmp = z * (((i * ((a * b) - (y * j))) / z) - (b * c))
    else if (y <= 1.7d-165) then
        tmp = t * ((c * j) - (x * a))
    else if (y <= 6.8d-46) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = (z * ((x * y) - (b * c))) - (j * (y * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -9.6e+60) {
		tmp = y * ((x * z) - (i * j));
	} else if (y <= -9e-177) {
		tmp = z * (((i * ((a * b) - (y * j))) / z) - (b * c));
	} else if (y <= 1.7e-165) {
		tmp = t * ((c * j) - (x * a));
	} else if (y <= 6.8e-46) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = (z * ((x * y) - (b * c))) - (j * (y * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -9.6e+60:
		tmp = y * ((x * z) - (i * j))
	elif y <= -9e-177:
		tmp = z * (((i * ((a * b) - (y * j))) / z) - (b * c))
	elif y <= 1.7e-165:
		tmp = t * ((c * j) - (x * a))
	elif y <= 6.8e-46:
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = (z * ((x * y) - (b * c))) - (j * (y * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -9.6e+60)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (y <= -9e-177)
		tmp = Float64(z * Float64(Float64(Float64(i * Float64(Float64(a * b) - Float64(y * j))) / z) - Float64(b * c)));
	elseif (y <= 1.7e-165)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (y <= 6.8e-46)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) - Float64(j * Float64(y * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -9.6e+60)
		tmp = y * ((x * z) - (i * j));
	elseif (y <= -9e-177)
		tmp = z * (((i * ((a * b) - (y * j))) / z) - (b * c));
	elseif (y <= 1.7e-165)
		tmp = t * ((c * j) - (x * a));
	elseif (y <= 6.8e-46)
		tmp = b * ((a * i) - (z * c));
	else
		tmp = (z * ((x * y) - (b * c))) - (j * (y * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -9.6e+60], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -9e-177], N[(z * N[(N[(N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e-165], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.8e-46], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -9.6000000000000001e60

   1. Initial program 56.4%

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

   3. Taylor expanded in y around inf 75.2%

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

      1. +-commutative 75.2%

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

      2. mul-1-neg 75.2%

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

      3. unsub-neg 75.2%

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

   5. Simplified 75.2%

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

   if -9.6000000000000001e60 < y < -9.0000000000000007e-177

   1. Initial program 72.9%

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

   3. Taylor expanded in c around 0 67.7%

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

   5. Simplified 65.8%

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

   6. Taylor expanded in t around 0 58.9%

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

      1. associate-*r* 58.9%

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

      2. neg-mul-1 58.9%

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

      3. *-commutative 58.9%

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

   8. Simplified 58.9%

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

   9. Taylor expanded in z around -inf 66.0%

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

   11. Simplified 75.0%

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

   12. Taylor expanded in x around 0 53.6%

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

       1. +-commutative 53.6%

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

       2. associate--r+ 53.6%

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

       3. div-sub 57.3%

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

       4. *-commutative 57.3%

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

       5. *-commutative 57.3%

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

       6. cancel-sign-sub-inv 57.3%

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

       7. associate-*r* 58.9%

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

       8. *-commutative 58.9%

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

       9. distribute-rgt-in 62.5%

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

       10. sub-neg 62.5%

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

       11. *-commutative 62.5%

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

       12. *-commutative 62.5%

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

   14. Simplified 62.5%

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

   if -9.0000000000000007e-177 < y < 1.7e-165

   1. Initial program 83.4%

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

   3. Taylor expanded in t around inf 62.6%

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

      1. +-commutative 62.6%

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

      2. mul-1-neg 62.6%

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

      3. unsub-neg 62.6%

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

      4. *-commutative 62.6%

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

   5. Simplified 62.6%

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

   if 1.7e-165 < y < 6.79999999999999992e-46

   1. Initial program 82.3%

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

   3. Taylor expanded in b around inf 68.7%

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

      1. *-commutative 68.7%

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

   5. Simplified 68.7%

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

   if 6.79999999999999992e-46 < y

   1. Initial program 52.5%

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

   3. Taylor expanded in c around 0 61.9%

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

   5. Simplified 67.9%

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

   6. Taylor expanded in t around 0 67.9%

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

      1. associate-*r* 67.9%

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

      2. neg-mul-1 67.9%

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

      3. *-commutative 67.9%

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

   8. Simplified 67.9%

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

   9. Taylor expanded in a around 0 57.2%

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

       1. mul-1-neg 57.2%

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

       2. associate-*r* 59.0%

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

       3. distribute-lft-neg-in 59.0%

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

       4. mul-1-neg 59.0%

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

       5. associate-*r* 63.5%

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

       6. distribute-rgt-in 69.7%

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

       7. *-commutative 69.7%

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

       8. associate-*l* 72.6%

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

       9. *-commutative 72.6%

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

       10. +-commutative 72.6%

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

       11. mul-1-neg 72.6%

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

       12. unsub-neg 72.6%

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

   11. Simplified 72.6%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.6 \cdot 10^{+60}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-177}:\\ \;\;\;\;z \cdot \left(\frac{i \cdot \left(a \cdot b - y \cdot j\right)}{z} - b \cdot c\right)\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-165}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-46}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - j \cdot \left(y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{+60}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-176}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{-166}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-45}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - j \cdot \left(y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= y -7.5e+60)
     (* y (- (* x z) (* i j)))
     (if (<= y -2.6e-176)
       t_1
       (if (<= y 1.08e-166)
         (* t (- (* c j) (* x a)))
         (if (<= y 1.95e-45)
           t_1
           (- (* z (- (* x y) (* b c))) (* j (* y i)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (y <= -7.5e+60) {
		tmp = y * ((x * z) - (i * j));
	} else if (y <= -2.6e-176) {
		tmp = t_1;
	} else if (y <= 1.08e-166) {
		tmp = t * ((c * j) - (x * a));
	} else if (y <= 1.95e-45) {
		tmp = t_1;
	} else {
		tmp = (z * ((x * y) - (b * c))) - (j * (y * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    if (y <= (-7.5d+60)) then
        tmp = y * ((x * z) - (i * j))
    else if (y <= (-2.6d-176)) then
        tmp = t_1
    else if (y <= 1.08d-166) then
        tmp = t * ((c * j) - (x * a))
    else if (y <= 1.95d-45) then
        tmp = t_1
    else
        tmp = (z * ((x * y) - (b * c))) - (j * (y * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (y <= -7.5e+60) {
		tmp = y * ((x * z) - (i * j));
	} else if (y <= -2.6e-176) {
		tmp = t_1;
	} else if (y <= 1.08e-166) {
		tmp = t * ((c * j) - (x * a));
	} else if (y <= 1.95e-45) {
		tmp = t_1;
	} else {
		tmp = (z * ((x * y) - (b * c))) - (j * (y * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	tmp = 0
	if y <= -7.5e+60:
		tmp = y * ((x * z) - (i * j))
	elif y <= -2.6e-176:
		tmp = t_1
	elif y <= 1.08e-166:
		tmp = t * ((c * j) - (x * a))
	elif y <= 1.95e-45:
		tmp = t_1
	else:
		tmp = (z * ((x * y) - (b * c))) - (j * (y * i))
	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 (y <= -7.5e+60)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (y <= -2.6e-176)
		tmp = t_1;
	elseif (y <= 1.08e-166)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (y <= 1.95e-45)
		tmp = t_1;
	else
		tmp = Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) - Float64(j * Float64(y * i)));
	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 (y <= -7.5e+60)
		tmp = y * ((x * z) - (i * j));
	elseif (y <= -2.6e-176)
		tmp = t_1;
	elseif (y <= 1.08e-166)
		tmp = t * ((c * j) - (x * a));
	elseif (y <= 1.95e-45)
		tmp = t_1;
	else
		tmp = (z * ((x * y) - (b * c))) - (j * (y * i));
	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[y, -7.5e+60], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.6e-176], t$95$1, If[LessEqual[y, 1.08e-166], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.95e-45], t$95$1, N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.5e60

   1. Initial program 56.4%

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

   3. Taylor expanded in y around inf 75.2%

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

      1. +-commutative 75.2%

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

      2. mul-1-neg 75.2%

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

      3. unsub-neg 75.2%

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

   5. Simplified 75.2%

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

   if -7.5e60 < y < -2.59999999999999992e-176 or 1.08e-166 < y < 1.95e-45

   1. Initial program 75.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   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 -2.59999999999999992e-176 < y < 1.08e-166

   1. Initial program 83.4%

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

   3. Taylor expanded in t around inf 62.6%

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

      1. +-commutative 62.6%

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

      2. mul-1-neg 62.6%

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

      3. unsub-neg 62.6%

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

      4. *-commutative 62.6%

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

   5. Simplified 62.6%

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

   if 1.95e-45 < y

   1. Initial program 52.5%

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

   3. Taylor expanded in c around 0 61.9%

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

   5. Simplified 67.9%

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

   6. Taylor expanded in t around 0 67.9%

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

      1. associate-*r* 67.9%

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

      2. neg-mul-1 67.9%

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

      3. *-commutative 67.9%

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

   8. Simplified 67.9%

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

   9. Taylor expanded in a around 0 57.2%

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

       1. mul-1-neg 57.2%

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

       2. associate-*r* 59.0%

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

       3. distribute-lft-neg-in 59.0%

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

       4. mul-1-neg 59.0%

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

       5. associate-*r* 63.5%

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

       6. distribute-rgt-in 69.7%

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

       7. *-commutative 69.7%

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

       8. associate-*l* 72.6%

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

       9. *-commutative 72.6%

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

       10. +-commutative 72.6%

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

       11. mul-1-neg 72.6%

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

       12. unsub-neg 72.6%

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

   11. Simplified 72.6%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+60}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-176}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{-166}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-45}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - j \cdot \left(y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_3 := t\_2 + t\_1\\ \mathbf{if}\;y \leq -1.46 \cdot 10^{-44}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-117}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + t\_1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+127}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c))))
        (t_2 (* y (- (* x z) (* i j))))
        (t_3 (+ t_2 t_1)))
   (if (<= y -1.46e-44)
     t_3
     (if (<= y 2.9e-117)
       (+ (* t (- (* c j) (* x a))) t_1)
       (if (<= y 5e+127) t_3 t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = t_2 + t_1;
	double tmp;
	if (y <= -1.46e-44) {
		tmp = t_3;
	} else if (y <= 2.9e-117) {
		tmp = (t * ((c * j) - (x * a))) + t_1;
	} else if (y <= 5e+127) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = y * ((x * z) - (i * j))
    t_3 = t_2 + t_1
    if (y <= (-1.46d-44)) then
        tmp = t_3
    else if (y <= 2.9d-117) then
        tmp = (t * ((c * j) - (x * a))) + t_1
    else if (y <= 5d+127) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = t_2 + t_1;
	double tmp;
	if (y <= -1.46e-44) {
		tmp = t_3;
	} else if (y <= 2.9e-117) {
		tmp = (t * ((c * j) - (x * a))) + t_1;
	} else if (y <= 5e+127) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = y * ((x * z) - (i * j))
	t_3 = t_2 + t_1
	tmp = 0
	if y <= -1.46e-44:
		tmp = t_3
	elif y <= 2.9e-117:
		tmp = (t * ((c * j) - (x * a))) + t_1
	elif y <= 5e+127:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_3 = Float64(t_2 + t_1)
	tmp = 0.0
	if (y <= -1.46e-44)
		tmp = t_3;
	elseif (y <= 2.9e-117)
		tmp = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) + t_1);
	elseif (y <= 5e+127)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = y * ((x * z) - (i * j));
	t_3 = t_2 + t_1;
	tmp = 0.0;
	if (y <= -1.46e-44)
		tmp = t_3;
	elseif (y <= 2.9e-117)
		tmp = (t * ((c * j) - (x * a))) + t_1;
	elseif (y <= 5e+127)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + t$95$1), $MachinePrecision]}, If[LessEqual[y, -1.46e-44], t$95$3, If[LessEqual[y, 2.9e-117], N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[y, 5e+127], t$95$3, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.46000000000000012e-44 or 2.9000000000000001e-117 < y < 5.0000000000000004e127

   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 0 68.3%

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

      1. mul-1-neg 68.3%

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

      2. *-commutative 68.3%

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

      3. distribute-rgt-neg-in 68.3%

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

      4. associate-*r* 63.8%

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

      5. *-commutative 63.8%

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

      6. associate-*l* 67.1%

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

      7. neg-mul-1 67.1%

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

      8. associate-*r* 67.1%

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

      9. *-commutative 67.1%

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

      10. associate-*l* 71.0%

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

      11. *-commutative 71.0%

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

      12. distribute-lft-in 73.4%

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

      13. +-commutative 73.4%

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

      14. mul-1-neg 73.4%

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

      15. unsub-neg 73.4%

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

      16. *-commutative 73.4%

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

   5. Simplified 73.4%

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

   if -1.46000000000000012e-44 < y < 2.9000000000000001e-117

   1. Initial program 83.4%

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

   3. Taylor expanded in y around 0 78.4%

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

      1. +-commutative 78.4%

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

      2. mul-1-neg 78.4%

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

      3. *-commutative 78.4%

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

      4. associate-*r* 79.4%

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

      5. *-commutative 79.4%

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

      6. associate-*l* 78.4%

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

      7. associate-*r* 76.3%

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

      8. *-commutative 76.3%

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

      9. associate-*l* 76.4%

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

      10. distribute-rgt-neg-in 76.4%

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

      11. mul-1-neg 76.4%

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

      12. distribute-lft-in 77.5%

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

      13. mul-1-neg 77.5%

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

      14. unsub-neg 77.5%

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

      15. *-commutative 77.5%

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

      16. *-commutative 77.5%

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

   5. Simplified 77.5%

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

   if 5.0000000000000004e127 < y

   1. Initial program 39.6%

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

   3. Taylor expanded in y around inf 79.0%

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

      1. +-commutative 79.0%

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

      2. mul-1-neg 79.0%

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

      3. unsub-neg 79.0%

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

   5. Simplified 79.0%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.46 \cdot 10^{-44}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-117}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+127}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -1.06 \cdot 10^{+61}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.08 \cdot 10^{-174}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-168}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+81}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))) (t_2 (* y (- (* x z) (* i j)))))
   (if (<= y -1.06e+61)
     t_2
     (if (<= y -1.08e-174)
       t_1
       (if (<= y 2.4e-168)
         (* t (- (* c j) (* x a)))
         (if (<= y 3.2e+81) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.06e+61) {
		tmp = t_2;
	} else if (y <= -1.08e-174) {
		tmp = t_1;
	} else if (y <= 2.4e-168) {
		tmp = t * ((c * j) - (x * a));
	} else if (y <= 3.2e+81) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = y * ((x * z) - (i * j))
    if (y <= (-1.06d+61)) then
        tmp = t_2
    else if (y <= (-1.08d-174)) then
        tmp = t_1
    else if (y <= 2.4d-168) then
        tmp = t * ((c * j) - (x * a))
    else if (y <= 3.2d+81) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.06e+61) {
		tmp = t_2;
	} else if (y <= -1.08e-174) {
		tmp = t_1;
	} else if (y <= 2.4e-168) {
		tmp = t * ((c * j) - (x * a));
	} else if (y <= 3.2e+81) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -1.06e+61:
		tmp = t_2
	elif y <= -1.08e-174:
		tmp = t_1
	elif y <= 2.4e-168:
		tmp = t * ((c * j) - (x * a))
	elif y <= 3.2e+81:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -1.06e+61)
		tmp = t_2;
	elseif (y <= -1.08e-174)
		tmp = t_1;
	elseif (y <= 2.4e-168)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (y <= 3.2e+81)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -1.06e+61)
		tmp = t_2;
	elseif (y <= -1.08e-174)
		tmp = t_1;
	elseif (y <= 2.4e-168)
		tmp = t * ((c * j) - (x * a));
	elseif (y <= 3.2e+81)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.06e+61], t$95$2, If[LessEqual[y, -1.08e-174], t$95$1, If[LessEqual[y, 2.4e-168], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e+81], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.0599999999999999e61 or 3.2e81 < y

   1. Initial program 49.8%

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

   3. Taylor expanded in y around inf 75.8%

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

      1. +-commutative 75.8%

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

      2. mul-1-neg 75.8%

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

      3. unsub-neg 75.8%

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

   5. Simplified 75.8%

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

   if -1.0599999999999999e61 < y < -1.08e-174 or 2.3999999999999999e-168 < y < 3.2e81

   1. Initial program 76.3%

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

   3. Taylor expanded in b around inf 58.0%

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

      1. *-commutative 58.0%

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

   5. Simplified 58.0%

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

   if -1.08e-174 < y < 2.3999999999999999e-168

   1. Initial program 83.4%

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

   3. Taylor expanded in t around inf 62.6%

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

      1. +-commutative 62.6%

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

      2. mul-1-neg 62.6%

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

      3. unsub-neg 62.6%

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

      4. *-commutative 62.6%

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

   5. Simplified 62.6%

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

Alternative 9: 65.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+61}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-44}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - j \cdot \left(y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -1.6e+61)
   (* y (- (* x z) (* i j)))
   (if (<= y 9e-44)
     (+ (* t (- (* c j) (* x a))) (* b (- (* a i) (* z c))))
     (- (* z (- (* x y) (* b c))) (* j (* y i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -1.6e+61) {
		tmp = y * ((x * z) - (i * j));
	} else if (y <= 9e-44) {
		tmp = (t * ((c * j) - (x * a))) + (b * ((a * i) - (z * c)));
	} else {
		tmp = (z * ((x * y) - (b * c))) - (j * (y * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-1.6d+61)) then
        tmp = y * ((x * z) - (i * j))
    else if (y <= 9d-44) then
        tmp = (t * ((c * j) - (x * a))) + (b * ((a * i) - (z * c)))
    else
        tmp = (z * ((x * y) - (b * c))) - (j * (y * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -1.6e+61) {
		tmp = y * ((x * z) - (i * j));
	} else if (y <= 9e-44) {
		tmp = (t * ((c * j) - (x * a))) + (b * ((a * i) - (z * c)));
	} else {
		tmp = (z * ((x * y) - (b * c))) - (j * (y * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -1.6e+61:
		tmp = y * ((x * z) - (i * j))
	elif y <= 9e-44:
		tmp = (t * ((c * j) - (x * a))) + (b * ((a * i) - (z * c)))
	else:
		tmp = (z * ((x * y) - (b * c))) - (j * (y * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -1.6e+61)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (y <= 9e-44)
		tmp = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	else
		tmp = Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) - Float64(j * Float64(y * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -1.6e+61)
		tmp = y * ((x * z) - (i * j));
	elseif (y <= 9e-44)
		tmp = (t * ((c * j) - (x * a))) + (b * ((a * i) - (z * c)));
	else
		tmp = (z * ((x * y) - (b * c))) - (j * (y * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -1.6e+61], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e-44], N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.5999999999999999e61

   1. Initial program 56.4%

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

   3. Taylor expanded in y around inf 75.2%

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

      1. +-commutative 75.2%

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

      2. mul-1-neg 75.2%

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

      3. unsub-neg 75.2%

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

   5. Simplified 75.2%

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

   if -1.5999999999999999e61 < y < 8.9999999999999997e-44

   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 y around 0 73.2%

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

      1. +-commutative 73.2%

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

      2. mul-1-neg 73.2%

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

      3. *-commutative 73.2%

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

      4. associate-*r* 73.1%

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

      5. *-commutative 73.1%

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

      6. associate-*l* 73.3%

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

      7. associate-*r* 70.4%

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

      8. *-commutative 70.4%

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

      9. associate-*l* 71.2%

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

      10. distribute-rgt-neg-in 71.2%

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

      11. mul-1-neg 71.2%

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

      12. distribute-lft-in 71.9%

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

      13. mul-1-neg 71.9%

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

      14. unsub-neg 71.9%

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

      15. *-commutative 71.9%

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

      16. *-commutative 71.9%

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

   5. Simplified 71.9%

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

   if 8.9999999999999997e-44 < y

   1. Initial program 52.5%

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

   3. Taylor expanded in c around 0 61.9%

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

   5. Simplified 67.9%

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

   6. Taylor expanded in t around 0 67.9%

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

      1. associate-*r* 67.9%

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

      2. neg-mul-1 67.9%

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

      3. *-commutative 67.9%

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

   8. Simplified 67.9%

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

   9. Taylor expanded in a around 0 57.2%

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

       1. mul-1-neg 57.2%

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

       2. associate-*r* 59.0%

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

       3. distribute-lft-neg-in 59.0%

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

       4. mul-1-neg 59.0%

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

       5. associate-*r* 63.5%

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

       6. distribute-rgt-in 69.7%

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

       7. *-commutative 69.7%

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

       8. associate-*l* 72.6%

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

       9. *-commutative 72.6%

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

       10. +-commutative 72.6%

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

       11. mul-1-neg 72.6%

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

       12. unsub-neg 72.6%

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

   11. Simplified 72.6%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+61}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-44}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - j \cdot \left(y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 30.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.15 \cdot 10^{+237}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{+61}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-46}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+83}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(-y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -3.15e+237)
   (* x (* y z))
   (if (<= y -1.15e+61)
     (* i (* y (- j)))
     (if (<= y 3.9e-46)
       (* b (* a i))
       (if (<= y 1.85e+83) (* (* z b) (- c)) (* j (- (* y i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -3.15e+237) {
		tmp = x * (y * z);
	} else if (y <= -1.15e+61) {
		tmp = i * (y * -j);
	} else if (y <= 3.9e-46) {
		tmp = b * (a * i);
	} else if (y <= 1.85e+83) {
		tmp = (z * b) * -c;
	} else {
		tmp = j * -(y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-3.15d+237)) then
        tmp = x * (y * z)
    else if (y <= (-1.15d+61)) then
        tmp = i * (y * -j)
    else if (y <= 3.9d-46) then
        tmp = b * (a * i)
    else if (y <= 1.85d+83) then
        tmp = (z * b) * -c
    else
        tmp = j * -(y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -3.15e+237) {
		tmp = x * (y * z);
	} else if (y <= -1.15e+61) {
		tmp = i * (y * -j);
	} else if (y <= 3.9e-46) {
		tmp = b * (a * i);
	} else if (y <= 1.85e+83) {
		tmp = (z * b) * -c;
	} else {
		tmp = j * -(y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -3.15e+237:
		tmp = x * (y * z)
	elif y <= -1.15e+61:
		tmp = i * (y * -j)
	elif y <= 3.9e-46:
		tmp = b * (a * i)
	elif y <= 1.85e+83:
		tmp = (z * b) * -c
	else:
		tmp = j * -(y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -3.15e+237)
		tmp = Float64(x * Float64(y * z));
	elseif (y <= -1.15e+61)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (y <= 3.9e-46)
		tmp = Float64(b * Float64(a * i));
	elseif (y <= 1.85e+83)
		tmp = Float64(Float64(z * b) * Float64(-c));
	else
		tmp = Float64(j * Float64(-Float64(y * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -3.15e+237)
		tmp = x * (y * z);
	elseif (y <= -1.15e+61)
		tmp = i * (y * -j);
	elseif (y <= 3.9e-46)
		tmp = b * (a * i);
	elseif (y <= 1.85e+83)
		tmp = (z * b) * -c;
	else
		tmp = j * -(y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -3.15e+237], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.15e+61], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.9e-46], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.85e+83], N[(N[(z * b), $MachinePrecision] * (-c)), $MachinePrecision], N[(j * (-N[(y * i), $MachinePrecision])), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.15000000000000004e237

   1. Initial program 55.4%

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

   3. Taylor expanded in c around 0 55.6%

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

   5. Simplified 66.7%

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

   6. Taylor expanded in x around inf 61.6%

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

   7. Taylor expanded in y around inf 61.7%

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

   if -3.15000000000000004e237 < y < -1.15e61

   1. Initial program 56.8%

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

   3. Taylor expanded in c around 0 59.4%

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

   5. Simplified 62.5%

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

   6. Taylor expanded in t around 0 57.7%

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

      1. associate-*r* 57.7%

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

      2. neg-mul-1 57.7%

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

      3. *-commutative 57.7%

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

   8. Simplified 57.7%

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

   9. Taylor expanded in j around inf 52.5%

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

       1. neg-mul-1 52.5%

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

       2. associate-*r* 45.9%

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

       3. distribute-lft-neg-out 45.9%

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

       4. *-commutative 45.9%

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

       5. distribute-lft-neg-in 45.9%

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

   11. Simplified 45.9%

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

   12. Taylor expanded in y around 0 52.5%

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

       1. mul-1-neg 52.5%

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

       2. *-commutative 52.5%

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

       3. distribute-rgt-neg-in 52.5%

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

       4. distribute-lft-neg-in 52.5%

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

       5. *-commutative 52.5%

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

   14. Simplified 52.5%

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

   if -1.15e61 < y < 3.9000000000000003e-46

   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 52.9%

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

      1. *-commutative 52.9%

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

   5. Simplified 52.9%

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

   6. Taylor expanded in a around inf 35.9%

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

   if 3.9000000000000003e-46 < y < 1.8500000000000001e83

   1. Initial program 79.0%

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

   3. Taylor expanded in c around 0 78.7%

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

   5. Simplified 78.7%

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

   6. Taylor expanded in t around 0 73.5%

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

      1. associate-*r* 73.5%

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

      2. neg-mul-1 73.5%

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

      3. *-commutative 73.5%

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

   8. Simplified 73.5%

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

   9. Taylor expanded in c around inf 42.5%

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

       1. mul-1-neg 42.5%

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

       2. *-commutative 42.5%

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

       3. associate-*r* 47.2%

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

       4. distribute-rgt-neg-in 47.2%

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

       5. *-commutative 47.2%

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

       6. distribute-rgt-neg-in 47.2%

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

   11. Simplified 47.2%

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

   if 1.8500000000000001e83 < y

   1. Initial program 41.6%

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

   3. Taylor expanded in c around 0 55.0%

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

   5. Simplified 63.5%

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

   6. Taylor expanded in t around 0 65.6%

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

      1. associate-*r* 65.6%

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

      2. neg-mul-1 65.6%

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

      3. *-commutative 65.6%

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

   8. Simplified 65.6%

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

   9. Taylor expanded in j around inf 43.2%

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

       1. neg-mul-1 43.2%

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

       2. associate-*r* 45.2%

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

       3. distribute-lft-neg-out 45.2%

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

       4. *-commutative 45.2%

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

       5. distribute-lft-neg-in 45.2%

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

   11. Simplified 45.2%

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

   12. Taylor expanded in y around 0 43.2%

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

       1. mul-1-neg 43.2%

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

       2. associate-*r* 45.2%

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

       3. *-commutative 45.2%

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

       4. associate-*r* 51.2%

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

       5. distribute-rgt-neg-in 51.2%

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

   14. Simplified 51.2%

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

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.15 \cdot 10^{+237}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{+61}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-46}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+83}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(-y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 52.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -4.5 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-261}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 134000000000:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= b -4.5e+44)
     t_1
     (if (<= b -1e-261)
       (* x (- (* y z) (* t a)))
       (if (<= b 134000000000.0) (* j (- (* t c) (* y i))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -4.5e+44) {
		tmp = t_1;
	} else if (b <= -1e-261) {
		tmp = x * ((y * z) - (t * a));
	} else if (b <= 134000000000.0) {
		tmp = j * ((t * c) - (y * 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 <= (-4.5d+44)) then
        tmp = t_1
    else if (b <= (-1d-261)) then
        tmp = x * ((y * z) - (t * a))
    else if (b <= 134000000000.0d0) then
        tmp = j * ((t * c) - (y * 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 <= -4.5e+44) {
		tmp = t_1;
	} else if (b <= -1e-261) {
		tmp = x * ((y * z) - (t * a));
	} else if (b <= 134000000000.0) {
		tmp = j * ((t * c) - (y * 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 <= -4.5e+44:
		tmp = t_1
	elif b <= -1e-261:
		tmp = x * ((y * z) - (t * a))
	elif b <= 134000000000.0:
		tmp = j * ((t * c) - (y * 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 <= -4.5e+44)
		tmp = t_1;
	elseif (b <= -1e-261)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (b <= 134000000000.0)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * 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 <= -4.5e+44)
		tmp = t_1;
	elseif (b <= -1e-261)
		tmp = x * ((y * z) - (t * a));
	elseif (b <= 134000000000.0)
		tmp = j * ((t * c) - (y * 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, -4.5e+44], t$95$1, If[LessEqual[b, -1e-261], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 134000000000.0], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.5e44 or 1.34e11 < b

   1. Initial program 68.6%

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

   3. Taylor expanded in b around inf 64.3%

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

      1. *-commutative 64.3%

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

   5. Simplified 64.3%

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

   if -4.5e44 < b < -9.99999999999999984e-262

   1. Initial program 69.1%

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

   3. Taylor expanded in c around 0 84.5%

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

   5. Simplified 86.3%

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

   6. Taylor expanded in x around inf 57.2%

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

   if -9.99999999999999984e-262 < b < 1.34e11

   1. Initial program 61.4%

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

   3. Taylor expanded in j around inf 60.1%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{+44}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-261}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 134000000000:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -14000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-137}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+52}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))))
   (if (<= a -14000.0)
     t_1
     (if (<= a -3.1e-137)
       (* b (- (* a i) (* z c)))
       (if (<= a 9.5e+52) (* c (- (* t j) (* z b))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -14000.0) {
		tmp = t_1;
	} else if (a <= -3.1e-137) {
		tmp = b * ((a * i) - (z * c));
	} else if (a <= 9.5e+52) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((b * i) - (x * t))
    if (a <= (-14000.0d0)) then
        tmp = t_1
    else if (a <= (-3.1d-137)) then
        tmp = b * ((a * i) - (z * c))
    else if (a <= 9.5d+52) then
        tmp = c * ((t * j) - (z * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -14000.0) {
		tmp = t_1;
	} else if (a <= -3.1e-137) {
		tmp = b * ((a * i) - (z * c));
	} else if (a <= 9.5e+52) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -14000.0:
		tmp = t_1
	elif a <= -3.1e-137:
		tmp = b * ((a * i) - (z * c))
	elif a <= 9.5e+52:
		tmp = c * ((t * j) - (z * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -14000.0)
		tmp = t_1;
	elseif (a <= -3.1e-137)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (a <= 9.5e+52)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -14000.0)
		tmp = t_1;
	elseif (a <= -3.1e-137)
		tmp = b * ((a * i) - (z * c));
	elseif (a <= 9.5e+52)
		tmp = c * ((t * j) - (z * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -14000.0], t$95$1, If[LessEqual[a, -3.1e-137], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.5e+52], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -14000 or 9.49999999999999994e52 < a

   1. Initial program 62.6%

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

   3. Taylor expanded in c around 0 68.5%

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

   5. Simplified 69.4%

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

   6. Taylor expanded in a around inf 62.5%

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

      1. +-commutative 62.5%

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

      2. mul-1-neg 62.5%

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

      3. unsub-neg 62.5%

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

      4. *-commutative 62.5%

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

   8. Simplified 62.5%

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

   if -14000 < a < -3.09999999999999978e-137

   1. Initial program 84.5%

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

   3. Taylor expanded in b around inf 52.1%

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

      1. *-commutative 52.1%

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

   5. Simplified 52.1%

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

   if -3.09999999999999978e-137 < a < 9.49999999999999994e52

   1. Initial program 66.3%

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

   3. Taylor expanded in c around inf 49.7%

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

      1. *-commutative 49.7%

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

      2. *-commutative 49.7%

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

   5. Simplified 49.7%

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

Alternative 13: 42.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+240}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{+61}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+57}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(-y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -2.1e+240)
   (* x (* y z))
   (if (<= y -1.5e+61)
     (* i (* y (- j)))
     (if (<= y 1.15e+57) (* a (- (* b i) (* x t))) (* j (- (* y i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -2.1e+240) {
		tmp = x * (y * z);
	} else if (y <= -1.5e+61) {
		tmp = i * (y * -j);
	} else if (y <= 1.15e+57) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = j * -(y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-2.1d+240)) then
        tmp = x * (y * z)
    else if (y <= (-1.5d+61)) then
        tmp = i * (y * -j)
    else if (y <= 1.15d+57) then
        tmp = a * ((b * i) - (x * t))
    else
        tmp = j * -(y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -2.1e+240) {
		tmp = x * (y * z);
	} else if (y <= -1.5e+61) {
		tmp = i * (y * -j);
	} else if (y <= 1.15e+57) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = j * -(y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -2.1e+240:
		tmp = x * (y * z)
	elif y <= -1.5e+61:
		tmp = i * (y * -j)
	elif y <= 1.15e+57:
		tmp = a * ((b * i) - (x * t))
	else:
		tmp = j * -(y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -2.1e+240)
		tmp = Float64(x * Float64(y * z));
	elseif (y <= -1.5e+61)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (y <= 1.15e+57)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	else
		tmp = Float64(j * Float64(-Float64(y * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -2.1e+240)
		tmp = x * (y * z);
	elseif (y <= -1.5e+61)
		tmp = i * (y * -j);
	elseif (y <= 1.15e+57)
		tmp = a * ((b * i) - (x * t));
	else
		tmp = j * -(y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -2.1e+240], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.5e+61], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e+57], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * (-N[(y * i), $MachinePrecision])), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.0999999999999999e240

   1. Initial program 55.4%

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

   3. Taylor expanded in c around 0 55.6%

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

   5. Simplified 66.7%

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

   6. Taylor expanded in x around inf 61.6%

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

   7. Taylor expanded in y around inf 61.7%

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

   if -2.0999999999999999e240 < y < -1.5e61

   1. Initial program 56.8%

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

   3. Taylor expanded in c around 0 59.4%

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

   5. Simplified 62.5%

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

   6. Taylor expanded in t around 0 57.7%

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

      1. associate-*r* 57.7%

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

      2. neg-mul-1 57.7%

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

      3. *-commutative 57.7%

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

   8. Simplified 57.7%

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

   9. Taylor expanded in j around inf 52.5%

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

       1. neg-mul-1 52.5%

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

       2. associate-*r* 45.9%

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

       3. distribute-lft-neg-out 45.9%

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

       4. *-commutative 45.9%

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

       5. distribute-lft-neg-in 45.9%

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

   11. Simplified 45.9%

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

   12. Taylor expanded in y around 0 52.5%

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

       1. mul-1-neg 52.5%

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

       2. *-commutative 52.5%

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

       3. distribute-rgt-neg-in 52.5%

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

       4. distribute-lft-neg-in 52.5%

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

       5. *-commutative 52.5%

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

   14. Simplified 52.5%

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

   if -1.5e61 < y < 1.1499999999999999e57

   1. Initial program 79.8%

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

   3. Taylor expanded in c around 0 76.9%

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

   5. Simplified 76.3%

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

   6. Taylor expanded in a around inf 49.7%

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

      1. +-commutative 49.7%

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

      2. mul-1-neg 49.7%

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

      3. unsub-neg 49.7%

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

      4. *-commutative 49.7%

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

   8. Simplified 49.7%

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

   if 1.1499999999999999e57 < y

   1. Initial program 41.1%

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

   3. Taylor expanded in c around 0 53.6%

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

   5. Simplified 61.6%

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

   6. Taylor expanded in t around 0 63.7%

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

      1. associate-*r* 63.7%

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

      2. neg-mul-1 63.7%

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

      3. *-commutative 63.7%

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

   8. Simplified 63.7%

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

   9. Taylor expanded in j around inf 44.7%

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

       1. neg-mul-1 44.7%

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

       2. associate-*r* 44.6%

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

       3. distribute-lft-neg-out 44.6%

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

       4. *-commutative 44.6%

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

       5. distribute-lft-neg-in 44.6%

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

   11. Simplified 44.6%

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

   12. Taylor expanded in y around 0 44.7%

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

       1. mul-1-neg 44.7%

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

       2. associate-*r* 44.6%

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

       3. *-commutative 44.6%

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

       4. associate-*r* 50.2%

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

       5. distribute-rgt-neg-in 50.2%

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

   14. Simplified 50.2%

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

4. Final simplification 51.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+240}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{+61}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+57}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(-y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 29.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-142}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+108}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -1.25e+17)
   (* x (* y z))
   (if (<= z -6.8e-142)
     (* i (* y (- j)))
     (if (<= z 7.8e+108) (* a (* b i)) (* (* z b) (- c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -1.25e+17) {
		tmp = x * (y * z);
	} else if (z <= -6.8e-142) {
		tmp = i * (y * -j);
	} else if (z <= 7.8e+108) {
		tmp = a * (b * i);
	} else {
		tmp = (z * b) * -c;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-1.25d+17)) then
        tmp = x * (y * z)
    else if (z <= (-6.8d-142)) then
        tmp = i * (y * -j)
    else if (z <= 7.8d+108) then
        tmp = a * (b * i)
    else
        tmp = (z * b) * -c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -1.25e+17) {
		tmp = x * (y * z);
	} else if (z <= -6.8e-142) {
		tmp = i * (y * -j);
	} else if (z <= 7.8e+108) {
		tmp = a * (b * i);
	} else {
		tmp = (z * b) * -c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -1.25e+17:
		tmp = x * (y * z)
	elif z <= -6.8e-142:
		tmp = i * (y * -j)
	elif z <= 7.8e+108:
		tmp = a * (b * i)
	else:
		tmp = (z * b) * -c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -1.25e+17)
		tmp = Float64(x * Float64(y * z));
	elseif (z <= -6.8e-142)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (z <= 7.8e+108)
		tmp = Float64(a * Float64(b * i));
	else
		tmp = Float64(Float64(z * b) * Float64(-c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -1.25e+17)
		tmp = x * (y * z);
	elseif (z <= -6.8e-142)
		tmp = i * (y * -j);
	elseif (z <= 7.8e+108)
		tmp = a * (b * i);
	else
		tmp = (z * b) * -c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -1.25e+17], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.8e-142], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.8e+108], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(N[(z * b), $MachinePrecision] * (-c)), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.25e17

   1. Initial program 66.2%

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

   3. Taylor expanded in c around 0 60.0%

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

   5. Simplified 66.5%

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

   6. Taylor expanded in x around inf 56.9%

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

   7. Taylor expanded in y around inf 50.7%

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

   if -1.25e17 < z < -6.80000000000000057e-142

   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 c around 0 72.0%

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

   5. Simplified 75.8%

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

   6. Taylor expanded in t around 0 64.3%

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

      1. associate-*r* 64.3%

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

      2. neg-mul-1 64.3%

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

      3. *-commutative 64.3%

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

   8. Simplified 64.3%

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

   9. Taylor expanded in j around inf 35.1%

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

       1. neg-mul-1 35.1%

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

       2. associate-*r* 38.7%

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

       3. distribute-lft-neg-out 38.7%

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

       4. *-commutative 38.7%

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

       5. distribute-lft-neg-in 38.7%

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

   11. Simplified 38.7%

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

   12. Taylor expanded in y around 0 35.1%

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

       1. mul-1-neg 35.1%

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

       2. *-commutative 35.1%

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

       3. distribute-rgt-neg-in 35.1%

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

       4. distribute-lft-neg-in 35.1%

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

       5. *-commutative 35.1%

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

   14. Simplified 35.1%

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

   if -6.80000000000000057e-142 < z < 7.79999999999999969e108

   1. Initial program 74.4%

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

   3. Taylor expanded in b around inf 43.5%

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

      1. *-commutative 43.5%

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

   5. Simplified 43.5%

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

   6. Taylor expanded in a around inf 35.8%

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

   if 7.79999999999999969e108 < z

   1. Initial program 42.5%

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

   3. Taylor expanded in c around 0 54.1%

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

   5. Simplified 56.5%

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

   6. Taylor expanded in t around 0 54.1%

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

      1. associate-*r* 54.1%

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

      2. neg-mul-1 54.1%

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

      3. *-commutative 54.1%

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

   8. Simplified 54.1%

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

   9. Taylor expanded in c around inf 45.4%

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

       1. mul-1-neg 45.4%

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

       2. *-commutative 45.4%

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

       3. associate-*r* 51.7%

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

       4. distribute-rgt-neg-in 51.7%

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

       5. *-commutative 51.7%

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

       6. distribute-rgt-neg-in 51.7%

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

   11. Simplified 51.7%

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

4. Final simplification 42.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-142}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+108}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 51.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3.65 \cdot 10^{+105} \lor \neg \left(c \leq 2.7 \cdot 10^{+67}\right):\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -3.65e+105) (not (<= c 2.7e+67)))
   (* c (- (* t j) (* z b)))
   (* i (- (* a b) (* y j)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -3.65e+105) || !(c <= 2.7e+67)) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = i * ((a * b) - (y * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((c <= (-3.65d+105)) .or. (.not. (c <= 2.7d+67))) then
        tmp = c * ((t * j) - (z * b))
    else
        tmp = i * ((a * b) - (y * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -3.65e+105) || !(c <= 2.7e+67)) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = i * ((a * b) - (y * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -3.65e+105) or not (c <= 2.7e+67):
		tmp = c * ((t * j) - (z * b))
	else:
		tmp = i * ((a * b) - (y * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -3.65e+105) || !(c <= 2.7e+67))
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	else
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -3.65e+105) || ~((c <= 2.7e+67)))
		tmp = c * ((t * j) - (z * b));
	else
		tmp = i * ((a * b) - (y * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -3.65e+105], N[Not[LessEqual[c, 2.7e+67]], $MachinePrecision]], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -3.65000000000000012e105 or 2.6999999999999999e67 < c

   1. Initial program 49.6%

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

   3. Taylor expanded in c around inf 66.2%

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

      1. *-commutative 66.2%

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

      2. *-commutative 66.2%

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

   5. Simplified 66.2%

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

   if -3.65000000000000012e105 < c < 2.6999999999999999e67

   1. Initial program 78.6%

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

   3. Taylor expanded in c around 0 68.9%

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

   5. Simplified 69.1%

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

   6. Taylor expanded in i around inf 52.5%

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

      1. *-commutative 52.5%

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

   8. Simplified 52.5%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.65 \cdot 10^{+105} \lor \neg \left(c \leq 2.7 \cdot 10^{+67}\right):\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 39.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2.85 \cdot 10^{-12}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+102}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x 2.85e-12)
   (* b (- (* a i) (* z c)))
   (if (<= x 1.65e+102) (* x (* y z)) (* a (- (* b i) (* x t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= 2.85e-12) {
		tmp = b * ((a * i) - (z * c));
	} else if (x <= 1.65e+102) {
		tmp = x * (y * z);
	} else {
		tmp = a * ((b * i) - (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (x <= 2.85d-12) then
        tmp = b * ((a * i) - (z * c))
    else if (x <= 1.65d+102) then
        tmp = x * (y * z)
    else
        tmp = a * ((b * i) - (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= 2.85e-12) {
		tmp = b * ((a * i) - (z * c));
	} else if (x <= 1.65e+102) {
		tmp = x * (y * z);
	} else {
		tmp = a * ((b * i) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if x <= 2.85e-12:
		tmp = b * ((a * i) - (z * c))
	elif x <= 1.65e+102:
		tmp = x * (y * z)
	else:
		tmp = a * ((b * i) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= 2.85e-12)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (x <= 1.65e+102)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (x <= 2.85e-12)
		tmp = b * ((a * i) - (z * c));
	elseif (x <= 1.65e+102)
		tmp = x * (y * z);
	else
		tmp = a * ((b * i) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, 2.85e-12], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.65e+102], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < 2.8500000000000002e-12

   1. Initial program 66.5%

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

   3. Taylor expanded in b around inf 48.1%

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

      1. *-commutative 48.1%

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

   5. Simplified 48.1%

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

   if 2.8500000000000002e-12 < x < 1.64999999999999999e102

   1. Initial program 64.8%

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

   3. Taylor expanded in c around 0 70.1%

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

   5. Simplified 75.2%

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

   6. Taylor expanded in x around inf 70.9%

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

   7. Taylor expanded in y around inf 65.9%

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

   if 1.64999999999999999e102 < x

   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 0 68.7%

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

   5. Simplified 74.7%

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

   6. Taylor expanded in a around inf 59.5%

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

      1. +-commutative 59.5%

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

      2. mul-1-neg 59.5%

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

      3. unsub-neg 59.5%

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

      4. *-commutative 59.5%

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

   8. Simplified 59.5%

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

Alternative 17: 29.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{+110}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -1.4e+17)
   (* x (* y z))
   (if (<= z 2.55e+110) (* a (* b i)) (* (* z b) (- c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -1.4e+17) {
		tmp = x * (y * z);
	} else if (z <= 2.55e+110) {
		tmp = a * (b * i);
	} else {
		tmp = (z * b) * -c;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-1.4d+17)) then
        tmp = x * (y * z)
    else if (z <= 2.55d+110) then
        tmp = a * (b * i)
    else
        tmp = (z * b) * -c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -1.4e+17) {
		tmp = x * (y * z);
	} else if (z <= 2.55e+110) {
		tmp = a * (b * i);
	} else {
		tmp = (z * b) * -c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -1.4e+17:
		tmp = x * (y * z)
	elif z <= 2.55e+110:
		tmp = a * (b * i)
	else:
		tmp = (z * b) * -c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -1.4e+17)
		tmp = Float64(x * Float64(y * z));
	elseif (z <= 2.55e+110)
		tmp = Float64(a * Float64(b * i));
	else
		tmp = Float64(Float64(z * b) * Float64(-c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -1.4e+17)
		tmp = x * (y * z);
	elseif (z <= 2.55e+110)
		tmp = a * (b * i);
	else
		tmp = (z * b) * -c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -1.4e+17], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.55e+110], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(N[(z * b), $MachinePrecision] * (-c)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.4e17

   1. Initial program 66.2%

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

   3. Taylor expanded in c around 0 60.0%

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

   5. Simplified 66.5%

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

   6. Taylor expanded in x around inf 56.9%

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

   7. Taylor expanded in y around inf 50.7%

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

   if -1.4e17 < z < 2.5500000000000001e110

   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 b around inf 40.5%

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

      1. *-commutative 40.5%

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

   5. Simplified 40.5%

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

   6. Taylor expanded in a around inf 32.8%

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

   if 2.5500000000000001e110 < z

   1. Initial program 42.5%

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

   3. Taylor expanded in c around 0 54.1%

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

   5. Simplified 56.5%

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

   6. Taylor expanded in t around 0 54.1%

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

      1. associate-*r* 54.1%

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

      2. neg-mul-1 54.1%

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

      3. *-commutative 54.1%

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

   8. Simplified 54.1%

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

   9. Taylor expanded in c around inf 45.4%

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

       1. mul-1-neg 45.4%

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

       2. *-commutative 45.4%

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

       3. associate-*r* 51.7%

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

       4. distribute-rgt-neg-in 51.7%

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

       5. *-commutative 51.7%

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

       6. distribute-rgt-neg-in 51.7%

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

   11. Simplified 51.7%

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

4. Final simplification 40.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{+110}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot b\right) \cdot \left(-c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 29.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 4.05 \cdot 10^{+108}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -1.02e+17)
   (* x (* y z))
   (if (<= z 4.05e+108) (* a (* b i)) (* b (* z (- c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -1.02e+17) {
		tmp = x * (y * z);
	} else if (z <= 4.05e+108) {
		tmp = a * (b * i);
	} else {
		tmp = b * (z * -c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-1.02d+17)) then
        tmp = x * (y * z)
    else if (z <= 4.05d+108) then
        tmp = a * (b * i)
    else
        tmp = b * (z * -c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -1.02e+17) {
		tmp = x * (y * z);
	} else if (z <= 4.05e+108) {
		tmp = a * (b * i);
	} else {
		tmp = b * (z * -c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -1.02e+17:
		tmp = x * (y * z)
	elif z <= 4.05e+108:
		tmp = a * (b * i)
	else:
		tmp = b * (z * -c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -1.02e+17)
		tmp = Float64(x * Float64(y * z));
	elseif (z <= 4.05e+108)
		tmp = Float64(a * Float64(b * i));
	else
		tmp = Float64(b * Float64(z * Float64(-c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -1.02e+17)
		tmp = x * (y * z);
	elseif (z <= 4.05e+108)
		tmp = a * (b * i);
	else
		tmp = b * (z * -c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -1.02e+17], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.05e+108], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.02e17

   1. Initial program 66.2%

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

   3. Taylor expanded in c around 0 60.0%

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

   5. Simplified 66.5%

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

   6. Taylor expanded in x around inf 56.9%

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

   7. Taylor expanded in y around inf 50.7%

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

   if -1.02e17 < z < 4.05e108

   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 b around inf 40.5%

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

      1. *-commutative 40.5%

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

   5. Simplified 40.5%

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

   6. Taylor expanded in a around inf 32.8%

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

   if 4.05e108 < z

   1. Initial program 42.5%

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

   3. Taylor expanded in b around inf 49.8%

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

      1. *-commutative 49.8%

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

   5. Simplified 49.8%

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

   6. Taylor expanded in a around 0 45.4%

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

      1. neg-mul-1 45.4%

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

      2. distribute-rgt-neg-in 45.4%

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

   8. Simplified 45.4%

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

4. Final simplification 39.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 4.05 \cdot 10^{+108}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 30.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+17} \lor \neg \left(z \leq 2.1 \cdot 10^{+80}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= z -1.45e+17) (not (<= z 2.1e+80))) (* x (* y z)) (* a (* b i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((z <= -1.45e+17) || !(z <= 2.1e+80)) {
		tmp = x * (y * z);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((z <= (-1.45d+17)) .or. (.not. (z <= 2.1d+80))) then
        tmp = x * (y * z)
    else
        tmp = a * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((z <= -1.45e+17) || !(z <= 2.1e+80)) {
		tmp = x * (y * z);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (z <= -1.45e+17) or not (z <= 2.1e+80):
		tmp = x * (y * z)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((z <= -1.45e+17) || !(z <= 2.1e+80))
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((z <= -1.45e+17) || ~((z <= 2.1e+80)))
		tmp = x * (y * z);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[z, -1.45e+17], N[Not[LessEqual[z, 2.1e+80]], $MachinePrecision]], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.45e17 or 2.10000000000000001e80 < z

   1. Initial program 57.1%

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

   3. Taylor expanded in c around 0 58.2%

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

   5. Simplified 62.0%

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

   6. Taylor expanded in x around inf 46.8%

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

   7. Taylor expanded in y around inf 41.4%

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

   if -1.45e17 < z < 2.10000000000000001e80

   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 b around inf 41.6%

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

      1. *-commutative 41.6%

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

   5. Simplified 41.6%

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

   6. Taylor expanded in a around inf 33.7%

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

4. Final simplification 37.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+17} \lor \neg \left(z \leq 2.1 \cdot 10^{+80}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 29.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+16}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+80}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -6.5e+16)
   (* x (* y z))
   (if (<= z 1.1e+80) (* a (* b i)) (* y (* x z)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -6.5e+16) {
		tmp = x * (y * z);
	} else if (z <= 1.1e+80) {
		tmp = a * (b * i);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-6.5d+16)) then
        tmp = x * (y * z)
    else if (z <= 1.1d+80) then
        tmp = a * (b * i)
    else
        tmp = y * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -6.5e+16) {
		tmp = x * (y * z);
	} else if (z <= 1.1e+80) {
		tmp = a * (b * i);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -6.5e+16:
		tmp = x * (y * z)
	elif z <= 1.1e+80:
		tmp = a * (b * i)
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -6.5e+16)
		tmp = Float64(x * Float64(y * z));
	elseif (z <= 1.1e+80)
		tmp = Float64(a * Float64(b * i));
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -6.5e+16)
		tmp = x * (y * z);
	elseif (z <= 1.1e+80)
		tmp = a * (b * i);
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -6.5e+16], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1e+80], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.5e16

   1. Initial program 66.2%

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

   3. Taylor expanded in c around 0 60.0%

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

   5. Simplified 66.5%

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

   6. Taylor expanded in x around inf 56.9%

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

   7. Taylor expanded in y around inf 50.7%

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

   if -6.5e16 < z < 1.10000000000000001e80

   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 b around inf 41.6%

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

      1. *-commutative 41.6%

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

   5. Simplified 41.6%

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

   6. Taylor expanded in a around inf 33.7%

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

   if 1.10000000000000001e80 < z

   1. Initial program 45.2%

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

   3. Taylor expanded in y around inf 50.3%

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

      1. +-commutative 50.3%

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

      2. mul-1-neg 50.3%

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

      3. unsub-neg 50.3%

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

   5. Simplified 50.3%

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

   6. Taylor expanded in x around inf 33.5%

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

Alternative 21: 22.2% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ b \cdot \left(a \cdot i\right) \end{array} \]

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 67.2%

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

3. Taylor expanded in b around inf 43.3%

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

   1. *-commutative 43.3%

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

5. Simplified 43.3%

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

6. Taylor expanded in a around inf 26.3%

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

Alternative 22: 22.4% 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 67.2%

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

3. Taylor expanded in b around inf 43.3%

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

   1. *-commutative 43.3%

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

5. Simplified 43.3%

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

6. Taylor expanded in a around inf 24.9%

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

Developer Target 1: 68.7% 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 2024185 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -1015122364899489/125000000000000000000000000000000000000000000000) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -942510763643697/2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2) (pow (* i y) 2))) (+ (* c t) (* i y)))) (if (< t -238547917063487/3125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 10535888557455487/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2) (pow (* i y) 2))) (+ (* 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)))))