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

Percentage Accurate: 73.3% → 72.7%

Time: 29.2s

Alternatives: 24

Speedup: 0.5×

• 58.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 72.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(z \cdot y - t \cdot a\right)\\ \mathbf{if}\;b \leq -1.9 \cdot 10^{+111}:\\ \;\;\;\;\left(b \cdot i\right) \cdot \left(t - \frac{c \cdot z}{i}\right)\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{-67}:\\ \;\;\;\;\left(t\_1 - t \cdot \left(c \cdot \frac{b \cdot z}{t} - b \cdot i\right)\right) + j \cdot \left(c \cdot a - i \cdot y\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+17}:\\ \;\;\;\;i \cdot \left(b \cdot t + \left(\frac{\mathsf{fma}\left(c, a \cdot j - b \cdot z, t\_1\right)}{i} - y \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(i \cdot t - c \cdot z\right) - y \cdot \left(i \cdot j - z \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* z y) (* t a)))))
   (if (<= b -1.9e+111)
     (* (* b i) (- t (/ (* c z) i)))
     (if (<= b 4.3e-67)
       (+
        (- t_1 (* t (- (* c (/ (* b z) t)) (* b i))))
        (* j (- (* c a) (* i y))))
       (if (<= b 6.5e+17)
         (* i (+ (* b t) (- (/ (fma c (- (* a j) (* b z)) t_1) i) (* y j))))
         (- (* b (- (* i t) (* c z))) (* y (- (* i j) (* z x)))))))))

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 * ((z * y) - (t * a));
	double tmp;
	if (b <= -1.9e+111) {
		tmp = (b * i) * (t - ((c * z) / i));
	} else if (b <= 4.3e-67) {
		tmp = (t_1 - (t * ((c * ((b * z) / t)) - (b * i)))) + (j * ((c * a) - (i * y)));
	} else if (b <= 6.5e+17) {
		tmp = i * ((b * t) + ((fma(c, ((a * j) - (b * z)), t_1) / i) - (y * j)));
	} else {
		tmp = (b * ((i * t) - (c * z))) - (y * ((i * j) - (z * x)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(z * y) - Float64(t * a)))
	tmp = 0.0
	if (b <= -1.9e+111)
		tmp = Float64(Float64(b * i) * Float64(t - Float64(Float64(c * z) / i)));
	elseif (b <= 4.3e-67)
		tmp = Float64(Float64(t_1 - Float64(t * Float64(Float64(c * Float64(Float64(b * z) / t)) - Float64(b * i)))) + Float64(j * Float64(Float64(c * a) - Float64(i * y))));
	elseif (b <= 6.5e+17)
		tmp = Float64(i * Float64(Float64(b * t) + Float64(Float64(fma(c, Float64(Float64(a * j) - Float64(b * z)), t_1) / i) - Float64(y * j))));
	else
		tmp = Float64(Float64(b * Float64(Float64(i * t) - Float64(c * z))) - Float64(y * Float64(Float64(i * j) - Float64(z * x))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(z * y), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.9e+111], N[(N[(b * i), $MachinePrecision] * N[(t - N[(N[(c * z), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.3e-67], N[(N[(t$95$1 - N[(t * N[(N[(c * N[(N[(b * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] - N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.5e+17], N[(i * N[(N[(b * t), $MachinePrecision] + N[(N[(N[(c * N[(N[(a * j), $MachinePrecision] - N[(b * z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] / i), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(N[(i * t), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(i * j), $MachinePrecision] - N[(z * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.89999999999999988e111

   1. Initial program 70.5%

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

      1. +-commutative 70.5%

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

      2. fma-define 72.4%

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

      3. *-commutative 72.4%

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

      4. *-commutative 72.4%

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

   3. Simplified 72.4%

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

   5. Taylor expanded in i around -inf 57.6%

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

   7. Simplified 63.5%

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

   8. Taylor expanded in b around inf 84.8%

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

      1. associate-*r* 86.7%

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

      2. mul-1-neg 86.7%

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

      3. unsub-neg 86.7%

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

   10. Simplified 86.7%

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

   if -1.89999999999999988e111 < b < 4.30000000000000027e-67

   1. Initial program 72.5%

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

   3. Taylor expanded in t around inf 78.7%

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

      1. mul-1-neg 78.7%

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

      2. +-commutative 78.7%

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

      3. unsub-neg 78.7%

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

      4. *-commutative 78.7%

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

      5. associate-*l* 83.4%

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

      6. *-commutative 83.4%

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

      7. associate-/l* 83.4%

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

      8. *-commutative 83.4%

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

   5. Simplified 83.4%

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

   if 4.30000000000000027e-67 < b < 6.5e17

   1. Initial program 67.9%

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

      1. +-commutative 67.9%

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

      2. fma-define 67.9%

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

      3. *-commutative 67.9%

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

      4. *-commutative 67.9%

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

   3. Simplified 67.9%

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

   5. Taylor expanded in i around -inf 66.8%

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

   7. Simplified 85.8%

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

   if 6.5e17 < b

   1. Initial program 69.7%

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

      1. +-commutative 69.7%

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

      2. fma-define 69.7%

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

      3. *-commutative 69.7%

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

      4. *-commutative 69.7%

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

   3. Simplified 69.7%

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

   5. Taylor expanded in a around 0 82.9%

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

      1. sub-neg 82.9%

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

      2. +-commutative 82.9%

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

      3. *-commutative 82.9%

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

      4. associate-*r* 84.6%

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

      5. associate-*r* 87.8%

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

      6. associate-*r* 87.8%

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

      7. distribute-rgt-in 89.5%

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

      8. mul-1-neg 89.5%

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

      9. unsub-neg 89.5%

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

      10. *-commutative 89.5%

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

      11. *-commutative 89.5%

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

      12. sub-neg 89.5%

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

      13. distribute-lft-out 84.3%

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

      14. distribute-rgt-neg-out 84.3%

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

      15. mul-1-neg 84.3%

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

      16. +-commutative 84.3%

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

      17. distribute-neg-in 84.3%

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

   7. Simplified 89.5%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.9 \cdot 10^{+111}:\\ \;\;\;\;\left(b \cdot i\right) \cdot \left(t - \frac{c \cdot z}{i}\right)\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{-67}:\\ \;\;\;\;\left(x \cdot \left(z \cdot y - t \cdot a\right) - t \cdot \left(c \cdot \frac{b \cdot z}{t} - b \cdot i\right)\right) + j \cdot \left(c \cdot a - i \cdot y\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+17}:\\ \;\;\;\;i \cdot \left(b \cdot t + \left(\frac{\mathsf{fma}\left(c, a \cdot j - b \cdot z, x \cdot \left(z \cdot y - t \cdot a\right)\right)}{i} - y \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(i \cdot t - c \cdot z\right) - y \cdot \left(i \cdot j - z \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 81.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 89.2%

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

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

   1. Initial program 0.0%

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

      1. +-commutative 0.0%

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

      2. fma-define 5.8%

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

      3. *-commutative 5.8%

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

      4. *-commutative 5.8%

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

   3. Simplified 5.8%

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

   5. Taylor expanded in y around inf 54.6%

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

      1. +-commutative 54.6%

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

      2. mul-1-neg 54.6%

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

      3. unsub-neg 54.6%

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

      4. *-commutative 54.6%

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

      5. *-commutative 54.6%

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

   7. Simplified 54.6%

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

4. Final simplification 82.1%

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

Alternative 3: 72.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{+109}:\\ \;\;\;\;\left(b \cdot i\right) \cdot \left(t - \frac{c \cdot z}{i}\right)\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{-24}:\\ \;\;\;\;\left(x \cdot \left(z \cdot y - t \cdot a\right) - t \cdot \left(c \cdot \frac{b \cdot z}{t} - b \cdot i\right)\right) + j \cdot \left(c \cdot a - i \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(i \cdot t - c \cdot z\right) - y \cdot \left(i \cdot j - z \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -2e+109)
   (* (* b i) (- t (/ (* c z) i)))
   (if (<= b 4.2e-24)
     (+
      (- (* x (- (* z y) (* t a))) (* t (- (* c (/ (* b z) t)) (* b i))))
      (* j (- (* c a) (* i y))))
     (- (* b (- (* i t) (* c z))) (* y (- (* i j) (* z x)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -2e+109) {
		tmp = (b * i) * (t - ((c * z) / i));
	} else if (b <= 4.2e-24) {
		tmp = ((x * ((z * y) - (t * a))) - (t * ((c * ((b * z) / t)) - (b * i)))) + (j * ((c * a) - (i * y)));
	} else {
		tmp = (b * ((i * t) - (c * z))) - (y * ((i * j) - (z * x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-2d+109)) then
        tmp = (b * i) * (t - ((c * z) / i))
    else if (b <= 4.2d-24) then
        tmp = ((x * ((z * y) - (t * a))) - (t * ((c * ((b * z) / t)) - (b * i)))) + (j * ((c * a) - (i * y)))
    else
        tmp = (b * ((i * t) - (c * z))) - (y * ((i * j) - (z * x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -2e+109) {
		tmp = (b * i) * (t - ((c * z) / i));
	} else if (b <= 4.2e-24) {
		tmp = ((x * ((z * y) - (t * a))) - (t * ((c * ((b * z) / t)) - (b * i)))) + (j * ((c * a) - (i * y)));
	} else {
		tmp = (b * ((i * t) - (c * z))) - (y * ((i * j) - (z * x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -2e+109:
		tmp = (b * i) * (t - ((c * z) / i))
	elif b <= 4.2e-24:
		tmp = ((x * ((z * y) - (t * a))) - (t * ((c * ((b * z) / t)) - (b * i)))) + (j * ((c * a) - (i * y)))
	else:
		tmp = (b * ((i * t) - (c * z))) - (y * ((i * j) - (z * x)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -2e+109)
		tmp = Float64(Float64(b * i) * Float64(t - Float64(Float64(c * z) / i)));
	elseif (b <= 4.2e-24)
		tmp = Float64(Float64(Float64(x * Float64(Float64(z * y) - Float64(t * a))) - Float64(t * Float64(Float64(c * Float64(Float64(b * z) / t)) - Float64(b * i)))) + Float64(j * Float64(Float64(c * a) - Float64(i * y))));
	else
		tmp = Float64(Float64(b * Float64(Float64(i * t) - Float64(c * z))) - Float64(y * Float64(Float64(i * j) - Float64(z * x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -2e+109)
		tmp = (b * i) * (t - ((c * z) / i));
	elseif (b <= 4.2e-24)
		tmp = ((x * ((z * y) - (t * a))) - (t * ((c * ((b * z) / t)) - (b * i)))) + (j * ((c * a) - (i * y)));
	else
		tmp = (b * ((i * t) - (c * z))) - (y * ((i * j) - (z * x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -2e+109], N[(N[(b * i), $MachinePrecision] * N[(t - N[(N[(c * z), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.2e-24], N[(N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(N[(c * N[(N[(b * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] - N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(N[(i * t), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(i * j), $MachinePrecision] - N[(z * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.99999999999999996e109

   1. Initial program 70.5%

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

      1. +-commutative 70.5%

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

      2. fma-define 72.4%

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

      3. *-commutative 72.4%

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

      4. *-commutative 72.4%

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

   3. Simplified 72.4%

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

   5. Taylor expanded in i around -inf 57.6%

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

   7. Simplified 63.5%

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

   8. Taylor expanded in b around inf 84.8%

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

      1. associate-*r* 86.7%

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

      2. mul-1-neg 86.7%

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

      3. unsub-neg 86.7%

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

   10. Simplified 86.7%

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

   if -1.99999999999999996e109 < b < 4.1999999999999999e-24

   1. Initial program 73.5%

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

   3. Taylor expanded in t around inf 77.8%

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

      1. mul-1-neg 77.8%

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

      2. +-commutative 77.8%

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

      3. unsub-neg 77.8%

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

      4. *-commutative 77.8%

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

      5. associate-*l* 82.0%

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

      6. *-commutative 82.0%

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

      7. associate-/l* 82.1%

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

      8. *-commutative 82.1%

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

   5. Simplified 82.1%

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

   if 4.1999999999999999e-24 < b

   1. Initial program 66.5%

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

      1. +-commutative 66.5%

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

      2. fma-define 66.5%

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

      3. *-commutative 66.5%

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

      4. *-commutative 66.5%

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

   3. Simplified 66.5%

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

   5. Taylor expanded in a around 0 79.3%

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

      1. sub-neg 79.3%

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

      2. +-commutative 79.3%

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

      3. *-commutative 79.3%

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

      4. associate-*r* 82.2%

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

      5. associate-*r* 83.5%

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

      6. associate-*r* 83.5%

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

      7. distribute-rgt-in 85.0%

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

      8. mul-1-neg 85.0%

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

      9. unsub-neg 85.0%

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

      10. *-commutative 85.0%

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

      11. *-commutative 85.0%

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

      12. sub-neg 85.0%

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

      13. distribute-lft-out 80.5%

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

      14. distribute-rgt-neg-out 80.5%

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

      15. mul-1-neg 80.5%

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

      16. +-commutative 80.5%

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

      17. distribute-neg-in 80.5%

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

   7. Simplified 85.0%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{+109}:\\ \;\;\;\;\left(b \cdot i\right) \cdot \left(t - \frac{c \cdot z}{i}\right)\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{-24}:\\ \;\;\;\;\left(x \cdot \left(z \cdot y - t \cdot a\right) - t \cdot \left(c \cdot \frac{b \cdot z}{t} - b \cdot i\right)\right) + j \cdot \left(c \cdot a - i \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(i \cdot t - c \cdot z\right) - y \cdot \left(i \cdot j - z \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 57.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \left(c \cdot a\right)\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{-55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-161}:\\ \;\;\;\;j \cdot \left(c \cdot a - i \cdot y\right) + b \cdot \left(i \cdot t\right)\\ \mathbf{elif}\;z \leq 1.28 \cdot 10^{-89}:\\ \;\;\;\;a \cdot \left(c \cdot j - t \cdot x\right)\\ \mathbf{elif}\;z \leq 1.62 \cdot 10^{+16}:\\ \;\;\;\;y \cdot \left(z \cdot x - i \cdot j\right)\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{+131}:\\ \;\;\;\;\left(b \cdot i\right) \cdot \left(t - \frac{c \cdot z}{i}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* z (- (* x y) (* b c))) (* j (* c a)))))
   (if (<= z -1.4e-55)
     t_1
     (if (<= z 4.8e-161)
       (+ (* j (- (* c a) (* i y))) (* b (* i t)))
       (if (<= z 1.28e-89)
         (* a (- (* c j) (* t x)))
         (if (<= z 1.62e+16)
           (* y (- (* z x) (* i j)))
           (if (<= z 3.05e+131) (* (* b i) (- t (/ (* c z) 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 = (z * ((x * y) - (b * c))) + (j * (c * a));
	double tmp;
	if (z <= -1.4e-55) {
		tmp = t_1;
	} else if (z <= 4.8e-161) {
		tmp = (j * ((c * a) - (i * y))) + (b * (i * t));
	} else if (z <= 1.28e-89) {
		tmp = a * ((c * j) - (t * x));
	} else if (z <= 1.62e+16) {
		tmp = y * ((z * x) - (i * j));
	} else if (z <= 3.05e+131) {
		tmp = (b * i) * (t - ((c * z) / 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 = (z * ((x * y) - (b * c))) + (j * (c * a))
    if (z <= (-1.4d-55)) then
        tmp = t_1
    else if (z <= 4.8d-161) then
        tmp = (j * ((c * a) - (i * y))) + (b * (i * t))
    else if (z <= 1.28d-89) then
        tmp = a * ((c * j) - (t * x))
    else if (z <= 1.62d+16) then
        tmp = y * ((z * x) - (i * j))
    else if (z <= 3.05d+131) then
        tmp = (b * i) * (t - ((c * z) / 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 = (z * ((x * y) - (b * c))) + (j * (c * a));
	double tmp;
	if (z <= -1.4e-55) {
		tmp = t_1;
	} else if (z <= 4.8e-161) {
		tmp = (j * ((c * a) - (i * y))) + (b * (i * t));
	} else if (z <= 1.28e-89) {
		tmp = a * ((c * j) - (t * x));
	} else if (z <= 1.62e+16) {
		tmp = y * ((z * x) - (i * j));
	} else if (z <= 3.05e+131) {
		tmp = (b * i) * (t - ((c * z) / i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (z * ((x * y) - (b * c))) + (j * (c * a))
	tmp = 0
	if z <= -1.4e-55:
		tmp = t_1
	elif z <= 4.8e-161:
		tmp = (j * ((c * a) - (i * y))) + (b * (i * t))
	elif z <= 1.28e-89:
		tmp = a * ((c * j) - (t * x))
	elif z <= 1.62e+16:
		tmp = y * ((z * x) - (i * j))
	elif z <= 3.05e+131:
		tmp = (b * i) * (t - ((c * z) / i))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) + Float64(j * Float64(c * a)))
	tmp = 0.0
	if (z <= -1.4e-55)
		tmp = t_1;
	elseif (z <= 4.8e-161)
		tmp = Float64(Float64(j * Float64(Float64(c * a) - Float64(i * y))) + Float64(b * Float64(i * t)));
	elseif (z <= 1.28e-89)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(t * x)));
	elseif (z <= 1.62e+16)
		tmp = Float64(y * Float64(Float64(z * x) - Float64(i * j)));
	elseif (z <= 3.05e+131)
		tmp = Float64(Float64(b * i) * Float64(t - Float64(Float64(c * z) / 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 = (z * ((x * y) - (b * c))) + (j * (c * a));
	tmp = 0.0;
	if (z <= -1.4e-55)
		tmp = t_1;
	elseif (z <= 4.8e-161)
		tmp = (j * ((c * a) - (i * y))) + (b * (i * t));
	elseif (z <= 1.28e-89)
		tmp = a * ((c * j) - (t * x));
	elseif (z <= 1.62e+16)
		tmp = y * ((z * x) - (i * j));
	elseif (z <= 3.05e+131)
		tmp = (b * i) * (t - ((c * z) / 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[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(c * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.4e-55], t$95$1, If[LessEqual[z, 4.8e-161], N[(N[(j * N[(N[(c * a), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(i * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.28e-89], N[(a * N[(N[(c * j), $MachinePrecision] - N[(t * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.62e+16], N[(y * N[(N[(z * x), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.05e+131], N[(N[(b * i), $MachinePrecision] * N[(t - N[(N[(c * z), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.39999999999999992e-55 or 3.0499999999999999e131 < z

   1. Initial program 62.4%

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

   3. Taylor expanded in z around inf 72.1%

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

      1. *-commutative 72.1%

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

      2. *-commutative 72.1%

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

   5. Simplified 72.1%

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

   6. Taylor expanded in c around inf 69.6%

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

      1. *-commutative 69.6%

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

   8. Simplified 69.6%

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

   if -1.39999999999999992e-55 < z < 4.79999999999999998e-161

   1. Initial program 79.8%

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

   3. Taylor expanded in i around inf 74.2%

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

   if 4.79999999999999998e-161 < z < 1.28000000000000003e-89

   1. Initial program 89.4%

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

      1. +-commutative 89.4%

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

      2. fma-define 89.4%

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

      3. *-commutative 89.4%

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

      4. *-commutative 89.4%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in a around inf 64.2%

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

      1. +-commutative 64.2%

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

      2. mul-1-neg 64.2%

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

      3. unsub-neg 64.2%

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

      4. *-commutative 64.2%

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

   7. Simplified 64.2%

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

   if 1.28000000000000003e-89 < z < 1.62e16

   1. Initial program 65.4%

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

      1. +-commutative 65.4%

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

      2. fma-define 65.4%

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

      3. *-commutative 65.4%

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

      4. *-commutative 65.4%

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

   3. Simplified 65.4%

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

   5. Taylor expanded in y around inf 71.3%

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

      1. +-commutative 71.3%

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

      2. mul-1-neg 71.3%

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

      3. unsub-neg 71.3%

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

      4. *-commutative 71.3%

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

      5. *-commutative 71.3%

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

   7. Simplified 71.3%

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

   if 1.62e16 < z < 3.0499999999999999e131

   1. Initial program 70.1%

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

      1. +-commutative 70.1%

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

      2. fma-define 73.6%

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

      3. *-commutative 73.6%

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

      4. *-commutative 73.6%

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

   3. Simplified 73.6%

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

   5. Taylor expanded in i around -inf 56.2%

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

   7. Simplified 59.6%

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

   8. Taylor expanded in b around inf 66.2%

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

      1. associate-*r* 69.2%

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

      2. mul-1-neg 69.2%

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

      3. unsub-neg 69.2%

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

   10. Simplified 69.2%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-55}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \left(c \cdot a\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-161}:\\ \;\;\;\;j \cdot \left(c \cdot a - i \cdot y\right) + b \cdot \left(i \cdot t\right)\\ \mathbf{elif}\;z \leq 1.28 \cdot 10^{-89}:\\ \;\;\;\;a \cdot \left(c \cdot j - t \cdot x\right)\\ \mathbf{elif}\;z \leq 1.62 \cdot 10^{+16}:\\ \;\;\;\;y \cdot \left(z \cdot x - i \cdot j\right)\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{+131}:\\ \;\;\;\;\left(b \cdot i\right) \cdot \left(t - \frac{c \cdot z}{i}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \left(c \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b \cdot i\right) \cdot \left(t - \frac{c \cdot z}{i}\right)\\ \mathbf{if}\;b \leq -5.2 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{-236}:\\ \;\;\;\;j \cdot \left(c \cdot a - i \cdot y\right)\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{-288}:\\ \;\;\;\;x \cdot \left(z \cdot y - t \cdot a\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-123}:\\ \;\;\;\;a \cdot \left(c \cdot j - t \cdot x\right)\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{+216}:\\ \;\;\;\;y \cdot \left(z \cdot x - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* b i) (- t (/ (* c z) i)))))
   (if (<= b -5.2e+43)
     t_1
     (if (<= b -6.5e-236)
       (* j (- (* c a) (* i y)))
       (if (<= b 5.8e-288)
         (* x (- (* z y) (* t a)))
         (if (<= b 4.5e-123)
           (* a (- (* c j) (* t x)))
           (if (<= b 6.2e+216) (* y (- (* z x) (* i j))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (b * i) * (t - ((c * z) / i));
	double tmp;
	if (b <= -5.2e+43) {
		tmp = t_1;
	} else if (b <= -6.5e-236) {
		tmp = j * ((c * a) - (i * y));
	} else if (b <= 5.8e-288) {
		tmp = x * ((z * y) - (t * a));
	} else if (b <= 4.5e-123) {
		tmp = a * ((c * j) - (t * x));
	} else if (b <= 6.2e+216) {
		tmp = y * ((z * x) - (i * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b * i) * (t - ((c * z) / i))
    if (b <= (-5.2d+43)) then
        tmp = t_1
    else if (b <= (-6.5d-236)) then
        tmp = j * ((c * a) - (i * y))
    else if (b <= 5.8d-288) then
        tmp = x * ((z * y) - (t * a))
    else if (b <= 4.5d-123) then
        tmp = a * ((c * j) - (t * x))
    else if (b <= 6.2d+216) then
        tmp = y * ((z * x) - (i * j))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (b * i) * (t - ((c * z) / i));
	double tmp;
	if (b <= -5.2e+43) {
		tmp = t_1;
	} else if (b <= -6.5e-236) {
		tmp = j * ((c * a) - (i * y));
	} else if (b <= 5.8e-288) {
		tmp = x * ((z * y) - (t * a));
	} else if (b <= 4.5e-123) {
		tmp = a * ((c * j) - (t * x));
	} else if (b <= 6.2e+216) {
		tmp = y * ((z * x) - (i * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (b * i) * (t - ((c * z) / i))
	tmp = 0
	if b <= -5.2e+43:
		tmp = t_1
	elif b <= -6.5e-236:
		tmp = j * ((c * a) - (i * y))
	elif b <= 5.8e-288:
		tmp = x * ((z * y) - (t * a))
	elif b <= 4.5e-123:
		tmp = a * ((c * j) - (t * x))
	elif b <= 6.2e+216:
		tmp = y * ((z * x) - (i * j))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(b * i) * Float64(t - Float64(Float64(c * z) / i)))
	tmp = 0.0
	if (b <= -5.2e+43)
		tmp = t_1;
	elseif (b <= -6.5e-236)
		tmp = Float64(j * Float64(Float64(c * a) - Float64(i * y)));
	elseif (b <= 5.8e-288)
		tmp = Float64(x * Float64(Float64(z * y) - Float64(t * a)));
	elseif (b <= 4.5e-123)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(t * x)));
	elseif (b <= 6.2e+216)
		tmp = Float64(y * Float64(Float64(z * x) - Float64(i * j)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (b * i) * (t - ((c * z) / i));
	tmp = 0.0;
	if (b <= -5.2e+43)
		tmp = t_1;
	elseif (b <= -6.5e-236)
		tmp = j * ((c * a) - (i * y));
	elseif (b <= 5.8e-288)
		tmp = x * ((z * y) - (t * a));
	elseif (b <= 4.5e-123)
		tmp = a * ((c * j) - (t * x));
	elseif (b <= 6.2e+216)
		tmp = y * ((z * x) - (i * j));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(b * i), $MachinePrecision] * N[(t - N[(N[(c * z), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.2e+43], t$95$1, If[LessEqual[b, -6.5e-236], N[(j * N[(N[(c * a), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.8e-288], N[(x * N[(N[(z * y), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.5e-123], N[(a * N[(N[(c * j), $MachinePrecision] - N[(t * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.2e+216], N[(y * N[(N[(z * x), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -5.20000000000000042e43 or 6.20000000000000007e216 < b

   1. Initial program 69.0%

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

      1. +-commutative 69.0%

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

      2. fma-define 70.3%

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

      3. *-commutative 70.3%

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

      4. *-commutative 70.3%

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

   3. Simplified 70.3%

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

   5. Taylor expanded in i around -inf 58.8%

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

   7. Simplified 62.5%

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

   8. Taylor expanded in b around inf 79.6%

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

      1. associate-*r* 79.7%

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

      2. mul-1-neg 79.7%

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

      3. unsub-neg 79.7%

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

   10. Simplified 79.7%

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

   if -5.20000000000000042e43 < b < -6.5000000000000001e-236

   1. Initial program 77.9%

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

   3. Taylor expanded in i around inf 65.8%

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

   4. Taylor expanded in b around 0 53.3%

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

      1. *-commutative 53.3%

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

      2. *-commutative 53.3%

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

   6. Simplified 53.3%

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

   if -6.5000000000000001e-236 < b < 5.8000000000000003e-288

   1. Initial program 55.8%

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

      1. +-commutative 55.8%

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

      2. fma-define 65.8%

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

      3. *-commutative 65.8%

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

      4. *-commutative 65.8%

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

   3. Simplified 65.8%

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

   5. Taylor expanded in i around -inf 41.4%

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

   7. Simplified 60.8%

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

   8. Taylor expanded in x around -inf 66.0%

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

      1. *-commutative 66.0%

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

   10. Simplified 66.0%

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

   if 5.8000000000000003e-288 < b < 4.49999999999999993e-123

   1. Initial program 75.1%

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

      1. +-commutative 75.1%

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

      2. fma-define 75.1%

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

      3. *-commutative 75.1%

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

      4. *-commutative 75.1%

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

   3. Simplified 75.1%

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

   5. Taylor expanded in a around inf 66.4%

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

      1. +-commutative 66.4%

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

      2. mul-1-neg 66.4%

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

      3. unsub-neg 66.4%

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

      4. *-commutative 66.4%

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

   7. Simplified 66.4%

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

   if 4.49999999999999993e-123 < b < 6.20000000000000007e216

   1. Initial program 70.7%

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

      1. +-commutative 70.7%

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

      2. fma-define 70.7%

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

      3. *-commutative 70.7%

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

      4. *-commutative 70.7%

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

   3. Simplified 70.7%

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

   5. Taylor expanded in y around inf 54.3%

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

      1. +-commutative 54.3%

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

      2. mul-1-neg 54.3%

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

      3. unsub-neg 54.3%

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

      4. *-commutative 54.3%

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

      5. *-commutative 54.3%

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

   7. Simplified 54.3%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{+43}:\\ \;\;\;\;\left(b \cdot i\right) \cdot \left(t - \frac{c \cdot z}{i}\right)\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{-236}:\\ \;\;\;\;j \cdot \left(c \cdot a - i \cdot y\right)\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{-288}:\\ \;\;\;\;x \cdot \left(z \cdot y - t \cdot a\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-123}:\\ \;\;\;\;a \cdot \left(c \cdot j - t \cdot x\right)\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{+216}:\\ \;\;\;\;y \cdot \left(z \cdot x - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot i\right) \cdot \left(t - \frac{c \cdot z}{i}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 30.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(b \cdot t\right)\\ \mathbf{if}\;t \leq -1.02 \cdot 10^{+251}:\\ \;\;\;\;b \cdot \left(i \cdot t\right)\\ \mathbf{elif}\;t \leq -7 \cdot 10^{+224}:\\ \;\;\;\;-a \cdot \left(t \cdot x\right)\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.35 \cdot 10^{-77}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-256}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-63}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* b t))))
   (if (<= t -1.02e+251)
     (* b (* i t))
     (if (<= t -7e+224)
       (- (* a (* t x)))
       (if (<= t -1.3e+78)
         t_1
         (if (<= t -2.35e-77)
           (* c (* z (- b)))
           (if (<= t 1.75e-256)
             (* x (* z y))
             (if (<= t 8.8e-63) (* c (* a j)) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (b * t);
	double tmp;
	if (t <= -1.02e+251) {
		tmp = b * (i * t);
	} else if (t <= -7e+224) {
		tmp = -(a * (t * x));
	} else if (t <= -1.3e+78) {
		tmp = t_1;
	} else if (t <= -2.35e-77) {
		tmp = c * (z * -b);
	} else if (t <= 1.75e-256) {
		tmp = x * (z * y);
	} else if (t <= 8.8e-63) {
		tmp = c * (a * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * (b * t)
    if (t <= (-1.02d+251)) then
        tmp = b * (i * t)
    else if (t <= (-7d+224)) then
        tmp = -(a * (t * x))
    else if (t <= (-1.3d+78)) then
        tmp = t_1
    else if (t <= (-2.35d-77)) then
        tmp = c * (z * -b)
    else if (t <= 1.75d-256) then
        tmp = x * (z * y)
    else if (t <= 8.8d-63) then
        tmp = c * (a * j)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (b * t);
	double tmp;
	if (t <= -1.02e+251) {
		tmp = b * (i * t);
	} else if (t <= -7e+224) {
		tmp = -(a * (t * x));
	} else if (t <= -1.3e+78) {
		tmp = t_1;
	} else if (t <= -2.35e-77) {
		tmp = c * (z * -b);
	} else if (t <= 1.75e-256) {
		tmp = x * (z * y);
	} else if (t <= 8.8e-63) {
		tmp = c * (a * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (b * t)
	tmp = 0
	if t <= -1.02e+251:
		tmp = b * (i * t)
	elif t <= -7e+224:
		tmp = -(a * (t * x))
	elif t <= -1.3e+78:
		tmp = t_1
	elif t <= -2.35e-77:
		tmp = c * (z * -b)
	elif t <= 1.75e-256:
		tmp = x * (z * y)
	elif t <= 8.8e-63:
		tmp = c * (a * j)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(b * t))
	tmp = 0.0
	if (t <= -1.02e+251)
		tmp = Float64(b * Float64(i * t));
	elseif (t <= -7e+224)
		tmp = Float64(-Float64(a * Float64(t * x)));
	elseif (t <= -1.3e+78)
		tmp = t_1;
	elseif (t <= -2.35e-77)
		tmp = Float64(c * Float64(z * Float64(-b)));
	elseif (t <= 1.75e-256)
		tmp = Float64(x * Float64(z * y));
	elseif (t <= 8.8e-63)
		tmp = Float64(c * Float64(a * j));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * (b * t);
	tmp = 0.0;
	if (t <= -1.02e+251)
		tmp = b * (i * t);
	elseif (t <= -7e+224)
		tmp = -(a * (t * x));
	elseif (t <= -1.3e+78)
		tmp = t_1;
	elseif (t <= -2.35e-77)
		tmp = c * (z * -b);
	elseif (t <= 1.75e-256)
		tmp = x * (z * y);
	elseif (t <= 8.8e-63)
		tmp = c * (a * j);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(b * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.02e+251], N[(b * N[(i * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -7e+224], (-N[(a * N[(t * x), $MachinePrecision]), $MachinePrecision]), If[LessEqual[t, -1.3e+78], t$95$1, If[LessEqual[t, -2.35e-77], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.75e-256], N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.8e-63], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -1.02e251

   1. Initial program 57.1%

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

   3. Taylor expanded in i around inf 65.0%

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

   4. Taylor expanded in b around inf 86.4%

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

      1. *-commutative 86.4%

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

   6. Simplified 86.4%

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

   if -1.02e251 < t < -7e224

   1. Initial program 60.0%

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

      1. +-commutative 60.0%

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

      2. fma-define 60.0%

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

      3. *-commutative 60.0%

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

      4. *-commutative 60.0%

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

   3. Simplified 60.0%

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

   5. Taylor expanded in a around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in j around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-lft-neg-out 100.0%

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

      3. *-commutative 100.0%

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

   10. Simplified 100.0%

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

   if -7e224 < t < -1.3e78 or 8.7999999999999998e-63 < t

   1. Initial program 66.0%

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

      1. +-commutative 66.0%

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

      2. fma-define 67.9%

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

      3. *-commutative 67.9%

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

      4. *-commutative 67.9%

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

   3. Simplified 67.9%

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

   5. Taylor expanded in i around -inf 61.7%

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

   7. Simplified 65.5%

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

   8. Taylor expanded in i around inf 54.0%

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

   9. Taylor expanded in b around inf 42.9%

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

   if -1.3e78 < t < -2.3499999999999999e-77

   1. Initial program 84.1%

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

      1. +-commutative 84.1%

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

      2. fma-define 84.1%

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

      3. *-commutative 84.1%

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

      4. *-commutative 84.1%

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

   3. Simplified 84.1%

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

   5. Taylor expanded in c around inf 57.7%

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

      1. *-commutative 57.7%

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

   7. Simplified 57.7%

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

   8. Taylor expanded in j around 0 41.6%

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

      1. mul-1-neg 41.6%

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

      2. distribute-rgt-neg-out 41.6%

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

   10. Simplified 41.6%

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

   if -2.3499999999999999e-77 < t < 1.75000000000000007e-256

   1. Initial program 77.4%

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

      1. +-commutative 77.4%

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

      2. fma-define 79.1%

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

      3. *-commutative 79.1%

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

      4. *-commutative 79.1%

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

   3. Simplified 79.1%

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

   5. Taylor expanded in y around inf 52.3%

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

      1. +-commutative 52.3%

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

      2. mul-1-neg 52.3%

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

      3. unsub-neg 52.3%

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

      4. *-commutative 52.3%

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

      5. *-commutative 52.3%

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

   7. Simplified 52.3%

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

   8. Taylor expanded in z around inf 37.7%

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

   if 1.75000000000000007e-256 < t < 8.7999999999999998e-63

   1. Initial program 69.7%

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

      1. +-commutative 69.7%

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

      2. fma-define 69.7%

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

      3. *-commutative 69.7%

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

      4. *-commutative 69.7%

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

   3. Simplified 69.7%

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

   5. Taylor expanded in c around inf 61.5%

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

      1. *-commutative 61.5%

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

   7. Simplified 61.5%

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

   8. Taylor expanded in j around inf 44.3%

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

4. Final simplification 45.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{+251}:\\ \;\;\;\;b \cdot \left(i \cdot t\right)\\ \mathbf{elif}\;t \leq -7 \cdot 10^{+224}:\\ \;\;\;\;-a \cdot \left(t \cdot x\right)\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{+78}:\\ \;\;\;\;i \cdot \left(b \cdot t\right)\\ \mathbf{elif}\;t \leq -2.35 \cdot 10^{-77}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-256}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-63}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(b \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 43.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j - b \cdot z\right)\\ t_2 := b \cdot \left(i \cdot t\right)\\ \mathbf{if}\;b \leq -8.4 \cdot 10^{+176}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{+136}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.55 \cdot 10^{+42}:\\ \;\;\;\;i \cdot \left(b \cdot t\right)\\ \mathbf{elif}\;b \leq 0.00285:\\ \;\;\;\;a \cdot \left(c \cdot j - t \cdot x\right)\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{+197}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* a j) (* b z)))) (t_2 (* b (* i t))))
   (if (<= b -8.4e+176)
     t_2
     (if (<= b -1.15e+136)
       t_1
       (if (<= b -2.55e+42)
         (* i (* b t))
         (if (<= b 0.00285)
           (* a (- (* c j) (* t x)))
           (if (<= b 9.2e+197) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (b * z));
	double t_2 = b * (i * t);
	double tmp;
	if (b <= -8.4e+176) {
		tmp = t_2;
	} else if (b <= -1.15e+136) {
		tmp = t_1;
	} else if (b <= -2.55e+42) {
		tmp = i * (b * t);
	} else if (b <= 0.00285) {
		tmp = a * ((c * j) - (t * x));
	} else if (b <= 9.2e+197) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * ((a * j) - (b * z))
    t_2 = b * (i * t)
    if (b <= (-8.4d+176)) then
        tmp = t_2
    else if (b <= (-1.15d+136)) then
        tmp = t_1
    else if (b <= (-2.55d+42)) then
        tmp = i * (b * t)
    else if (b <= 0.00285d0) then
        tmp = a * ((c * j) - (t * x))
    else if (b <= 9.2d+197) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (b * z));
	double t_2 = b * (i * t);
	double tmp;
	if (b <= -8.4e+176) {
		tmp = t_2;
	} else if (b <= -1.15e+136) {
		tmp = t_1;
	} else if (b <= -2.55e+42) {
		tmp = i * (b * t);
	} else if (b <= 0.00285) {
		tmp = a * ((c * j) - (t * x));
	} else if (b <= 9.2e+197) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((a * j) - (b * z))
	t_2 = b * (i * t)
	tmp = 0
	if b <= -8.4e+176:
		tmp = t_2
	elif b <= -1.15e+136:
		tmp = t_1
	elif b <= -2.55e+42:
		tmp = i * (b * t)
	elif b <= 0.00285:
		tmp = a * ((c * j) - (t * x))
	elif b <= 9.2e+197:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(a * j) - Float64(b * z)))
	t_2 = Float64(b * Float64(i * t))
	tmp = 0.0
	if (b <= -8.4e+176)
		tmp = t_2;
	elseif (b <= -1.15e+136)
		tmp = t_1;
	elseif (b <= -2.55e+42)
		tmp = Float64(i * Float64(b * t));
	elseif (b <= 0.00285)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(t * x)));
	elseif (b <= 9.2e+197)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((a * j) - (b * z));
	t_2 = b * (i * t);
	tmp = 0.0;
	if (b <= -8.4e+176)
		tmp = t_2;
	elseif (b <= -1.15e+136)
		tmp = t_1;
	elseif (b <= -2.55e+42)
		tmp = i * (b * t);
	elseif (b <= 0.00285)
		tmp = a * ((c * j) - (t * x));
	elseif (b <= 9.2e+197)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(i * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8.4e+176], t$95$2, If[LessEqual[b, -1.15e+136], t$95$1, If[LessEqual[b, -2.55e+42], N[(i * N[(b * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 0.00285], N[(a * N[(N[(c * j), $MachinePrecision] - N[(t * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.2e+197], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -8.3999999999999996e176 or 9.2000000000000002e197 < b

   1. Initial program 73.7%

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

   3. Taylor expanded in i around inf 56.4%

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

   4. Taylor expanded in b around inf 58.4%

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

      1. *-commutative 58.4%

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

   6. Simplified 58.4%

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

   if -8.3999999999999996e176 < b < -1.15e136 or 0.0028500000000000001 < b < 9.2000000000000002e197

   1. Initial program 63.2%

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

      1. +-commutative 63.2%

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

      2. fma-define 63.2%

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

      3. *-commutative 63.2%

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

      4. *-commutative 63.2%

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

   3. Simplified 63.2%

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

   5. Taylor expanded in c around inf 54.0%

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

      1. *-commutative 54.0%

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

   7. Simplified 54.0%

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

   if -1.15e136 < b < -2.55e42

   1. Initial program 59.8%

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

      1. +-commutative 59.8%

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

      2. fma-define 59.8%

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

      3. *-commutative 59.8%

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

      4. *-commutative 59.8%

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

   3. Simplified 59.8%

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

   5. Taylor expanded in i around -inf 66.5%

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

   7. Simplified 73.2%

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

   8. Taylor expanded in i around inf 67.0%

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

   9. Taylor expanded in b around inf 54.2%

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

   if -2.55e42 < b < 0.0028500000000000001

   1. Initial program 73.7%

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

      1. +-commutative 73.7%

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

      2. fma-define 75.2%

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

      3. *-commutative 75.2%

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

      4. *-commutative 75.2%

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

   3. Simplified 75.2%

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

   5. Taylor expanded in a around inf 51.9%

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

      1. +-commutative 51.9%

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

      2. mul-1-neg 51.9%

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

      3. unsub-neg 51.9%

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

      4. *-commutative 51.9%

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

   7. Simplified 51.9%

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

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.4 \cdot 10^{+176}:\\ \;\;\;\;b \cdot \left(i \cdot t\right)\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{+136}:\\ \;\;\;\;c \cdot \left(a \cdot j - b \cdot z\right)\\ \mathbf{elif}\;b \leq -2.55 \cdot 10^{+42}:\\ \;\;\;\;i \cdot \left(b \cdot t\right)\\ \mathbf{elif}\;b \leq 0.00285:\\ \;\;\;\;a \cdot \left(c \cdot j - t \cdot x\right)\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{+197}:\\ \;\;\;\;c \cdot \left(a \cdot j - b \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(i \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(z \cdot y - t \cdot a\right)\\ t_2 := i \cdot \left(b \cdot t - y \cdot j\right)\\ t_3 := c \cdot \left(a \cdot j - b \cdot z\right)\\ \mathbf{if}\;c \leq -1.4 \cdot 10^{-45}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq -1.15 \cdot 10^{-175}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -4.5 \cdot 10^{-247}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 3.55 \cdot 10^{-255}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 3.6 \cdot 10^{-56}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* z y) (* t a))))
        (t_2 (* i (- (* b t) (* y j))))
        (t_3 (* c (- (* a j) (* b z)))))
   (if (<= c -1.4e-45)
     t_3
     (if (<= c -1.15e-175)
       t_2
       (if (<= c -4.5e-247)
         t_1
         (if (<= c 3.55e-255) t_2 (if (<= c 3.6e-56) 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 = x * ((z * y) - (t * a));
	double t_2 = i * ((b * t) - (y * j));
	double t_3 = c * ((a * j) - (b * z));
	double tmp;
	if (c <= -1.4e-45) {
		tmp = t_3;
	} else if (c <= -1.15e-175) {
		tmp = t_2;
	} else if (c <= -4.5e-247) {
		tmp = t_1;
	} else if (c <= 3.55e-255) {
		tmp = t_2;
	} else if (c <= 3.6e-56) {
		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 = x * ((z * y) - (t * a))
    t_2 = i * ((b * t) - (y * j))
    t_3 = c * ((a * j) - (b * z))
    if (c <= (-1.4d-45)) then
        tmp = t_3
    else if (c <= (-1.15d-175)) then
        tmp = t_2
    else if (c <= (-4.5d-247)) then
        tmp = t_1
    else if (c <= 3.55d-255) then
        tmp = t_2
    else if (c <= 3.6d-56) 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 = x * ((z * y) - (t * a));
	double t_2 = i * ((b * t) - (y * j));
	double t_3 = c * ((a * j) - (b * z));
	double tmp;
	if (c <= -1.4e-45) {
		tmp = t_3;
	} else if (c <= -1.15e-175) {
		tmp = t_2;
	} else if (c <= -4.5e-247) {
		tmp = t_1;
	} else if (c <= 3.55e-255) {
		tmp = t_2;
	} else if (c <= 3.6e-56) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((z * y) - (t * a))
	t_2 = i * ((b * t) - (y * j))
	t_3 = c * ((a * j) - (b * z))
	tmp = 0
	if c <= -1.4e-45:
		tmp = t_3
	elif c <= -1.15e-175:
		tmp = t_2
	elif c <= -4.5e-247:
		tmp = t_1
	elif c <= 3.55e-255:
		tmp = t_2
	elif c <= 3.6e-56:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(z * y) - Float64(t * a)))
	t_2 = Float64(i * Float64(Float64(b * t) - Float64(y * j)))
	t_3 = Float64(c * Float64(Float64(a * j) - Float64(b * z)))
	tmp = 0.0
	if (c <= -1.4e-45)
		tmp = t_3;
	elseif (c <= -1.15e-175)
		tmp = t_2;
	elseif (c <= -4.5e-247)
		tmp = t_1;
	elseif (c <= 3.55e-255)
		tmp = t_2;
	elseif (c <= 3.6e-56)
		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 = x * ((z * y) - (t * a));
	t_2 = i * ((b * t) - (y * j));
	t_3 = c * ((a * j) - (b * z));
	tmp = 0.0;
	if (c <= -1.4e-45)
		tmp = t_3;
	elseif (c <= -1.15e-175)
		tmp = t_2;
	elseif (c <= -4.5e-247)
		tmp = t_1;
	elseif (c <= 3.55e-255)
		tmp = t_2;
	elseif (c <= 3.6e-56)
		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[(x * N[(N[(z * y), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(b * t), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.4e-45], t$95$3, If[LessEqual[c, -1.15e-175], t$95$2, If[LessEqual[c, -4.5e-247], t$95$1, If[LessEqual[c, 3.55e-255], t$95$2, If[LessEqual[c, 3.6e-56], t$95$1, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.4000000000000001e-45 or 3.59999999999999978e-56 < c

   1. Initial program 65.4%

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

      1. +-commutative 65.4%

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

      2. fma-define 66.8%

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

      3. *-commutative 66.8%

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

      4. *-commutative 66.8%

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

   3. Simplified 66.8%

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

   5. Taylor expanded in c around inf 57.2%

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

      1. *-commutative 57.2%

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

   7. Simplified 57.2%

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

   if -1.4000000000000001e-45 < c < -1.15e-175 or -4.5000000000000002e-247 < c < 3.5499999999999998e-255

   1. Initial program 76.4%

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

      1. +-commutative 76.4%

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

      2. fma-define 76.4%

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

      3. *-commutative 76.4%

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

      4. *-commutative 76.4%

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

   3. Simplified 76.4%

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

   5. Taylor expanded in i around -inf 79.9%

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

   7. Simplified 71.3%

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

   8. Taylor expanded in i around inf 66.7%

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

   if -1.15e-175 < c < -4.5000000000000002e-247 or 3.5499999999999998e-255 < c < 3.59999999999999978e-56

   1. Initial program 79.8%

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

      1. +-commutative 79.8%

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

      2. fma-define 81.6%

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

      3. *-commutative 81.6%

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

      4. *-commutative 81.6%

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

   3. Simplified 81.6%

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

   5. Taylor expanded in i around -inf 70.5%

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

   7. Simplified 68.6%

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

   8. Taylor expanded in x around -inf 61.4%

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

      1. *-commutative 61.4%

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

   10. Simplified 61.4%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.4 \cdot 10^{-45}:\\ \;\;\;\;c \cdot \left(a \cdot j - b \cdot z\right)\\ \mathbf{elif}\;c \leq -1.15 \cdot 10^{-175}:\\ \;\;\;\;i \cdot \left(b \cdot t - y \cdot j\right)\\ \mathbf{elif}\;c \leq -4.5 \cdot 10^{-247}:\\ \;\;\;\;x \cdot \left(z \cdot y - t \cdot a\right)\\ \mathbf{elif}\;c \leq 3.55 \cdot 10^{-255}:\\ \;\;\;\;i \cdot \left(b \cdot t - y \cdot j\right)\\ \mathbf{elif}\;c \leq 3.6 \cdot 10^{-56}:\\ \;\;\;\;x \cdot \left(z \cdot y - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - b \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 52.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j - b \cdot z\right)\\ t_2 := i \cdot \left(b \cdot t - y \cdot j\right)\\ \mathbf{if}\;i \leq -6.6 \cdot 10^{+16}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -2.4 \cdot 10^{-119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -5.1 \cdot 10^{-195}:\\ \;\;\;\;x \cdot \left(z \cdot y - t \cdot a\right)\\ \mathbf{elif}\;i \leq -4 \cdot 10^{-257}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 1.2 \cdot 10^{+69}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* a j) (* b z)))) (t_2 (* i (- (* b t) (* y j)))))
   (if (<= i -6.6e+16)
     t_2
     (if (<= i -2.4e-119)
       t_1
       (if (<= i -5.1e-195)
         (* x (- (* z y) (* t a)))
         (if (<= i -4e-257)
           t_1
           (if (<= i 1.2e+69) (* z (- (* x y) (* b c))) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (b * z));
	double t_2 = i * ((b * t) - (y * j));
	double tmp;
	if (i <= -6.6e+16) {
		tmp = t_2;
	} else if (i <= -2.4e-119) {
		tmp = t_1;
	} else if (i <= -5.1e-195) {
		tmp = x * ((z * y) - (t * a));
	} else if (i <= -4e-257) {
		tmp = t_1;
	} else if (i <= 1.2e+69) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * ((a * j) - (b * z))
    t_2 = i * ((b * t) - (y * j))
    if (i <= (-6.6d+16)) then
        tmp = t_2
    else if (i <= (-2.4d-119)) then
        tmp = t_1
    else if (i <= (-5.1d-195)) then
        tmp = x * ((z * y) - (t * a))
    else if (i <= (-4d-257)) then
        tmp = t_1
    else if (i <= 1.2d+69) then
        tmp = z * ((x * y) - (b * c))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (b * z));
	double t_2 = i * ((b * t) - (y * j));
	double tmp;
	if (i <= -6.6e+16) {
		tmp = t_2;
	} else if (i <= -2.4e-119) {
		tmp = t_1;
	} else if (i <= -5.1e-195) {
		tmp = x * ((z * y) - (t * a));
	} else if (i <= -4e-257) {
		tmp = t_1;
	} else if (i <= 1.2e+69) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((a * j) - (b * z))
	t_2 = i * ((b * t) - (y * j))
	tmp = 0
	if i <= -6.6e+16:
		tmp = t_2
	elif i <= -2.4e-119:
		tmp = t_1
	elif i <= -5.1e-195:
		tmp = x * ((z * y) - (t * a))
	elif i <= -4e-257:
		tmp = t_1
	elif i <= 1.2e+69:
		tmp = z * ((x * y) - (b * c))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(a * j) - Float64(b * z)))
	t_2 = Float64(i * Float64(Float64(b * t) - Float64(y * j)))
	tmp = 0.0
	if (i <= -6.6e+16)
		tmp = t_2;
	elseif (i <= -2.4e-119)
		tmp = t_1;
	elseif (i <= -5.1e-195)
		tmp = Float64(x * Float64(Float64(z * y) - Float64(t * a)));
	elseif (i <= -4e-257)
		tmp = t_1;
	elseif (i <= 1.2e+69)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((a * j) - (b * z));
	t_2 = i * ((b * t) - (y * j));
	tmp = 0.0;
	if (i <= -6.6e+16)
		tmp = t_2;
	elseif (i <= -2.4e-119)
		tmp = t_1;
	elseif (i <= -5.1e-195)
		tmp = x * ((z * y) - (t * a));
	elseif (i <= -4e-257)
		tmp = t_1;
	elseif (i <= 1.2e+69)
		tmp = z * ((x * y) - (b * c));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(b * t), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -6.6e+16], t$95$2, If[LessEqual[i, -2.4e-119], t$95$1, If[LessEqual[i, -5.1e-195], N[(x * N[(N[(z * y), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -4e-257], t$95$1, If[LessEqual[i, 1.2e+69], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -6.6e16 or 1.2000000000000001e69 < i

   1. Initial program 58.3%

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

      1. +-commutative 58.3%

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

      2. fma-define 59.9%

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

      3. *-commutative 59.9%

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

      4. *-commutative 59.9%

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

   3. Simplified 59.9%

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

   5. Taylor expanded in i around -inf 73.3%

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

   7. Simplified 78.3%

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

   8. Taylor expanded in i around inf 65.8%

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

   if -6.6e16 < i < -2.40000000000000009e-119 or -5.1e-195 < i < -3.9999999999999999e-257

   1. Initial program 84.6%

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

      1. +-commutative 84.6%

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

      2. fma-define 84.6%

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

      3. *-commutative 84.6%

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

      4. *-commutative 84.6%

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

   3. Simplified 84.6%

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

   5. Taylor expanded in c around inf 62.9%

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

      1. *-commutative 62.9%

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

   7. Simplified 62.9%

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

   if -2.40000000000000009e-119 < i < -5.1e-195

   1. Initial program 87.8%

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

      1. +-commutative 87.8%

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

      2. fma-define 87.8%

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

      3. *-commutative 87.8%

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

      4. *-commutative 87.8%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in i around -inf 61.8%

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

   7. Simplified 61.8%

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

   8. Taylor expanded in x around -inf 55.7%

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

      1. *-commutative 55.7%

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

   10. Simplified 55.7%

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

   if -3.9999999999999999e-257 < i < 1.2000000000000001e69

   1. Initial program 80.1%

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

      1. +-commutative 80.1%

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

      2. fma-define 81.3%

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

      3. *-commutative 81.3%

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

      4. *-commutative 81.3%

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

   3. Simplified 81.3%

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

   5. Taylor expanded in i around -inf 56.3%

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

   7. Simplified 61.3%

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

   8. Taylor expanded in z around inf 39.2%

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

      1. +-commutative 39.2%

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

      2. mul-1-neg 39.2%

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

      3. unsub-neg 39.2%

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

      4. div-sub 44.2%

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

      5. associate-/l* 44.3%

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

      6. associate-/l* 44.2%

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

      7. *-commutative 44.2%

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

   10. Simplified 44.2%

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

   11. Taylor expanded in i around 0 52.1%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -6.6 \cdot 10^{+16}:\\ \;\;\;\;i \cdot \left(b \cdot t - y \cdot j\right)\\ \mathbf{elif}\;i \leq -2.4 \cdot 10^{-119}:\\ \;\;\;\;c \cdot \left(a \cdot j - b \cdot z\right)\\ \mathbf{elif}\;i \leq -5.1 \cdot 10^{-195}:\\ \;\;\;\;x \cdot \left(z \cdot y - t \cdot a\right)\\ \mathbf{elif}\;i \leq -4 \cdot 10^{-257}:\\ \;\;\;\;c \cdot \left(a \cdot j - b \cdot z\right)\\ \mathbf{elif}\;i \leq 1.2 \cdot 10^{+69}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(b \cdot t - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 67.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(c \cdot a - i \cdot y\right)\\ \mathbf{if}\;b \leq -1.05 \cdot 10^{+117}:\\ \;\;\;\;\left(b \cdot i\right) \cdot \left(t - \frac{c \cdot z}{i}\right)\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-282}:\\ \;\;\;\;t\_1 + t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{-9}:\\ \;\;\;\;t\_1 + x \cdot \left(z \cdot y - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(i \cdot t - c \cdot z\right) - y \cdot \left(i \cdot j - z \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* c a) (* i y)))))
   (if (<= b -1.05e+117)
     (* (* b i) (- t (/ (* c z) i)))
     (if (<= b -1e-282)
       (+ t_1 (* t (- (* b i) (* x a))))
       (if (<= b 1.55e-9)
         (+ t_1 (* x (- (* z y) (* t a))))
         (- (* b (- (* i t) (* c z))) (* y (- (* i j) (* z x)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (i * y));
	double tmp;
	if (b <= -1.05e+117) {
		tmp = (b * i) * (t - ((c * z) / i));
	} else if (b <= -1e-282) {
		tmp = t_1 + (t * ((b * i) - (x * a)));
	} else if (b <= 1.55e-9) {
		tmp = t_1 + (x * ((z * y) - (t * a)));
	} else {
		tmp = (b * ((i * t) - (c * z))) - (y * ((i * j) - (z * x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((c * a) - (i * y))
    if (b <= (-1.05d+117)) then
        tmp = (b * i) * (t - ((c * z) / i))
    else if (b <= (-1d-282)) then
        tmp = t_1 + (t * ((b * i) - (x * a)))
    else if (b <= 1.55d-9) then
        tmp = t_1 + (x * ((z * y) - (t * a)))
    else
        tmp = (b * ((i * t) - (c * z))) - (y * ((i * j) - (z * x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (i * y));
	double tmp;
	if (b <= -1.05e+117) {
		tmp = (b * i) * (t - ((c * z) / i));
	} else if (b <= -1e-282) {
		tmp = t_1 + (t * ((b * i) - (x * a)));
	} else if (b <= 1.55e-9) {
		tmp = t_1 + (x * ((z * y) - (t * a)));
	} else {
		tmp = (b * ((i * t) - (c * z))) - (y * ((i * j) - (z * x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((c * a) - (i * y))
	tmp = 0
	if b <= -1.05e+117:
		tmp = (b * i) * (t - ((c * z) / i))
	elif b <= -1e-282:
		tmp = t_1 + (t * ((b * i) - (x * a)))
	elif b <= 1.55e-9:
		tmp = t_1 + (x * ((z * y) - (t * a)))
	else:
		tmp = (b * ((i * t) - (c * z))) - (y * ((i * j) - (z * x)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(c * a) - Float64(i * y)))
	tmp = 0.0
	if (b <= -1.05e+117)
		tmp = Float64(Float64(b * i) * Float64(t - Float64(Float64(c * z) / i)));
	elseif (b <= -1e-282)
		tmp = Float64(t_1 + Float64(t * Float64(Float64(b * i) - Float64(x * a))));
	elseif (b <= 1.55e-9)
		tmp = Float64(t_1 + Float64(x * Float64(Float64(z * y) - Float64(t * a))));
	else
		tmp = Float64(Float64(b * Float64(Float64(i * t) - Float64(c * z))) - Float64(y * Float64(Float64(i * j) - Float64(z * x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((c * a) - (i * y));
	tmp = 0.0;
	if (b <= -1.05e+117)
		tmp = (b * i) * (t - ((c * z) / i));
	elseif (b <= -1e-282)
		tmp = t_1 + (t * ((b * i) - (x * a)));
	elseif (b <= 1.55e-9)
		tmp = t_1 + (x * ((z * y) - (t * a)));
	else
		tmp = (b * ((i * t) - (c * z))) - (y * ((i * j) - (z * x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(c * a), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.05e+117], N[(N[(b * i), $MachinePrecision] * N[(t - N[(N[(c * z), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1e-282], N[(t$95$1 + N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.55e-9], N[(t$95$1 + N[(x * N[(N[(z * y), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(N[(i * t), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(i * j), $MachinePrecision] - N[(z * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.0500000000000001e117

   1. Initial program 69.9%

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

      1. +-commutative 69.9%

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

      2. fma-define 71.9%

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

      3. *-commutative 71.9%

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

      4. *-commutative 71.9%

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

   3. Simplified 71.9%

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

   5. Taylor expanded in i around -inf 56.8%

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

   7. Simplified 62.7%

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

   8. Taylor expanded in b around inf 86.4%

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

      1. associate-*r* 86.4%

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

      2. mul-1-neg 86.4%

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

      3. unsub-neg 86.4%

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

   10. Simplified 86.4%

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

   if -1.0500000000000001e117 < b < -1e-282

   1. Initial program 71.5%

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

   3. Taylor expanded in t around -inf 77.1%

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

   if -1e-282 < b < 1.55000000000000002e-9

   1. Initial program 74.6%

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

      1. +-commutative 74.6%

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

      2. fma-define 74.6%

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

      3. *-commutative 74.6%

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

      4. *-commutative 74.6%

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

   3. Simplified 74.6%

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

   5. Taylor expanded in b around 0 79.0%

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

   if 1.55000000000000002e-9 < b

   1. Initial program 67.6%

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

      1. +-commutative 67.6%

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

      2. fma-define 67.6%

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

      3. *-commutative 67.6%

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

      4. *-commutative 67.6%

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

   3. Simplified 67.6%

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

   5. Taylor expanded in a around 0 81.1%

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

      1. sub-neg 81.1%

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

      2. +-commutative 81.1%

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

      3. *-commutative 81.1%

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

      4. associate-*r* 84.3%

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

      5. associate-*r* 85.6%

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

      6. associate-*r* 85.6%

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

      7. distribute-rgt-in 87.2%

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

      8. mul-1-neg 87.2%

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

      9. unsub-neg 87.2%

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

      10. *-commutative 87.2%

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

      11. *-commutative 87.2%

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

      12. sub-neg 87.2%

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

      13. distribute-lft-out 82.5%

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

      14. distribute-rgt-neg-out 82.5%

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

      15. mul-1-neg 82.5%

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

      16. +-commutative 82.5%

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

      17. distribute-neg-in 82.5%

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

   7. Simplified 87.2%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.05 \cdot 10^{+117}:\\ \;\;\;\;\left(b \cdot i\right) \cdot \left(t - \frac{c \cdot z}{i}\right)\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-282}:\\ \;\;\;\;j \cdot \left(c \cdot a - i \cdot y\right) + t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{-9}:\\ \;\;\;\;j \cdot \left(c \cdot a - i \cdot y\right) + x \cdot \left(z \cdot y - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(i \cdot t - c \cdot z\right) - y \cdot \left(i \cdot j - z \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b \cdot i\right) \cdot \left(t - \frac{c \cdot z}{i}\right)\\ \mathbf{if}\;b \leq -6.5 \cdot 10^{+113}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 0.0138:\\ \;\;\;\;j \cdot \left(c \cdot a - i \cdot y\right) + x \cdot \left(z \cdot y - t \cdot a\right)\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{+197}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+252}:\\ \;\;\;\;y \cdot \left(b \cdot \left(i \cdot \frac{t}{y}\right) - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* b i) (- t (/ (* c z) i)))))
   (if (<= b -6.5e+113)
     t_1
     (if (<= b 0.0138)
       (+ (* j (- (* c a) (* i y))) (* x (- (* z y) (* t a))))
       (if (<= b 9.2e+197)
         (* z (- (* x y) (* b c)))
         (if (<= b 5.2e+252) (* y (- (* b (* i (/ t y))) (* i j))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (b * i) * (t - ((c * z) / i));
	double tmp;
	if (b <= -6.5e+113) {
		tmp = t_1;
	} else if (b <= 0.0138) {
		tmp = (j * ((c * a) - (i * y))) + (x * ((z * y) - (t * a)));
	} else if (b <= 9.2e+197) {
		tmp = z * ((x * y) - (b * c));
	} else if (b <= 5.2e+252) {
		tmp = y * ((b * (i * (t / y))) - (i * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b * i) * (t - ((c * z) / i))
    if (b <= (-6.5d+113)) then
        tmp = t_1
    else if (b <= 0.0138d0) then
        tmp = (j * ((c * a) - (i * y))) + (x * ((z * y) - (t * a)))
    else if (b <= 9.2d+197) then
        tmp = z * ((x * y) - (b * c))
    else if (b <= 5.2d+252) then
        tmp = y * ((b * (i * (t / y))) - (i * j))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (b * i) * (t - ((c * z) / i));
	double tmp;
	if (b <= -6.5e+113) {
		tmp = t_1;
	} else if (b <= 0.0138) {
		tmp = (j * ((c * a) - (i * y))) + (x * ((z * y) - (t * a)));
	} else if (b <= 9.2e+197) {
		tmp = z * ((x * y) - (b * c));
	} else if (b <= 5.2e+252) {
		tmp = y * ((b * (i * (t / y))) - (i * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (b * i) * (t - ((c * z) / i))
	tmp = 0
	if b <= -6.5e+113:
		tmp = t_1
	elif b <= 0.0138:
		tmp = (j * ((c * a) - (i * y))) + (x * ((z * y) - (t * a)))
	elif b <= 9.2e+197:
		tmp = z * ((x * y) - (b * c))
	elif b <= 5.2e+252:
		tmp = y * ((b * (i * (t / y))) - (i * j))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(b * i) * Float64(t - Float64(Float64(c * z) / i)))
	tmp = 0.0
	if (b <= -6.5e+113)
		tmp = t_1;
	elseif (b <= 0.0138)
		tmp = Float64(Float64(j * Float64(Float64(c * a) - Float64(i * y))) + Float64(x * Float64(Float64(z * y) - Float64(t * a))));
	elseif (b <= 9.2e+197)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (b <= 5.2e+252)
		tmp = Float64(y * Float64(Float64(b * Float64(i * Float64(t / y))) - Float64(i * j)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (b * i) * (t - ((c * z) / i));
	tmp = 0.0;
	if (b <= -6.5e+113)
		tmp = t_1;
	elseif (b <= 0.0138)
		tmp = (j * ((c * a) - (i * y))) + (x * ((z * y) - (t * a)));
	elseif (b <= 9.2e+197)
		tmp = z * ((x * y) - (b * c));
	elseif (b <= 5.2e+252)
		tmp = y * ((b * (i * (t / y))) - (i * j));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(b * i), $MachinePrecision] * N[(t - N[(N[(c * z), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.5e+113], t$95$1, If[LessEqual[b, 0.0138], N[(N[(j * N[(N[(c * a), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(z * y), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.2e+197], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.2e+252], N[(y * N[(N[(b * N[(i * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -6.5000000000000001e113 or 5.20000000000000035e252 < b

   1. Initial program 70.2%

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

      1. +-commutative 70.2%

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

      2. fma-define 71.8%

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

      3. *-commutative 71.8%

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

      4. *-commutative 71.8%

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

   3. Simplified 71.8%

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

   5. Taylor expanded in i around -inf 56.8%

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

   7. Simplified 63.1%

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

   8. Taylor expanded in b around inf 86.3%

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

      1. associate-*r* 86.4%

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

      2. mul-1-neg 86.4%

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

      3. unsub-neg 86.4%

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

   10. Simplified 86.4%

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

   if -6.5000000000000001e113 < b < 0.0138

   1. Initial program 72.6%

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

      1. +-commutative 72.6%

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

      2. fma-define 73.9%

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

      3. *-commutative 73.9%

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

      4. *-commutative 73.9%

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

   3. Simplified 73.9%

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

   5. Taylor expanded in b around 0 72.2%

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

   if 0.0138 < b < 9.2000000000000002e197

   1. Initial program 67.0%

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

      1. +-commutative 67.0%

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

      2. fma-define 67.0%

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

      3. *-commutative 67.0%

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

      4. *-commutative 67.0%

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

   3. Simplified 67.0%

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

   5. Taylor expanded in i around -inf 66.2%

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

   7. Simplified 60.6%

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

   8. Taylor expanded in z around inf 47.3%

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

      1. +-commutative 47.3%

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

      2. mul-1-neg 47.3%

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

      3. unsub-neg 47.3%

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

      4. div-sub 50.1%

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

      5. associate-/l* 50.1%

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

      6. associate-/l* 50.1%

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

      7. *-commutative 50.1%

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

   10. Simplified 50.1%

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

   11. Taylor expanded in i around 0 60.9%

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

   if 9.2000000000000002e197 < b < 5.20000000000000035e252

   1. Initial program 69.4%

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

      1. +-commutative 69.4%

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

      2. fma-define 69.4%

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

      3. *-commutative 69.4%

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

      4. *-commutative 69.4%

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

   3. Simplified 69.4%

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

   5. Taylor expanded in i around -inf 56.1%

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

   7. Simplified 48.4%

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

   8. Taylor expanded in i around inf 72.0%

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

   9. Taylor expanded in y around -inf 92.4%

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

       1. mul-1-neg 92.4%

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

       2. *-commutative 92.4%

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

       3. distribute-rgt-neg-in 92.4%

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

       4. +-commutative 92.4%

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

       5. mul-1-neg 92.4%

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

       6. unsub-neg 92.4%

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

       7. associate-/l* 92.3%

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

       8. associate-/l* 92.3%

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

   11. Simplified 92.3%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.5 \cdot 10^{+113}:\\ \;\;\;\;\left(b \cdot i\right) \cdot \left(t - \frac{c \cdot z}{i}\right)\\ \mathbf{elif}\;b \leq 0.0138:\\ \;\;\;\;j \cdot \left(c \cdot a - i \cdot y\right) + x \cdot \left(z \cdot y - t \cdot a\right)\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{+197}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+252}:\\ \;\;\;\;y \cdot \left(b \cdot \left(i \cdot \frac{t}{y}\right) - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot i\right) \cdot \left(t - \frac{c \cdot z}{i}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 29.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(b \cdot t\right)\\ \mathbf{if}\;t \leq -1.45 \cdot 10^{+249}:\\ \;\;\;\;b \cdot \left(i \cdot t\right)\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{+224}:\\ \;\;\;\;-a \cdot \left(t \cdot x\right)\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-256}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-66}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* b t))))
   (if (<= t -1.45e+249)
     (* b (* i t))
     (if (<= t -5.5e+224)
       (- (* a (* t x)))
       (if (<= t -5e-57)
         t_1
         (if (<= t 1.1e-256)
           (* x (* z y))
           (if (<= t 5.2e-66) (* c (* a j)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (b * t);
	double tmp;
	if (t <= -1.45e+249) {
		tmp = b * (i * t);
	} else if (t <= -5.5e+224) {
		tmp = -(a * (t * x));
	} else if (t <= -5e-57) {
		tmp = t_1;
	} else if (t <= 1.1e-256) {
		tmp = x * (z * y);
	} else if (t <= 5.2e-66) {
		tmp = c * (a * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * (b * t)
    if (t <= (-1.45d+249)) then
        tmp = b * (i * t)
    else if (t <= (-5.5d+224)) then
        tmp = -(a * (t * x))
    else if (t <= (-5d-57)) then
        tmp = t_1
    else if (t <= 1.1d-256) then
        tmp = x * (z * y)
    else if (t <= 5.2d-66) then
        tmp = c * (a * j)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (b * t);
	double tmp;
	if (t <= -1.45e+249) {
		tmp = b * (i * t);
	} else if (t <= -5.5e+224) {
		tmp = -(a * (t * x));
	} else if (t <= -5e-57) {
		tmp = t_1;
	} else if (t <= 1.1e-256) {
		tmp = x * (z * y);
	} else if (t <= 5.2e-66) {
		tmp = c * (a * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (b * t)
	tmp = 0
	if t <= -1.45e+249:
		tmp = b * (i * t)
	elif t <= -5.5e+224:
		tmp = -(a * (t * x))
	elif t <= -5e-57:
		tmp = t_1
	elif t <= 1.1e-256:
		tmp = x * (z * y)
	elif t <= 5.2e-66:
		tmp = c * (a * j)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(b * t))
	tmp = 0.0
	if (t <= -1.45e+249)
		tmp = Float64(b * Float64(i * t));
	elseif (t <= -5.5e+224)
		tmp = Float64(-Float64(a * Float64(t * x)));
	elseif (t <= -5e-57)
		tmp = t_1;
	elseif (t <= 1.1e-256)
		tmp = Float64(x * Float64(z * y));
	elseif (t <= 5.2e-66)
		tmp = Float64(c * Float64(a * j));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * (b * t);
	tmp = 0.0;
	if (t <= -1.45e+249)
		tmp = b * (i * t);
	elseif (t <= -5.5e+224)
		tmp = -(a * (t * x));
	elseif (t <= -5e-57)
		tmp = t_1;
	elseif (t <= 1.1e-256)
		tmp = x * (z * y);
	elseif (t <= 5.2e-66)
		tmp = c * (a * j);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(b * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.45e+249], N[(b * N[(i * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.5e+224], (-N[(a * N[(t * x), $MachinePrecision]), $MachinePrecision]), If[LessEqual[t, -5e-57], t$95$1, If[LessEqual[t, 1.1e-256], N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.2e-66], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.45000000000000008e249

   1. Initial program 57.1%

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

   3. Taylor expanded in i around inf 65.0%

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

   4. Taylor expanded in b around inf 86.4%

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

      1. *-commutative 86.4%

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

   6. Simplified 86.4%

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

   if -1.45000000000000008e249 < t < -5.50000000000000035e224

   1. Initial program 60.0%

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

      1. +-commutative 60.0%

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

      2. fma-define 60.0%

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

      3. *-commutative 60.0%

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

      4. *-commutative 60.0%

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

   3. Simplified 60.0%

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

   5. Taylor expanded in a around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in j around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-lft-neg-out 100.0%

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

      3. *-commutative 100.0%

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

   10. Simplified 100.0%

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

   if -5.50000000000000035e224 < t < -5.0000000000000002e-57 or 5.1999999999999998e-66 < t

   1. Initial program 69.4%

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

      1. +-commutative 69.4%

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

      2. fma-define 70.8%

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

      3. *-commutative 70.8%

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

      4. *-commutative 70.8%

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

   3. Simplified 70.8%

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

   5. Taylor expanded in i around -inf 59.7%

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

   7. Simplified 65.5%

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

   8. Taylor expanded in i around inf 49.5%

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

   9. Taylor expanded in b around inf 38.2%

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

   if -5.0000000000000002e-57 < t < 1.10000000000000005e-256

   1. Initial program 79.5%

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

      1. +-commutative 79.5%

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

      2. fma-define 81.1%

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

      3. *-commutative 81.1%

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

      4. *-commutative 81.1%

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

   3. Simplified 81.1%

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

   5. Taylor expanded in y around inf 52.4%

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

      1. +-commutative 52.4%

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

      2. mul-1-neg 52.4%

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

      3. unsub-neg 52.4%

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

      4. *-commutative 52.4%

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

      5. *-commutative 52.4%

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

   7. Simplified 52.4%

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

   8. Taylor expanded in z around inf 35.8%

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

   if 1.10000000000000005e-256 < t < 5.1999999999999998e-66

   1. Initial program 69.7%

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

      1. +-commutative 69.7%

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

      2. fma-define 69.7%

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

      3. *-commutative 69.7%

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

      4. *-commutative 69.7%

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

   3. Simplified 69.7%

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

   5. Taylor expanded in c around inf 61.5%

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

      1. *-commutative 61.5%

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

   7. Simplified 61.5%

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

   8. Taylor expanded in j around inf 44.3%

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

4. Final simplification 42.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+249}:\\ \;\;\;\;b \cdot \left(i \cdot t\right)\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{+224}:\\ \;\;\;\;-a \cdot \left(t \cdot x\right)\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-57}:\\ \;\;\;\;i \cdot \left(b \cdot t\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-256}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-66}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(b \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 49.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - t \cdot x\right)\\ \mathbf{if}\;a \leq -1.45 \cdot 10^{+134}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.35 \cdot 10^{+81}:\\ \;\;\;\;c \cdot \left(a \cdot j - b \cdot z\right)\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-95} \lor \neg \left(a \leq 4.6 \cdot 10^{+123}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(b \cdot t - y \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* t x)))))
   (if (<= a -1.45e+134)
     t_1
     (if (<= a -2.35e+81)
       (* c (- (* a j) (* b z)))
       (if (or (<= a -1.9e-95) (not (<= a 4.6e+123)))
         t_1
         (* i (- (* b t) (* y j))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (t * x));
	double tmp;
	if (a <= -1.45e+134) {
		tmp = t_1;
	} else if (a <= -2.35e+81) {
		tmp = c * ((a * j) - (b * z));
	} else if ((a <= -1.9e-95) || !(a <= 4.6e+123)) {
		tmp = t_1;
	} else {
		tmp = i * ((b * t) - (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) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (t * x))
    if (a <= (-1.45d+134)) then
        tmp = t_1
    else if (a <= (-2.35d+81)) then
        tmp = c * ((a * j) - (b * z))
    else if ((a <= (-1.9d-95)) .or. (.not. (a <= 4.6d+123))) then
        tmp = t_1
    else
        tmp = i * ((b * t) - (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 t_1 = a * ((c * j) - (t * x));
	double tmp;
	if (a <= -1.45e+134) {
		tmp = t_1;
	} else if (a <= -2.35e+81) {
		tmp = c * ((a * j) - (b * z));
	} else if ((a <= -1.9e-95) || !(a <= 4.6e+123)) {
		tmp = t_1;
	} else {
		tmp = i * ((b * t) - (y * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (t * x))
	tmp = 0
	if a <= -1.45e+134:
		tmp = t_1
	elif a <= -2.35e+81:
		tmp = c * ((a * j) - (b * z))
	elif (a <= -1.9e-95) or not (a <= 4.6e+123):
		tmp = t_1
	else:
		tmp = i * ((b * t) - (y * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(t * x)))
	tmp = 0.0
	if (a <= -1.45e+134)
		tmp = t_1;
	elseif (a <= -2.35e+81)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(b * z)));
	elseif ((a <= -1.9e-95) || !(a <= 4.6e+123))
		tmp = t_1;
	else
		tmp = Float64(i * Float64(Float64(b * t) - Float64(y * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (t * x));
	tmp = 0.0;
	if (a <= -1.45e+134)
		tmp = t_1;
	elseif (a <= -2.35e+81)
		tmp = c * ((a * j) - (b * z));
	elseif ((a <= -1.9e-95) || ~((a <= 4.6e+123)))
		tmp = t_1;
	else
		tmp = i * ((b * t) - (y * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(t * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.45e+134], t$95$1, If[LessEqual[a, -2.35e+81], N[(c * N[(N[(a * j), $MachinePrecision] - N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, -1.9e-95], N[Not[LessEqual[a, 4.6e+123]], $MachinePrecision]], t$95$1, N[(i * N[(N[(b * t), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.45000000000000006e134 or -2.3500000000000001e81 < a < -1.8999999999999999e-95 or 4.59999999999999981e123 < a

   1. Initial program 63.6%

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

      1. +-commutative 63.6%

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

      2. fma-define 65.4%

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

      3. *-commutative 65.4%

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

      4. *-commutative 65.4%

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

   3. Simplified 65.4%

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

   5. Taylor expanded in a around inf 63.3%

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

      1. +-commutative 63.3%

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

      2. mul-1-neg 63.3%

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

      3. unsub-neg 63.3%

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

      4. *-commutative 63.3%

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

   7. Simplified 63.3%

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

   if -1.45000000000000006e134 < a < -2.3500000000000001e81

   1. Initial program 50.4%

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

      1. +-commutative 50.4%

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

      2. fma-define 50.4%

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

      3. *-commutative 50.4%

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

      4. *-commutative 50.4%

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

   3. Simplified 50.4%

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

   5. Taylor expanded in c around inf 72.1%

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

      1. *-commutative 72.1%

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

   7. Simplified 72.1%

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

   if -1.8999999999999999e-95 < a < 4.59999999999999981e123

   1. Initial program 79.4%

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

      1. +-commutative 79.4%

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

      2. fma-define 80.1%

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

      3. *-commutative 80.1%

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

      4. *-commutative 80.1%

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

   3. Simplified 80.1%

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

   5. Taylor expanded in i around -inf 64.7%

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

   7. Simplified 73.0%

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

   8. Taylor expanded in i around inf 51.3%

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

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{+134}:\\ \;\;\;\;a \cdot \left(c \cdot j - t \cdot x\right)\\ \mathbf{elif}\;a \leq -2.35 \cdot 10^{+81}:\\ \;\;\;\;c \cdot \left(a \cdot j - b \cdot z\right)\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-95} \lor \neg \left(a \leq 4.6 \cdot 10^{+123}\right):\\ \;\;\;\;a \cdot \left(c \cdot j - t \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(b \cdot t - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 49.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z \cdot x - i \cdot j\right)\\ \mathbf{if}\;y \leq -41000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-294}:\\ \;\;\;\;c \cdot \left(a \cdot j - b \cdot z\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-167}:\\ \;\;\;\;i \cdot \left(b \cdot t - y \cdot j\right)\\ \mathbf{elif}\;y \leq 270000000:\\ \;\;\;\;a \cdot \left(c \cdot j - t \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* z x) (* i j)))))
   (if (<= y -41000.0)
     t_1
     (if (<= y 9.2e-294)
       (* c (- (* a j) (* b z)))
       (if (<= y 1.4e-167)
         (* i (- (* b t) (* y j)))
         (if (<= y 270000000.0) (* a (- (* c j) (* t x))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((z * x) - (i * j));
	double tmp;
	if (y <= -41000.0) {
		tmp = t_1;
	} else if (y <= 9.2e-294) {
		tmp = c * ((a * j) - (b * z));
	} else if (y <= 1.4e-167) {
		tmp = i * ((b * t) - (y * j));
	} else if (y <= 270000000.0) {
		tmp = a * ((c * j) - (t * x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z * x) - (i * j))
    if (y <= (-41000.0d0)) then
        tmp = t_1
    else if (y <= 9.2d-294) then
        tmp = c * ((a * j) - (b * z))
    else if (y <= 1.4d-167) then
        tmp = i * ((b * t) - (y * j))
    else if (y <= 270000000.0d0) then
        tmp = a * ((c * j) - (t * x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((z * x) - (i * j));
	double tmp;
	if (y <= -41000.0) {
		tmp = t_1;
	} else if (y <= 9.2e-294) {
		tmp = c * ((a * j) - (b * z));
	} else if (y <= 1.4e-167) {
		tmp = i * ((b * t) - (y * j));
	} else if (y <= 270000000.0) {
		tmp = a * ((c * j) - (t * x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((z * x) - (i * j))
	tmp = 0
	if y <= -41000.0:
		tmp = t_1
	elif y <= 9.2e-294:
		tmp = c * ((a * j) - (b * z))
	elif y <= 1.4e-167:
		tmp = i * ((b * t) - (y * j))
	elif y <= 270000000.0:
		tmp = a * ((c * j) - (t * x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(z * x) - Float64(i * j)))
	tmp = 0.0
	if (y <= -41000.0)
		tmp = t_1;
	elseif (y <= 9.2e-294)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(b * z)));
	elseif (y <= 1.4e-167)
		tmp = Float64(i * Float64(Float64(b * t) - Float64(y * j)));
	elseif (y <= 270000000.0)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(t * x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((z * x) - (i * j));
	tmp = 0.0;
	if (y <= -41000.0)
		tmp = t_1;
	elseif (y <= 9.2e-294)
		tmp = c * ((a * j) - (b * z));
	elseif (y <= 1.4e-167)
		tmp = i * ((b * t) - (y * j));
	elseif (y <= 270000000.0)
		tmp = a * ((c * j) - (t * x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(N[(z * x), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -41000.0], t$95$1, If[LessEqual[y, 9.2e-294], N[(c * N[(N[(a * j), $MachinePrecision] - N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.4e-167], N[(i * N[(N[(b * t), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 270000000.0], N[(a * N[(N[(c * j), $MachinePrecision] - N[(t * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -41000 or 2.7e8 < y

   1. Initial program 60.2%

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

      1. +-commutative 60.2%

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

      2. fma-define 61.0%

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

      3. *-commutative 61.0%

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

      4. *-commutative 61.0%

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

   3. Simplified 61.0%

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

   5. Taylor expanded in y around inf 61.6%

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

      1. +-commutative 61.6%

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

      2. mul-1-neg 61.6%

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

      3. unsub-neg 61.6%

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

      4. *-commutative 61.6%

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

      5. *-commutative 61.6%

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

   7. Simplified 61.6%

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

   if -41000 < y < 9.20000000000000064e-294

   1. Initial program 83.7%

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

      1. +-commutative 83.7%

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

      2. fma-define 85.1%

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

      3. *-commutative 85.1%

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

      4. *-commutative 85.1%

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

   3. Simplified 85.1%

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

   5. Taylor expanded in c around inf 55.0%

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

      1. *-commutative 55.0%

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

   7. Simplified 55.0%

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

   if 9.20000000000000064e-294 < y < 1.39999999999999993e-167

   1. Initial program 88.0%

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

      1. +-commutative 88.0%

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

      2. fma-define 88.0%

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

      3. *-commutative 88.0%

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

      4. *-commutative 88.0%

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

   3. Simplified 88.0%

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

   5. Taylor expanded in i around -inf 79.1%

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

   7. Simplified 75.9%

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

   8. Taylor expanded in i around inf 58.9%

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

   if 1.39999999999999993e-167 < y < 2.7e8

   1. Initial program 64.7%

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

      1. +-commutative 64.7%

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

      2. fma-define 67.6%

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

      3. *-commutative 67.6%

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

      4. *-commutative 67.6%

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

   3. Simplified 67.6%

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

   5. Taylor expanded in a around inf 62.6%

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

      1. +-commutative 62.6%

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

      2. mul-1-neg 62.6%

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

      3. unsub-neg 62.6%

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

      4. *-commutative 62.6%

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

   7. Simplified 62.6%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -41000:\\ \;\;\;\;y \cdot \left(z \cdot x - i \cdot j\right)\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-294}:\\ \;\;\;\;c \cdot \left(a \cdot j - b \cdot z\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-167}:\\ \;\;\;\;i \cdot \left(b \cdot t - y \cdot j\right)\\ \mathbf{elif}\;y \leq 270000000:\\ \;\;\;\;a \cdot \left(c \cdot j - t \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot x - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 68.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+112}:\\ \;\;\;\;\left(b \cdot i\right) \cdot \left(t - \frac{c \cdot z}{i}\right)\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{-10}:\\ \;\;\;\;j \cdot \left(c \cdot a - i \cdot y\right) + x \cdot \left(z \cdot y - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(i \cdot t - c \cdot z\right) - y \cdot \left(i \cdot j - z \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -7.5e+112)
   (* (* b i) (- t (/ (* c z) i)))
   (if (<= b 9.2e-10)
     (+ (* j (- (* c a) (* i y))) (* x (- (* z y) (* t a))))
     (- (* b (- (* i t) (* c z))) (* y (- (* i j) (* z x)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -7.5e+112) {
		tmp = (b * i) * (t - ((c * z) / i));
	} else if (b <= 9.2e-10) {
		tmp = (j * ((c * a) - (i * y))) + (x * ((z * y) - (t * a)));
	} else {
		tmp = (b * ((i * t) - (c * z))) - (y * ((i * j) - (z * x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-7.5d+112)) then
        tmp = (b * i) * (t - ((c * z) / i))
    else if (b <= 9.2d-10) then
        tmp = (j * ((c * a) - (i * y))) + (x * ((z * y) - (t * a)))
    else
        tmp = (b * ((i * t) - (c * z))) - (y * ((i * j) - (z * x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -7.5e+112) {
		tmp = (b * i) * (t - ((c * z) / i));
	} else if (b <= 9.2e-10) {
		tmp = (j * ((c * a) - (i * y))) + (x * ((z * y) - (t * a)));
	} else {
		tmp = (b * ((i * t) - (c * z))) - (y * ((i * j) - (z * x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -7.5e+112:
		tmp = (b * i) * (t - ((c * z) / i))
	elif b <= 9.2e-10:
		tmp = (j * ((c * a) - (i * y))) + (x * ((z * y) - (t * a)))
	else:
		tmp = (b * ((i * t) - (c * z))) - (y * ((i * j) - (z * x)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -7.5e+112)
		tmp = Float64(Float64(b * i) * Float64(t - Float64(Float64(c * z) / i)));
	elseif (b <= 9.2e-10)
		tmp = Float64(Float64(j * Float64(Float64(c * a) - Float64(i * y))) + Float64(x * Float64(Float64(z * y) - Float64(t * a))));
	else
		tmp = Float64(Float64(b * Float64(Float64(i * t) - Float64(c * z))) - Float64(y * Float64(Float64(i * j) - Float64(z * x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -7.5e+112)
		tmp = (b * i) * (t - ((c * z) / i));
	elseif (b <= 9.2e-10)
		tmp = (j * ((c * a) - (i * y))) + (x * ((z * y) - (t * a)));
	else
		tmp = (b * ((i * t) - (c * z))) - (y * ((i * j) - (z * x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -7.5e+112], N[(N[(b * i), $MachinePrecision] * N[(t - N[(N[(c * z), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.2e-10], N[(N[(j * N[(N[(c * a), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(z * y), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(N[(i * t), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(i * j), $MachinePrecision] - N[(z * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.5e112

   1. Initial program 69.9%

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

      1. +-commutative 69.9%

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

      2. fma-define 71.9%

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

      3. *-commutative 71.9%

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

      4. *-commutative 71.9%

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

   3. Simplified 71.9%

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

   5. Taylor expanded in i around -inf 56.8%

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

   7. Simplified 62.7%

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

   8. Taylor expanded in b around inf 86.4%

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

      1. associate-*r* 86.4%

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

      2. mul-1-neg 86.4%

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

      3. unsub-neg 86.4%

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

   10. Simplified 86.4%

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

   if -7.5e112 < b < 9.20000000000000028e-10

   1. Initial program 73.0%

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

      1. +-commutative 73.0%

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

      2. fma-define 74.4%

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

      3. *-commutative 74.4%

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

      4. *-commutative 74.4%

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

   3. Simplified 74.4%

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

   5. Taylor expanded in b around 0 72.6%

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

   if 9.20000000000000028e-10 < b

   1. Initial program 67.6%

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

      1. +-commutative 67.6%

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

      2. fma-define 67.6%

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

      3. *-commutative 67.6%

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

      4. *-commutative 67.6%

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

   3. Simplified 67.6%

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

   5. Taylor expanded in a around 0 81.1%

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

      1. sub-neg 81.1%

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

      2. +-commutative 81.1%

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

      3. *-commutative 81.1%

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

      4. associate-*r* 84.3%

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

      5. associate-*r* 85.6%

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

      6. associate-*r* 85.6%

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

      7. distribute-rgt-in 87.2%

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

      8. mul-1-neg 87.2%

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

      9. unsub-neg 87.2%

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

      10. *-commutative 87.2%

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

      11. *-commutative 87.2%

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

      12. sub-neg 87.2%

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

      13. distribute-lft-out 82.5%

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

      14. distribute-rgt-neg-out 82.5%

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

      15. mul-1-neg 82.5%

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

      16. +-commutative 82.5%

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

      17. distribute-neg-in 82.5%

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

   7. Simplified 87.2%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+112}:\\ \;\;\;\;\left(b \cdot i\right) \cdot \left(t - \frac{c \cdot z}{i}\right)\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{-10}:\\ \;\;\;\;j \cdot \left(c \cdot a - i \cdot y\right) + x \cdot \left(z \cdot y - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(i \cdot t - c \cdot z\right) - y \cdot \left(i \cdot j - z \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 58.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+121} \lor \neg \left(x \leq 9 \cdot 10^{+140}\right):\\ \;\;\;\;x \cdot \left(z \cdot y - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(c \cdot a - i \cdot y\right) + b \cdot \left(i \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= x -3.2e+121) (not (<= x 9e+140)))
   (* x (- (* z y) (* t a)))
   (+ (* j (- (* c a) (* i y))) (* b (* i 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 <= -3.2e+121) || !(x <= 9e+140)) {
		tmp = x * ((z * y) - (t * a));
	} else {
		tmp = (j * ((c * a) - (i * y))) + (b * (i * 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 <= (-3.2d+121)) .or. (.not. (x <= 9d+140))) then
        tmp = x * ((z * y) - (t * a))
    else
        tmp = (j * ((c * a) - (i * y))) + (b * (i * 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 <= -3.2e+121) || !(x <= 9e+140)) {
		tmp = x * ((z * y) - (t * a));
	} else {
		tmp = (j * ((c * a) - (i * y))) + (b * (i * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (x <= -3.2e+121) or not (x <= 9e+140):
		tmp = x * ((z * y) - (t * a))
	else:
		tmp = (j * ((c * a) - (i * y))) + (b * (i * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((x <= -3.2e+121) || !(x <= 9e+140))
		tmp = Float64(x * Float64(Float64(z * y) - Float64(t * a)));
	else
		tmp = Float64(Float64(j * Float64(Float64(c * a) - Float64(i * y))) + Float64(b * Float64(i * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((x <= -3.2e+121) || ~((x <= 9e+140)))
		tmp = x * ((z * y) - (t * a));
	else
		tmp = (j * ((c * a) - (i * y))) + (b * (i * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[x, -3.2e+121], N[Not[LessEqual[x, 9e+140]], $MachinePrecision]], N[(x * N[(N[(z * y), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(N[(c * a), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(i * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.1999999999999999e121 or 9.0000000000000003e140 < x

   1. Initial program 68.7%

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

      1. +-commutative 68.7%

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

      2. fma-define 71.4%

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

      3. *-commutative 71.4%

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

      4. *-commutative 71.4%

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

   3. Simplified 71.4%

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

   5. Taylor expanded in i around -inf 70.6%

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

   7. Simplified 73.2%

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

   8. Taylor expanded in x around -inf 73.9%

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

      1. *-commutative 73.9%

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

   10. Simplified 73.9%

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

   if -3.1999999999999999e121 < x < 9.0000000000000003e140

   1. Initial program 72.0%

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

   3. Taylor expanded in i around inf 61.9%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+121} \lor \neg \left(x \leq 9 \cdot 10^{+140}\right):\\ \;\;\;\;x \cdot \left(z \cdot y - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(c \cdot a - i \cdot y\right) + b \cdot \left(i \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 29.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.4 \cdot 10^{-46}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq -5 \cdot 10^{-194}:\\ \;\;\;\;i \cdot \left(b \cdot t\right)\\ \mathbf{elif}\;j \leq 3.6 \cdot 10^{-26}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -1.4e-46)
   (* a (* c j))
   (if (<= j -5e-194)
     (* i (* b t))
     (if (<= j 3.6e-26) (* y (* z x)) (* (* i j) (- y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -1.4e-46) {
		tmp = a * (c * j);
	} else if (j <= -5e-194) {
		tmp = i * (b * t);
	} else if (j <= 3.6e-26) {
		tmp = y * (z * x);
	} else {
		tmp = (i * j) * -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (j <= (-1.4d-46)) then
        tmp = a * (c * j)
    else if (j <= (-5d-194)) then
        tmp = i * (b * t)
    else if (j <= 3.6d-26) then
        tmp = y * (z * x)
    else
        tmp = (i * j) * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -1.4e-46) {
		tmp = a * (c * j);
	} else if (j <= -5e-194) {
		tmp = i * (b * t);
	} else if (j <= 3.6e-26) {
		tmp = y * (z * x);
	} else {
		tmp = (i * j) * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -1.4e-46:
		tmp = a * (c * j)
	elif j <= -5e-194:
		tmp = i * (b * t)
	elif j <= 3.6e-26:
		tmp = y * (z * x)
	else:
		tmp = (i * j) * -y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -1.4e-46)
		tmp = Float64(a * Float64(c * j));
	elseif (j <= -5e-194)
		tmp = Float64(i * Float64(b * t));
	elseif (j <= 3.6e-26)
		tmp = Float64(y * Float64(z * x));
	else
		tmp = Float64(Float64(i * j) * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -1.4e-46)
		tmp = a * (c * j);
	elseif (j <= -5e-194)
		tmp = i * (b * t);
	elseif (j <= 3.6e-26)
		tmp = y * (z * x);
	else
		tmp = (i * j) * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -1.4e-46], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -5e-194], N[(i * N[(b * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.6e-26], N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision], N[(N[(i * j), $MachinePrecision] * (-y)), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.3999999999999999e-46

   1. Initial program 70.5%

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

      1. +-commutative 70.5%

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

      2. fma-define 72.0%

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

      3. *-commutative 72.0%

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

      4. *-commutative 72.0%

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

   3. Simplified 72.0%

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

   5. Taylor expanded in a around inf 51.0%

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

      1. +-commutative 51.0%

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

      2. mul-1-neg 51.0%

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

      3. unsub-neg 51.0%

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

      4. *-commutative 51.0%

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

   7. Simplified 51.0%

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

   8. Taylor expanded in j around inf 40.2%

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

   if -1.3999999999999999e-46 < j < -5.0000000000000002e-194

   1. Initial program 65.8%

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

      1. +-commutative 65.8%

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

      2. fma-define 65.8%

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

      3. *-commutative 65.8%

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

      4. *-commutative 65.8%

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

   3. Simplified 65.8%

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

   5. Taylor expanded in i around -inf 81.0%

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

   7. Simplified 81.0%

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

   8. Taylor expanded in i around inf 55.2%

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

   9. Taylor expanded in b around inf 50.6%

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

   if -5.0000000000000002e-194 < j < 3.6000000000000001e-26

   1. Initial program 65.7%

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

      1. +-commutative 65.7%

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

      2. fma-define 65.7%

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

      3. *-commutative 65.7%

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

      4. *-commutative 65.7%

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

   3. Simplified 65.7%

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

   5. Taylor expanded in y around inf 37.7%

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

      1. +-commutative 37.7%

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

      2. mul-1-neg 37.7%

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

      3. unsub-neg 37.7%

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

      4. *-commutative 37.7%

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

      5. *-commutative 37.7%

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

   7. Simplified 37.7%

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

   8. Taylor expanded in z around inf 37.6%

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

      1. *-commutative 37.6%

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

   10. Simplified 37.6%

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

   if 3.6000000000000001e-26 < j

   1. Initial program 78.9%

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

      1. +-commutative 78.9%

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

      2. fma-define 81.4%

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

      3. *-commutative 81.4%

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

      4. *-commutative 81.4%

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

   3. Simplified 81.4%

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

   5. Taylor expanded in y around inf 50.5%

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

      1. +-commutative 50.5%

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

      2. mul-1-neg 50.5%

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

      3. unsub-neg 50.5%

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

      4. *-commutative 50.5%

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

      5. *-commutative 50.5%

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

   7. Simplified 50.5%

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

   8. Taylor expanded in z around 0 39.0%

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

      1. associate-*r* 39.0%

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

      2. neg-mul-1 39.0%

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

      3. *-commutative 39.0%

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

      4. *-commutative 39.0%

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

      5. associate-*r* 44.8%

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

   10. Simplified 44.8%

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

4. Final simplification 41.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.4 \cdot 10^{-46}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq -5 \cdot 10^{-194}:\\ \;\;\;\;i \cdot \left(b \cdot t\right)\\ \mathbf{elif}\;j \leq 3.6 \cdot 10^{-26}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 41.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(i \cdot t\right)\\ \mathbf{if}\;b \leq -3.1 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 0.0285:\\ \;\;\;\;a \cdot \left(c \cdot j - t \cdot x\right)\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{+197}:\\ \;\;\;\;b \cdot \left(c \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* i t))))
   (if (<= b -3.1e+43)
     t_1
     (if (<= b 0.0285)
       (* a (- (* c j) (* t x)))
       (if (<= b 9.2e+197) (* b (* c (- z))) 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 * (i * t);
	double tmp;
	if (b <= -3.1e+43) {
		tmp = t_1;
	} else if (b <= 0.0285) {
		tmp = a * ((c * j) - (t * x));
	} else if (b <= 9.2e+197) {
		tmp = b * (c * -z);
	} 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 * (i * t)
    if (b <= (-3.1d+43)) then
        tmp = t_1
    else if (b <= 0.0285d0) then
        tmp = a * ((c * j) - (t * x))
    else if (b <= 9.2d+197) then
        tmp = b * (c * -z)
    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 * (i * t);
	double tmp;
	if (b <= -3.1e+43) {
		tmp = t_1;
	} else if (b <= 0.0285) {
		tmp = a * ((c * j) - (t * x));
	} else if (b <= 9.2e+197) {
		tmp = b * (c * -z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (i * t)
	tmp = 0
	if b <= -3.1e+43:
		tmp = t_1
	elif b <= 0.0285:
		tmp = a * ((c * j) - (t * x))
	elif b <= 9.2e+197:
		tmp = b * (c * -z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(i * t))
	tmp = 0.0
	if (b <= -3.1e+43)
		tmp = t_1;
	elseif (b <= 0.0285)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(t * x)));
	elseif (b <= 9.2e+197)
		tmp = Float64(b * Float64(c * Float64(-z)));
	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 * (i * t);
	tmp = 0.0;
	if (b <= -3.1e+43)
		tmp = t_1;
	elseif (b <= 0.0285)
		tmp = a * ((c * j) - (t * x));
	elseif (b <= 9.2e+197)
		tmp = b * (c * -z);
	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[(i * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.1e+43], t$95$1, If[LessEqual[b, 0.0285], N[(a * N[(N[(c * j), $MachinePrecision] - N[(t * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.2e+197], N[(b * N[(c * (-z)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.1000000000000002e43 or 9.2000000000000002e197 < b

   1. Initial program 68.6%

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

   3. Taylor expanded in i around inf 55.3%

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

   4. Taylor expanded in b around inf 53.5%

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

      1. *-commutative 53.5%

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

   6. Simplified 53.5%

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

   if -3.1000000000000002e43 < b < 0.028500000000000001

   1. Initial program 73.7%

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

      1. +-commutative 73.7%

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

      2. fma-define 75.2%

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

      3. *-commutative 75.2%

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

      4. *-commutative 75.2%

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

   3. Simplified 75.2%

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

   5. Taylor expanded in a around inf 51.9%

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

      1. +-commutative 51.9%

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

      2. mul-1-neg 51.9%

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

      3. unsub-neg 51.9%

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

      4. *-commutative 51.9%

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

   7. Simplified 51.9%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   if 0.028500000000000001 < b < 9.2000000000000002e197

   1. Initial program 67.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 67.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-define 67.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 67.0%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 67.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 67.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 46.2%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 46.2%

         \[\leadsto c \cdot \left(\color{blue}{j \cdot a} - b \cdot z\right) \]

   7. Simplified 46.2%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a - b \cdot z\right)} \]

   8. Taylor expanded in j around 0 41.1%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 41.1%

         \[\leadsto \color{blue}{\left(-1 \cdot b\right) \cdot \left(c \cdot z\right)} \]

      2. neg-mul-1 41.1%

         \[\leadsto \color{blue}{\left(-b\right)} \cdot \left(c \cdot z\right) \]

   10. Simplified 41.1%

       \[\leadsto \color{blue}{\left(-b\right) \cdot \left(c \cdot z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 51.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.1 \cdot 10^{+43}:\\ \;\;\;\;b \cdot \left(i \cdot t\right)\\ \mathbf{elif}\;b \leq 0.0285:\\ \;\;\;\;a \cdot \left(c \cdot j - t \cdot x\right)\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{+197}:\\ \;\;\;\;b \cdot \left(c \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(i \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 29.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{-58}:\\ \;\;\;\;b \cdot \left(i \cdot t\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-257}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-65}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(b \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -3.8e-58)
   (* b (* i t))
   (if (<= t 5.2e-257)
     (* x (* z y))
     (if (<= t 2.9e-65) (* c (* a j)) (* i (* b 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 (t <= -3.8e-58) {
		tmp = b * (i * t);
	} else if (t <= 5.2e-257) {
		tmp = x * (z * y);
	} else if (t <= 2.9e-65) {
		tmp = c * (a * j);
	} else {
		tmp = i * (b * 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 (t <= (-3.8d-58)) then
        tmp = b * (i * t)
    else if (t <= 5.2d-257) then
        tmp = x * (z * y)
    else if (t <= 2.9d-65) then
        tmp = c * (a * j)
    else
        tmp = i * (b * 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 (t <= -3.8e-58) {
		tmp = b * (i * t);
	} else if (t <= 5.2e-257) {
		tmp = x * (z * y);
	} else if (t <= 2.9e-65) {
		tmp = c * (a * j);
	} else {
		tmp = i * (b * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -3.8e-58:
		tmp = b * (i * t)
	elif t <= 5.2e-257:
		tmp = x * (z * y)
	elif t <= 2.9e-65:
		tmp = c * (a * j)
	else:
		tmp = i * (b * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -3.8e-58)
		tmp = Float64(b * Float64(i * t));
	elseif (t <= 5.2e-257)
		tmp = Float64(x * Float64(z * y));
	elseif (t <= 2.9e-65)
		tmp = Float64(c * Float64(a * j));
	else
		tmp = Float64(i * Float64(b * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -3.8e-58)
		tmp = b * (i * t);
	elseif (t <= 5.2e-257)
		tmp = x * (z * y);
	elseif (t <= 2.9e-65)
		tmp = c * (a * j);
	else
		tmp = i * (b * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -3.8e-58], N[(b * N[(i * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.2e-257], N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.9e-65], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], N[(i * N[(b * t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.7999999999999997e-58

   1. Initial program 66.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 48.1%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Taylor expanded in b around inf 36.9%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   5. Step-by-step derivation

      1. *-commutative 36.9%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   6. Simplified 36.9%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]

   if -3.7999999999999997e-58 < t < 5.2000000000000002e-257

   1. Initial program 79.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 79.5%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-define 81.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 81.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 81.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 81.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 52.4%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   6. Step-by-step derivation

      1. +-commutative 52.4%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 52.4%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 52.4%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 52.4%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

      5. *-commutative 52.4%

         \[\leadsto y \cdot \left(z \cdot x - \color{blue}{j \cdot i}\right) \]

   7. Simplified 52.4%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - j \cdot i\right)} \]

   8. Taylor expanded in z around inf 35.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   if 5.2000000000000002e-257 < t < 2.8999999999999998e-65

   1. Initial program 69.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 69.7%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-define 69.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 69.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 69.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 69.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 61.5%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 61.5%

         \[\leadsto c \cdot \left(\color{blue}{j \cdot a} - b \cdot z\right) \]

   7. Simplified 61.5%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a - b \cdot z\right)} \]

   8. Taylor expanded in j around inf 44.3%

      \[\leadsto c \cdot \color{blue}{\left(a \cdot j\right)} \]

   if 2.8999999999999998e-65 < t

   1. Initial program 69.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 69.5%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-define 72.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 72.0%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 72.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 72.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 61.5%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(-1 \cdot \frac{\left(a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) - b \cdot \left(c \cdot z\right)}{i} + j \cdot y\right) - b \cdot t\right)\right)} \]

   7. Simplified 62.8%

      \[\leadsto \color{blue}{i \cdot \left(-\left(\left(j \cdot y - \frac{\mathsf{fma}\left(c, j \cdot a - b \cdot z, x \cdot \left(y \cdot z - a \cdot t\right)\right)}{i}\right) - b \cdot t\right)\right)} \]

   8. Taylor expanded in i around inf 54.4%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot t - j \cdot y\right)} \]

   9. Taylor expanded in b around inf 44.3%

      \[\leadsto i \cdot \color{blue}{\left(b \cdot t\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 40.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{-58}:\\ \;\;\;\;b \cdot \left(i \cdot t\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-257}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-65}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(b \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 30.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.86 \cdot 10^{-53} \lor \neg \left(t \leq 9 \cdot 10^{-64}\right):\\ \;\;\;\;b \cdot \left(i \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -1.86e-53) (not (<= t 9e-64))) (* b (* i t)) (* a (* c 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 ((t <= -1.86e-53) || !(t <= 9e-64)) {
		tmp = b * (i * t);
	} else {
		tmp = a * (c * 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 ((t <= (-1.86d-53)) .or. (.not. (t <= 9d-64))) then
        tmp = b * (i * t)
    else
        tmp = a * (c * 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 ((t <= -1.86e-53) || !(t <= 9e-64)) {
		tmp = b * (i * t);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -1.86e-53) or not (t <= 9e-64):
		tmp = b * (i * t)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -1.86e-53) || !(t <= 9e-64))
		tmp = Float64(b * Float64(i * t));
	else
		tmp = Float64(a * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -1.86e-53) || ~((t <= 9e-64)))
		tmp = b * (i * t);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -1.86e-53], N[Not[LessEqual[t, 9e-64]], $MachinePrecision]], N[(b * N[(i * t), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.8599999999999999e-53 or 9.00000000000000019e-64 < t

   1. Initial program 68.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 51.1%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Taylor expanded in b around inf 40.5%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   5. Step-by-step derivation

      1. *-commutative 40.5%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   6. Simplified 40.5%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]

   if -1.8599999999999999e-53 < t < 9.00000000000000019e-64

   1. Initial program 75.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 75.5%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-define 76.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 76.5%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 76.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 76.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 36.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   6. Step-by-step derivation

      1. +-commutative 36.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 36.8%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 36.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 36.8%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   7. Simplified 36.8%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   8. Taylor expanded in j around inf 31.8%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.86 \cdot 10^{-53} \lor \neg \left(t \leq 9 \cdot 10^{-64}\right):\\ \;\;\;\;b \cdot \left(i \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 30.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-54} \lor \neg \left(t \leq 7.2 \cdot 10^{-63}\right):\\ \;\;\;\;b \cdot \left(i \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -8.5e-54) (not (<= t 7.2e-63))) (* b (* i t)) (* c (* a 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 ((t <= -8.5e-54) || !(t <= 7.2e-63)) {
		tmp = b * (i * t);
	} else {
		tmp = c * (a * 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 ((t <= (-8.5d-54)) .or. (.not. (t <= 7.2d-63))) then
        tmp = b * (i * t)
    else
        tmp = c * (a * 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 ((t <= -8.5e-54) || !(t <= 7.2e-63)) {
		tmp = b * (i * t);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -8.5e-54) or not (t <= 7.2e-63):
		tmp = b * (i * t)
	else:
		tmp = c * (a * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -8.5e-54) || !(t <= 7.2e-63))
		tmp = Float64(b * Float64(i * t));
	else
		tmp = Float64(c * Float64(a * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -8.5e-54) || ~((t <= 7.2e-63)))
		tmp = b * (i * t);
	else
		tmp = c * (a * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -8.5e-54], N[Not[LessEqual[t, 7.2e-63]], $MachinePrecision]], N[(b * N[(i * t), $MachinePrecision]), $MachinePrecision], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.5e-54 or 7.20000000000000016e-63 < t

   1. Initial program 68.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 51.1%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Taylor expanded in b around inf 40.5%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   5. Step-by-step derivation

      1. *-commutative 40.5%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   6. Simplified 40.5%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]

   if -8.5e-54 < t < 7.20000000000000016e-63

   1. Initial program 75.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 75.5%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-define 76.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 76.5%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 76.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 76.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 48.1%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 48.1%

         \[\leadsto c \cdot \left(\color{blue}{j \cdot a} - b \cdot z\right) \]

   7. Simplified 48.1%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a - b \cdot z\right)} \]

   8. Taylor expanded in j around inf 32.8%

      \[\leadsto c \cdot \color{blue}{\left(a \cdot j\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-54} \lor \neg \left(t \leq 7.2 \cdot 10^{-63}\right):\\ \;\;\;\;b \cdot \left(i \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 30.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{-54}:\\ \;\;\;\;b \cdot \left(i \cdot t\right)\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-62}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(b \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -8.8e-54)
   (* b (* i t))
   (if (<= t 2.2e-62) (* c (* a j)) (* i (* b 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 (t <= -8.8e-54) {
		tmp = b * (i * t);
	} else if (t <= 2.2e-62) {
		tmp = c * (a * j);
	} else {
		tmp = i * (b * 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 (t <= (-8.8d-54)) then
        tmp = b * (i * t)
    else if (t <= 2.2d-62) then
        tmp = c * (a * j)
    else
        tmp = i * (b * 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 (t <= -8.8e-54) {
		tmp = b * (i * t);
	} else if (t <= 2.2e-62) {
		tmp = c * (a * j);
	} else {
		tmp = i * (b * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -8.8e-54:
		tmp = b * (i * t)
	elif t <= 2.2e-62:
		tmp = c * (a * j)
	else:
		tmp = i * (b * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -8.8e-54)
		tmp = Float64(b * Float64(i * t));
	elseif (t <= 2.2e-62)
		tmp = Float64(c * Float64(a * j));
	else
		tmp = Float64(i * Float64(b * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -8.8e-54)
		tmp = b * (i * t);
	elseif (t <= 2.2e-62)
		tmp = c * (a * j);
	else
		tmp = i * (b * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -8.8e-54], N[(b * N[(i * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.2e-62], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], N[(i * N[(b * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.7999999999999998e-54

   1. Initial program 66.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 48.1%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Taylor expanded in b around inf 37.9%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   5. Step-by-step derivation

      1. *-commutative 37.9%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   6. Simplified 37.9%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]

   if -8.7999999999999998e-54 < t < 2.20000000000000017e-62

   1. Initial program 75.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 75.5%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-define 76.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 76.5%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 76.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 76.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 48.1%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 48.1%

         \[\leadsto c \cdot \left(\color{blue}{j \cdot a} - b \cdot z\right) \]

   7. Simplified 48.1%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a - b \cdot z\right)} \]

   8. Taylor expanded in j around inf 32.8%

      \[\leadsto c \cdot \color{blue}{\left(a \cdot j\right)} \]

   if 2.20000000000000017e-62 < t

   1. Initial program 69.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 69.5%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-define 72.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 72.0%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 72.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 72.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around -inf 61.5%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(\left(-1 \cdot \frac{\left(a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) - b \cdot \left(c \cdot z\right)}{i} + j \cdot y\right) - b \cdot t\right)\right)} \]

   7. Simplified 62.8%

      \[\leadsto \color{blue}{i \cdot \left(-\left(\left(j \cdot y - \frac{\mathsf{fma}\left(c, j \cdot a - b \cdot z, x \cdot \left(y \cdot z - a \cdot t\right)\right)}{i}\right) - b \cdot t\right)\right)} \]

   8. Taylor expanded in i around inf 54.4%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot t - j \cdot y\right)} \]

   9. Taylor expanded in b around inf 44.3%

      \[\leadsto i \cdot \color{blue}{\left(b \cdot t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 37.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{-54}:\\ \;\;\;\;b \cdot \left(i \cdot t\right)\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-62}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(b \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 20.9% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 7.4 \cdot 10^{+36}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b 7.4e+36) (* a (* c j)) (* a (* t x))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= 7.4e+36) {
		tmp = a * (c * j);
	} else {
		tmp = a * (t * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= 7.4d+36) then
        tmp = a * (c * j)
    else
        tmp = a * (t * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= 7.4e+36) {
		tmp = a * (c * j);
	} else {
		tmp = a * (t * x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= 7.4e+36:
		tmp = a * (c * j)
	else:
		tmp = a * (t * x)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= 7.4e+36)
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(a * Float64(t * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= 7.4e+36)
		tmp = a * (c * j);
	else
		tmp = a * (t * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, 7.4e+36], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(a * N[(t * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 7.40000000000000058e36

   1. Initial program 71.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 71.4%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-define 72.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 72.9%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 72.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 72.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 41.4%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   6. Step-by-step derivation

      1. +-commutative 41.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 41.4%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 41.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 41.4%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   7. Simplified 41.4%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   8. Taylor expanded in j around inf 24.9%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]

   if 7.40000000000000058e36 < b

   1. Initial program 69.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 69.9%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-define 69.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 69.9%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 69.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 69.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 19.6%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   6. Step-by-step derivation

      1. +-commutative 19.6%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 19.6%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 19.6%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 19.6%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   7. Simplified 19.6%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   8. Taylor expanded in j around 0 16.2%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 16.2%

         \[\leadsto a \cdot \color{blue}{\left(-t \cdot x\right)} \]

      2. distribute-lft-neg-out 16.2%

         \[\leadsto a \cdot \color{blue}{\left(\left(-t\right) \cdot x\right)} \]

      3. *-commutative 16.2%

         \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   10. Simplified 16.2%

       \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]
   11. Step-by-step derivation

       1. pow1 16.2%

          \[\leadsto \color{blue}{{\left(a \cdot \left(x \cdot \left(-t\right)\right)\right)}^{1}} \]

       2. associate-*r* 19.9%

          \[\leadsto {\color{blue}{\left(\left(a \cdot x\right) \cdot \left(-t\right)\right)}}^{1} \]

       3. add-sqr-sqrt 9.7%

          \[\leadsto {\left(\left(a \cdot x\right) \cdot \color{blue}{\left(\sqrt{-t} \cdot \sqrt{-t}\right)}\right)}^{1} \]

       4. sqrt-unprod 19.0%

          \[\leadsto {\left(\left(a \cdot x\right) \cdot \color{blue}{\sqrt{\left(-t\right) \cdot \left(-t\right)}}\right)}^{1} \]

       5. sqr-neg 19.0%

          \[\leadsto {\left(\left(a \cdot x\right) \cdot \sqrt{\color{blue}{t \cdot t}}\right)}^{1} \]

       6. sqrt-unprod 7.7%

          \[\leadsto {\left(\left(a \cdot x\right) \cdot \color{blue}{\left(\sqrt{t} \cdot \sqrt{t}\right)}\right)}^{1} \]

       7. add-sqr-sqrt 12.9%

          \[\leadsto {\left(\left(a \cdot x\right) \cdot \color{blue}{t}\right)}^{1} \]

   12. Applied egg-rr 12.9%

       \[\leadsto \color{blue}{{\left(\left(a \cdot x\right) \cdot t\right)}^{1}} \]
   13. Step-by-step derivation

       1. unpow1 12.9%

          \[\leadsto \color{blue}{\left(a \cdot x\right) \cdot t} \]

       2. associate-*l* 16.4%

          \[\leadsto \color{blue}{a \cdot \left(x \cdot t\right)} \]

       3. *-commutative 16.4%

          \[\leadsto a \cdot \color{blue}{\left(t \cdot x\right)} \]

   14. Simplified 16.4%

       \[\leadsto \color{blue}{a \cdot \left(t \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 23.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 7.4 \cdot 10^{+36}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 22.9% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(c \cdot j\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* c j)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = a * (c * j)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (c * j)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(c * j))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (c * j);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 71.1%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
2. Step-by-step derivation

   1. +-commutative 71.1%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

   2. fma-define 72.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

   3. *-commutative 72.2%

      \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

   4. *-commutative 72.2%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

3. Simplified 72.2%

   \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
4. Add Preprocessing

5. Taylor expanded in a around inf 36.7%

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
6. Step-by-step derivation

   1. +-commutative 36.7%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

   2. mul-1-neg 36.7%

      \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

   3. unsub-neg 36.7%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. *-commutative 36.7%

      \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

7. Simplified 36.7%

   \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

8. Taylor expanded in j around inf 21.0%

   \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]

9. Final simplification 21.0%

   \[\leadsto a \cdot \left(c \cdot j\right) \]
10. Add Preprocessing

Developer target: 59.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right)\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + t\_1\\ \mathbf{if}\;x < -1.469694296777705 \cdot 10^{-64}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x < 3.2113527362226803 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* c a) (* y i))))
        (t_2
         (+
          (-
           (* x (- (* y z) (* t a)))
           (/
            (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0)))
            (+ (* c z) (* t i))))
          t_1)))
   (if (< x -1.469694296777705e-64)
     t_2
     (if (< x 3.2113527362226803e-147)
       (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) t_1))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (pow((c * z), 2.0) - pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((c * a) - (y * i))
    t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ** 2.0d0) - ((t * i) ** 2.0d0))) / ((c * z) + (t * i)))) + t_1
    if (x < (-1.469694296777705d-64)) then
        tmp = t_2
    else if (x < 3.2113527362226803d-147) then
        tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (Math.pow((c * z), 2.0) - Math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((c * a) - (y * i))
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (math.pow((c * z), 2.0) - math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1
	tmp = 0
	if x < -1.469694296777705e-64:
		tmp = t_2
	elif x < 3.2113527362226803e-147:
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(c * a) - Float64(y * i)))
	t_2 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(Float64(b * Float64((Float64(c * z) ^ 2.0) - (Float64(t * i) ^ 2.0))) / Float64(Float64(c * z) + Float64(t * i)))) + t_1)
	tmp = 0.0
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = Float64(Float64(Float64(Float64(b * i) - Float64(x * a)) * t) - Float64(Float64(z * Float64(c * b)) - t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((c * a) - (y * i));
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ^ 2.0) - ((t * i) ^ 2.0))) / ((c * z) + (t * i)))) + t_1;
	tmp = 0.0;
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[Power[N[(c * z), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(t * i), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * z), $MachinePrecision] + N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[Less[x, -1.469694296777705e-64], t$95$2, If[Less[x, 3.2113527362226803e-147], N[(N[(N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] - N[(N[(z * N[(c * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024071 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :alt
  (if (< x -1.469694296777705e-64) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 3.2113527362226803e-147) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i)))))