Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 72.6% → 84.3%

Time: 22.7s

Alternatives: 31

Speedup: 0.5×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 72.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 84.3% accurate, 0.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 92.9%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in c around inf 17.7%

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

      1. *-commutative 17.7%

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

      2. associate-*r* 12.9%

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

      3. *-commutative 12.9%

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

      4. associate-*r* 16.1%

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

   5. Simplified 16.1%

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

   6. Taylor expanded in a around inf 29.0%

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

      1. sub-neg 29.0%

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

      2. +-commutative 29.0%

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

      3. mul-1-neg 29.0%

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

      4. unsub-neg 29.0%

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

      5. +-commutative 29.0%

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

      6. *-commutative 29.0%

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

      7. associate-*r* 29.0%

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

      8. *-commutative 29.0%

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

      9. neg-mul-1 29.0%

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

   8. Simplified 29.0%

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

   9. Taylor expanded in t around inf 33.9%

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

   11. Simplified 55.1%

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

4. Final simplification 83.8%

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

Alternative 2: 81.0% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 92.9%

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

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

   1. Initial program 0.0%

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

      1. +-commutative 0.0%

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

      2. fma-define 9.7%

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

      3. *-commutative 9.7%

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

      4. *-commutative 9.7%

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

      5. cancel-sign-sub-inv 9.7%

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

      6. cancel-sign-sub 9.7%

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

      7. fmm-def 12.9%

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

      8. distribute-rgt-neg-out 12.9%

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

      9. remove-double-neg 12.9%

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

      10. *-commutative 12.9%

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

      11. *-commutative 12.9%

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

   3. Simplified 12.9%

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

   5. Taylor expanded in i around inf 49.1%

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

      1. distribute-lft-out-- 49.1%

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

      2. *-commutative 49.1%

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

   7. Simplified 49.1%

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

4. Final simplification 82.3%

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

Alternative 3: 66.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot z - t \cdot a\\ \mathbf{if}\;c \leq -7.8 \cdot 10^{+192}:\\ \;\;\;\;t \cdot \left(c \cdot j - b \cdot \frac{z \cdot c}{t}\right)\\ \mathbf{elif}\;c \leq -8.2 \cdot 10^{-41}:\\ \;\;\;\;x \cdot \left(t\_1 + c \cdot \frac{t \cdot j - z \cdot b}{x}\right)\\ \mathbf{elif}\;c \leq -2.7 \cdot 10^{-146}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 2.55 \cdot 10^{+132}:\\ \;\;\;\;t \cdot \left(c \cdot j\right) + \left(x \cdot t\_1 + b \cdot \left(a \cdot i - z \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot c\right) \cdot \left(j - b \cdot \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* y z) (* t a))))
   (if (<= c -7.8e+192)
     (* t (- (* c j) (* b (/ (* z c) t))))
     (if (<= c -8.2e-41)
       (* x (+ t_1 (* c (/ (- (* t j) (* z b)) x))))
       (if (<= c -2.7e-146)
         (+ (* j (- (* t c) (* y i))) (* a (- (* b i) (* x t))))
         (if (<= c 2.55e+132)
           (+ (* t (* c j)) (+ (* x t_1) (* b (- (* a i) (* z c)))))
           (* (* t c) (- j (* b (/ z t))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * z) - (t * a);
	double tmp;
	if (c <= -7.8e+192) {
		tmp = t * ((c * j) - (b * ((z * c) / t)));
	} else if (c <= -8.2e-41) {
		tmp = x * (t_1 + (c * (((t * j) - (z * b)) / x)));
	} else if (c <= -2.7e-146) {
		tmp = (j * ((t * c) - (y * i))) + (a * ((b * i) - (x * t)));
	} else if (c <= 2.55e+132) {
		tmp = (t * (c * j)) + ((x * t_1) + (b * ((a * i) - (z * c))));
	} else {
		tmp = (t * c) * (j - (b * (z / t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * z) - (t * a)
    if (c <= (-7.8d+192)) then
        tmp = t * ((c * j) - (b * ((z * c) / t)))
    else if (c <= (-8.2d-41)) then
        tmp = x * (t_1 + (c * (((t * j) - (z * b)) / x)))
    else if (c <= (-2.7d-146)) then
        tmp = (j * ((t * c) - (y * i))) + (a * ((b * i) - (x * t)))
    else if (c <= 2.55d+132) then
        tmp = (t * (c * j)) + ((x * t_1) + (b * ((a * i) - (z * c))))
    else
        tmp = (t * c) * (j - (b * (z / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * z) - (t * a);
	double tmp;
	if (c <= -7.8e+192) {
		tmp = t * ((c * j) - (b * ((z * c) / t)));
	} else if (c <= -8.2e-41) {
		tmp = x * (t_1 + (c * (((t * j) - (z * b)) / x)));
	} else if (c <= -2.7e-146) {
		tmp = (j * ((t * c) - (y * i))) + (a * ((b * i) - (x * t)));
	} else if (c <= 2.55e+132) {
		tmp = (t * (c * j)) + ((x * t_1) + (b * ((a * i) - (z * c))));
	} else {
		tmp = (t * c) * (j - (b * (z / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (y * z) - (t * a)
	tmp = 0
	if c <= -7.8e+192:
		tmp = t * ((c * j) - (b * ((z * c) / t)))
	elif c <= -8.2e-41:
		tmp = x * (t_1 + (c * (((t * j) - (z * b)) / x)))
	elif c <= -2.7e-146:
		tmp = (j * ((t * c) - (y * i))) + (a * ((b * i) - (x * t)))
	elif c <= 2.55e+132:
		tmp = (t * (c * j)) + ((x * t_1) + (b * ((a * i) - (z * c))))
	else:
		tmp = (t * c) * (j - (b * (z / t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(y * z) - Float64(t * a))
	tmp = 0.0
	if (c <= -7.8e+192)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(b * Float64(Float64(z * c) / t))));
	elseif (c <= -8.2e-41)
		tmp = Float64(x * Float64(t_1 + Float64(c * Float64(Float64(Float64(t * j) - Float64(z * b)) / x))));
	elseif (c <= -2.7e-146)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(a * Float64(Float64(b * i) - Float64(x * t))));
	elseif (c <= 2.55e+132)
		tmp = Float64(Float64(t * Float64(c * j)) + Float64(Float64(x * t_1) + Float64(b * Float64(Float64(a * i) - Float64(z * c)))));
	else
		tmp = Float64(Float64(t * c) * Float64(j - Float64(b * Float64(z / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (y * z) - (t * a);
	tmp = 0.0;
	if (c <= -7.8e+192)
		tmp = t * ((c * j) - (b * ((z * c) / t)));
	elseif (c <= -8.2e-41)
		tmp = x * (t_1 + (c * (((t * j) - (z * b)) / x)));
	elseif (c <= -2.7e-146)
		tmp = (j * ((t * c) - (y * i))) + (a * ((b * i) - (x * t)));
	elseif (c <= 2.55e+132)
		tmp = (t * (c * j)) + ((x * t_1) + (b * ((a * i) - (z * c))));
	else
		tmp = (t * c) * (j - (b * (z / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -7.8e+192], N[(t * N[(N[(c * j), $MachinePrecision] - N[(b * N[(N[(z * c), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -8.2e-41], N[(x * N[(t$95$1 + N[(c * N[(N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.7e-146], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.55e+132], N[(N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision] + N[(N[(x * t$95$1), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * c), $MachinePrecision] * N[(j - N[(b * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -7.7999999999999996e192

   1. Initial program 54.4%

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

      1. +-commutative 54.4%

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

      2. fma-define 58.2%

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

      3. *-commutative 58.2%

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

      4. *-commutative 58.2%

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

      5. cancel-sign-sub-inv 58.2%

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

      6. cancel-sign-sub 58.2%

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

      7. fmm-def 58.2%

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

      8. distribute-rgt-neg-out 58.2%

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

      9. remove-double-neg 58.2%

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

      10. *-commutative 58.2%

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

      11. *-commutative 58.2%

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

   3. Simplified 58.2%

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

   5. Taylor expanded in c around inf 80.6%

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

      1. *-commutative 80.6%

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

      2. *-commutative 80.6%

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

   7. Simplified 80.6%

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

   8. Taylor expanded in t around inf 88.6%

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

      1. +-commutative 88.6%

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

      2. mul-1-neg 88.6%

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

      3. unsub-neg 88.6%

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

      4. associate-/l* 88.6%

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

   10. Simplified 88.6%

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

   if -7.7999999999999996e192 < c < -8.20000000000000028e-41

   1. Initial program 65.2%

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

   3. Taylor expanded in c around inf 73.7%

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

      1. *-commutative 73.7%

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

      2. associate-*r* 69.5%

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

      3. *-commutative 69.5%

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

      4. associate-*r* 69.4%

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

   5. Simplified 69.4%

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

   6. Taylor expanded in x around -inf 67.8%

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

      1. mul-1-neg 67.8%

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

      2. *-commutative 67.8%

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

      3. distribute-rgt-neg-in 67.8%

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

   8. Simplified 63.5%

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

   9. Taylor expanded in c around inf 76.5%

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

       1. associate-/l* 78.7%

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

       2. *-commutative 78.7%

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

       3. *-commutative 78.7%

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

   11. Simplified 78.7%

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

   if -8.20000000000000028e-41 < c < -2.69999999999999995e-146

   1. Initial program 65.8%

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

      1. cancel-sign-sub-inv 65.8%

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

      2. cancel-sign-sub 65.8%

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

      3. *-commutative 65.8%

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

      4. fmm-def 65.8%

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

      5. distribute-rgt-neg-in 65.8%

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

      6. remove-double-neg 65.8%

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

      7. *-commutative 65.8%

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

      8. *-commutative 65.8%

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

      9. *-commutative 65.8%

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

      10. *-commutative 65.8%

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

   3. Simplified 65.8%

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

   5. Taylor expanded in a around -inf 77.0%

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

   if -2.69999999999999995e-146 < c < 2.55e132

   1. Initial program 81.4%

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

   3. Taylor expanded in c around inf 73.9%

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

      1. *-commutative 73.9%

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

      2. associate-*r* 74.8%

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

      3. *-commutative 74.8%

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

      4. associate-*r* 75.7%

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

   5. Simplified 75.7%

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

   if 2.55e132 < c

   1. Initial program 59.2%

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

      1. +-commutative 59.2%

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

      2. fma-define 59.2%

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

      3. *-commutative 59.2%

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

      4. *-commutative 59.2%

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

      5. cancel-sign-sub-inv 59.2%

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

      6. cancel-sign-sub 59.2%

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

      7. fmm-def 59.2%

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

      8. distribute-rgt-neg-out 59.2%

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

      9. remove-double-neg 59.2%

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

      10. *-commutative 59.2%

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

      11. *-commutative 59.2%

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

   3. Simplified 59.2%

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

   5. Taylor expanded in c around inf 72.7%

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

      1. *-commutative 72.7%

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

      2. *-commutative 72.7%

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

   7. Simplified 72.7%

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

   8. Taylor expanded in t around inf 62.3%

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

      1. +-commutative 62.3%

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

      2. mul-1-neg 62.3%

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

      3. unsub-neg 62.3%

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

      4. associate-/l* 62.3%

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

   10. Simplified 62.3%

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

   11. Taylor expanded in c around 0 72.7%

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

       1. associate-*r* 72.9%

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

       2. *-commutative 72.9%

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

       3. associate-/l* 75.0%

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

   13. Simplified 75.0%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -7.8 \cdot 10^{+192}:\\ \;\;\;\;t \cdot \left(c \cdot j - b \cdot \frac{z \cdot c}{t}\right)\\ \mathbf{elif}\;c \leq -8.2 \cdot 10^{-41}:\\ \;\;\;\;x \cdot \left(\left(y \cdot z - t \cdot a\right) + c \cdot \frac{t \cdot j - z \cdot b}{x}\right)\\ \mathbf{elif}\;c \leq -2.7 \cdot 10^{-146}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 2.55 \cdot 10^{+132}:\\ \;\;\;\;t \cdot \left(c \cdot j\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot c\right) \cdot \left(j - b \cdot \frac{z}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -4.8 \cdot 10^{+111}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -1.7 \cdot 10^{-66}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq -1.75 \cdot 10^{-163}:\\ \;\;\;\;i \cdot \left(j \cdot \left(a \cdot \frac{b}{j} - y\right)\right)\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{-178}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 2750:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 3.3 \cdot 10^{+90}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j)))) (t_2 (* c (- (* t j) (* z b)))))
   (if (<= c -4.8e+111)
     t_2
     (if (<= c -1.7e-66)
       (* x (- (* y z) (* t a)))
       (if (<= c -1.75e-163)
         (* i (* j (- (* a (/ b j)) y)))
         (if (<= c 1.55e-178)
           t_1
           (if (<= c 2750.0)
             (* a (- (* b i) (* x t)))
             (if (<= c 3.3e+90) 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 = y * ((x * z) - (i * j));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -4.8e+111) {
		tmp = t_2;
	} else if (c <= -1.7e-66) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= -1.75e-163) {
		tmp = i * (j * ((a * (b / j)) - y));
	} else if (c <= 1.55e-178) {
		tmp = t_1;
	} else if (c <= 2750.0) {
		tmp = a * ((b * i) - (x * t));
	} else if (c <= 3.3e+90) {
		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 = y * ((x * z) - (i * j))
    t_2 = c * ((t * j) - (z * b))
    if (c <= (-4.8d+111)) then
        tmp = t_2
    else if (c <= (-1.7d-66)) then
        tmp = x * ((y * z) - (t * a))
    else if (c <= (-1.75d-163)) then
        tmp = i * (j * ((a * (b / j)) - y))
    else if (c <= 1.55d-178) then
        tmp = t_1
    else if (c <= 2750.0d0) then
        tmp = a * ((b * i) - (x * t))
    else if (c <= 3.3d+90) 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 = y * ((x * z) - (i * j));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -4.8e+111) {
		tmp = t_2;
	} else if (c <= -1.7e-66) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= -1.75e-163) {
		tmp = i * (j * ((a * (b / j)) - y));
	} else if (c <= 1.55e-178) {
		tmp = t_1;
	} else if (c <= 2750.0) {
		tmp = a * ((b * i) - (x * t));
	} else if (c <= 3.3e+90) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	t_2 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -4.8e+111:
		tmp = t_2
	elif c <= -1.7e-66:
		tmp = x * ((y * z) - (t * a))
	elif c <= -1.75e-163:
		tmp = i * (j * ((a * (b / j)) - y))
	elif c <= 1.55e-178:
		tmp = t_1
	elif c <= 2750.0:
		tmp = a * ((b * i) - (x * t))
	elif c <= 3.3e+90:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -4.8e+111)
		tmp = t_2;
	elseif (c <= -1.7e-66)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (c <= -1.75e-163)
		tmp = Float64(i * Float64(j * Float64(Float64(a * Float64(b / j)) - y)));
	elseif (c <= 1.55e-178)
		tmp = t_1;
	elseif (c <= 2750.0)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (c <= 3.3e+90)
		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 = y * ((x * z) - (i * j));
	t_2 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -4.8e+111)
		tmp = t_2;
	elseif (c <= -1.7e-66)
		tmp = x * ((y * z) - (t * a));
	elseif (c <= -1.75e-163)
		tmp = i * (j * ((a * (b / j)) - y));
	elseif (c <= 1.55e-178)
		tmp = t_1;
	elseif (c <= 2750.0)
		tmp = a * ((b * i) - (x * t));
	elseif (c <= 3.3e+90)
		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[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4.8e+111], t$95$2, If[LessEqual[c, -1.7e-66], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.75e-163], N[(i * N[(j * N[(N[(a * N[(b / j), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.55e-178], t$95$1, If[LessEqual[c, 2750.0], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.3e+90], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -4.80000000000000011e111 or 3.30000000000000008e90 < c

   1. Initial program 60.9%

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

      1. +-commutative 60.9%

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

      2. fma-define 64.5%

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

      3. *-commutative 64.5%

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

      4. *-commutative 64.5%

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

      5. cancel-sign-sub-inv 64.5%

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

      6. cancel-sign-sub 64.5%

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

      7. fmm-def 64.5%

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

      8. distribute-rgt-neg-out 64.5%

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

      9. remove-double-neg 64.5%

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

      10. *-commutative 64.5%

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

      11. *-commutative 64.5%

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

   3. Simplified 64.5%

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

   5. Taylor expanded in c around inf 73.9%

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

      1. *-commutative 73.9%

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

      2. *-commutative 73.9%

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

   7. Simplified 73.9%

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

   if -4.80000000000000011e111 < c < -1.69999999999999999e-66

   1. Initial program 61.9%

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

   3. Taylor expanded in a around inf 64.4%

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

      1. mul-1-neg 64.4%

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

      2. +-commutative 64.4%

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

      3. unsub-neg 64.4%

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

      4. *-commutative 64.4%

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

      5. *-commutative 64.4%

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

      6. associate-*r* 64.3%

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

      7. *-commutative 64.3%

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

   5. Simplified 64.3%

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

   6. Taylor expanded in x around inf 56.5%

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

      1. *-commutative 56.5%

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

   8. Simplified 56.5%

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

   if -1.69999999999999999e-66 < c < -1.75000000000000014e-163

   1. Initial program 76.1%

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

      1. +-commutative 76.1%

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

      2. fma-define 76.0%

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

      3. *-commutative 76.0%

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

      4. *-commutative 76.0%

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

      5. cancel-sign-sub-inv 76.0%

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

      6. cancel-sign-sub 76.0%

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

      7. fmm-def 76.0%

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

      8. distribute-rgt-neg-out 76.0%

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

      9. remove-double-neg 76.0%

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

      10. *-commutative 76.0%

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

      11. *-commutative 76.0%

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

   3. Simplified 76.0%

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

   5. Taylor expanded in i around inf 58.5%

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

      1. distribute-lft-out-- 58.5%

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

      2. *-commutative 58.5%

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

   7. Simplified 58.5%

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

   8. Taylor expanded in j around inf 55.2%

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

      1. +-commutative 55.2%

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

      2. mul-1-neg 55.2%

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

      3. unsub-neg 55.2%

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

      4. associate-/l* 58.7%

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

   10. Simplified 58.7%

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

   if -1.75000000000000014e-163 < c < 1.55e-178 or 2750 < c < 3.30000000000000008e90

   1. Initial program 78.5%

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

      1. +-commutative 78.5%

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

      2. fma-define 80.1%

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

      3. *-commutative 80.1%

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

      4. *-commutative 80.1%

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

      5. cancel-sign-sub-inv 80.1%

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

      6. cancel-sign-sub 80.1%

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

      7. fmm-def 83.5%

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

      8. distribute-rgt-neg-out 83.5%

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

      9. remove-double-neg 83.5%

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

      10. *-commutative 83.5%

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

      11. *-commutative 83.5%

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

   3. Simplified 83.5%

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

   5. Taylor expanded in y around inf 61.0%

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

      1. +-commutative 61.0%

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

      2. mul-1-neg 61.0%

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

      3. unsub-neg 61.0%

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

   7. Simplified 61.0%

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

   if 1.55e-178 < c < 2750

   1. Initial program 82.9%

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

   3. Taylor expanded in a around inf 63.8%

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

      1. mul-1-neg 63.8%

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

      2. +-commutative 63.8%

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

      3. unsub-neg 63.8%

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

      4. *-commutative 63.8%

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

      5. *-commutative 63.8%

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

      6. associate-*r* 63.9%

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

      7. *-commutative 63.9%

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

   5. Simplified 63.9%

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

   6. Taylor expanded in a around inf 54.0%

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

      1. +-commutative 54.0%

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

      2. mul-1-neg 54.0%

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

      3. unsub-neg 54.0%

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

   8. Simplified 54.0%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.8 \cdot 10^{+111}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -1.7 \cdot 10^{-66}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq -1.75 \cdot 10^{-163}:\\ \;\;\;\;i \cdot \left(j \cdot \left(a \cdot \frac{b}{j} - y\right)\right)\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{-178}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 2750:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 3.3 \cdot 10^{+90}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -2.15 \cdot 10^{+114}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -6.8 \cdot 10^{-65}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq -6 \cdot 10^{-162}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 1.02 \cdot 10^{-180}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 22000000:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 1.65 \cdot 10^{+92}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j)))) (t_2 (* c (- (* t j) (* z b)))))
   (if (<= c -2.15e+114)
     t_2
     (if (<= c -6.8e-65)
       (* x (- (* y z) (* t a)))
       (if (<= c -6e-162)
         (* i (- (* a b) (* y j)))
         (if (<= c 1.02e-180)
           t_1
           (if (<= c 22000000.0)
             (* a (- (* b i) (* x t)))
             (if (<= c 1.65e+92) 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 = y * ((x * z) - (i * j));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -2.15e+114) {
		tmp = t_2;
	} else if (c <= -6.8e-65) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= -6e-162) {
		tmp = i * ((a * b) - (y * j));
	} else if (c <= 1.02e-180) {
		tmp = t_1;
	} else if (c <= 22000000.0) {
		tmp = a * ((b * i) - (x * t));
	} else if (c <= 1.65e+92) {
		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 = y * ((x * z) - (i * j))
    t_2 = c * ((t * j) - (z * b))
    if (c <= (-2.15d+114)) then
        tmp = t_2
    else if (c <= (-6.8d-65)) then
        tmp = x * ((y * z) - (t * a))
    else if (c <= (-6d-162)) then
        tmp = i * ((a * b) - (y * j))
    else if (c <= 1.02d-180) then
        tmp = t_1
    else if (c <= 22000000.0d0) then
        tmp = a * ((b * i) - (x * t))
    else if (c <= 1.65d+92) 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 = y * ((x * z) - (i * j));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -2.15e+114) {
		tmp = t_2;
	} else if (c <= -6.8e-65) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= -6e-162) {
		tmp = i * ((a * b) - (y * j));
	} else if (c <= 1.02e-180) {
		tmp = t_1;
	} else if (c <= 22000000.0) {
		tmp = a * ((b * i) - (x * t));
	} else if (c <= 1.65e+92) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	t_2 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -2.15e+114:
		tmp = t_2
	elif c <= -6.8e-65:
		tmp = x * ((y * z) - (t * a))
	elif c <= -6e-162:
		tmp = i * ((a * b) - (y * j))
	elif c <= 1.02e-180:
		tmp = t_1
	elif c <= 22000000.0:
		tmp = a * ((b * i) - (x * t))
	elif c <= 1.65e+92:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -2.15e+114)
		tmp = t_2;
	elseif (c <= -6.8e-65)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (c <= -6e-162)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (c <= 1.02e-180)
		tmp = t_1;
	elseif (c <= 22000000.0)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (c <= 1.65e+92)
		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 = y * ((x * z) - (i * j));
	t_2 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -2.15e+114)
		tmp = t_2;
	elseif (c <= -6.8e-65)
		tmp = x * ((y * z) - (t * a));
	elseif (c <= -6e-162)
		tmp = i * ((a * b) - (y * j));
	elseif (c <= 1.02e-180)
		tmp = t_1;
	elseif (c <= 22000000.0)
		tmp = a * ((b * i) - (x * t));
	elseif (c <= 1.65e+92)
		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[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.15e+114], t$95$2, If[LessEqual[c, -6.8e-65], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -6e-162], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.02e-180], t$95$1, If[LessEqual[c, 22000000.0], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.65e+92], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -2.15e114 or 1.64999999999999987e92 < c

   1. Initial program 60.9%

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

      1. +-commutative 60.9%

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

      2. fma-define 64.5%

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

      3. *-commutative 64.5%

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

      4. *-commutative 64.5%

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

      5. cancel-sign-sub-inv 64.5%

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

      6. cancel-sign-sub 64.5%

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

      7. fmm-def 64.5%

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

      8. distribute-rgt-neg-out 64.5%

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

      9. remove-double-neg 64.5%

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

      10. *-commutative 64.5%

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

      11. *-commutative 64.5%

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

   3. Simplified 64.5%

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

   5. Taylor expanded in c around inf 73.9%

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

      1. *-commutative 73.9%

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

      2. *-commutative 73.9%

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

   7. Simplified 73.9%

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

   if -2.15e114 < c < -6.79999999999999973e-65

   1. Initial program 61.9%

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

   3. Taylor expanded in a around inf 64.4%

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

      1. mul-1-neg 64.4%

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

      2. +-commutative 64.4%

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

      3. unsub-neg 64.4%

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

      4. *-commutative 64.4%

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

      5. *-commutative 64.4%

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

      6. associate-*r* 64.3%

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

      7. *-commutative 64.3%

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

   5. Simplified 64.3%

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

   6. Taylor expanded in x around inf 56.5%

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

      1. *-commutative 56.5%

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

   8. Simplified 56.5%

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

   if -6.79999999999999973e-65 < c < -5.99999999999999997e-162

   1. Initial program 76.1%

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

      1. +-commutative 76.1%

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

      2. fma-define 76.0%

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

      3. *-commutative 76.0%

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

      4. *-commutative 76.0%

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

      5. cancel-sign-sub-inv 76.0%

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

      6. cancel-sign-sub 76.0%

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

      7. fmm-def 76.0%

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

      8. distribute-rgt-neg-out 76.0%

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

      9. remove-double-neg 76.0%

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

      10. *-commutative 76.0%

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

      11. *-commutative 76.0%

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

   3. Simplified 76.0%

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

   5. Taylor expanded in i around inf 58.5%

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

      1. distribute-lft-out-- 58.5%

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

      2. *-commutative 58.5%

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

   7. Simplified 58.5%

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

   if -5.99999999999999997e-162 < c < 1.0199999999999999e-180 or 2.2e7 < c < 1.64999999999999987e92

   1. Initial program 78.5%

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

      1. +-commutative 78.5%

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

      2. fma-define 80.1%

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

      3. *-commutative 80.1%

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

      4. *-commutative 80.1%

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

      5. cancel-sign-sub-inv 80.1%

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

      6. cancel-sign-sub 80.1%

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

      7. fmm-def 83.5%

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

      8. distribute-rgt-neg-out 83.5%

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

      9. remove-double-neg 83.5%

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

      10. *-commutative 83.5%

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

      11. *-commutative 83.5%

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

   3. Simplified 83.5%

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

   5. Taylor expanded in y around inf 61.0%

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

      1. +-commutative 61.0%

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

      2. mul-1-neg 61.0%

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

      3. unsub-neg 61.0%

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

   7. Simplified 61.0%

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

   if 1.0199999999999999e-180 < c < 2.2e7

   1. Initial program 82.9%

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

   3. Taylor expanded in a around inf 63.8%

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

      1. mul-1-neg 63.8%

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

      2. +-commutative 63.8%

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

      3. unsub-neg 63.8%

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

      4. *-commutative 63.8%

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

      5. *-commutative 63.8%

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

      6. associate-*r* 63.9%

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

      7. *-commutative 63.9%

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

   5. Simplified 63.9%

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

   6. Taylor expanded in a around inf 54.0%

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

      1. +-commutative 54.0%

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

      2. mul-1-neg 54.0%

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

      3. unsub-neg 54.0%

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

   8. Simplified 54.0%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.15 \cdot 10^{+114}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -6.8 \cdot 10^{-65}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq -6 \cdot 10^{-162}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 1.02 \cdot 10^{-180}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 22000000:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 1.65 \cdot 10^{+92}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 63.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot z - t \cdot a\\ \mathbf{if}\;c \leq -6.5 \cdot 10^{+192}:\\ \;\;\;\;t \cdot \left(c \cdot j - b \cdot \frac{z \cdot c}{t}\right)\\ \mathbf{elif}\;c \leq -1.45 \cdot 10^{-41}:\\ \;\;\;\;x \cdot \left(t\_1 + c \cdot \frac{t \cdot j - z \cdot b}{x}\right)\\ \mathbf{elif}\;c \leq -4 \cdot 10^{-148}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 4 \cdot 10^{+132}:\\ \;\;\;\;x \cdot t\_1 + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot c\right) \cdot \left(j - b \cdot \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* y z) (* t a))))
   (if (<= c -6.5e+192)
     (* t (- (* c j) (* b (/ (* z c) t))))
     (if (<= c -1.45e-41)
       (* x (+ t_1 (* c (/ (- (* t j) (* z b)) x))))
       (if (<= c -4e-148)
         (+ (* j (- (* t c) (* y i))) (* a (- (* b i) (* x t))))
         (if (<= c 4e+132)
           (+ (* x t_1) (* b (- (* a i) (* z c))))
           (* (* t c) (- j (* b (/ z t))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * z) - (t * a);
	double tmp;
	if (c <= -6.5e+192) {
		tmp = t * ((c * j) - (b * ((z * c) / t)));
	} else if (c <= -1.45e-41) {
		tmp = x * (t_1 + (c * (((t * j) - (z * b)) / x)));
	} else if (c <= -4e-148) {
		tmp = (j * ((t * c) - (y * i))) + (a * ((b * i) - (x * t)));
	} else if (c <= 4e+132) {
		tmp = (x * t_1) + (b * ((a * i) - (z * c)));
	} else {
		tmp = (t * c) * (j - (b * (z / t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * z) - (t * a)
    if (c <= (-6.5d+192)) then
        tmp = t * ((c * j) - (b * ((z * c) / t)))
    else if (c <= (-1.45d-41)) then
        tmp = x * (t_1 + (c * (((t * j) - (z * b)) / x)))
    else if (c <= (-4d-148)) then
        tmp = (j * ((t * c) - (y * i))) + (a * ((b * i) - (x * t)))
    else if (c <= 4d+132) then
        tmp = (x * t_1) + (b * ((a * i) - (z * c)))
    else
        tmp = (t * c) * (j - (b * (z / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * z) - (t * a);
	double tmp;
	if (c <= -6.5e+192) {
		tmp = t * ((c * j) - (b * ((z * c) / t)));
	} else if (c <= -1.45e-41) {
		tmp = x * (t_1 + (c * (((t * j) - (z * b)) / x)));
	} else if (c <= -4e-148) {
		tmp = (j * ((t * c) - (y * i))) + (a * ((b * i) - (x * t)));
	} else if (c <= 4e+132) {
		tmp = (x * t_1) + (b * ((a * i) - (z * c)));
	} else {
		tmp = (t * c) * (j - (b * (z / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (y * z) - (t * a)
	tmp = 0
	if c <= -6.5e+192:
		tmp = t * ((c * j) - (b * ((z * c) / t)))
	elif c <= -1.45e-41:
		tmp = x * (t_1 + (c * (((t * j) - (z * b)) / x)))
	elif c <= -4e-148:
		tmp = (j * ((t * c) - (y * i))) + (a * ((b * i) - (x * t)))
	elif c <= 4e+132:
		tmp = (x * t_1) + (b * ((a * i) - (z * c)))
	else:
		tmp = (t * c) * (j - (b * (z / t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(y * z) - Float64(t * a))
	tmp = 0.0
	if (c <= -6.5e+192)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(b * Float64(Float64(z * c) / t))));
	elseif (c <= -1.45e-41)
		tmp = Float64(x * Float64(t_1 + Float64(c * Float64(Float64(Float64(t * j) - Float64(z * b)) / x))));
	elseif (c <= -4e-148)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(a * Float64(Float64(b * i) - Float64(x * t))));
	elseif (c <= 4e+132)
		tmp = Float64(Float64(x * t_1) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	else
		tmp = Float64(Float64(t * c) * Float64(j - Float64(b * Float64(z / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (y * z) - (t * a);
	tmp = 0.0;
	if (c <= -6.5e+192)
		tmp = t * ((c * j) - (b * ((z * c) / t)));
	elseif (c <= -1.45e-41)
		tmp = x * (t_1 + (c * (((t * j) - (z * b)) / x)));
	elseif (c <= -4e-148)
		tmp = (j * ((t * c) - (y * i))) + (a * ((b * i) - (x * t)));
	elseif (c <= 4e+132)
		tmp = (x * t_1) + (b * ((a * i) - (z * c)));
	else
		tmp = (t * c) * (j - (b * (z / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -6.5e+192], N[(t * N[(N[(c * j), $MachinePrecision] - N[(b * N[(N[(z * c), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.45e-41], N[(x * N[(t$95$1 + N[(c * N[(N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -4e-148], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4e+132], N[(N[(x * t$95$1), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * c), $MachinePrecision] * N[(j - N[(b * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -6.50000000000000033e192

   1. Initial program 54.4%

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

      1. +-commutative 54.4%

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

      2. fma-define 58.2%

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

      3. *-commutative 58.2%

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

      4. *-commutative 58.2%

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

      5. cancel-sign-sub-inv 58.2%

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

      6. cancel-sign-sub 58.2%

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

      7. fmm-def 58.2%

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

      8. distribute-rgt-neg-out 58.2%

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

      9. remove-double-neg 58.2%

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

      10. *-commutative 58.2%

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

      11. *-commutative 58.2%

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

   3. Simplified 58.2%

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

   5. Taylor expanded in c around inf 80.6%

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

      1. *-commutative 80.6%

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

      2. *-commutative 80.6%

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

   7. Simplified 80.6%

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

   8. Taylor expanded in t around inf 88.6%

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

      1. +-commutative 88.6%

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

      2. mul-1-neg 88.6%

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

      3. unsub-neg 88.6%

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

      4. associate-/l* 88.6%

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

   10. Simplified 88.6%

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

   if -6.50000000000000033e192 < c < -1.44999999999999989e-41

   1. Initial program 65.2%

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

   3. Taylor expanded in c around inf 73.7%

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

      1. *-commutative 73.7%

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

      2. associate-*r* 69.5%

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

      3. *-commutative 69.5%

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

      4. associate-*r* 69.4%

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

   5. Simplified 69.4%

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

   6. Taylor expanded in x around -inf 67.8%

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

      1. mul-1-neg 67.8%

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

      2. *-commutative 67.8%

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

      3. distribute-rgt-neg-in 67.8%

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

   8. Simplified 63.5%

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

   9. Taylor expanded in c around inf 76.5%

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

       1. associate-/l* 78.7%

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

       2. *-commutative 78.7%

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

       3. *-commutative 78.7%

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

   11. Simplified 78.7%

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

   if -1.44999999999999989e-41 < c < -3.99999999999999974e-148

   1. Initial program 65.8%

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

      1. cancel-sign-sub-inv 65.8%

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

      2. cancel-sign-sub 65.8%

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

      3. *-commutative 65.8%

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

      4. fmm-def 65.8%

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

      5. distribute-rgt-neg-in 65.8%

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

      6. remove-double-neg 65.8%

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

      7. *-commutative 65.8%

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

      8. *-commutative 65.8%

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

      9. *-commutative 65.8%

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

      10. *-commutative 65.8%

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

   3. Simplified 65.8%

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

   5. Taylor expanded in a around -inf 77.0%

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

   if -3.99999999999999974e-148 < c < 3.99999999999999996e132

   1. Initial program 81.4%

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

   3. Taylor expanded in j around 0 70.4%

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

   if 3.99999999999999996e132 < c

   1. Initial program 59.2%

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

      1. +-commutative 59.2%

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

      2. fma-define 59.2%

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

      3. *-commutative 59.2%

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

      4. *-commutative 59.2%

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

      5. cancel-sign-sub-inv 59.2%

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

      6. cancel-sign-sub 59.2%

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

      7. fmm-def 59.2%

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

      8. distribute-rgt-neg-out 59.2%

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

      9. remove-double-neg 59.2%

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

      10. *-commutative 59.2%

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

      11. *-commutative 59.2%

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

   3. Simplified 59.2%

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

   5. Taylor expanded in c around inf 72.7%

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

      1. *-commutative 72.7%

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

      2. *-commutative 72.7%

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

   7. Simplified 72.7%

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

   8. Taylor expanded in t around inf 62.3%

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

      1. +-commutative 62.3%

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

      2. mul-1-neg 62.3%

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

      3. unsub-neg 62.3%

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

      4. associate-/l* 62.3%

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

   10. Simplified 62.3%

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

   11. Taylor expanded in c around 0 72.7%

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

       1. associate-*r* 72.9%

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

       2. *-commutative 72.9%

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

       3. associate-/l* 75.0%

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

   13. Simplified 75.0%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.5 \cdot 10^{+192}:\\ \;\;\;\;t \cdot \left(c \cdot j - b \cdot \frac{z \cdot c}{t}\right)\\ \mathbf{elif}\;c \leq -1.45 \cdot 10^{-41}:\\ \;\;\;\;x \cdot \left(\left(y \cdot z - t \cdot a\right) + c \cdot \frac{t \cdot j - z \cdot b}{x}\right)\\ \mathbf{elif}\;c \leq -4 \cdot 10^{-148}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 4 \cdot 10^{+132}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot c\right) \cdot \left(j - b \cdot \frac{z}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := t\_1 + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;c \leq -7 \cdot 10^{+202}:\\ \;\;\;\;t \cdot \left(c \cdot j - b \cdot \frac{z \cdot c}{t}\right)\\ \mathbf{elif}\;c \leq -3.3 \cdot 10^{+72}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -1.55 \cdot 10^{-139}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + t\_1\\ \mathbf{elif}\;c \leq 3 \cdot 10^{+131}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot c\right) \cdot \left(j - b \cdot \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (+ t_1 (* b (- (* a i) (* z c))))))
   (if (<= c -7e+202)
     (* t (- (* c j) (* b (/ (* z c) t))))
     (if (<= c -3.3e+72)
       t_2
       (if (<= c -1.55e-139)
         (+ (* j (- (* t c) (* y i))) t_1)
         (if (<= c 3e+131) t_2 (* (* t c) (- j (* b (/ z t))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = t_1 + (b * ((a * i) - (z * c)));
	double tmp;
	if (c <= -7e+202) {
		tmp = t * ((c * j) - (b * ((z * c) / t)));
	} else if (c <= -3.3e+72) {
		tmp = t_2;
	} else if (c <= -1.55e-139) {
		tmp = (j * ((t * c) - (y * i))) + t_1;
	} else if (c <= 3e+131) {
		tmp = t_2;
	} else {
		tmp = (t * c) * (j - (b * (z / t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = t_1 + (b * ((a * i) - (z * c)))
    if (c <= (-7d+202)) then
        tmp = t * ((c * j) - (b * ((z * c) / t)))
    else if (c <= (-3.3d+72)) then
        tmp = t_2
    else if (c <= (-1.55d-139)) then
        tmp = (j * ((t * c) - (y * i))) + t_1
    else if (c <= 3d+131) then
        tmp = t_2
    else
        tmp = (t * c) * (j - (b * (z / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = t_1 + (b * ((a * i) - (z * c)));
	double tmp;
	if (c <= -7e+202) {
		tmp = t * ((c * j) - (b * ((z * c) / t)));
	} else if (c <= -3.3e+72) {
		tmp = t_2;
	} else if (c <= -1.55e-139) {
		tmp = (j * ((t * c) - (y * i))) + t_1;
	} else if (c <= 3e+131) {
		tmp = t_2;
	} else {
		tmp = (t * c) * (j - (b * (z / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = t_1 + (b * ((a * i) - (z * c)))
	tmp = 0
	if c <= -7e+202:
		tmp = t * ((c * j) - (b * ((z * c) / t)))
	elif c <= -3.3e+72:
		tmp = t_2
	elif c <= -1.55e-139:
		tmp = (j * ((t * c) - (y * i))) + t_1
	elif c <= 3e+131:
		tmp = t_2
	else:
		tmp = (t * c) * (j - (b * (z / t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(t_1 + Float64(b * Float64(Float64(a * i) - Float64(z * c))))
	tmp = 0.0
	if (c <= -7e+202)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(b * Float64(Float64(z * c) / t))));
	elseif (c <= -3.3e+72)
		tmp = t_2;
	elseif (c <= -1.55e-139)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + t_1);
	elseif (c <= 3e+131)
		tmp = t_2;
	else
		tmp = Float64(Float64(t * c) * Float64(j - Float64(b * Float64(z / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = t_1 + (b * ((a * i) - (z * c)));
	tmp = 0.0;
	if (c <= -7e+202)
		tmp = t * ((c * j) - (b * ((z * c) / t)));
	elseif (c <= -3.3e+72)
		tmp = t_2;
	elseif (c <= -1.55e-139)
		tmp = (j * ((t * c) - (y * i))) + t_1;
	elseif (c <= 3e+131)
		tmp = t_2;
	else
		tmp = (t * c) * (j - (b * (z / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -7e+202], N[(t * N[(N[(c * j), $MachinePrecision] - N[(b * N[(N[(z * c), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -3.3e+72], t$95$2, If[LessEqual[c, -1.55e-139], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[c, 3e+131], t$95$2, N[(N[(t * c), $MachinePrecision] * N[(j - N[(b * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -6.99999999999999975e202

   1. Initial program 54.8%

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

      1. +-commutative 54.8%

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

      2. fma-define 54.8%

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

      3. *-commutative 54.8%

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

      4. *-commutative 54.8%

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

      5. cancel-sign-sub-inv 54.8%

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

      6. cancel-sign-sub 54.8%

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

      7. fmm-def 54.8%

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

      8. distribute-rgt-neg-out 54.8%

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

      9. remove-double-neg 54.8%

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

      10. *-commutative 54.8%

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

      11. *-commutative 54.8%

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

   3. Simplified 54.8%

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

   5. Taylor expanded in c around inf 83.6%

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

      1. *-commutative 83.6%

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

      2. *-commutative 83.6%

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

   7. Simplified 83.6%

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

   8. Taylor expanded in t around inf 88.5%

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

      1. +-commutative 88.5%

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

      2. mul-1-neg 88.5%

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

      3. unsub-neg 88.5%

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

      4. associate-/l* 88.5%

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

   10. Simplified 88.5%

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

   if -6.99999999999999975e202 < c < -3.3e72 or -1.55e-139 < c < 3.0000000000000001e131

   1. Initial program 75.5%

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

   3. Taylor expanded in j around 0 70.7%

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

   if -3.3e72 < c < -1.55e-139

   1. Initial program 72.2%

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

   3. Taylor expanded in b around 0 74.7%

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

   if 3.0000000000000001e131 < c

   1. Initial program 59.2%

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

      1. +-commutative 59.2%

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

      2. fma-define 59.2%

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

      3. *-commutative 59.2%

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

      4. *-commutative 59.2%

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

      5. cancel-sign-sub-inv 59.2%

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

      6. cancel-sign-sub 59.2%

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

      7. fmm-def 59.2%

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

      8. distribute-rgt-neg-out 59.2%

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

      9. remove-double-neg 59.2%

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

      10. *-commutative 59.2%

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

      11. *-commutative 59.2%

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

   3. Simplified 59.2%

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

   5. Taylor expanded in c around inf 72.7%

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

      1. *-commutative 72.7%

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

      2. *-commutative 72.7%

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

   7. Simplified 72.7%

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

   8. Taylor expanded in t around inf 62.3%

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

      1. +-commutative 62.3%

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

      2. mul-1-neg 62.3%

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

      3. unsub-neg 62.3%

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

      4. associate-/l* 62.3%

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

   10. Simplified 62.3%

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

   11. Taylor expanded in c around 0 72.7%

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

       1. associate-*r* 72.9%

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

       2. *-commutative 72.9%

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

       3. associate-/l* 75.0%

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

   13. Simplified 75.0%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -7 \cdot 10^{+202}:\\ \;\;\;\;t \cdot \left(c \cdot j - b \cdot \frac{z \cdot c}{t}\right)\\ \mathbf{elif}\;c \leq -3.3 \cdot 10^{+72}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq -1.55 \cdot 10^{-139}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 3 \cdot 10^{+131}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot c\right) \cdot \left(j - b \cdot \frac{z}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 60.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+208}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{+159}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-5} \lor \neg \left(t \leq 250\right):\\ \;\;\;\;t \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -3.8e+208)
   (* t (- (* c j) (* x a)))
   (if (<= t -2.9e+159)
     (+ (* j (- (* t c) (* y i))) (* a (* b i)))
     (if (or (<= t -1.15e-5) (not (<= t 250.0)))
       (+ (* t (* c j)) (* x (- (* y z) (* t a))))
       (+ (* x (* y z)) (* b (- (* a i) (* z c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -3.8e+208) {
		tmp = t * ((c * j) - (x * a));
	} else if (t <= -2.9e+159) {
		tmp = (j * ((t * c) - (y * i))) + (a * (b * i));
	} else if ((t <= -1.15e-5) || !(t <= 250.0)) {
		tmp = (t * (c * j)) + (x * ((y * z) - (t * a)));
	} else {
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (t <= (-3.8d+208)) then
        tmp = t * ((c * j) - (x * a))
    else if (t <= (-2.9d+159)) then
        tmp = (j * ((t * c) - (y * i))) + (a * (b * i))
    else if ((t <= (-1.15d-5)) .or. (.not. (t <= 250.0d0))) then
        tmp = (t * (c * j)) + (x * ((y * z) - (t * a)))
    else
        tmp = (x * (y * z)) + (b * ((a * i) - (z * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -3.8e+208) {
		tmp = t * ((c * j) - (x * a));
	} else if (t <= -2.9e+159) {
		tmp = (j * ((t * c) - (y * i))) + (a * (b * i));
	} else if ((t <= -1.15e-5) || !(t <= 250.0)) {
		tmp = (t * (c * j)) + (x * ((y * z) - (t * a)));
	} else {
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -3.8e+208:
		tmp = t * ((c * j) - (x * a))
	elif t <= -2.9e+159:
		tmp = (j * ((t * c) - (y * i))) + (a * (b * i))
	elif (t <= -1.15e-5) or not (t <= 250.0):
		tmp = (t * (c * j)) + (x * ((y * z) - (t * a)))
	else:
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -3.8e+208)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (t <= -2.9e+159)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(a * Float64(b * i)));
	elseif ((t <= -1.15e-5) || !(t <= 250.0))
		tmp = Float64(Float64(t * Float64(c * j)) + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	else
		tmp = Float64(Float64(x * Float64(y * z)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -3.8e+208)
		tmp = t * ((c * j) - (x * a));
	elseif (t <= -2.9e+159)
		tmp = (j * ((t * c) - (y * i))) + (a * (b * i));
	elseif ((t <= -1.15e-5) || ~((t <= 250.0)))
		tmp = (t * (c * j)) + (x * ((y * z) - (t * a)));
	else
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -3.8e+208], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.9e+159], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -1.15e-5], N[Not[LessEqual[t, 250.0]], $MachinePrecision]], N[(N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.8000000000000002e208

   1. Initial program 38.0%

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

      1. +-commutative 38.0%

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

      2. fma-define 42.2%

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

      3. *-commutative 42.2%

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

      4. *-commutative 42.2%

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

      5. cancel-sign-sub-inv 42.2%

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

      6. cancel-sign-sub 42.2%

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

      7. fmm-def 50.5%

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

      8. distribute-rgt-neg-out 50.5%

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

      9. remove-double-neg 50.5%

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

      10. *-commutative 50.5%

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

      11. *-commutative 50.5%

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

   3. Simplified 50.5%

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

   5. Taylor expanded in t around inf 75.5%

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

      1. +-commutative 75.5%

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

      2. mul-1-neg 75.5%

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

      3. unsub-neg 75.5%

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

      4. *-commutative 75.5%

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

   7. Simplified 75.5%

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

   if -3.8000000000000002e208 < t < -2.90000000000000014e159

   1. Initial program 36.2%

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

      1. cancel-sign-sub-inv 36.2%

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

      2. cancel-sign-sub 36.2%

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

      3. *-commutative 36.2%

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

      4. fmm-def 36.2%

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

      5. distribute-rgt-neg-in 36.2%

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

      6. remove-double-neg 36.2%

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

      7. *-commutative 36.2%

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

      8. *-commutative 36.2%

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

      9. *-commutative 36.2%

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

      10. *-commutative 36.2%

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

   3. Simplified 36.2%

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

   5. Taylor expanded in i around inf 81.7%

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

   if -2.90000000000000014e159 < t < -1.15e-5 or 250 < t

   1. Initial program 68.0%

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

   3. Taylor expanded in b around 0 69.6%

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

   4. Taylor expanded in c around inf 63.8%

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

      1. *-commutative 68.0%

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

      2. associate-*r* 65.7%

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

      3. *-commutative 65.7%

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

      4. associate-*r* 71.4%

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

   6. Simplified 66.1%

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

   if -1.15e-5 < t < 250

   1. Initial program 80.3%

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

   3. Taylor expanded in c around inf 71.6%

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

      1. *-commutative 71.6%

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

      2. associate-*r* 72.1%

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

      3. *-commutative 72.1%

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

      4. associate-*r* 69.3%

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

   5. Simplified 69.3%

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

   6. Taylor expanded in t around 0 62.0%

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

      1. *-commutative 62.0%

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

   8. Simplified 62.0%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+208}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{+159}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-5} \lor \neg \left(t \leq 250\right):\\ \;\;\;\;t \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 51.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -8.2 \cdot 10^{+107}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -3.4 \cdot 10^{-52}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 1.68 \cdot 10^{-187}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 61:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 2.6 \cdot 10^{+90}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j)))) (t_2 (* c (- (* t j) (* z b)))))
   (if (<= c -8.2e+107)
     t_2
     (if (<= c -3.4e-52)
       (* x (- (* y z) (* t a)))
       (if (<= c 1.68e-187)
         t_1
         (if (<= c 61.0)
           (* a (- (* b i) (* x t)))
           (if (<= c 2.6e+90) 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 = y * ((x * z) - (i * j));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -8.2e+107) {
		tmp = t_2;
	} else if (c <= -3.4e-52) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= 1.68e-187) {
		tmp = t_1;
	} else if (c <= 61.0) {
		tmp = a * ((b * i) - (x * t));
	} else if (c <= 2.6e+90) {
		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 = y * ((x * z) - (i * j))
    t_2 = c * ((t * j) - (z * b))
    if (c <= (-8.2d+107)) then
        tmp = t_2
    else if (c <= (-3.4d-52)) then
        tmp = x * ((y * z) - (t * a))
    else if (c <= 1.68d-187) then
        tmp = t_1
    else if (c <= 61.0d0) then
        tmp = a * ((b * i) - (x * t))
    else if (c <= 2.6d+90) 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 = y * ((x * z) - (i * j));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -8.2e+107) {
		tmp = t_2;
	} else if (c <= -3.4e-52) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= 1.68e-187) {
		tmp = t_1;
	} else if (c <= 61.0) {
		tmp = a * ((b * i) - (x * t));
	} else if (c <= 2.6e+90) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	t_2 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -8.2e+107:
		tmp = t_2
	elif c <= -3.4e-52:
		tmp = x * ((y * z) - (t * a))
	elif c <= 1.68e-187:
		tmp = t_1
	elif c <= 61.0:
		tmp = a * ((b * i) - (x * t))
	elif c <= 2.6e+90:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -8.2e+107)
		tmp = t_2;
	elseif (c <= -3.4e-52)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (c <= 1.68e-187)
		tmp = t_1;
	elseif (c <= 61.0)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (c <= 2.6e+90)
		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 = y * ((x * z) - (i * j));
	t_2 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -8.2e+107)
		tmp = t_2;
	elseif (c <= -3.4e-52)
		tmp = x * ((y * z) - (t * a));
	elseif (c <= 1.68e-187)
		tmp = t_1;
	elseif (c <= 61.0)
		tmp = a * ((b * i) - (x * t));
	elseif (c <= 2.6e+90)
		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[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -8.2e+107], t$95$2, If[LessEqual[c, -3.4e-52], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.68e-187], t$95$1, If[LessEqual[c, 61.0], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.6e+90], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -8.1999999999999998e107 or 2.5999999999999998e90 < c

   1. Initial program 60.9%

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

      1. +-commutative 60.9%

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

      2. fma-define 64.5%

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

      3. *-commutative 64.5%

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

      4. *-commutative 64.5%

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

      5. cancel-sign-sub-inv 64.5%

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

      6. cancel-sign-sub 64.5%

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

      7. fmm-def 64.5%

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

      8. distribute-rgt-neg-out 64.5%

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

      9. remove-double-neg 64.5%

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

      10. *-commutative 64.5%

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

      11. *-commutative 64.5%

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

   3. Simplified 64.5%

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

   5. Taylor expanded in c around inf 73.9%

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

      1. *-commutative 73.9%

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

      2. *-commutative 73.9%

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

   7. Simplified 73.9%

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

   if -8.1999999999999998e107 < c < -3.40000000000000017e-52

   1. Initial program 65.7%

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

   3. Taylor expanded in a around inf 65.9%

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

      1. mul-1-neg 65.9%

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

      2. +-commutative 65.9%

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

      3. unsub-neg 65.9%

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

      4. *-commutative 65.9%

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

      5. *-commutative 65.9%

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

      6. associate-*r* 65.9%

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

      7. *-commutative 65.9%

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

   5. Simplified 65.9%

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

   6. Taylor expanded in x around inf 54.4%

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

      1. *-commutative 54.4%

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

   8. Simplified 54.4%

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

   if -3.40000000000000017e-52 < c < 1.6799999999999999e-187 or 61 < c < 2.5999999999999998e90

   1. Initial program 75.4%

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

      1. +-commutative 75.4%

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

      2. fma-define 76.5%

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

      3. *-commutative 76.5%

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

      4. *-commutative 76.5%

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

      5. cancel-sign-sub-inv 76.5%

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

      6. cancel-sign-sub 76.5%

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

      7. fmm-def 78.6%

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

      8. distribute-rgt-neg-out 78.6%

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

      9. remove-double-neg 78.6%

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

      10. *-commutative 78.6%

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

      11. *-commutative 78.6%

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

   3. Simplified 78.6%

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

   5. Taylor expanded in y around inf 54.2%

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

      1. +-commutative 54.2%

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

      2. mul-1-neg 54.2%

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

      3. unsub-neg 54.2%

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

   7. Simplified 54.2%

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

   if 1.6799999999999999e-187 < c < 61

   1. Initial program 82.9%

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

   3. Taylor expanded in a around inf 63.8%

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

      1. mul-1-neg 63.8%

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

      2. +-commutative 63.8%

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

      3. unsub-neg 63.8%

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

      4. *-commutative 63.8%

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

      5. *-commutative 63.8%

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

      6. associate-*r* 63.9%

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

      7. *-commutative 63.9%

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

   5. Simplified 63.9%

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

   6. Taylor expanded in a around inf 54.0%

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

      1. +-commutative 54.0%

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

      2. mul-1-neg 54.0%

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

      3. unsub-neg 54.0%

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

   8. Simplified 54.0%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -8.2 \cdot 10^{+107}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -3.4 \cdot 10^{-52}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 1.68 \cdot 10^{-187}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 61:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 2.6 \cdot 10^{+90}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 67.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := t\_1 + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;j \leq -3.6 \cdot 10^{+33}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 1.25 \cdot 10^{-108}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 5.4 \cdot 10^{+127}:\\ \;\;\;\;t\_1 + a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i))))
        (t_2 (+ t_1 (* z (- (* x y) (* b c))))))
   (if (<= j -3.6e+33)
     t_2
     (if (<= j 1.25e-108)
       (+ (* x (- (* y z) (* t a))) (* b (- (* a i) (* z c))))
       (if (<= j 5.4e+127) (+ t_1 (* a (- (* b i) (* x t)))) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = t_1 + (z * ((x * y) - (b * c)));
	double tmp;
	if (j <= -3.6e+33) {
		tmp = t_2;
	} else if (j <= 1.25e-108) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	} else if (j <= 5.4e+127) {
		tmp = t_1 + (a * ((b * i) - (x * t)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = t_1 + (z * ((x * y) - (b * c)))
    if (j <= (-3.6d+33)) then
        tmp = t_2
    else if (j <= 1.25d-108) then
        tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))
    else if (j <= 5.4d+127) then
        tmp = t_1 + (a * ((b * i) - (x * t)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = t_1 + (z * ((x * y) - (b * c)));
	double tmp;
	if (j <= -3.6e+33) {
		tmp = t_2;
	} else if (j <= 1.25e-108) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	} else if (j <= 5.4e+127) {
		tmp = t_1 + (a * ((b * i) - (x * t)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = t_1 + (z * ((x * y) - (b * c)))
	tmp = 0
	if j <= -3.6e+33:
		tmp = t_2
	elif j <= 1.25e-108:
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))
	elif j <= 5.4e+127:
		tmp = t_1 + (a * ((b * i) - (x * t)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(t_1 + Float64(z * Float64(Float64(x * y) - Float64(b * c))))
	tmp = 0.0
	if (j <= -3.6e+33)
		tmp = t_2;
	elseif (j <= 1.25e-108)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (j <= 5.4e+127)
		tmp = Float64(t_1 + Float64(a * Float64(Float64(b * i) - Float64(x * t))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = t_1 + (z * ((x * y) - (b * c)));
	tmp = 0.0;
	if (j <= -3.6e+33)
		tmp = t_2;
	elseif (j <= 1.25e-108)
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	elseif (j <= 5.4e+127)
		tmp = t_1 + (a * ((b * i) - (x * t)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.6e+33], t$95$2, If[LessEqual[j, 1.25e-108], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.4e+127], N[(t$95$1 + N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -3.6000000000000003e33 or 5.4000000000000004e127 < j

   1. Initial program 65.0%

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

      1. cancel-sign-sub-inv 65.0%

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

      2. cancel-sign-sub 65.0%

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

      3. *-commutative 65.0%

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

      4. fmm-def 66.1%

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

      5. distribute-rgt-neg-in 66.1%

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

      6. remove-double-neg 66.1%

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

      7. *-commutative 66.1%

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

      8. *-commutative 66.1%

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

      9. *-commutative 66.1%

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

      10. *-commutative 66.1%

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

   3. Simplified 66.1%

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

   5. Taylor expanded in z around inf 72.8%

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

   if -3.6000000000000003e33 < j < 1.25e-108

   1. Initial program 72.1%

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

   3. Taylor expanded in j around 0 71.0%

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

   if 1.25e-108 < j < 5.4000000000000004e127

   1. Initial program 76.4%

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

      1. cancel-sign-sub-inv 76.4%

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

      2. cancel-sign-sub 76.4%

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

      3. *-commutative 76.4%

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

      4. fmm-def 78.4%

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

      5. distribute-rgt-neg-in 78.4%

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

      6. remove-double-neg 78.4%

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

      7. *-commutative 78.4%

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

      8. *-commutative 78.4%

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

      9. *-commutative 78.4%

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

      10. *-commutative 78.4%

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

   3. Simplified 78.4%

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

   5. Taylor expanded in a around -inf 75.1%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.6 \cdot 10^{+33}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 1.25 \cdot 10^{-108}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 5.4 \cdot 10^{+127}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -88:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-199}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+20}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* t (* c j)) (* x (- (* y z) (* t a))))))
   (if (<= x -88.0)
     t_1
     (if (<= x -1.6e-199)
       (+ (* x (* y z)) (* b (- (* a i) (* z c))))
       (if (<= x 8.5e+20) (- (* j (- (* t c) (* y i))) (* z (* b c))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (t * (c * j)) + (x * ((y * z) - (t * a)));
	double tmp;
	if (x <= -88.0) {
		tmp = t_1;
	} else if (x <= -1.6e-199) {
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)));
	} else if (x <= 8.5e+20) {
		tmp = (j * ((t * c) - (y * i))) - (z * (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t * (c * j)) + (x * ((y * z) - (t * a)))
    if (x <= (-88.0d0)) then
        tmp = t_1
    else if (x <= (-1.6d-199)) then
        tmp = (x * (y * z)) + (b * ((a * i) - (z * c)))
    else if (x <= 8.5d+20) then
        tmp = (j * ((t * c) - (y * i))) - (z * (b * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (t * (c * j)) + (x * ((y * z) - (t * a)));
	double tmp;
	if (x <= -88.0) {
		tmp = t_1;
	} else if (x <= -1.6e-199) {
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)));
	} else if (x <= 8.5e+20) {
		tmp = (j * ((t * c) - (y * i))) - (z * (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (t * (c * j)) + (x * ((y * z) - (t * a)))
	tmp = 0
	if x <= -88.0:
		tmp = t_1
	elif x <= -1.6e-199:
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)))
	elif x <= 8.5e+20:
		tmp = (j * ((t * c) - (y * i))) - (z * (b * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(t * Float64(c * j)) + Float64(x * Float64(Float64(y * z) - Float64(t * a))))
	tmp = 0.0
	if (x <= -88.0)
		tmp = t_1;
	elseif (x <= -1.6e-199)
		tmp = Float64(Float64(x * Float64(y * z)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (x <= 8.5e+20)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) - Float64(z * Float64(b * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (t * (c * j)) + (x * ((y * z) - (t * a)));
	tmp = 0.0;
	if (x <= -88.0)
		tmp = t_1;
	elseif (x <= -1.6e-199)
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)));
	elseif (x <= 8.5e+20)
		tmp = (j * ((t * c) - (y * i))) - (z * (b * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -88.0], t$95$1, If[LessEqual[x, -1.6e-199], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.5e+20], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -88 or 8.5e20 < x

   1. Initial program 68.0%

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

   3. Taylor expanded in b around 0 66.0%

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

   4. Taylor expanded in c around inf 64.6%

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

      1. *-commutative 68.8%

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

      2. associate-*r* 66.6%

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

      3. *-commutative 66.6%

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

      4. associate-*r* 69.5%

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

   6. Simplified 66.1%

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

   if -88 < x < -1.6e-199

   1. Initial program 77.5%

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

   3. Taylor expanded in c around inf 77.4%

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

      1. *-commutative 77.4%

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

      2. associate-*r* 74.7%

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

      3. *-commutative 74.7%

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

      4. associate-*r* 74.6%

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

   5. Simplified 74.6%

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

   6. Taylor expanded in t around 0 64.9%

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

      1. *-commutative 64.9%

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

   8. Simplified 64.9%

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

   if -1.6e-199 < x < 8.5e20

   1. Initial program 71.3%

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

      1. cancel-sign-sub-inv 71.3%

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

      2. cancel-sign-sub 71.3%

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

      3. *-commutative 71.3%

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

      4. fmm-def 71.3%

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

      5. distribute-rgt-neg-in 71.3%

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

      6. remove-double-neg 71.3%

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

      7. *-commutative 71.3%

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

      8. *-commutative 71.3%

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

      9. *-commutative 71.3%

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

      10. *-commutative 71.3%

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

   3. Simplified 71.3%

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

   5. Taylor expanded in c around inf 60.6%

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

      1. mul-1-neg 60.6%

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

      2. *-commutative 60.6%

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

      3. *-commutative 60.6%

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

      4. associate-*r* 64.7%

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

      5. *-commutative 64.7%

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

      6. distribute-rgt-neg-out 64.7%

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

      7. distribute-rgt-neg-in 64.7%

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

   7. Simplified 64.7%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -88:\\ \;\;\;\;t \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-199}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+20}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+103}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-183}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-205}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))) (t_2 (* z (- (* x y) (* b c)))))
   (if (<= z -4.2e+103)
     t_2
     (if (<= z -8.2e-183)
       t_1
       (if (<= z 6.2e-205)
         (* a (- (* b i) (* x t)))
         (if (<= z 1.06e+63) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -4.2e+103) {
		tmp = t_2;
	} else if (z <= -8.2e-183) {
		tmp = t_1;
	} else if (z <= 6.2e-205) {
		tmp = a * ((b * i) - (x * t));
	} else if (z <= 1.06e+63) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = z * ((x * y) - (b * c))
    if (z <= (-4.2d+103)) then
        tmp = t_2
    else if (z <= (-8.2d-183)) then
        tmp = t_1
    else if (z <= 6.2d-205) then
        tmp = a * ((b * i) - (x * t))
    else if (z <= 1.06d+63) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -4.2e+103) {
		tmp = t_2;
	} else if (z <= -8.2e-183) {
		tmp = t_1;
	} else if (z <= 6.2e-205) {
		tmp = a * ((b * i) - (x * t));
	} else if (z <= 1.06e+63) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -4.2e+103:
		tmp = t_2
	elif z <= -8.2e-183:
		tmp = t_1
	elif z <= 6.2e-205:
		tmp = a * ((b * i) - (x * t))
	elif z <= 1.06e+63:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (z <= -4.2e+103)
		tmp = t_2;
	elseif (z <= -8.2e-183)
		tmp = t_1;
	elseif (z <= 6.2e-205)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (z <= 1.06e+63)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -4.2e+103)
		tmp = t_2;
	elseif (z <= -8.2e-183)
		tmp = t_1;
	elseif (z <= 6.2e-205)
		tmp = a * ((b * i) - (x * t));
	elseif (z <= 1.06e+63)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.2e+103], t$95$2, If[LessEqual[z, -8.2e-183], t$95$1, If[LessEqual[z, 6.2e-205], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.06e+63], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.2000000000000003e103 or 1.0600000000000001e63 < z

   1. Initial program 60.1%

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

   3. Taylor expanded in a around inf 48.7%

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

      1. mul-1-neg 48.7%

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

      2. +-commutative 48.7%

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

      3. unsub-neg 48.7%

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

      4. *-commutative 48.7%

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

      5. *-commutative 48.7%

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

      6. associate-*r* 49.6%

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

      7. *-commutative 49.6%

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

   5. Simplified 49.6%

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

   6. Taylor expanded in z around inf 68.3%

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

      1. *-commutative 68.3%

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

   8. Simplified 68.3%

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

   if -4.2000000000000003e103 < z < -8.1999999999999996e-183 or 6.19999999999999965e-205 < z < 1.0600000000000001e63

   1. Initial program 73.0%

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

      1. +-commutative 73.0%

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

      2. fma-define 73.9%

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

      3. *-commutative 73.9%

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

      4. *-commutative 73.9%

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

      5. cancel-sign-sub-inv 73.9%

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

      6. cancel-sign-sub 73.9%

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

      7. fmm-def 74.9%

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

      8. distribute-rgt-neg-out 74.9%

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

      9. remove-double-neg 74.9%

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

      10. *-commutative 74.9%

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

      11. *-commutative 74.9%

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

   3. Simplified 74.9%

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

   5. Taylor expanded in j around inf 50.0%

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

      1. *-commutative 50.0%

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

      2. *-commutative 50.0%

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

   7. Simplified 50.0%

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

   if -8.1999999999999996e-183 < z < 6.19999999999999965e-205

   1. Initial program 87.1%

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

   3. Taylor expanded in a around inf 87.0%

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

      1. mul-1-neg 87.0%

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

      2. +-commutative 87.0%

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

      3. unsub-neg 87.0%

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

      4. *-commutative 87.0%

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

      5. *-commutative 87.0%

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

      6. associate-*r* 84.9%

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

      7. *-commutative 84.9%

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

   5. Simplified 84.9%

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

   6. Taylor expanded in a around inf 63.3%

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

      1. +-commutative 63.3%

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

      2. mul-1-neg 63.3%

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

      3. unsub-neg 63.3%

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

   8. Simplified 63.3%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+103}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-183}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-205}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{+63}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 64.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+117} \lor \neg \left(z \leq 1.35 \cdot 10^{+78}\right):\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= z -3.9e+117) (not (<= z 1.35e+78)))
   (* z (- (* x y) (* b c)))
   (+ (* j (- (* t c) (* y i))) (* x (- (* y z) (* t a))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((z <= -3.9e+117) || !(z <= 1.35e+78)) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((z <= (-3.9d+117)) .or. (.not. (z <= 1.35d+78))) then
        tmp = z * ((x * y) - (b * c))
    else
        tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((z <= -3.9e+117) || !(z <= 1.35e+78)) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (z <= -3.9e+117) or not (z <= 1.35e+78):
		tmp = z * ((x * y) - (b * c))
	else:
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((z <= -3.9e+117) || !(z <= 1.35e+78))
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	else
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((z <= -3.9e+117) || ~((z <= 1.35e+78)))
		tmp = z * ((x * y) - (b * c));
	else
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[z, -3.9e+117], N[Not[LessEqual[z, 1.35e+78]], $MachinePrecision]], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.8999999999999999e117 or 1.35000000000000002e78 < z

   1. Initial program 59.0%

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

   3. Taylor expanded in a around inf 47.1%

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

      1. mul-1-neg 47.1%

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

      2. +-commutative 47.1%

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

      3. unsub-neg 47.1%

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

      4. *-commutative 47.1%

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

      5. *-commutative 47.1%

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

      6. associate-*r* 48.1%

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

      7. *-commutative 48.1%

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

   5. Simplified 48.1%

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

   6. Taylor expanded in z around inf 69.6%

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

      1. *-commutative 69.6%

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

   8. Simplified 69.6%

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

   if -3.8999999999999999e117 < z < 1.35000000000000002e78

   1. Initial program 77.4%

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

   3. Taylor expanded in b around 0 65.5%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+117} \lor \neg \left(z \leq 1.35 \cdot 10^{+78}\right):\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 61.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{-20} \lor \neg \left(a \leq 2.6 \cdot 10^{+61}\right):\\ \;\;\;\;a \cdot \left(\left(b \cdot i + \frac{x \cdot \left(y \cdot z\right)}{a}\right) - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -1.5e-20) (not (<= a 2.6e+61)))
   (* a (- (+ (* b i) (/ (* x (* y z)) a)) (* x t)))
   (- (* j (- (* t c) (* y i))) (* b (* z c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -1.5e-20) || !(a <= 2.6e+61)) {
		tmp = a * (((b * i) + ((x * (y * z)) / a)) - (x * t));
	} else {
		tmp = (j * ((t * c) - (y * i))) - (b * (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((a <= (-1.5d-20)) .or. (.not. (a <= 2.6d+61))) then
        tmp = a * (((b * i) + ((x * (y * z)) / a)) - (x * t))
    else
        tmp = (j * ((t * c) - (y * i))) - (b * (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -1.5e-20) || !(a <= 2.6e+61)) {
		tmp = a * (((b * i) + ((x * (y * z)) / a)) - (x * t));
	} else {
		tmp = (j * ((t * c) - (y * i))) - (b * (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (a <= -1.5e-20) or not (a <= 2.6e+61):
		tmp = a * (((b * i) + ((x * (y * z)) / a)) - (x * t))
	else:
		tmp = (j * ((t * c) - (y * i))) - (b * (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -1.5e-20) || !(a <= 2.6e+61))
		tmp = Float64(a * Float64(Float64(Float64(b * i) + Float64(Float64(x * Float64(y * z)) / a)) - Float64(x * t)));
	else
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) - Float64(b * Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((a <= -1.5e-20) || ~((a <= 2.6e+61)))
		tmp = a * (((b * i) + ((x * (y * z)) / a)) - (x * t));
	else
		tmp = (j * ((t * c) - (y * i))) - (b * (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -1.5e-20], N[Not[LessEqual[a, 2.6e+61]], $MachinePrecision]], N[(a * N[(N[(N[(b * i), $MachinePrecision] + N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.50000000000000014e-20 or 2.59999999999999973e61 < a

   1. Initial program 62.1%

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

   3. Taylor expanded in c around inf 62.8%

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

      1. *-commutative 62.8%

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

      2. associate-*r* 61.4%

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

      3. *-commutative 61.4%

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

      4. associate-*r* 59.9%

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

   5. Simplified 59.9%

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

   6. Taylor expanded in a around inf 71.2%

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

      1. sub-neg 71.2%

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

      2. +-commutative 71.2%

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

      3. mul-1-neg 71.2%

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

      4. unsub-neg 71.2%

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

      5. +-commutative 71.2%

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

      6. *-commutative 71.2%

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

      7. associate-*r* 70.5%

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

      8. *-commutative 70.5%

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

      9. neg-mul-1 70.5%

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

   8. Simplified 70.4%

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

   9. Taylor expanded in c around 0 68.1%

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

   if -1.50000000000000014e-20 < a < 2.59999999999999973e61

   1. Initial program 79.2%

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

      1. cancel-sign-sub-inv 79.2%

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

      2. cancel-sign-sub 79.2%

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

      3. *-commutative 79.2%

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

      4. fmm-def 79.2%

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

      5. distribute-rgt-neg-in 79.2%

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

      6. remove-double-neg 79.2%

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

      7. *-commutative 79.2%

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

      8. *-commutative 79.2%

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

      9. *-commutative 79.2%

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

      10. *-commutative 79.2%

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

   3. Simplified 79.2%

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

   5. Taylor expanded in c around inf 62.9%

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

      1. associate-*r* 62.9%

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

      2. neg-mul-1 62.9%

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

      3. *-commutative 62.9%

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

   7. Simplified 62.9%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{-20} \lor \neg \left(a \leq 2.6 \cdot 10^{+61}\right):\\ \;\;\;\;a \cdot \left(\left(b \cdot i + \frac{x \cdot \left(y \cdot z\right)}{a}\right) - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 29.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+117}:\\ \;\;\;\;z \cdot \left(-b \cdot c\right)\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-185}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+24}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+160}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -6.4e+117)
   (* z (- (* b c)))
   (if (<= z -5.4e-185)
     (* y (* i (- j)))
     (if (<= z 1.55e+24)
       (* (* x t) (- a))
       (if (<= z 4.3e+160) (* z (* x y)) (* c (* z (- b))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -6.4e+117) {
		tmp = z * -(b * c);
	} else if (z <= -5.4e-185) {
		tmp = y * (i * -j);
	} else if (z <= 1.55e+24) {
		tmp = (x * t) * -a;
	} else if (z <= 4.3e+160) {
		tmp = z * (x * y);
	} else {
		tmp = c * (z * -b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-6.4d+117)) then
        tmp = z * -(b * c)
    else if (z <= (-5.4d-185)) then
        tmp = y * (i * -j)
    else if (z <= 1.55d+24) then
        tmp = (x * t) * -a
    else if (z <= 4.3d+160) then
        tmp = z * (x * y)
    else
        tmp = c * (z * -b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -6.4e+117) {
		tmp = z * -(b * c);
	} else if (z <= -5.4e-185) {
		tmp = y * (i * -j);
	} else if (z <= 1.55e+24) {
		tmp = (x * t) * -a;
	} else if (z <= 4.3e+160) {
		tmp = z * (x * y);
	} else {
		tmp = c * (z * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -6.4e+117:
		tmp = z * -(b * c)
	elif z <= -5.4e-185:
		tmp = y * (i * -j)
	elif z <= 1.55e+24:
		tmp = (x * t) * -a
	elif z <= 4.3e+160:
		tmp = z * (x * y)
	else:
		tmp = c * (z * -b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -6.4e+117)
		tmp = Float64(z * Float64(-Float64(b * c)));
	elseif (z <= -5.4e-185)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (z <= 1.55e+24)
		tmp = Float64(Float64(x * t) * Float64(-a));
	elseif (z <= 4.3e+160)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = Float64(c * Float64(z * Float64(-b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -6.4e+117)
		tmp = z * -(b * c);
	elseif (z <= -5.4e-185)
		tmp = y * (i * -j);
	elseif (z <= 1.55e+24)
		tmp = (x * t) * -a;
	elseif (z <= 4.3e+160)
		tmp = z * (x * y);
	else
		tmp = c * (z * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -6.4e+117], N[(z * (-N[(b * c), $MachinePrecision])), $MachinePrecision], If[LessEqual[z, -5.4e-185], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e+24], N[(N[(x * t), $MachinePrecision] * (-a)), $MachinePrecision], If[LessEqual[z, 4.3e+160], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -6.4000000000000001e117

   1. Initial program 51.2%

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

   3. Taylor expanded in a around inf 39.4%

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

      1. mul-1-neg 39.4%

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

      2. +-commutative 39.4%

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

      3. unsub-neg 39.4%

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

      4. *-commutative 39.4%

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

      5. *-commutative 39.4%

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

      6. associate-*r* 41.3%

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

      7. *-commutative 41.3%

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

   5. Simplified 41.3%

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

   6. Taylor expanded in z around inf 67.3%

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

      1. *-commutative 67.3%

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

   8. Simplified 67.3%

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

   9. Taylor expanded in y around 0 44.0%

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

       1. neg-mul-1 44.0%

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

       2. distribute-lft-neg-in 44.0%

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

       3. *-commutative 44.0%

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

   11. Simplified 44.0%

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

   if -6.4000000000000001e117 < z < -5.39999999999999976e-185

   1. Initial program 69.7%

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

   3. Taylor expanded in a around inf 75.1%

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

      1. mul-1-neg 75.1%

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

      2. +-commutative 75.1%

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

      3. unsub-neg 75.1%

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

      4. *-commutative 75.1%

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

      5. *-commutative 75.1%

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

      6. associate-*r* 73.5%

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

      7. *-commutative 73.5%

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

   5. Simplified 73.5%

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

   6. Taylor expanded in y around inf 49.6%

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

      1. +-commutative 49.6%

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

      2. mul-1-neg 49.6%

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

      3. unsub-neg 49.6%

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

      4. *-commutative 49.6%

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

   8. Simplified 49.6%

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

   9. Taylor expanded in z around 0 33.4%

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

       1. neg-mul-1 33.4%

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

       2. distribute-rgt-neg-in 33.4%

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

   11. Simplified 33.4%

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

   if -5.39999999999999976e-185 < z < 1.55000000000000005e24

   1. Initial program 81.1%

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

   3. Taylor expanded in b around 0 66.1%

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

   4. Taylor expanded in a around inf 33.4%

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

      1. associate-*r* 33.4%

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

      2. neg-mul-1 33.4%

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

   6. Simplified 33.4%

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

   if 1.55000000000000005e24 < z < 4.29999999999999989e160

   1. Initial program 79.6%

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

   3. Taylor expanded in a around inf 72.7%

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

      1. mul-1-neg 72.7%

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

      2. +-commutative 72.7%

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

      3. unsub-neg 72.7%

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

      4. *-commutative 72.7%

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

      5. *-commutative 72.7%

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

      6. associate-*r* 72.8%

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

      7. *-commutative 72.8%

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

   5. Simplified 72.8%

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

   6. Taylor expanded in y around inf 51.0%

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

      1. +-commutative 51.0%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 51.0%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 51.0%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 51.0%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   8. Simplified 51.0%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   9. Taylor expanded in z around inf 34.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 41.0%

          \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot z} \]

       2. *-commutative 41.0%

          \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]

   11. Simplified 41.0%

       \[\leadsto \color{blue}{\left(y \cdot x\right) \cdot z} \]

   if 4.29999999999999989e160 < z

   1. Initial program 59.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 59.4%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 63.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 63.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 63.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 63.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 63.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fmm-def 63.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. distribute-rgt-neg-out 63.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. remove-double-neg 63.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. *-commutative 63.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 63.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 63.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 66.5%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 66.5%

         \[\leadsto c \cdot \left(\color{blue}{t \cdot j} - b \cdot z\right) \]

      2. *-commutative 66.5%

         \[\leadsto c \cdot \left(t \cdot j - \color{blue}{z \cdot b}\right) \]

   7. Simplified 66.5%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   8. Taylor expanded in t around 0 66.3%

      \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(b \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 66.3%

         \[\leadsto c \cdot \color{blue}{\left(-b \cdot z\right)} \]

      2. distribute-rgt-neg-in 66.3%

         \[\leadsto c \cdot \color{blue}{\left(b \cdot \left(-z\right)\right)} \]

   10. Simplified 66.3%

       \[\leadsto c \cdot \color{blue}{\left(b \cdot \left(-z\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 39.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+117}:\\ \;\;\;\;z \cdot \left(-b \cdot c\right)\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-185}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+24}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+160}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 29.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -2.7 \cdot 10^{+62}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 3.1 \cdot 10^{-289}:\\ \;\;\;\;z \cdot \left(-b \cdot c\right)\\ \mathbf{elif}\;i \leq 4 \cdot 10^{-135}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 2.6 \cdot 10^{+71}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -2.7e+62)
   (* a (* b i))
   (if (<= i 3.1e-289)
     (* z (- (* b c)))
     (if (<= i 4e-135)
       (* z (* x y))
       (if (<= i 2.6e+71) (* c (* z (- b))) (* y (* i (- 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 (i <= -2.7e+62) {
		tmp = a * (b * i);
	} else if (i <= 3.1e-289) {
		tmp = z * -(b * c);
	} else if (i <= 4e-135) {
		tmp = z * (x * y);
	} else if (i <= 2.6e+71) {
		tmp = c * (z * -b);
	} else {
		tmp = y * (i * -j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (i <= (-2.7d+62)) then
        tmp = a * (b * i)
    else if (i <= 3.1d-289) then
        tmp = z * -(b * c)
    else if (i <= 4d-135) then
        tmp = z * (x * y)
    else if (i <= 2.6d+71) then
        tmp = c * (z * -b)
    else
        tmp = y * (i * -j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -2.7e+62) {
		tmp = a * (b * i);
	} else if (i <= 3.1e-289) {
		tmp = z * -(b * c);
	} else if (i <= 4e-135) {
		tmp = z * (x * y);
	} else if (i <= 2.6e+71) {
		tmp = c * (z * -b);
	} else {
		tmp = y * (i * -j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -2.7e+62:
		tmp = a * (b * i)
	elif i <= 3.1e-289:
		tmp = z * -(b * c)
	elif i <= 4e-135:
		tmp = z * (x * y)
	elif i <= 2.6e+71:
		tmp = c * (z * -b)
	else:
		tmp = y * (i * -j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -2.7e+62)
		tmp = Float64(a * Float64(b * i));
	elseif (i <= 3.1e-289)
		tmp = Float64(z * Float64(-Float64(b * c)));
	elseif (i <= 4e-135)
		tmp = Float64(z * Float64(x * y));
	elseif (i <= 2.6e+71)
		tmp = Float64(c * Float64(z * Float64(-b)));
	else
		tmp = Float64(y * Float64(i * Float64(-j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -2.7e+62)
		tmp = a * (b * i);
	elseif (i <= 3.1e-289)
		tmp = z * -(b * c);
	elseif (i <= 4e-135)
		tmp = z * (x * y);
	elseif (i <= 2.6e+71)
		tmp = c * (z * -b);
	else
		tmp = y * (i * -j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -2.7e+62], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.1e-289], N[(z * (-N[(b * c), $MachinePrecision])), $MachinePrecision], If[LessEqual[i, 4e-135], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.6e+71], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -2.7e62

   1. Initial program 54.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 54.8%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 57.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 57.0%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 57.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 57.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 57.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fmm-def 59.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. distribute-rgt-neg-out 59.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. remove-double-neg 59.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. *-commutative 59.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 59.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 59.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around inf 65.9%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. distribute-lft-out-- 65.9%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. *-commutative 65.9%

         \[\leadsto i \cdot \left(-1 \cdot \left(\color{blue}{y \cdot j} - a \cdot b\right)\right) \]

   7. Simplified 65.9%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j - a \cdot b\right)\right)} \]

   8. Taylor expanded in y around 0 40.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

   if -2.7e62 < i < 3.1e-289

   1. Initial program 82.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 77.1%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{a \cdot \left(-1 \cdot \left(b \cdot i\right) + \frac{b \cdot \left(c \cdot z\right)}{a}\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg 77.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\color{blue}{\left(-b \cdot i\right)} + \frac{b \cdot \left(c \cdot z\right)}{a}\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. +-commutative 77.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \color{blue}{\left(\frac{b \cdot \left(c \cdot z\right)}{a} + \left(-b \cdot i\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      3. unsub-neg 77.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \color{blue}{\left(\frac{b \cdot \left(c \cdot z\right)}{a} - b \cdot i\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 77.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{\color{blue}{\left(c \cdot z\right) \cdot b}}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      5. *-commutative 77.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{\color{blue}{\left(z \cdot c\right)} \cdot b}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      6. associate-*r* 78.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{\color{blue}{z \cdot \left(c \cdot b\right)}}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      7. *-commutative 78.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{z \cdot \color{blue}{\left(b \cdot c\right)}}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 78.2%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{a \cdot \left(\frac{z \cdot \left(b \cdot c\right)}{a} - b \cdot i\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   6. Taylor expanded in z around inf 45.6%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   7. Step-by-step derivation

      1. *-commutative 45.6%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

   8. Simplified 45.6%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - b \cdot c\right)} \]

   9. Taylor expanded in y around 0 32.0%

      \[\leadsto z \cdot \color{blue}{\left(-1 \cdot \left(b \cdot c\right)\right)} \]
   10. Step-by-step derivation

       1. neg-mul-1 32.0%

          \[\leadsto z \cdot \color{blue}{\left(-b \cdot c\right)} \]

       2. distribute-lft-neg-in 32.0%

          \[\leadsto z \cdot \color{blue}{\left(\left(-b\right) \cdot c\right)} \]

       3. *-commutative 32.0%

          \[\leadsto z \cdot \color{blue}{\left(c \cdot \left(-b\right)\right)} \]

   11. Simplified 32.0%

       \[\leadsto z \cdot \color{blue}{\left(c \cdot \left(-b\right)\right)} \]

   if 3.1e-289 < i < 4.0000000000000002e-135

   1. Initial program 78.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 78.4%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{a \cdot \left(-1 \cdot \left(b \cdot i\right) + \frac{b \cdot \left(c \cdot z\right)}{a}\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg 78.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\color{blue}{\left(-b \cdot i\right)} + \frac{b \cdot \left(c \cdot z\right)}{a}\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. +-commutative 78.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \color{blue}{\left(\frac{b \cdot \left(c \cdot z\right)}{a} + \left(-b \cdot i\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      3. unsub-neg 78.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \color{blue}{\left(\frac{b \cdot \left(c \cdot z\right)}{a} - b \cdot i\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 78.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{\color{blue}{\left(c \cdot z\right) \cdot b}}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      5. *-commutative 78.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{\color{blue}{\left(z \cdot c\right)} \cdot b}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      6. associate-*r* 75.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{\color{blue}{z \cdot \left(c \cdot b\right)}}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      7. *-commutative 75.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{z \cdot \color{blue}{\left(b \cdot c\right)}}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 75.7%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{a \cdot \left(\frac{z \cdot \left(b \cdot c\right)}{a} - b \cdot i\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   6. Taylor expanded in y around inf 48.5%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   7. Step-by-step derivation

      1. +-commutative 48.5%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 48.5%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 48.5%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 48.5%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   8. Simplified 48.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   9. Taylor expanded in z around inf 40.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 43.3%

          \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot z} \]

       2. *-commutative 43.3%

          \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]

   11. Simplified 43.3%

       \[\leadsto \color{blue}{\left(y \cdot x\right) \cdot z} \]

   if 4.0000000000000002e-135 < i < 2.59999999999999991e71

   1. Initial program 80.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 80.6%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 83.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 83.3%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 83.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 83.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 83.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fmm-def 86.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. distribute-rgt-neg-out 86.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. remove-double-neg 86.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. *-commutative 86.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 86.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 86.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 59.5%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 59.5%

         \[\leadsto c \cdot \left(\color{blue}{t \cdot j} - b \cdot z\right) \]

      2. *-commutative 59.5%

         \[\leadsto c \cdot \left(t \cdot j - \color{blue}{z \cdot b}\right) \]

   7. Simplified 59.5%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   8. Taylor expanded in t around 0 46.2%

      \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(b \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 46.2%

         \[\leadsto c \cdot \color{blue}{\left(-b \cdot z\right)} \]

      2. distribute-rgt-neg-in 46.2%

         \[\leadsto c \cdot \color{blue}{\left(b \cdot \left(-z\right)\right)} \]

   10. Simplified 46.2%

       \[\leadsto c \cdot \color{blue}{\left(b \cdot \left(-z\right)\right)} \]

   if 2.59999999999999991e71 < i

   1. Initial program 53.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 50.1%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{a \cdot \left(-1 \cdot \left(b \cdot i\right) + \frac{b \cdot \left(c \cdot z\right)}{a}\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg 50.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\color{blue}{\left(-b \cdot i\right)} + \frac{b \cdot \left(c \cdot z\right)}{a}\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. +-commutative 50.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \color{blue}{\left(\frac{b \cdot \left(c \cdot z\right)}{a} + \left(-b \cdot i\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      3. unsub-neg 50.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \color{blue}{\left(\frac{b \cdot \left(c \cdot z\right)}{a} - b \cdot i\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 50.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{\color{blue}{\left(c \cdot z\right) \cdot b}}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      5. *-commutative 50.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{\color{blue}{\left(z \cdot c\right)} \cdot b}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      6. associate-*r* 50.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{\color{blue}{z \cdot \left(c \cdot b\right)}}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      7. *-commutative 50.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{z \cdot \color{blue}{\left(b \cdot c\right)}}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 50.1%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{a \cdot \left(\frac{z \cdot \left(b \cdot c\right)}{a} - b \cdot i\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   6. Taylor expanded in y around inf 52.8%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   7. Step-by-step derivation

      1. +-commutative 52.8%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 52.8%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 52.8%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 52.8%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   8. Simplified 52.8%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   9. Taylor expanded in z around 0 41.5%

      \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)} \]
   10. Step-by-step derivation

       1. neg-mul-1 41.5%

          \[\leadsto y \cdot \color{blue}{\left(-i \cdot j\right)} \]

       2. distribute-rgt-neg-in 41.5%

          \[\leadsto y \cdot \color{blue}{\left(i \cdot \left(-j\right)\right)} \]

   11. Simplified 41.5%

       \[\leadsto y \cdot \color{blue}{\left(i \cdot \left(-j\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 39.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.7 \cdot 10^{+62}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 3.1 \cdot 10^{-289}:\\ \;\;\;\;z \cdot \left(-b \cdot c\right)\\ \mathbf{elif}\;i \leq 4 \cdot 10^{-135}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 2.6 \cdot 10^{+71}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 29.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{if}\;i \leq -8.6 \cdot 10^{+63}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 5.1 \cdot 10^{-290}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 6.6 \cdot 10^{-135}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 6 \cdot 10^{+73}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* z (- b)))))
   (if (<= i -8.6e+63)
     (* a (* b i))
     (if (<= i 5.1e-290)
       t_1
       (if (<= i 6.6e-135)
         (* z (* x y))
         (if (<= i 6e+73) t_1 (* y (* i (- j)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (z * -b);
	double tmp;
	if (i <= -8.6e+63) {
		tmp = a * (b * i);
	} else if (i <= 5.1e-290) {
		tmp = t_1;
	} else if (i <= 6.6e-135) {
		tmp = z * (x * y);
	} else if (i <= 6e+73) {
		tmp = t_1;
	} else {
		tmp = y * (i * -j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (z * -b)
    if (i <= (-8.6d+63)) then
        tmp = a * (b * i)
    else if (i <= 5.1d-290) then
        tmp = t_1
    else if (i <= 6.6d-135) then
        tmp = z * (x * y)
    else if (i <= 6d+73) then
        tmp = t_1
    else
        tmp = y * (i * -j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (z * -b);
	double tmp;
	if (i <= -8.6e+63) {
		tmp = a * (b * i);
	} else if (i <= 5.1e-290) {
		tmp = t_1;
	} else if (i <= 6.6e-135) {
		tmp = z * (x * y);
	} else if (i <= 6e+73) {
		tmp = t_1;
	} else {
		tmp = y * (i * -j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (z * -b)
	tmp = 0
	if i <= -8.6e+63:
		tmp = a * (b * i)
	elif i <= 5.1e-290:
		tmp = t_1
	elif i <= 6.6e-135:
		tmp = z * (x * y)
	elif i <= 6e+73:
		tmp = t_1
	else:
		tmp = y * (i * -j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(z * Float64(-b)))
	tmp = 0.0
	if (i <= -8.6e+63)
		tmp = Float64(a * Float64(b * i));
	elseif (i <= 5.1e-290)
		tmp = t_1;
	elseif (i <= 6.6e-135)
		tmp = Float64(z * Float64(x * y));
	elseif (i <= 6e+73)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(i * Float64(-j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (z * -b);
	tmp = 0.0;
	if (i <= -8.6e+63)
		tmp = a * (b * i);
	elseif (i <= 5.1e-290)
		tmp = t_1;
	elseif (i <= 6.6e-135)
		tmp = z * (x * y);
	elseif (i <= 6e+73)
		tmp = t_1;
	else
		tmp = y * (i * -j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -8.6e+63], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5.1e-290], t$95$1, If[LessEqual[i, 6.6e-135], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 6e+73], t$95$1, N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -8.6000000000000001e63

   1. Initial program 54.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 54.8%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 57.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 57.0%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 57.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 57.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 57.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fmm-def 59.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. distribute-rgt-neg-out 59.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. remove-double-neg 59.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. *-commutative 59.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 59.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 59.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around inf 65.9%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. distribute-lft-out-- 65.9%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. *-commutative 65.9%

         \[\leadsto i \cdot \left(-1 \cdot \left(\color{blue}{y \cdot j} - a \cdot b\right)\right) \]

   7. Simplified 65.9%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j - a \cdot b\right)\right)} \]

   8. Taylor expanded in y around 0 40.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

   if -8.6000000000000001e63 < i < 5.1e-290 or 6.5999999999999999e-135 < i < 6.00000000000000021e73

   1. Initial program 82.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 82.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 83.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 83.0%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 83.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 83.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 83.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fmm-def 83.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. distribute-rgt-neg-out 83.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. remove-double-neg 83.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. *-commutative 83.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 83.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 83.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 50.0%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 50.0%

         \[\leadsto c \cdot \left(\color{blue}{t \cdot j} - b \cdot z\right) \]

      2. *-commutative 50.0%

         \[\leadsto c \cdot \left(t \cdot j - \color{blue}{z \cdot b}\right) \]

   7. Simplified 50.0%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   8. Taylor expanded in t around 0 35.6%

      \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(b \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 35.6%

         \[\leadsto c \cdot \color{blue}{\left(-b \cdot z\right)} \]

      2. distribute-rgt-neg-in 35.6%

         \[\leadsto c \cdot \color{blue}{\left(b \cdot \left(-z\right)\right)} \]

   10. Simplified 35.6%

       \[\leadsto c \cdot \color{blue}{\left(b \cdot \left(-z\right)\right)} \]

   if 5.1e-290 < i < 6.5999999999999999e-135

   1. Initial program 78.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 78.4%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{a \cdot \left(-1 \cdot \left(b \cdot i\right) + \frac{b \cdot \left(c \cdot z\right)}{a}\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg 78.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\color{blue}{\left(-b \cdot i\right)} + \frac{b \cdot \left(c \cdot z\right)}{a}\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. +-commutative 78.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \color{blue}{\left(\frac{b \cdot \left(c \cdot z\right)}{a} + \left(-b \cdot i\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      3. unsub-neg 78.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \color{blue}{\left(\frac{b \cdot \left(c \cdot z\right)}{a} - b \cdot i\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 78.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{\color{blue}{\left(c \cdot z\right) \cdot b}}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      5. *-commutative 78.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{\color{blue}{\left(z \cdot c\right)} \cdot b}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      6. associate-*r* 75.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{\color{blue}{z \cdot \left(c \cdot b\right)}}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      7. *-commutative 75.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{z \cdot \color{blue}{\left(b \cdot c\right)}}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 75.7%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{a \cdot \left(\frac{z \cdot \left(b \cdot c\right)}{a} - b \cdot i\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   6. Taylor expanded in y around inf 48.5%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   7. Step-by-step derivation

      1. +-commutative 48.5%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 48.5%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 48.5%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 48.5%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   8. Simplified 48.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   9. Taylor expanded in z around inf 40.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 43.3%

          \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot z} \]

       2. *-commutative 43.3%

          \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]

   11. Simplified 43.3%

       \[\leadsto \color{blue}{\left(y \cdot x\right) \cdot z} \]

   if 6.00000000000000021e73 < i

   1. Initial program 53.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 50.1%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{a \cdot \left(-1 \cdot \left(b \cdot i\right) + \frac{b \cdot \left(c \cdot z\right)}{a}\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg 50.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\color{blue}{\left(-b \cdot i\right)} + \frac{b \cdot \left(c \cdot z\right)}{a}\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. +-commutative 50.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \color{blue}{\left(\frac{b \cdot \left(c \cdot z\right)}{a} + \left(-b \cdot i\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      3. unsub-neg 50.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \color{blue}{\left(\frac{b \cdot \left(c \cdot z\right)}{a} - b \cdot i\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 50.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{\color{blue}{\left(c \cdot z\right) \cdot b}}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      5. *-commutative 50.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{\color{blue}{\left(z \cdot c\right)} \cdot b}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      6. associate-*r* 50.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{\color{blue}{z \cdot \left(c \cdot b\right)}}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      7. *-commutative 50.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{z \cdot \color{blue}{\left(b \cdot c\right)}}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 50.1%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{a \cdot \left(\frac{z \cdot \left(b \cdot c\right)}{a} - b \cdot i\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   6. Taylor expanded in y around inf 52.8%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   7. Step-by-step derivation

      1. +-commutative 52.8%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 52.8%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 52.8%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 52.8%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   8. Simplified 52.8%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   9. Taylor expanded in z around 0 41.5%

      \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)} \]
   10. Step-by-step derivation

       1. neg-mul-1 41.5%

          \[\leadsto y \cdot \color{blue}{\left(-i \cdot j\right)} \]

       2. distribute-rgt-neg-in 41.5%

          \[\leadsto y \cdot \color{blue}{\left(i \cdot \left(-j\right)\right)} \]

   11. Simplified 41.5%

       \[\leadsto y \cdot \color{blue}{\left(i \cdot \left(-j\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 38.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -8.6 \cdot 10^{+63}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 5.1 \cdot 10^{-290}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;i \leq 6.6 \cdot 10^{-135}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 6 \cdot 10^{+73}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 30.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{if}\;z \leq -1.45 \cdot 10^{+274}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{-94}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+161}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* z (- b)))))
   (if (<= z -1.45e+274)
     (* x (* y z))
     (if (<= z -2.7e+15)
       t_1
       (if (<= z 1.52e-94)
         (* t (* c j))
         (if (<= z 2.15e+161) (* z (* x y)) 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 = c * (z * -b);
	double tmp;
	if (z <= -1.45e+274) {
		tmp = x * (y * z);
	} else if (z <= -2.7e+15) {
		tmp = t_1;
	} else if (z <= 1.52e-94) {
		tmp = t * (c * j);
	} else if (z <= 2.15e+161) {
		tmp = z * (x * y);
	} 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 = c * (z * -b)
    if (z <= (-1.45d+274)) then
        tmp = x * (y * z)
    else if (z <= (-2.7d+15)) then
        tmp = t_1
    else if (z <= 1.52d-94) then
        tmp = t * (c * j)
    else if (z <= 2.15d+161) then
        tmp = z * (x * y)
    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 = c * (z * -b);
	double tmp;
	if (z <= -1.45e+274) {
		tmp = x * (y * z);
	} else if (z <= -2.7e+15) {
		tmp = t_1;
	} else if (z <= 1.52e-94) {
		tmp = t * (c * j);
	} else if (z <= 2.15e+161) {
		tmp = z * (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (z * -b)
	tmp = 0
	if z <= -1.45e+274:
		tmp = x * (y * z)
	elif z <= -2.7e+15:
		tmp = t_1
	elif z <= 1.52e-94:
		tmp = t * (c * j)
	elif z <= 2.15e+161:
		tmp = z * (x * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(z * Float64(-b)))
	tmp = 0.0
	if (z <= -1.45e+274)
		tmp = Float64(x * Float64(y * z));
	elseif (z <= -2.7e+15)
		tmp = t_1;
	elseif (z <= 1.52e-94)
		tmp = Float64(t * Float64(c * j));
	elseif (z <= 2.15e+161)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (z * -b);
	tmp = 0.0;
	if (z <= -1.45e+274)
		tmp = x * (y * z);
	elseif (z <= -2.7e+15)
		tmp = t_1;
	elseif (z <= 1.52e-94)
		tmp = t * (c * j);
	elseif (z <= 2.15e+161)
		tmp = z * (x * y);
	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[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.45e+274], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.7e+15], t$95$1, If[LessEqual[z, 1.52e-94], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.15e+161], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.45e274

   1. Initial program 56.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 42.7%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   4. Taylor expanded in z around inf 85.6%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   5. Step-by-step derivation

      1. *-commutative 85.6%

         \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

   6. Simplified 85.6%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y\right)} \]

   if -1.45e274 < z < -2.7e15 or 2.15e161 < z

   1. Initial program 56.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 56.7%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 61.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 61.4%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 61.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 61.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 61.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fmm-def 63.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. distribute-rgt-neg-out 63.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. remove-double-neg 63.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. *-commutative 63.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 63.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 63.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 51.5%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 51.5%

         \[\leadsto c \cdot \left(\color{blue}{t \cdot j} - b \cdot z\right) \]

      2. *-commutative 51.5%

         \[\leadsto c \cdot \left(t \cdot j - \color{blue}{z \cdot b}\right) \]

   7. Simplified 51.5%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   8. Taylor expanded in t around 0 47.8%

      \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(b \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 47.8%

         \[\leadsto c \cdot \color{blue}{\left(-b \cdot z\right)} \]

      2. distribute-rgt-neg-in 47.8%

         \[\leadsto c \cdot \color{blue}{\left(b \cdot \left(-z\right)\right)} \]

   10. Simplified 47.8%

       \[\leadsto c \cdot \color{blue}{\left(b \cdot \left(-z\right)\right)} \]

   if -2.7e15 < z < 1.5199999999999999e-94

   1. Initial program 79.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 79.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 80.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 80.2%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 80.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 80.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 80.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fmm-def 80.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. distribute-rgt-neg-out 80.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. remove-double-neg 80.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. *-commutative 80.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 80.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 80.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 32.4%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 32.4%

         \[\leadsto c \cdot \left(\color{blue}{t \cdot j} - b \cdot z\right) \]

      2. *-commutative 32.4%

         \[\leadsto c \cdot \left(t \cdot j - \color{blue}{z \cdot b}\right) \]

   7. Simplified 32.4%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   8. Taylor expanded in t around inf 27.2%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 28.9%

         \[\leadsto \color{blue}{\left(c \cdot j\right) \cdot t} \]

      2. *-commutative 28.9%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j\right)} \]

   10. Simplified 28.9%

       \[\leadsto \color{blue}{t \cdot \left(c \cdot j\right)} \]

   if 1.5199999999999999e-94 < z < 2.15e161

   1. Initial program 75.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 72.0%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{a \cdot \left(-1 \cdot \left(b \cdot i\right) + \frac{b \cdot \left(c \cdot z\right)}{a}\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg 72.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\color{blue}{\left(-b \cdot i\right)} + \frac{b \cdot \left(c \cdot z\right)}{a}\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. +-commutative 72.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \color{blue}{\left(\frac{b \cdot \left(c \cdot z\right)}{a} + \left(-b \cdot i\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      3. unsub-neg 72.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \color{blue}{\left(\frac{b \cdot \left(c \cdot z\right)}{a} - b \cdot i\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 72.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{\color{blue}{\left(c \cdot z\right) \cdot b}}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      5. *-commutative 72.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{\color{blue}{\left(z \cdot c\right)} \cdot b}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      6. associate-*r* 72.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{\color{blue}{z \cdot \left(c \cdot b\right)}}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      7. *-commutative 72.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{z \cdot \color{blue}{\left(b \cdot c\right)}}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 72.0%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{a \cdot \left(\frac{z \cdot \left(b \cdot c\right)}{a} - b \cdot i\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   6. Taylor expanded in y around inf 49.2%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   7. Step-by-step derivation

      1. +-commutative 49.2%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 49.2%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 49.2%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 49.2%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   8. Simplified 49.2%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   9. Taylor expanded in z around inf 31.2%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 32.8%

          \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot z} \]

       2. *-commutative 32.8%

          \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]

   11. Simplified 32.8%

       \[\leadsto \color{blue}{\left(y \cdot x\right) \cdot z} \]
3. Recombined 4 regimes into one program.

4. Final simplification 37.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+274}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{+15}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{-94}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+161}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 59.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.65 \cdot 10^{-135} \lor \neg \left(x \leq 12500000000000\right):\\ \;\;\;\;t \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= x -2.65e-135) (not (<= x 12500000000000.0)))
   (+ (* t (* c j)) (* x (- (* y z) (* t a))))
   (+ (* j (- (* t c) (* y i))) (* a (* b i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((x <= -2.65e-135) || !(x <= 12500000000000.0)) {
		tmp = (t * (c * j)) + (x * ((y * z) - (t * a)));
	} else {
		tmp = (j * ((t * c) - (y * i))) + (a * (b * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((x <= (-2.65d-135)) .or. (.not. (x <= 12500000000000.0d0))) then
        tmp = (t * (c * j)) + (x * ((y * z) - (t * a)))
    else
        tmp = (j * ((t * c) - (y * i))) + (a * (b * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((x <= -2.65e-135) || !(x <= 12500000000000.0)) {
		tmp = (t * (c * j)) + (x * ((y * z) - (t * a)));
	} else {
		tmp = (j * ((t * c) - (y * i))) + (a * (b * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (x <= -2.65e-135) or not (x <= 12500000000000.0):
		tmp = (t * (c * j)) + (x * ((y * z) - (t * a)))
	else:
		tmp = (j * ((t * c) - (y * i))) + (a * (b * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((x <= -2.65e-135) || !(x <= 12500000000000.0))
		tmp = Float64(Float64(t * Float64(c * j)) + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	else
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(a * Float64(b * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((x <= -2.65e-135) || ~((x <= 12500000000000.0)))
		tmp = (t * (c * j)) + (x * ((y * z) - (t * a)));
	else
		tmp = (j * ((t * c) - (y * i))) + (a * (b * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[x, -2.65e-135], N[Not[LessEqual[x, 12500000000000.0]], $MachinePrecision]], N[(N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.65e-135 or 1.25e13 < x

   1. Initial program 69.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 63.9%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   4. Taylor expanded in c around inf 61.6%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} + x \cdot \left(y \cdot z - a \cdot t\right) \]
   5. Step-by-step derivation

      1. *-commutative 70.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + c \cdot \color{blue}{\left(t \cdot j\right)} \]

      2. associate-*r* 68.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{\left(c \cdot t\right) \cdot j} \]

      3. *-commutative 68.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{\left(t \cdot c\right)} \cdot j \]

      4. associate-*r* 71.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{t \cdot \left(c \cdot j\right)} \]

   6. Simplified 64.0%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j\right)} + x \cdot \left(y \cdot z - a \cdot t\right) \]

   if -2.65e-135 < x < 1.25e13

   1. Initial program 71.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub-inv 71.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. cancel-sign-sub 71.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      3. *-commutative 71.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      4. fmm-def 72.3%

         \[\leadsto \left(x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      5. distribute-rgt-neg-in 72.3%

         \[\leadsto \left(x \cdot \mathsf{fma}\left(y, z, \color{blue}{a \cdot \left(-t\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      6. remove-double-neg 72.3%

         \[\leadsto \left(x \cdot \mathsf{fma}\left(y, z, a \cdot \left(-t\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      7. *-commutative 72.3%

         \[\leadsto \left(x \cdot \mathsf{fma}\left(y, z, a \cdot \left(-t\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      8. *-commutative 72.3%

         \[\leadsto \left(x \cdot \mathsf{fma}\left(y, z, a \cdot \left(-t\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      9. *-commutative 72.3%

         \[\leadsto \left(x \cdot \mathsf{fma}\left(y, z, a \cdot \left(-t\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      10. *-commutative 72.3%

          \[\leadsto \left(x \cdot \mathsf{fma}\left(y, z, a \cdot \left(-t\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 72.3%

      \[\leadsto \color{blue}{\left(x \cdot \mathsf{fma}\left(y, z, a \cdot \left(-t\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around inf 57.1%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.65 \cdot 10^{-135} \lor \neg \left(x \leq 12500000000000\right):\\ \;\;\;\;t \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 60.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-11} \lor \neg \left(z \leq 7 \cdot 10^{+79}\right):\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= z -5.5e-11) (not (<= z 7e+79)))
   (* z (- (* x y) (* b c)))
   (+ (* j (- (* t c) (* y i))) (* a (* b i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((z <= -5.5e-11) || !(z <= 7e+79)) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = (j * ((t * c) - (y * i))) + (a * (b * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((z <= (-5.5d-11)) .or. (.not. (z <= 7d+79))) then
        tmp = z * ((x * y) - (b * c))
    else
        tmp = (j * ((t * c) - (y * i))) + (a * (b * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((z <= -5.5e-11) || !(z <= 7e+79)) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = (j * ((t * c) - (y * i))) + (a * (b * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (z <= -5.5e-11) or not (z <= 7e+79):
		tmp = z * ((x * y) - (b * c))
	else:
		tmp = (j * ((t * c) - (y * i))) + (a * (b * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((z <= -5.5e-11) || !(z <= 7e+79))
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	else
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(a * Float64(b * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((z <= -5.5e-11) || ~((z <= 7e+79)))
		tmp = z * ((x * y) - (b * c));
	else
		tmp = (j * ((t * c) - (y * i))) + (a * (b * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[z, -5.5e-11], N[Not[LessEqual[z, 7e+79]], $MachinePrecision]], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.49999999999999975e-11 or 6.99999999999999961e79 < z

   1. Initial program 60.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 50.2%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{a \cdot \left(-1 \cdot \left(b \cdot i\right) + \frac{b \cdot \left(c \cdot z\right)}{a}\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg 50.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\color{blue}{\left(-b \cdot i\right)} + \frac{b \cdot \left(c \cdot z\right)}{a}\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. +-commutative 50.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \color{blue}{\left(\frac{b \cdot \left(c \cdot z\right)}{a} + \left(-b \cdot i\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      3. unsub-neg 50.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \color{blue}{\left(\frac{b \cdot \left(c \cdot z\right)}{a} - b \cdot i\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 50.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{\color{blue}{\left(c \cdot z\right) \cdot b}}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      5. *-commutative 50.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{\color{blue}{\left(z \cdot c\right)} \cdot b}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      6. associate-*r* 51.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{\color{blue}{z \cdot \left(c \cdot b\right)}}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      7. *-commutative 51.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{z \cdot \color{blue}{\left(b \cdot c\right)}}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 51.0%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{a \cdot \left(\frac{z \cdot \left(b \cdot c\right)}{a} - b \cdot i\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   6. Taylor expanded in z around inf 64.6%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   7. Step-by-step derivation

      1. *-commutative 64.6%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

   8. Simplified 64.6%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - b \cdot c\right)} \]

   if -5.49999999999999975e-11 < z < 6.99999999999999961e79

   1. Initial program 79.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub-inv 79.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. cancel-sign-sub 79.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      3. *-commutative 79.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      4. fmm-def 79.5%

         \[\leadsto \left(x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      5. distribute-rgt-neg-in 79.5%

         \[\leadsto \left(x \cdot \mathsf{fma}\left(y, z, \color{blue}{a \cdot \left(-t\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      6. remove-double-neg 79.5%

         \[\leadsto \left(x \cdot \mathsf{fma}\left(y, z, a \cdot \left(-t\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      7. *-commutative 79.5%

         \[\leadsto \left(x \cdot \mathsf{fma}\left(y, z, a \cdot \left(-t\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      8. *-commutative 79.5%

         \[\leadsto \left(x \cdot \mathsf{fma}\left(y, z, a \cdot \left(-t\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      9. *-commutative 79.5%

         \[\leadsto \left(x \cdot \mathsf{fma}\left(y, z, a \cdot \left(-t\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      10. *-commutative 79.5%

          \[\leadsto \left(x \cdot \mathsf{fma}\left(y, z, a \cdot \left(-t\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 79.5%

      \[\leadsto \color{blue}{\left(x \cdot \mathsf{fma}\left(y, z, a \cdot \left(-t\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around inf 56.1%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-11} \lor \neg \left(z \leq 7 \cdot 10^{+79}\right):\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 51.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.45 \cdot 10^{+51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-184}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 18000000000:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= b -1.45e+51)
     t_1
     (if (<= b -2.4e-184)
       (* x (- (* y z) (* t a)))
       (if (<= b 18000000000.0) (* j (- (* t c) (* y i))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.45e+51) {
		tmp = t_1;
	} else if (b <= -2.4e-184) {
		tmp = x * ((y * z) - (t * a));
	} else if (b <= 18000000000.0) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    if (b <= (-1.45d+51)) then
        tmp = t_1
    else if (b <= (-2.4d-184)) then
        tmp = x * ((y * z) - (t * a))
    else if (b <= 18000000000.0d0) then
        tmp = j * ((t * c) - (y * i))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.45e+51) {
		tmp = t_1;
	} else if (b <= -2.4e-184) {
		tmp = x * ((y * z) - (t * a));
	} else if (b <= 18000000000.0) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -1.45e+51:
		tmp = t_1
	elif b <= -2.4e-184:
		tmp = x * ((y * z) - (t * a))
	elif b <= 18000000000.0:
		tmp = j * ((t * c) - (y * i))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -1.45e+51)
		tmp = t_1;
	elseif (b <= -2.4e-184)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (b <= 18000000000.0)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -1.45e+51)
		tmp = t_1;
	elseif (b <= -2.4e-184)
		tmp = x * ((y * z) - (t * a));
	elseif (b <= 18000000000.0)
		tmp = j * ((t * c) - (y * i));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.45e+51], t$95$1, If[LessEqual[b, -2.4e-184], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 18000000000.0], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.4499999999999999e51 or 1.8e10 < b

   1. Initial program 74.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 76.0%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{c \cdot \left(j \cdot t\right)} \]
   4. Step-by-step derivation

      1. *-commutative 76.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + c \cdot \color{blue}{\left(t \cdot j\right)} \]

      2. associate-*r* 74.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{\left(c \cdot t\right) \cdot j} \]

      3. *-commutative 74.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{\left(t \cdot c\right)} \cdot j \]

      4. associate-*r* 76.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{t \cdot \left(c \cdot j\right)} \]

   5. Simplified 76.0%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{t \cdot \left(c \cdot j\right)} \]

   6. Taylor expanded in b around inf 64.6%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]

   if -1.4499999999999999e51 < b < -2.40000000000000024e-184

   1. Initial program 67.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 66.2%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{a \cdot \left(-1 \cdot \left(b \cdot i\right) + \frac{b \cdot \left(c \cdot z\right)}{a}\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg 66.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\color{blue}{\left(-b \cdot i\right)} + \frac{b \cdot \left(c \cdot z\right)}{a}\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. +-commutative 66.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \color{blue}{\left(\frac{b \cdot \left(c \cdot z\right)}{a} + \left(-b \cdot i\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      3. unsub-neg 66.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \color{blue}{\left(\frac{b \cdot \left(c \cdot z\right)}{a} - b \cdot i\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 66.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{\color{blue}{\left(c \cdot z\right) \cdot b}}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      5. *-commutative 66.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{\color{blue}{\left(z \cdot c\right)} \cdot b}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      6. associate-*r* 66.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{\color{blue}{z \cdot \left(c \cdot b\right)}}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      7. *-commutative 66.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{z \cdot \color{blue}{\left(b \cdot c\right)}}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 66.2%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{a \cdot \left(\frac{z \cdot \left(b \cdot c\right)}{a} - b \cdot i\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   6. Taylor expanded in x around inf 53.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 53.8%

         \[\leadsto x \cdot \left(\color{blue}{z \cdot y} - a \cdot t\right) \]

   8. Simplified 53.8%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y - a \cdot t\right)} \]

   if -2.40000000000000024e-184 < b < 1.8e10

   1. Initial program 67.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 67.4%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 67.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 67.4%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 67.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 67.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 67.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fmm-def 68.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. distribute-rgt-neg-out 68.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. remove-double-neg 68.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. *-commutative 68.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 68.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 68.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in j around inf 48.2%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]
   6. Step-by-step derivation

      1. *-commutative 48.2%

         \[\leadsto j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      2. *-commutative 48.2%

         \[\leadsto j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   7. Simplified 48.2%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot c - y \cdot i\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.45 \cdot 10^{+51}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-184}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 18000000000:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 51.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -5 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{-173}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 7600000000:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= b -5e+62)
     t_1
     (if (<= b -5.8e-173)
       (* t (- (* c j) (* x a)))
       (if (<= b 7600000000.0) (* j (- (* t c) (* y i))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -5e+62) {
		tmp = t_1;
	} else if (b <= -5.8e-173) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= 7600000000.0) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    if (b <= (-5d+62)) then
        tmp = t_1
    else if (b <= (-5.8d-173)) then
        tmp = t * ((c * j) - (x * a))
    else if (b <= 7600000000.0d0) then
        tmp = j * ((t * c) - (y * i))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -5e+62) {
		tmp = t_1;
	} else if (b <= -5.8e-173) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= 7600000000.0) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -5e+62:
		tmp = t_1
	elif b <= -5.8e-173:
		tmp = t * ((c * j) - (x * a))
	elif b <= 7600000000.0:
		tmp = j * ((t * c) - (y * i))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -5e+62)
		tmp = t_1;
	elseif (b <= -5.8e-173)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (b <= 7600000000.0)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -5e+62)
		tmp = t_1;
	elseif (b <= -5.8e-173)
		tmp = t * ((c * j) - (x * a));
	elseif (b <= 7600000000.0)
		tmp = j * ((t * c) - (y * i));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5e+62], t$95$1, If[LessEqual[b, -5.8e-173], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7600000000.0], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.00000000000000029e62 or 7.6e9 < b

   1. Initial program 73.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 75.1%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{c \cdot \left(j \cdot t\right)} \]
   4. Step-by-step derivation

      1. *-commutative 75.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + c \cdot \color{blue}{\left(t \cdot j\right)} \]

      2. associate-*r* 73.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{\left(c \cdot t\right) \cdot j} \]

      3. *-commutative 73.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{\left(t \cdot c\right)} \cdot j \]

      4. associate-*r* 75.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{t \cdot \left(c \cdot j\right)} \]

   5. Simplified 75.2%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{t \cdot \left(c \cdot j\right)} \]

   6. Taylor expanded in b around inf 65.1%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]

   if -5.00000000000000029e62 < b < -5.7999999999999997e-173

   1. Initial program 67.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 67.9%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 69.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 69.8%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 69.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 69.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 69.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fmm-def 69.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. distribute-rgt-neg-out 69.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. remove-double-neg 69.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. *-commutative 69.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 69.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 69.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 45.5%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   6. Step-by-step derivation

      1. +-commutative 45.5%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 45.5%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 45.5%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

      4. *-commutative 45.5%

         \[\leadsto t \cdot \left(c \cdot j - \color{blue}{x \cdot a}\right) \]

   7. Simplified 45.5%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - x \cdot a\right)} \]

   if -5.7999999999999997e-173 < b < 7.6e9

   1. Initial program 68.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 68.7%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 68.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 68.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 68.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 68.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 68.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fmm-def 69.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. distribute-rgt-neg-out 69.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. remove-double-neg 69.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. *-commutative 69.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 69.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 69.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in j around inf 48.4%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]
   6. Step-by-step derivation

      1. *-commutative 48.4%

         \[\leadsto j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      2. *-commutative 48.4%

         \[\leadsto j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   7. Simplified 48.4%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot c - y \cdot i\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+62}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{-173}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 7600000000:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 51.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -2.6 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -4.9 \cdot 10^{-54}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;b \leq 4100000000:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= b -2.6e+43)
     t_1
     (if (<= b -4.9e-54)
       (* a (- (* b i) (* x t)))
       (if (<= b 4100000000.0) (* j (- (* t c) (* y i))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -2.6e+43) {
		tmp = t_1;
	} else if (b <= -4.9e-54) {
		tmp = a * ((b * i) - (x * t));
	} else if (b <= 4100000000.0) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    if (b <= (-2.6d+43)) then
        tmp = t_1
    else if (b <= (-4.9d-54)) then
        tmp = a * ((b * i) - (x * t))
    else if (b <= 4100000000.0d0) then
        tmp = j * ((t * c) - (y * i))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -2.6e+43) {
		tmp = t_1;
	} else if (b <= -4.9e-54) {
		tmp = a * ((b * i) - (x * t));
	} else if (b <= 4100000000.0) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -2.6e+43:
		tmp = t_1
	elif b <= -4.9e-54:
		tmp = a * ((b * i) - (x * t))
	elif b <= 4100000000.0:
		tmp = j * ((t * c) - (y * i))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -2.6e+43)
		tmp = t_1;
	elseif (b <= -4.9e-54)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (b <= 4100000000.0)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -2.6e+43)
		tmp = t_1;
	elseif (b <= -4.9e-54)
		tmp = a * ((b * i) - (x * t));
	elseif (b <= 4100000000.0)
		tmp = j * ((t * c) - (y * i));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.6e+43], t$95$1, If[LessEqual[b, -4.9e-54], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4100000000.0], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.60000000000000021e43 or 4.1e9 < b

   1. Initial program 73.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 75.5%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{c \cdot \left(j \cdot t\right)} \]
   4. Step-by-step derivation

      1. *-commutative 75.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + c \cdot \color{blue}{\left(t \cdot j\right)} \]

      2. associate-*r* 73.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{\left(c \cdot t\right) \cdot j} \]

      3. *-commutative 73.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{\left(t \cdot c\right)} \cdot j \]

      4. associate-*r* 75.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{t \cdot \left(c \cdot j\right)} \]

   5. Simplified 75.6%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{t \cdot \left(c \cdot j\right)} \]

   6. Taylor expanded in b around inf 63.5%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]

   if -2.60000000000000021e43 < b < -4.90000000000000021e-54

   1. Initial program 84.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 79.6%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{a \cdot \left(-1 \cdot \left(b \cdot i\right) + \frac{b \cdot \left(c \cdot z\right)}{a}\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg 79.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\color{blue}{\left(-b \cdot i\right)} + \frac{b \cdot \left(c \cdot z\right)}{a}\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. +-commutative 79.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \color{blue}{\left(\frac{b \cdot \left(c \cdot z\right)}{a} + \left(-b \cdot i\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      3. unsub-neg 79.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \color{blue}{\left(\frac{b \cdot \left(c \cdot z\right)}{a} - b \cdot i\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 79.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{\color{blue}{\left(c \cdot z\right) \cdot b}}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      5. *-commutative 79.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{\color{blue}{\left(z \cdot c\right)} \cdot b}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      6. associate-*r* 79.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{\color{blue}{z \cdot \left(c \cdot b\right)}}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      7. *-commutative 79.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{z \cdot \color{blue}{\left(b \cdot c\right)}}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 79.6%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{a \cdot \left(\frac{z \cdot \left(b \cdot c\right)}{a} - b \cdot i\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   6. Taylor expanded in a around inf 53.3%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + b \cdot i\right)} \]
   7. Step-by-step derivation

      1. +-commutative 53.3%

         \[\leadsto a \cdot \color{blue}{\left(b \cdot i + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 53.3%

         \[\leadsto a \cdot \left(b \cdot i + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 53.3%

         \[\leadsto a \cdot \color{blue}{\left(b \cdot i - t \cdot x\right)} \]

   8. Simplified 53.3%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   if -4.90000000000000021e-54 < b < 4.1e9

   1. Initial program 65.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 65.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 65.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 65.9%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 65.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 65.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 65.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fmm-def 66.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. distribute-rgt-neg-out 66.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. remove-double-neg 66.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. *-commutative 66.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 66.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 66.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in j around inf 45.7%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]
   6. Step-by-step derivation

      1. *-commutative 45.7%

         \[\leadsto j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      2. *-commutative 45.7%

         \[\leadsto j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   7. Simplified 45.7%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot c - y \cdot i\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.6 \cdot 10^{+43}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -4.9 \cdot 10^{-54}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;b \leq 4100000000:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 64.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{-15}:\\ \;\;\;\;a \cdot \left(\left(b \cdot i + \frac{x \cdot \left(y \cdot z\right)}{a}\right) - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -8.5e-15)
   (* a (- (+ (* b i) (/ (* x (* y z)) a)) (* x t)))
   (+ (* j (- (* t c) (* y i))) (* z (- (* x y) (* b c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -8.5e-15) {
		tmp = a * (((b * i) + ((x * (y * z)) / a)) - (x * t));
	} else {
		tmp = (j * ((t * c) - (y * i))) + (z * ((x * y) - (b * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (a <= (-8.5d-15)) then
        tmp = a * (((b * i) + ((x * (y * z)) / a)) - (x * t))
    else
        tmp = (j * ((t * c) - (y * i))) + (z * ((x * y) - (b * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -8.5e-15) {
		tmp = a * (((b * i) + ((x * (y * z)) / a)) - (x * t));
	} else {
		tmp = (j * ((t * c) - (y * i))) + (z * ((x * y) - (b * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -8.5e-15:
		tmp = a * (((b * i) + ((x * (y * z)) / a)) - (x * t))
	else:
		tmp = (j * ((t * c) - (y * i))) + (z * ((x * y) - (b * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -8.5e-15)
		tmp = Float64(a * Float64(Float64(Float64(b * i) + Float64(Float64(x * Float64(y * z)) / a)) - Float64(x * t)));
	else
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(z * Float64(Float64(x * y) - Float64(b * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -8.5e-15)
		tmp = a * (((b * i) + ((x * (y * z)) / a)) - (x * t));
	else
		tmp = (j * ((t * c) - (y * i))) + (z * ((x * y) - (b * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -8.5e-15], N[(a * N[(N[(N[(b * i), $MachinePrecision] + N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -8.50000000000000007e-15

   1. Initial program 64.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 64.0%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{c \cdot \left(j \cdot t\right)} \]
   4. Step-by-step derivation

      1. *-commutative 64.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + c \cdot \color{blue}{\left(t \cdot j\right)} \]

      2. associate-*r* 61.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{\left(c \cdot t\right) \cdot j} \]

      3. *-commutative 61.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{\left(t \cdot c\right)} \cdot j \]

      4. associate-*r* 60.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{t \cdot \left(c \cdot j\right)} \]

   5. Simplified 60.4%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{t \cdot \left(c \cdot j\right)} \]

   6. Taylor expanded in a around inf 75.2%

      \[\leadsto \color{blue}{a \cdot \left(\left(-1 \cdot \left(t \cdot x\right) + \left(\frac{c \cdot \left(j \cdot t\right)}{a} + \frac{x \cdot \left(y \cdot z\right)}{a}\right)\right) - \left(-1 \cdot \left(b \cdot i\right) + \frac{b \cdot \left(c \cdot z\right)}{a}\right)\right)} \]
   7. Step-by-step derivation

      1. sub-neg 75.2%

         \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot \left(t \cdot x\right) + \left(\frac{c \cdot \left(j \cdot t\right)}{a} + \frac{x \cdot \left(y \cdot z\right)}{a}\right)\right) + \left(-\left(-1 \cdot \left(b \cdot i\right) + \frac{b \cdot \left(c \cdot z\right)}{a}\right)\right)\right)} \]

      2. +-commutative 75.2%

         \[\leadsto a \cdot \left(\color{blue}{\left(\left(\frac{c \cdot \left(j \cdot t\right)}{a} + \frac{x \cdot \left(y \cdot z\right)}{a}\right) + -1 \cdot \left(t \cdot x\right)\right)} + \left(-\left(-1 \cdot \left(b \cdot i\right) + \frac{b \cdot \left(c \cdot z\right)}{a}\right)\right)\right) \]

      3. mul-1-neg 75.2%

         \[\leadsto a \cdot \left(\left(\left(\frac{c \cdot \left(j \cdot t\right)}{a} + \frac{x \cdot \left(y \cdot z\right)}{a}\right) + \color{blue}{\left(-t \cdot x\right)}\right) + \left(-\left(-1 \cdot \left(b \cdot i\right) + \frac{b \cdot \left(c \cdot z\right)}{a}\right)\right)\right) \]

      4. unsub-neg 75.2%

         \[\leadsto a \cdot \left(\color{blue}{\left(\left(\frac{c \cdot \left(j \cdot t\right)}{a} + \frac{x \cdot \left(y \cdot z\right)}{a}\right) - t \cdot x\right)} + \left(-\left(-1 \cdot \left(b \cdot i\right) + \frac{b \cdot \left(c \cdot z\right)}{a}\right)\right)\right) \]

      5. +-commutative 75.2%

         \[\leadsto a \cdot \left(\left(\color{blue}{\left(\frac{x \cdot \left(y \cdot z\right)}{a} + \frac{c \cdot \left(j \cdot t\right)}{a}\right)} - t \cdot x\right) + \left(-\left(-1 \cdot \left(b \cdot i\right) + \frac{b \cdot \left(c \cdot z\right)}{a}\right)\right)\right) \]

      6. *-commutative 75.2%

         \[\leadsto a \cdot \left(\left(\left(\frac{x \cdot \color{blue}{\left(z \cdot y\right)}}{a} + \frac{c \cdot \left(j \cdot t\right)}{a}\right) - t \cdot x\right) + \left(-\left(-1 \cdot \left(b \cdot i\right) + \frac{b \cdot \left(c \cdot z\right)}{a}\right)\right)\right) \]

      7. associate-*r* 72.8%

         \[\leadsto a \cdot \left(\left(\left(\frac{x \cdot \left(z \cdot y\right)}{a} + \frac{\color{blue}{\left(c \cdot j\right) \cdot t}}{a}\right) - t \cdot x\right) + \left(-\left(-1 \cdot \left(b \cdot i\right) + \frac{b \cdot \left(c \cdot z\right)}{a}\right)\right)\right) \]

      8. *-commutative 72.8%

         \[\leadsto a \cdot \left(\left(\left(\frac{x \cdot \left(z \cdot y\right)}{a} + \frac{\color{blue}{t \cdot \left(c \cdot j\right)}}{a}\right) - t \cdot x\right) + \left(-\left(-1 \cdot \left(b \cdot i\right) + \frac{b \cdot \left(c \cdot z\right)}{a}\right)\right)\right) \]

      9. neg-mul-1 72.8%

         \[\leadsto a \cdot \left(\left(\left(\frac{x \cdot \left(z \cdot y\right)}{a} + \frac{t \cdot \left(c \cdot j\right)}{a}\right) - t \cdot x\right) + \left(-\left(\color{blue}{\left(-b \cdot i\right)} + \frac{b \cdot \left(c \cdot z\right)}{a}\right)\right)\right) \]

   8. Simplified 72.8%

      \[\leadsto \color{blue}{a \cdot \left(\left(\left(\frac{x \cdot \left(z \cdot y\right)}{a} + \frac{t \cdot \left(c \cdot j\right)}{a}\right) - t \cdot x\right) + \left(b \cdot i - b \cdot \frac{c \cdot z}{a}\right)\right)} \]

   9. Taylor expanded in c around 0 72.8%

      \[\leadsto \color{blue}{a \cdot \left(\left(b \cdot i + \frac{x \cdot \left(y \cdot z\right)}{a}\right) - t \cdot x\right)} \]

   if -8.50000000000000007e-15 < a

   1. Initial program 73.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub-inv 73.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. cancel-sign-sub 73.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      3. *-commutative 73.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      4. fmm-def 73.9%

         \[\leadsto \left(x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      5. distribute-rgt-neg-in 73.9%

         \[\leadsto \left(x \cdot \mathsf{fma}\left(y, z, \color{blue}{a \cdot \left(-t\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      6. remove-double-neg 73.9%

         \[\leadsto \left(x \cdot \mathsf{fma}\left(y, z, a \cdot \left(-t\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      7. *-commutative 73.9%

         \[\leadsto \left(x \cdot \mathsf{fma}\left(y, z, a \cdot \left(-t\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      8. *-commutative 73.9%

         \[\leadsto \left(x \cdot \mathsf{fma}\left(y, z, a \cdot \left(-t\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      9. *-commutative 73.9%

         \[\leadsto \left(x \cdot \mathsf{fma}\left(y, z, a \cdot \left(-t\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      10. *-commutative 73.9%

          \[\leadsto \left(x \cdot \mathsf{fma}\left(y, z, a \cdot \left(-t\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 73.9%

      \[\leadsto \color{blue}{\left(x \cdot \mathsf{fma}\left(y, z, a \cdot \left(-t\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 65.3%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{-15}:\\ \;\;\;\;a \cdot \left(\left(b \cdot i + \frac{x \cdot \left(y \cdot z\right)}{a}\right) - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 41.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{+216}:\\ \;\;\;\;z \cdot \left(-b \cdot c\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+94}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{+160}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -1.16e+216)
   (* z (- (* b c)))
   (if (<= z 2.4e+94)
     (* a (- (* b i) (* x t)))
     (if (<= z 1.16e+160) (* z (* x y)) (* c (* z (- b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -1.16e+216) {
		tmp = z * -(b * c);
	} else if (z <= 2.4e+94) {
		tmp = a * ((b * i) - (x * t));
	} else if (z <= 1.16e+160) {
		tmp = z * (x * y);
	} else {
		tmp = c * (z * -b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-1.16d+216)) then
        tmp = z * -(b * c)
    else if (z <= 2.4d+94) then
        tmp = a * ((b * i) - (x * t))
    else if (z <= 1.16d+160) then
        tmp = z * (x * y)
    else
        tmp = c * (z * -b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -1.16e+216) {
		tmp = z * -(b * c);
	} else if (z <= 2.4e+94) {
		tmp = a * ((b * i) - (x * t));
	} else if (z <= 1.16e+160) {
		tmp = z * (x * y);
	} else {
		tmp = c * (z * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -1.16e+216:
		tmp = z * -(b * c)
	elif z <= 2.4e+94:
		tmp = a * ((b * i) - (x * t))
	elif z <= 1.16e+160:
		tmp = z * (x * y)
	else:
		tmp = c * (z * -b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -1.16e+216)
		tmp = Float64(z * Float64(-Float64(b * c)));
	elseif (z <= 2.4e+94)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (z <= 1.16e+160)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = Float64(c * Float64(z * Float64(-b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -1.16e+216)
		tmp = z * -(b * c);
	elseif (z <= 2.4e+94)
		tmp = a * ((b * i) - (x * t));
	elseif (z <= 1.16e+160)
		tmp = z * (x * y);
	else
		tmp = c * (z * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -1.16e+216], N[(z * (-N[(b * c), $MachinePrecision])), $MachinePrecision], If[LessEqual[z, 2.4e+94], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.16e+160], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.16e216

   1. Initial program 52.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 36.6%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{a \cdot \left(-1 \cdot \left(b \cdot i\right) + \frac{b \cdot \left(c \cdot z\right)}{a}\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg 36.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\color{blue}{\left(-b \cdot i\right)} + \frac{b \cdot \left(c \cdot z\right)}{a}\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. +-commutative 36.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \color{blue}{\left(\frac{b \cdot \left(c \cdot z\right)}{a} + \left(-b \cdot i\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      3. unsub-neg 36.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \color{blue}{\left(\frac{b \cdot \left(c \cdot z\right)}{a} - b \cdot i\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 36.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{\color{blue}{\left(c \cdot z\right) \cdot b}}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      5. *-commutative 36.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{\color{blue}{\left(z \cdot c\right)} \cdot b}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      6. associate-*r* 40.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{\color{blue}{z \cdot \left(c \cdot b\right)}}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      7. *-commutative 40.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{z \cdot \color{blue}{\left(b \cdot c\right)}}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 40.4%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{a \cdot \left(\frac{z \cdot \left(b \cdot c\right)}{a} - b \cdot i\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   6. Taylor expanded in z around inf 83.9%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   7. Step-by-step derivation

      1. *-commutative 83.9%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

   8. Simplified 83.9%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - b \cdot c\right)} \]

   9. Taylor expanded in y around 0 56.9%

      \[\leadsto z \cdot \color{blue}{\left(-1 \cdot \left(b \cdot c\right)\right)} \]
   10. Step-by-step derivation

       1. neg-mul-1 56.9%

          \[\leadsto z \cdot \color{blue}{\left(-b \cdot c\right)} \]

       2. distribute-lft-neg-in 56.9%

          \[\leadsto z \cdot \color{blue}{\left(\left(-b\right) \cdot c\right)} \]

       3. *-commutative 56.9%

          \[\leadsto z \cdot \color{blue}{\left(c \cdot \left(-b\right)\right)} \]

   11. Simplified 56.9%

       \[\leadsto z \cdot \color{blue}{\left(c \cdot \left(-b\right)\right)} \]

   if -1.16e216 < z < 2.39999999999999983e94

   1. Initial program 74.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 74.1%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{a \cdot \left(-1 \cdot \left(b \cdot i\right) + \frac{b \cdot \left(c \cdot z\right)}{a}\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg 74.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\color{blue}{\left(-b \cdot i\right)} + \frac{b \cdot \left(c \cdot z\right)}{a}\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. +-commutative 74.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \color{blue}{\left(\frac{b \cdot \left(c \cdot z\right)}{a} + \left(-b \cdot i\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      3. unsub-neg 74.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \color{blue}{\left(\frac{b \cdot \left(c \cdot z\right)}{a} - b \cdot i\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 74.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{\color{blue}{\left(c \cdot z\right) \cdot b}}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      5. *-commutative 74.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{\color{blue}{\left(z \cdot c\right)} \cdot b}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      6. associate-*r* 73.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{\color{blue}{z \cdot \left(c \cdot b\right)}}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      7. *-commutative 73.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{z \cdot \color{blue}{\left(b \cdot c\right)}}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 73.1%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{a \cdot \left(\frac{z \cdot \left(b \cdot c\right)}{a} - b \cdot i\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   6. Taylor expanded in a around inf 43.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + b \cdot i\right)} \]
   7. Step-by-step derivation

      1. +-commutative 43.0%

         \[\leadsto a \cdot \color{blue}{\left(b \cdot i + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 43.0%

         \[\leadsto a \cdot \left(b \cdot i + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 43.0%

         \[\leadsto a \cdot \color{blue}{\left(b \cdot i - t \cdot x\right)} \]

   8. Simplified 43.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   if 2.39999999999999983e94 < z < 1.16000000000000006e160

   1. Initial program 74.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 64.0%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{a \cdot \left(-1 \cdot \left(b \cdot i\right) + \frac{b \cdot \left(c \cdot z\right)}{a}\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg 64.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\color{blue}{\left(-b \cdot i\right)} + \frac{b \cdot \left(c \cdot z\right)}{a}\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. +-commutative 64.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \color{blue}{\left(\frac{b \cdot \left(c \cdot z\right)}{a} + \left(-b \cdot i\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      3. unsub-neg 64.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \color{blue}{\left(\frac{b \cdot \left(c \cdot z\right)}{a} - b \cdot i\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 64.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{\color{blue}{\left(c \cdot z\right) \cdot b}}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      5. *-commutative 64.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{\color{blue}{\left(z \cdot c\right)} \cdot b}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      6. associate-*r* 64.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{\color{blue}{z \cdot \left(c \cdot b\right)}}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      7. *-commutative 64.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{z \cdot \color{blue}{\left(b \cdot c\right)}}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 64.1%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{a \cdot \left(\frac{z \cdot \left(b \cdot c\right)}{a} - b \cdot i\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   6. Taylor expanded in y around inf 53.9%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   7. Step-by-step derivation

      1. +-commutative 53.9%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 53.9%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 53.9%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 53.9%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   8. Simplified 53.9%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   9. Taylor expanded in z around inf 45.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 54.7%

          \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot z} \]

       2. *-commutative 54.7%

          \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]

   11. Simplified 54.7%

       \[\leadsto \color{blue}{\left(y \cdot x\right) \cdot z} \]

   if 1.16000000000000006e160 < z

   1. Initial program 59.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 59.4%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 63.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 63.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 63.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 63.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 63.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fmm-def 63.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. distribute-rgt-neg-out 63.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. remove-double-neg 63.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. *-commutative 63.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 63.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 63.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 66.5%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 66.5%

         \[\leadsto c \cdot \left(\color{blue}{t \cdot j} - b \cdot z\right) \]

      2. *-commutative 66.5%

         \[\leadsto c \cdot \left(t \cdot j - \color{blue}{z \cdot b}\right) \]

   7. Simplified 66.5%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   8. Taylor expanded in t around 0 66.3%

      \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(b \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 66.3%

         \[\leadsto c \cdot \color{blue}{\left(-b \cdot z\right)} \]

      2. distribute-rgt-neg-in 66.3%

         \[\leadsto c \cdot \color{blue}{\left(b \cdot \left(-z\right)\right)} \]

   10. Simplified 66.3%

       \[\leadsto c \cdot \color{blue}{\left(b \cdot \left(-z\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 47.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{+216}:\\ \;\;\;\;z \cdot \left(-b \cdot c\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+94}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{+160}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 52.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{-15} \lor \neg \left(a \leq 9.5 \cdot 10^{+59}\right):\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -1.6e-15) (not (<= a 9.5e+59)))
   (* a (- (* b i) (* x t)))
   (* c (- (* t j) (* z b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -1.6e-15) || !(a <= 9.5e+59)) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = c * ((t * j) - (z * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((a <= (-1.6d-15)) .or. (.not. (a <= 9.5d+59))) then
        tmp = a * ((b * i) - (x * t))
    else
        tmp = c * ((t * j) - (z * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -1.6e-15) || !(a <= 9.5e+59)) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = c * ((t * j) - (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (a <= -1.6e-15) or not (a <= 9.5e+59):
		tmp = a * ((b * i) - (x * t))
	else:
		tmp = c * ((t * j) - (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -1.6e-15) || !(a <= 9.5e+59))
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	else
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((a <= -1.6e-15) || ~((a <= 9.5e+59)))
		tmp = a * ((b * i) - (x * t));
	else
		tmp = c * ((t * j) - (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -1.6e-15], N[Not[LessEqual[a, 9.5e+59]], $MachinePrecision]], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.6e-15 or 9.50000000000000023e59 < a

   1. Initial program 62.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 67.4%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{a \cdot \left(-1 \cdot \left(b \cdot i\right) + \frac{b \cdot \left(c \cdot z\right)}{a}\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg 67.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\color{blue}{\left(-b \cdot i\right)} + \frac{b \cdot \left(c \cdot z\right)}{a}\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. +-commutative 67.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \color{blue}{\left(\frac{b \cdot \left(c \cdot z\right)}{a} + \left(-b \cdot i\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      3. unsub-neg 67.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \color{blue}{\left(\frac{b \cdot \left(c \cdot z\right)}{a} - b \cdot i\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 67.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{\color{blue}{\left(c \cdot z\right) \cdot b}}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      5. *-commutative 67.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{\color{blue}{\left(z \cdot c\right)} \cdot b}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      6. associate-*r* 67.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{\color{blue}{z \cdot \left(c \cdot b\right)}}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      7. *-commutative 67.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{z \cdot \color{blue}{\left(b \cdot c\right)}}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 67.4%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{a \cdot \left(\frac{z \cdot \left(b \cdot c\right)}{a} - b \cdot i\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   6. Taylor expanded in a around inf 55.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + b \cdot i\right)} \]
   7. Step-by-step derivation

      1. +-commutative 55.5%

         \[\leadsto a \cdot \color{blue}{\left(b \cdot i + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 55.5%

         \[\leadsto a \cdot \left(b \cdot i + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 55.5%

         \[\leadsto a \cdot \color{blue}{\left(b \cdot i - t \cdot x\right)} \]

   8. Simplified 55.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   if -1.6e-15 < a < 9.50000000000000023e59

   1. Initial program 79.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 79.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 81.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 81.5%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 81.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 81.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 81.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fmm-def 81.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. distribute-rgt-neg-out 81.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. remove-double-neg 81.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. *-commutative 81.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 81.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 81.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 48.6%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 48.6%

         \[\leadsto c \cdot \left(\color{blue}{t \cdot j} - b \cdot z\right) \]

      2. *-commutative 48.6%

         \[\leadsto c \cdot \left(t \cdot j - \color{blue}{z \cdot b}\right) \]

   7. Simplified 48.6%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{-15} \lor \neg \left(a \leq 9.5 \cdot 10^{+59}\right):\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 44.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{+44} \lor \neg \left(b \leq 8.5 \cdot 10^{-196}\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -1.3e+44) (not (<= b 8.5e-196)))
   (* b (- (* a i) (* z c)))
   (* a (- (* b i) (* x t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -1.3e+44) || !(b <= 8.5e-196)) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = a * ((b * i) - (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-1.3d+44)) .or. (.not. (b <= 8.5d-196))) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = a * ((b * i) - (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -1.3e+44) || !(b <= 8.5e-196)) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = a * ((b * i) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -1.3e+44) or not (b <= 8.5e-196):
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = a * ((b * i) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -1.3e+44) || !(b <= 8.5e-196))
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -1.3e+44) || ~((b <= 8.5e-196)))
		tmp = b * ((a * i) - (z * c));
	else
		tmp = a * ((b * i) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -1.3e+44], N[Not[LessEqual[b, 8.5e-196]], $MachinePrecision]], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.3e44 or 8.50000000000000004e-196 < b

   1. Initial program 72.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 70.8%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{c \cdot \left(j \cdot t\right)} \]
   4. Step-by-step derivation

      1. *-commutative 70.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + c \cdot \color{blue}{\left(t \cdot j\right)} \]

      2. associate-*r* 68.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{\left(c \cdot t\right) \cdot j} \]

      3. *-commutative 68.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{\left(t \cdot c\right)} \cdot j \]

      4. associate-*r* 71.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{t \cdot \left(c \cdot j\right)} \]

   5. Simplified 71.2%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{t \cdot \left(c \cdot j\right)} \]

   6. Taylor expanded in b around inf 53.7%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]

   if -1.3e44 < b < 8.50000000000000004e-196

   1. Initial program 67.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 73.7%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{a \cdot \left(-1 \cdot \left(b \cdot i\right) + \frac{b \cdot \left(c \cdot z\right)}{a}\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. mul-1-neg 73.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\color{blue}{\left(-b \cdot i\right)} + \frac{b \cdot \left(c \cdot z\right)}{a}\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. +-commutative 73.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \color{blue}{\left(\frac{b \cdot \left(c \cdot z\right)}{a} + \left(-b \cdot i\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      3. unsub-neg 73.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \color{blue}{\left(\frac{b \cdot \left(c \cdot z\right)}{a} - b \cdot i\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 73.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{\color{blue}{\left(c \cdot z\right) \cdot b}}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      5. *-commutative 73.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{\color{blue}{\left(z \cdot c\right)} \cdot b}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      6. associate-*r* 74.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{\color{blue}{z \cdot \left(c \cdot b\right)}}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

      7. *-commutative 74.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - a \cdot \left(\frac{z \cdot \color{blue}{\left(b \cdot c\right)}}{a} - b \cdot i\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 74.7%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{a \cdot \left(\frac{z \cdot \left(b \cdot c\right)}{a} - b \cdot i\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   6. Taylor expanded in a around inf 39.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + b \cdot i\right)} \]
   7. Step-by-step derivation

      1. +-commutative 39.2%

         \[\leadsto a \cdot \color{blue}{\left(b \cdot i + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 39.2%

         \[\leadsto a \cdot \left(b \cdot i + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 39.2%

         \[\leadsto a \cdot \color{blue}{\left(b \cdot i - t \cdot x\right)} \]

   8. Simplified 39.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 48.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{+44} \lor \neg \left(b \leq 8.5 \cdot 10^{-196}\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 29.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -9.2 \cdot 10^{+118} \lor \neg \left(c \leq 10^{+149}\right):\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -9.2e+118) (not (<= c 1e+149))) (* t (* c j)) (* a (* b i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -9.2e+118) || !(c <= 1e+149)) {
		tmp = t * (c * j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((c <= (-9.2d+118)) .or. (.not. (c <= 1d+149))) then
        tmp = t * (c * j)
    else
        tmp = a * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -9.2e+118) || !(c <= 1e+149)) {
		tmp = t * (c * j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -9.2e+118) or not (c <= 1e+149):
		tmp = t * (c * j)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -9.2e+118) || !(c <= 1e+149))
		tmp = Float64(t * Float64(c * j));
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -9.2e+118) || ~((c <= 1e+149)))
		tmp = t * (c * j);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -9.2e+118], N[Not[LessEqual[c, 1e+149]], $MachinePrecision]], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -9.20000000000000063e118 or 1.00000000000000005e149 < c

   1. Initial program 61.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 61.7%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 64.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 64.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 64.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 64.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 64.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fmm-def 64.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. distribute-rgt-neg-out 64.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. remove-double-neg 64.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. *-commutative 64.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 64.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 64.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 75.7%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 75.7%

         \[\leadsto c \cdot \left(\color{blue}{t \cdot j} - b \cdot z\right) \]

      2. *-commutative 75.7%

         \[\leadsto c \cdot \left(t \cdot j - \color{blue}{z \cdot b}\right) \]

   7. Simplified 75.7%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   8. Taylor expanded in t around inf 41.8%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 45.8%

         \[\leadsto \color{blue}{\left(c \cdot j\right) \cdot t} \]

      2. *-commutative 45.8%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j\right)} \]

   10. Simplified 45.8%

       \[\leadsto \color{blue}{t \cdot \left(c \cdot j\right)} \]

   if -9.20000000000000063e118 < c < 1.00000000000000005e149

   1. Initial program 73.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 73.7%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 75.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 75.8%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 75.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 75.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 75.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fmm-def 76.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. distribute-rgt-neg-out 76.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. remove-double-neg 76.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. *-commutative 76.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 76.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 76.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around inf 40.5%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. distribute-lft-out-- 40.5%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. *-commutative 40.5%

         \[\leadsto i \cdot \left(-1 \cdot \left(\color{blue}{y \cdot j} - a \cdot b\right)\right) \]

   7. Simplified 40.5%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j - a \cdot b\right)\right)} \]

   8. Taylor expanded in y around 0 24.3%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 30.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -9.2 \cdot 10^{+118} \lor \neg \left(c \leq 10^{+149}\right):\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 28.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{-72} \lor \neg \left(a \leq 1.65 \cdot 10^{-105}\right):\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -3.7e-72) (not (<= a 1.65e-105))) (* a (* b i)) (* c (* t j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -3.7e-72) || !(a <= 1.65e-105)) {
		tmp = a * (b * i);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((a <= (-3.7d-72)) .or. (.not. (a <= 1.65d-105))) then
        tmp = a * (b * i)
    else
        tmp = c * (t * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -3.7e-72) || !(a <= 1.65e-105)) {
		tmp = a * (b * i);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (a <= -3.7e-72) or not (a <= 1.65e-105):
		tmp = a * (b * i)
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -3.7e-72) || !(a <= 1.65e-105))
		tmp = Float64(a * Float64(b * i));
	else
		tmp = Float64(c * Float64(t * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((a <= -3.7e-72) || ~((a <= 1.65e-105)))
		tmp = a * (b * i);
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -3.7e-72], N[Not[LessEqual[a, 1.65e-105]], $MachinePrecision]], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.6999999999999998e-72 or 1.6499999999999999e-105 < a

   1. Initial program 66.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 66.8%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 69.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 69.2%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 69.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 69.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 69.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fmm-def 70.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. distribute-rgt-neg-out 70.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. remove-double-neg 70.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. *-commutative 70.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 70.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 70.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around inf 45.4%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. distribute-lft-out-- 45.4%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. *-commutative 45.4%

         \[\leadsto i \cdot \left(-1 \cdot \left(\color{blue}{y \cdot j} - a \cdot b\right)\right) \]

   7. Simplified 45.4%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j - a \cdot b\right)\right)} \]

   8. Taylor expanded in y around 0 29.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

   if -3.6999999999999998e-72 < a < 1.6499999999999999e-105

   1. Initial program 77.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 77.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 79.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 79.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 79.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 79.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 79.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fmm-def 79.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. distribute-rgt-neg-out 79.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. remove-double-neg 79.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. *-commutative 79.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 79.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 79.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 52.3%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 52.3%

         \[\leadsto c \cdot \left(\color{blue}{t \cdot j} - b \cdot z\right) \]

      2. *-commutative 52.3%

         \[\leadsto c \cdot \left(t \cdot j - \color{blue}{z \cdot b}\right) \]

   7. Simplified 52.3%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   8. Taylor expanded in t around inf 31.5%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 29.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{-72} \lor \neg \left(a \leq 1.65 \cdot 10^{-105}\right):\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 29.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+89}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq 700:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -6.8e+89)
   (* c (* t j))
   (if (<= t 700.0) (* x (* y z)) (* t (* 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 <= -6.8e+89) {
		tmp = c * (t * j);
	} else if (t <= 700.0) {
		tmp = x * (y * z);
	} else {
		tmp = t * (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 <= (-6.8d+89)) then
        tmp = c * (t * j)
    else if (t <= 700.0d0) then
        tmp = x * (y * z)
    else
        tmp = t * (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 <= -6.8e+89) {
		tmp = c * (t * j);
	} else if (t <= 700.0) {
		tmp = x * (y * z);
	} else {
		tmp = t * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -6.8e+89:
		tmp = c * (t * j)
	elif t <= 700.0:
		tmp = x * (y * z)
	else:
		tmp = t * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -6.8e+89)
		tmp = Float64(c * Float64(t * j));
	elseif (t <= 700.0)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(t * 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 <= -6.8e+89)
		tmp = c * (t * j);
	elseif (t <= 700.0)
		tmp = x * (y * z);
	else
		tmp = t * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -6.8e+89], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 700.0], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.8000000000000004e89

   1. Initial program 46.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 46.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 50.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 50.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 50.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 50.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 50.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fmm-def 54.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. distribute-rgt-neg-out 54.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. remove-double-neg 54.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. *-commutative 54.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 54.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 54.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 43.2%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 43.2%

         \[\leadsto c \cdot \left(\color{blue}{t \cdot j} - b \cdot z\right) \]

      2. *-commutative 43.2%

         \[\leadsto c \cdot \left(t \cdot j - \color{blue}{z \cdot b}\right) \]

   7. Simplified 43.2%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   8. Taylor expanded in t around inf 35.4%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]

   if -6.8000000000000004e89 < t < 700

   1. Initial program 79.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 55.1%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   4. Taylor expanded in z around inf 29.7%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   5. Step-by-step derivation

      1. *-commutative 29.7%

         \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

   6. Simplified 29.7%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y\right)} \]

   if 700 < t

   1. Initial program 67.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 67.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 68.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 68.9%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 68.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 68.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 68.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. fmm-def 68.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. distribute-rgt-neg-out 68.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. remove-double-neg 68.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. *-commutative 68.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      11. *-commutative 68.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 68.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 54.7%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 54.7%

         \[\leadsto c \cdot \left(\color{blue}{t \cdot j} - b \cdot z\right) \]

      2. *-commutative 54.7%

         \[\leadsto c \cdot \left(t \cdot j - \color{blue}{z \cdot b}\right) \]

   7. Simplified 54.7%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   8. Taylor expanded in t around inf 38.6%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 38.9%

         \[\leadsto \color{blue}{\left(c \cdot j\right) \cdot t} \]

      2. *-commutative 38.9%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j\right)} \]

   10. Simplified 38.9%

       \[\leadsto \color{blue}{t \cdot \left(c \cdot j\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 32.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+89}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq 700:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 31: 22.5% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(b \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* b i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (b * i);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = a * (b * i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (b * i);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (b * i)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(b * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (b * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 70.4%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
2. Step-by-step derivation

   1. +-commutative 70.4%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

   2. fma-define 72.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

   3. *-commutative 72.8%

      \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

   4. *-commutative 72.8%

      \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

   5. cancel-sign-sub-inv 72.8%

      \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

   6. cancel-sign-sub 72.8%

      \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

   7. fmm-def 73.5%

      \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

   8. distribute-rgt-neg-out 73.5%

      \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

   9. remove-double-neg 73.5%

      \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

   10. *-commutative 73.5%

       \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

   11. *-commutative 73.5%

       \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

3. Simplified 73.5%

   \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
4. Add Preprocessing

5. Taylor expanded in i around inf 36.8%

   \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
6. Step-by-step derivation

   1. distribute-lft-out-- 36.8%

      \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

   2. *-commutative 36.8%

      \[\leadsto i \cdot \left(-1 \cdot \left(\color{blue}{y \cdot j} - a \cdot b\right)\right) \]

7. Simplified 36.8%

   \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j - a \cdot b\right)\right)} \]

8. Taylor expanded in y around 0 20.5%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
9. Add Preprocessing

Developer Target 1: 67.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ t_2 := x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{if}\;t < -8.120978919195912 \cdot 10^{-33}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < -4.712553818218485 \cdot 10^{-169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t < -7.633533346031584 \cdot 10^{-308}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 1.0535888557455487 \cdot 10^{-139}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
          (/
           (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0)))
           (+ (* c t) (* i y)))))
        (t_2
         (-
          (* x (- (* z y) (* a t)))
          (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))
   (if (< t -8.120978919195912e-33)
     t_2
     (if (< t -4.712553818218485e-169)
       t_1
       (if (< t -7.633533346031584e-308)
         t_2
         (if (< t 1.0535888557455487e-139) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (pow((c * t), 2.0) - pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ** 2.0d0) - ((i * y) ** 2.0d0))) / ((c * t) + (i * y)))
    t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
    if (t < (-8.120978919195912d-33)) then
        tmp = t_2
    else if (t < (-4.712553818218485d-169)) then
        tmp = t_1
    else if (t < (-7.633533346031584d-308)) then
        tmp = t_2
    else if (t < 1.0535888557455487d-139) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (Math.pow((c * t), 2.0) - Math.pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (math.pow((c * t), 2.0) - math.pow((i * y), 2.0))) / ((c * t) + (i * y)))
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
	tmp = 0
	if t < -8.120978919195912e-33:
		tmp = t_2
	elif t < -4.712553818218485e-169:
		tmp = t_1
	elif t < -7.633533346031584e-308:
		tmp = t_2
	elif t < 1.0535888557455487e-139:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(Float64(j * Float64((Float64(c * t) ^ 2.0) - (Float64(i * y) ^ 2.0))) / Float64(Float64(c * t) + Float64(i * y))))
	t_2 = Float64(Float64(x * Float64(Float64(z * y) - Float64(a * t))) - Float64(Float64(b * Float64(Float64(z * c) - Float64(a * i))) - Float64(Float64(Float64(c * t) - Float64(y * i)) * j)))
	tmp = 0.0
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ^ 2.0) - ((i * y) ^ 2.0))) / ((c * t) + (i * y)));
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	tmp = 0.0;
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[Power[N[(c * t), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(i * y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * t), $MachinePrecision] + N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(c * t), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -8.120978919195912e-33], t$95$2, If[Less[t, -4.712553818218485e-169], t$95$1, If[Less[t, -7.633533346031584e-308], t$95$2, If[Less[t, 1.0535888557455487e-139], t$95$1, t$95$2]]]]]]

Reproduce

herbie shell --seed 2024165 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -1015122364899489/125000000000000000000000000000000000000000000000) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -942510763643697/2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2) (pow (* i y) 2))) (+ (* c t) (* i y)))) (if (< t -238547917063487/3125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 10535888557455487/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2) (pow (* i y) 2))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))