Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 74.0% → 83.0%

Time: 21.3s

Alternatives: 23

Speedup: 0.5×

• 58.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 74.0% 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: 83.0% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(b * Float64(Float64(a * i) - Float64(z * c))) - Float64(x * Float64(Float64(t * a) - Float64(y * z)))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(a * Float64(Float64(b * Float64(i / t)) - x)));
	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))) - (x * ((t * a) - (y * z)))) + (j * ((t * c) - (y * i)));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = t * (a * ((b * (i / t)) - x));
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 91.8%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in c around 0 31.5%

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

   4. Taylor expanded in a around -inf 50.8%

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

      1. associate-*r* 50.8%

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

      2. neg-mul-1 50.8%

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

      3. *-commutative 50.8%

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

   6. Simplified 50.8%

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

   7. Taylor expanded in t around 0 39.7%

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

      1. +-commutative 39.7%

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

      2. mul-1-neg 39.7%

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

      3. unsub-neg 39.7%

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

      4. associate-*r* 37.9%

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

      5. *-commutative 37.9%

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

      6. associate-*r* 35.8%

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

      7. *-commutative 35.8%

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

   9. Simplified 35.8%

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

   10. Taylor expanded in t around inf 46.9%

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

       1. associate-/l* 50.5%

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

       2. distribute-lft-out-- 57.9%

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

       3. associate-/l* 58.0%

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

   12. Simplified 58.0%

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

4. Final simplification 84.6%

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

Alternative 2: 66.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.12 \cdot 10^{-50}:\\ \;\;\;\;a \cdot \left(t \cdot \left(b \cdot \frac{i}{t} - x\right)\right)\\ \mathbf{elif}\;a \leq 2900000000:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+183}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -1.12e-50)
   (* a (* t (- (* b (/ i t)) x)))
   (if (<= a 2900000000.0)
     (+ (* j (- (* t c) (* y i))) (* z (- (* x y) (* b c))))
     (if (<= a 6.2e+183)
       (- (* b (- (* a i) (* z c))) (* x (- (* t a) (* y z))))
       (* a (- (* b i) (* x t)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -1.12e-50) {
		tmp = a * (t * ((b * (i / t)) - x));
	} else if (a <= 2900000000.0) {
		tmp = (j * ((t * c) - (y * i))) + (z * ((x * y) - (b * c)));
	} else if (a <= 6.2e+183) {
		tmp = (b * ((a * i) - (z * c))) - (x * ((t * a) - (y * z)));
	} else {
		tmp = a * ((b * i) - (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (a <= (-1.12d-50)) then
        tmp = a * (t * ((b * (i / t)) - x))
    else if (a <= 2900000000.0d0) then
        tmp = (j * ((t * c) - (y * i))) + (z * ((x * y) - (b * c)))
    else if (a <= 6.2d+183) then
        tmp = (b * ((a * i) - (z * c))) - (x * ((t * a) - (y * z)))
    else
        tmp = a * ((b * i) - (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -1.12e-50) {
		tmp = a * (t * ((b * (i / t)) - x));
	} else if (a <= 2900000000.0) {
		tmp = (j * ((t * c) - (y * i))) + (z * ((x * y) - (b * c)));
	} else if (a <= 6.2e+183) {
		tmp = (b * ((a * i) - (z * c))) - (x * ((t * a) - (y * z)));
	} else {
		tmp = a * ((b * i) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -1.12e-50:
		tmp = a * (t * ((b * (i / t)) - x))
	elif a <= 2900000000.0:
		tmp = (j * ((t * c) - (y * i))) + (z * ((x * y) - (b * c)))
	elif a <= 6.2e+183:
		tmp = (b * ((a * i) - (z * c))) - (x * ((t * a) - (y * z)))
	else:
		tmp = a * ((b * i) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -1.12e-50)
		tmp = Float64(a * Float64(t * Float64(Float64(b * Float64(i / t)) - x)));
	elseif (a <= 2900000000.0)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(z * Float64(Float64(x * y) - Float64(b * c))));
	elseif (a <= 6.2e+183)
		tmp = Float64(Float64(b * Float64(Float64(a * i) - Float64(z * c))) - Float64(x * Float64(Float64(t * a) - Float64(y * z))));
	else
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -1.12e-50)
		tmp = a * (t * ((b * (i / t)) - x));
	elseif (a <= 2900000000.0)
		tmp = (j * ((t * c) - (y * i))) + (z * ((x * y) - (b * c)));
	elseif (a <= 6.2e+183)
		tmp = (b * ((a * i) - (z * c))) - (x * ((t * a) - (y * z)));
	else
		tmp = a * ((b * i) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -1.12e-50], N[(a * N[(t * N[(N[(b * N[(i / t), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2900000000.0], 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], If[LessEqual[a, 6.2e+183], N[(N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.12e-50

   1. Initial program 56.6%

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

   3. Taylor expanded in c around 0 59.6%

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

   4. Taylor expanded in a around -inf 65.8%

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

      1. associate-*r* 65.8%

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

      2. neg-mul-1 65.8%

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

      3. *-commutative 65.8%

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

   6. Simplified 65.8%

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

   7. Taylor expanded in t around inf 71.4%

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

      1. mul-1-neg 71.4%

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

      2. unsub-neg 71.4%

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

      3. associate-/l* 68.8%

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

   9. Simplified 68.8%

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

   if -1.12e-50 < a < 2.9e9

   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. Step-by-step derivation

      1. cancel-sign-sub-inv 81.4%

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

      2. cancel-sign-sub 81.4%

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

      3. fmm-def 81.4%

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

      4. distribute-lft-neg-out 81.4%

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

      5. *-commutative 81.4%

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

      6. remove-double-neg 81.4%

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

      7. *-commutative 81.4%

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

      8. *-commutative 81.4%

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

      9. *-commutative 81.4%

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

      10. *-commutative 81.4%

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

   3. Simplified 81.4%

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

   5. Taylor expanded in z around inf 76.4%

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

   if 2.9e9 < a < 6.1999999999999997e183

   1. Initial program 82.4%

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

   3. Taylor expanded in j around 0 76.3%

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

   if 6.1999999999999997e183 < a

   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. Add Preprocessing

   3. Taylor expanded in c around 0 58.6%

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

   4. Taylor expanded in a around -inf 91.8%

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

      1. associate-*r* 91.8%

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

      2. neg-mul-1 91.8%

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

      3. *-commutative 91.8%

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

   6. Simplified 91.8%

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

   7. Taylor expanded in t around 0 71.0%

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

      1. +-commutative 71.0%

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

      2. mul-1-neg 71.0%

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

      3. unsub-neg 71.0%

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

      4. associate-*r* 71.0%

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

      5. *-commutative 71.0%

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

      6. associate-*r* 63.0%

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

      7. *-commutative 63.0%

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

   9. Simplified 63.0%

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

   10. Taylor expanded in b around 0 71.0%

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

       1. distribute-lft-out-- 91.8%

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

   12. Simplified 91.8%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.12 \cdot 10^{-50}:\\ \;\;\;\;a \cdot \left(t \cdot \left(b \cdot \frac{i}{t} - x\right)\right)\\ \mathbf{elif}\;a \leq 2900000000:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+183}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 59.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t \cdot \left(b \cdot \frac{i}{t} - x\right)\right)\\ \mathbf{if}\;a \leq -1.2 \cdot 10^{-50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-255}:\\ \;\;\;\;y \cdot \left(x \cdot z + \left(c \cdot \left(j \cdot \frac{t}{y}\right) - i \cdot j\right)\right)\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+133}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* t (- (* b (/ i t)) x)))))
   (if (<= a -1.2e-50)
     t_1
     (if (<= a -1.2e-255)
       (* y (+ (* x z) (- (* c (* j (/ t y))) (* i j))))
       (if (<= a 1.9e+133)
         (- (* j (- (* t c) (* y i))) (* x (- (* t a) (* y z))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (t * ((b * (i / t)) - x));
	double tmp;
	if (a <= -1.2e-50) {
		tmp = t_1;
	} else if (a <= -1.2e-255) {
		tmp = y * ((x * z) + ((c * (j * (t / y))) - (i * j)));
	} else if (a <= 1.9e+133) {
		tmp = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (t * ((b * (i / t)) - x))
    if (a <= (-1.2d-50)) then
        tmp = t_1
    else if (a <= (-1.2d-255)) then
        tmp = y * ((x * z) + ((c * (j * (t / y))) - (i * j)))
    else if (a <= 1.9d+133) then
        tmp = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (t * ((b * (i / t)) - x));
	double tmp;
	if (a <= -1.2e-50) {
		tmp = t_1;
	} else if (a <= -1.2e-255) {
		tmp = y * ((x * z) + ((c * (j * (t / y))) - (i * j)));
	} else if (a <= 1.9e+133) {
		tmp = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (t * ((b * (i / t)) - x))
	tmp = 0
	if a <= -1.2e-50:
		tmp = t_1
	elif a <= -1.2e-255:
		tmp = y * ((x * z) + ((c * (j * (t / y))) - (i * j)))
	elif a <= 1.9e+133:
		tmp = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(t * Float64(Float64(b * Float64(i / t)) - x)))
	tmp = 0.0
	if (a <= -1.2e-50)
		tmp = t_1;
	elseif (a <= -1.2e-255)
		tmp = Float64(y * Float64(Float64(x * z) + Float64(Float64(c * Float64(j * Float64(t / y))) - Float64(i * j))));
	elseif (a <= 1.9e+133)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) - Float64(x * Float64(Float64(t * a) - Float64(y * z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (t * ((b * (i / t)) - x));
	tmp = 0.0;
	if (a <= -1.2e-50)
		tmp = t_1;
	elseif (a <= -1.2e-255)
		tmp = y * ((x * z) + ((c * (j * (t / y))) - (i * j)));
	elseif (a <= 1.9e+133)
		tmp = (j * ((t * c) - (y * i))) - (x * ((t * a) - (y * z)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(t * N[(N[(b * N[(i / t), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.2e-50], t$95$1, If[LessEqual[a, -1.2e-255], N[(y * N[(N[(x * z), $MachinePrecision] + N[(N[(c * N[(j * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.9e+133], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.20000000000000001e-50 or 1.9000000000000001e133 < a

   1. Initial program 57.1%

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

   3. Taylor expanded in c around 0 60.9%

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

   4. Taylor expanded in a around -inf 70.0%

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

      1. associate-*r* 70.0%

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

      2. neg-mul-1 70.0%

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

      3. *-commutative 70.0%

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

   6. Simplified 70.0%

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

   7. Taylor expanded in t around inf 73.4%

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

      1. mul-1-neg 73.4%

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

      2. unsub-neg 73.4%

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

      3. associate-/l* 72.6%

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

   9. Simplified 72.6%

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

   if -1.20000000000000001e-50 < a < -1.1999999999999999e-255

   1. Initial program 71.0%

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

   3. Taylor expanded in b around 0 51.3%

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

   4. Taylor expanded in y around inf 49.0%

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

      1. associate-*r* 58.5%

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

      2. *-commutative 58.5%

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

   6. Simplified 58.5%

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

   7. Taylor expanded in y around -inf 64.5%

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

      1. mul-1-neg 64.5%

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

      2. distribute-rgt-neg-in 64.5%

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

      3. +-commutative 64.5%

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

      4. mul-1-neg 64.5%

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

      5. unsub-neg 64.5%

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

   9. Simplified 63.5%

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

   if -1.1999999999999999e-255 < a < 1.9000000000000001e133

   1. Initial program 88.1%

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

   3. Taylor expanded in b around 0 72.4%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{-50}:\\ \;\;\;\;a \cdot \left(t \cdot \left(b \cdot \frac{i}{t} - x\right)\right)\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-255}:\\ \;\;\;\;y \cdot \left(x \cdot z + \left(c \cdot \left(j \cdot \frac{t}{y}\right) - i \cdot j\right)\right)\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+133}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(b \cdot \frac{i}{t} - x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 29.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i\right)\\ t_2 := t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{if}\;a \leq -1.3 \cdot 10^{+131}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-295}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-53}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+130}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* a i))) (t_2 (* t (* x (- a)))))
   (if (<= a -1.3e+131)
     t_2
     (if (<= a -1.3e-30)
       t_1
       (if (<= a 5.2e-295)
         (* t (* c j))
         (if (<= a 1.8e-53)
           (* (* i j) (- y))
           (if (<= a 1.9e+130) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (a * i);
	double t_2 = t * (x * -a);
	double tmp;
	if (a <= -1.3e+131) {
		tmp = t_2;
	} else if (a <= -1.3e-30) {
		tmp = t_1;
	} else if (a <= 5.2e-295) {
		tmp = t * (c * j);
	} else if (a <= 1.8e-53) {
		tmp = (i * j) * -y;
	} else if (a <= 1.9e+130) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (a * i)
    t_2 = t * (x * -a)
    if (a <= (-1.3d+131)) then
        tmp = t_2
    else if (a <= (-1.3d-30)) then
        tmp = t_1
    else if (a <= 5.2d-295) then
        tmp = t * (c * j)
    else if (a <= 1.8d-53) then
        tmp = (i * j) * -y
    else if (a <= 1.9d+130) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (a * i);
	double t_2 = t * (x * -a);
	double tmp;
	if (a <= -1.3e+131) {
		tmp = t_2;
	} else if (a <= -1.3e-30) {
		tmp = t_1;
	} else if (a <= 5.2e-295) {
		tmp = t * (c * j);
	} else if (a <= 1.8e-53) {
		tmp = (i * j) * -y;
	} else if (a <= 1.9e+130) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (a * i)
	t_2 = t * (x * -a)
	tmp = 0
	if a <= -1.3e+131:
		tmp = t_2
	elif a <= -1.3e-30:
		tmp = t_1
	elif a <= 5.2e-295:
		tmp = t * (c * j)
	elif a <= 1.8e-53:
		tmp = (i * j) * -y
	elif a <= 1.9e+130:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(a * i))
	t_2 = Float64(t * Float64(x * Float64(-a)))
	tmp = 0.0
	if (a <= -1.3e+131)
		tmp = t_2;
	elseif (a <= -1.3e-30)
		tmp = t_1;
	elseif (a <= 5.2e-295)
		tmp = Float64(t * Float64(c * j));
	elseif (a <= 1.8e-53)
		tmp = Float64(Float64(i * j) * Float64(-y));
	elseif (a <= 1.9e+130)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (a * i);
	t_2 = t * (x * -a);
	tmp = 0.0;
	if (a <= -1.3e+131)
		tmp = t_2;
	elseif (a <= -1.3e-30)
		tmp = t_1;
	elseif (a <= 5.2e-295)
		tmp = t * (c * j);
	elseif (a <= 1.8e-53)
		tmp = (i * j) * -y;
	elseif (a <= 1.9e+130)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.3e+131], t$95$2, If[LessEqual[a, -1.3e-30], t$95$1, If[LessEqual[a, 5.2e-295], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.8e-53], N[(N[(i * j), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[a, 1.9e+130], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.3e131 or 1.7999999999999999e-53 < a < 1.9000000000000001e130

   1. Initial program 68.5%

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

   3. Taylor expanded in c around 0 61.1%

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

   4. Taylor expanded in a around -inf 53.1%

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

      1. associate-*r* 53.1%

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

      2. neg-mul-1 53.1%

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

      3. *-commutative 53.1%

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

   6. Simplified 53.1%

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

   7. Taylor expanded in t around 0 51.9%

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

      1. +-commutative 51.9%

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

      2. mul-1-neg 51.9%

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

      3. unsub-neg 51.9%

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

      4. associate-*r* 49.4%

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

      5. *-commutative 49.4%

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

      6. associate-*r* 48.1%

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

      7. *-commutative 48.1%

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

   9. Simplified 48.1%

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

   10. Taylor expanded in b around 0 39.6%

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

       1. mul-1-neg 39.6%

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

       2. associate-*r* 38.3%

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

       3. *-commutative 38.3%

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

       4. associate-*r* 45.7%

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

       5. distribute-rgt-neg-in 45.7%

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

       6. distribute-rgt-neg-in 45.7%

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

   12. Simplified 45.7%

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

   if -1.3e131 < a < -1.29999999999999993e-30 or 1.9000000000000001e130 < a

   1. Initial program 62.6%

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

      1. +-commutative 62.6%

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

      2. fma-define 65.6%

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

      3. *-commutative 65.6%

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

      4. *-commutative 65.6%

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

      5. cancel-sign-sub-inv 65.6%

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

      6. cancel-sign-sub 65.6%

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

      7. sub-neg 65.6%

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

      8. sub-neg 65.6%

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

      9. *-commutative 65.6%

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

      10. fmm-def 65.6%

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

      11. *-commutative 65.6%

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

      12. distribute-rgt-neg-out 65.6%

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

      13. remove-double-neg 65.6%

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

      14. *-commutative 65.6%

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

      15. *-commutative 65.6%

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

   3. Simplified 65.6%

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

   5. Taylor expanded in i around inf 62.4%

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

      1. distribute-lft-out-- 62.4%

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

      2. *-commutative 62.4%

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

   7. Simplified 62.4%

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

   8. Taylor expanded in y around 0 51.2%

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

      1. *-commutative 51.2%

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

      2. associate-*r* 52.7%

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

      3. *-commutative 52.7%

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

   10. Simplified 52.7%

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

   if -1.29999999999999993e-30 < a < 5.1999999999999997e-295

   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. Step-by-step derivation

      1. +-commutative 74.1%

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

      2. fma-define 75.7%

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

      3. *-commutative 75.7%

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

      4. *-commutative 75.7%

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

      5. cancel-sign-sub-inv 75.7%

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

      6. cancel-sign-sub 75.7%

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

      7. sub-neg 75.7%

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

      8. sub-neg 75.7%

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

      9. *-commutative 75.7%

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

      10. fmm-def 75.7%

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

      11. *-commutative 75.7%

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

      12. distribute-rgt-neg-out 75.7%

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

      13. remove-double-neg 75.7%

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

      14. *-commutative 75.7%

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

      15. *-commutative 75.7%

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

   3. Simplified 75.7%

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

   5. Taylor expanded in c around inf 49.8%

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

      1. *-commutative 49.8%

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

      2. *-commutative 49.8%

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

   7. Simplified 49.8%

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

   8. Taylor expanded in t around inf 29.2%

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

      1. associate-*r* 33.0%

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

      2. *-commutative 33.0%

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

   10. Simplified 33.0%

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

   if 5.1999999999999997e-295 < a < 1.7999999999999999e-53

   1. Initial program 89.9%

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

   3. Taylor expanded in b around 0 74.4%

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

   4. Taylor expanded in y around inf 74.5%

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

      1. associate-*r* 68.4%

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

      2. *-commutative 68.4%

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

   6. Simplified 68.4%

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

   7. Taylor expanded in y around -inf 72.2%

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

      1. mul-1-neg 72.2%

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

      2. distribute-rgt-neg-in 72.2%

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

      3. +-commutative 72.2%

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

      4. mul-1-neg 72.2%

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

      5. unsub-neg 72.2%

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

   9. Simplified 74.0%

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

   10. Taylor expanded in i around inf 40.4%

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

       1. *-commutative 40.4%

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

   12. Simplified 40.4%

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

4. Final simplification 43.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{+131}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-30}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-295}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-53}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+130}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 58.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{-50}:\\ \;\;\;\;a \cdot \left(t \cdot \left(b \cdot \frac{i}{t} - x\right)\right)\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-42}:\\ \;\;\;\;y \cdot \left(x \cdot z + \left(c \cdot \left(j \cdot \frac{t}{y}\right) - i \cdot j\right)\right)\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{+182}:\\ \;\;\;\;a \cdot \left(b \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -1.2e-50)
   (* a (* t (- (* b (/ i t)) x)))
   (if (<= a 2.6e-42)
     (* y (+ (* x z) (- (* c (* j (/ t y))) (* i j))))
     (if (<= a 2.45e+182)
       (- (* a (* b i)) (* x (- (* t a) (* y z))))
       (* a (- (* b i) (* x t)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -1.2e-50) {
		tmp = a * (t * ((b * (i / t)) - x));
	} else if (a <= 2.6e-42) {
		tmp = y * ((x * z) + ((c * (j * (t / y))) - (i * j)));
	} else if (a <= 2.45e+182) {
		tmp = (a * (b * i)) - (x * ((t * a) - (y * z)));
	} else {
		tmp = a * ((b * i) - (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (a <= (-1.2d-50)) then
        tmp = a * (t * ((b * (i / t)) - x))
    else if (a <= 2.6d-42) then
        tmp = y * ((x * z) + ((c * (j * (t / y))) - (i * j)))
    else if (a <= 2.45d+182) then
        tmp = (a * (b * i)) - (x * ((t * a) - (y * z)))
    else
        tmp = a * ((b * i) - (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -1.2e-50) {
		tmp = a * (t * ((b * (i / t)) - x));
	} else if (a <= 2.6e-42) {
		tmp = y * ((x * z) + ((c * (j * (t / y))) - (i * j)));
	} else if (a <= 2.45e+182) {
		tmp = (a * (b * i)) - (x * ((t * a) - (y * z)));
	} else {
		tmp = a * ((b * i) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -1.2e-50:
		tmp = a * (t * ((b * (i / t)) - x))
	elif a <= 2.6e-42:
		tmp = y * ((x * z) + ((c * (j * (t / y))) - (i * j)))
	elif a <= 2.45e+182:
		tmp = (a * (b * i)) - (x * ((t * a) - (y * z)))
	else:
		tmp = a * ((b * i) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -1.2e-50)
		tmp = Float64(a * Float64(t * Float64(Float64(b * Float64(i / t)) - x)));
	elseif (a <= 2.6e-42)
		tmp = Float64(y * Float64(Float64(x * z) + Float64(Float64(c * Float64(j * Float64(t / y))) - Float64(i * j))));
	elseif (a <= 2.45e+182)
		tmp = Float64(Float64(a * Float64(b * i)) - Float64(x * Float64(Float64(t * a) - Float64(y * z))));
	else
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -1.2e-50)
		tmp = a * (t * ((b * (i / t)) - x));
	elseif (a <= 2.6e-42)
		tmp = y * ((x * z) + ((c * (j * (t / y))) - (i * j)));
	elseif (a <= 2.45e+182)
		tmp = (a * (b * i)) - (x * ((t * a) - (y * z)));
	else
		tmp = a * ((b * i) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -1.2e-50], N[(a * N[(t * N[(N[(b * N[(i / t), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.6e-42], N[(y * N[(N[(x * z), $MachinePrecision] + N[(N[(c * N[(j * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.45e+182], N[(N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.20000000000000001e-50

   1. Initial program 56.6%

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

   3. Taylor expanded in c around 0 59.6%

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

   4. Taylor expanded in a around -inf 65.8%

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

      1. associate-*r* 65.8%

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

      2. neg-mul-1 65.8%

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

      3. *-commutative 65.8%

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

   6. Simplified 65.8%

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

   7. Taylor expanded in t around inf 71.4%

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

      1. mul-1-neg 71.4%

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

      2. unsub-neg 71.4%

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

      3. associate-/l* 68.8%

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

   9. Simplified 68.8%

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

   if -1.20000000000000001e-50 < a < 2.6e-42

   1. Initial program 81.9%

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

   3. Taylor expanded in b around 0 64.9%

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

   4. Taylor expanded in y around inf 63.7%

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

      1. associate-*r* 64.6%

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

      2. *-commutative 64.6%

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

   6. Simplified 64.6%

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

   7. Taylor expanded in y around -inf 66.6%

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

      1. mul-1-neg 66.6%

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

      2. distribute-rgt-neg-in 66.6%

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

      3. +-commutative 66.6%

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

      4. mul-1-neg 66.6%

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

      5. unsub-neg 66.6%

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

   9. Simplified 67.9%

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

   if 2.6e-42 < a < 2.45e182

   1. Initial program 81.3%

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

   3. Taylor expanded in c around 0 72.2%

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

   4. Taylor expanded in j around 0 65.2%

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

   if 2.45e182 < a

   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. Add Preprocessing

   3. Taylor expanded in c around 0 58.6%

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

   4. Taylor expanded in a around -inf 91.8%

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

      1. associate-*r* 91.8%

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

      2. neg-mul-1 91.8%

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

      3. *-commutative 91.8%

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

   6. Simplified 91.8%

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

   7. Taylor expanded in t around 0 71.0%

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

      1. +-commutative 71.0%

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

      2. mul-1-neg 71.0%

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

      3. unsub-neg 71.0%

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

      4. associate-*r* 71.0%

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

      5. *-commutative 71.0%

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

      6. associate-*r* 63.0%

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

      7. *-commutative 63.0%

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

   9. Simplified 63.0%

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

   10. Taylor expanded in b around 0 71.0%

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

       1. distribute-lft-out-- 91.8%

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

   12. Simplified 91.8%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{-50}:\\ \;\;\;\;a \cdot \left(t \cdot \left(b \cdot \frac{i}{t} - x\right)\right)\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-42}:\\ \;\;\;\;y \cdot \left(x \cdot z + \left(c \cdot \left(j \cdot \frac{t}{y}\right) - i \cdot j\right)\right)\\ \mathbf{elif}\;a \leq 2.45 \cdot 10^{+182}:\\ \;\;\;\;a \cdot \left(b \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 59.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{-51}:\\ \;\;\;\;a \cdot \left(t \cdot \left(b \cdot \frac{i}{t} - x\right)\right)\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-45}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{+181}:\\ \;\;\;\;a \cdot \left(b \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -5e-51)
   (* a (* t (- (* b (/ i t)) x)))
   (if (<= a 7.5e-45)
     (+ (* j (- (* t c) (* y i))) (* z (* x y)))
     (if (<= a 3.9e+181)
       (- (* a (* b i)) (* x (- (* t a) (* y z))))
       (* a (- (* b i) (* x t)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -5e-51) {
		tmp = a * (t * ((b * (i / t)) - x));
	} else if (a <= 7.5e-45) {
		tmp = (j * ((t * c) - (y * i))) + (z * (x * y));
	} else if (a <= 3.9e+181) {
		tmp = (a * (b * i)) - (x * ((t * a) - (y * z)));
	} else {
		tmp = a * ((b * i) - (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (a <= (-5d-51)) then
        tmp = a * (t * ((b * (i / t)) - x))
    else if (a <= 7.5d-45) then
        tmp = (j * ((t * c) - (y * i))) + (z * (x * y))
    else if (a <= 3.9d+181) then
        tmp = (a * (b * i)) - (x * ((t * a) - (y * z)))
    else
        tmp = a * ((b * i) - (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -5e-51) {
		tmp = a * (t * ((b * (i / t)) - x));
	} else if (a <= 7.5e-45) {
		tmp = (j * ((t * c) - (y * i))) + (z * (x * y));
	} else if (a <= 3.9e+181) {
		tmp = (a * (b * i)) - (x * ((t * a) - (y * z)));
	} else {
		tmp = a * ((b * i) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -5e-51:
		tmp = a * (t * ((b * (i / t)) - x))
	elif a <= 7.5e-45:
		tmp = (j * ((t * c) - (y * i))) + (z * (x * y))
	elif a <= 3.9e+181:
		tmp = (a * (b * i)) - (x * ((t * a) - (y * z)))
	else:
		tmp = a * ((b * i) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -5e-51)
		tmp = Float64(a * Float64(t * Float64(Float64(b * Float64(i / t)) - x)));
	elseif (a <= 7.5e-45)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(z * Float64(x * y)));
	elseif (a <= 3.9e+181)
		tmp = Float64(Float64(a * Float64(b * i)) - Float64(x * Float64(Float64(t * a) - Float64(y * z))));
	else
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -5e-51)
		tmp = a * (t * ((b * (i / t)) - x));
	elseif (a <= 7.5e-45)
		tmp = (j * ((t * c) - (y * i))) + (z * (x * y));
	elseif (a <= 3.9e+181)
		tmp = (a * (b * i)) - (x * ((t * a) - (y * z)));
	else
		tmp = a * ((b * i) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -5e-51], N[(a * N[(t * N[(N[(b * N[(i / t), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.5e-45], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.9e+181], N[(N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -5.00000000000000004e-51

   1. Initial program 56.6%

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

   3. Taylor expanded in c around 0 59.6%

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

   4. Taylor expanded in a around -inf 65.8%

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

      1. associate-*r* 65.8%

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

      2. neg-mul-1 65.8%

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

      3. *-commutative 65.8%

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

   6. Simplified 65.8%

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

   7. Taylor expanded in t around inf 71.4%

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

      1. mul-1-neg 71.4%

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

      2. unsub-neg 71.4%

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

      3. associate-/l* 68.8%

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

   9. Simplified 68.8%

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

   if -5.00000000000000004e-51 < a < 7.5000000000000006e-45

   1. Initial program 81.9%

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

   3. Taylor expanded in b around 0 64.9%

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

   4. Taylor expanded in y around inf 63.7%

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

      1. associate-*r* 64.6%

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

      2. *-commutative 64.6%

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

   6. Simplified 64.6%

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

   if 7.5000000000000006e-45 < a < 3.9e181

   1. Initial program 81.3%

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

   3. Taylor expanded in c around 0 72.2%

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

   4. Taylor expanded in j around 0 65.2%

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

   if 3.9e181 < a

   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. Add Preprocessing

   3. Taylor expanded in c around 0 58.6%

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

   4. Taylor expanded in a around -inf 91.8%

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

      1. associate-*r* 91.8%

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

      2. neg-mul-1 91.8%

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

      3. *-commutative 91.8%

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

   6. Simplified 91.8%

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

   7. Taylor expanded in t around 0 71.0%

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

      1. +-commutative 71.0%

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

      2. mul-1-neg 71.0%

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

      3. unsub-neg 71.0%

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

      4. associate-*r* 71.0%

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

      5. *-commutative 71.0%

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

      6. associate-*r* 63.0%

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

      7. *-commutative 63.0%

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

   9. Simplified 63.0%

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

   10. Taylor expanded in b around 0 71.0%

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

       1. distribute-lft-out-- 91.8%

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

   12. Simplified 91.8%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{-51}:\\ \;\;\;\;a \cdot \left(t \cdot \left(b \cdot \frac{i}{t} - x\right)\right)\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-45}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{+181}:\\ \;\;\;\;a \cdot \left(b \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -2.05 \cdot 10^{-41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-304}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-41}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+129}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))))
   (if (<= a -2.05e-41)
     t_1
     (if (<= a 8e-304)
       (* c (- (* t j) (* z b)))
       (if (<= a 6.5e-41)
         (* j (- (* t c) (* y i)))
         (if (<= a 3.5e+129) (* x (- (* y z) (* t a))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -2.05e-41) {
		tmp = t_1;
	} else if (a <= 8e-304) {
		tmp = c * ((t * j) - (z * b));
	} else if (a <= 6.5e-41) {
		tmp = j * ((t * c) - (y * i));
	} else if (a <= 3.5e+129) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((b * i) - (x * t))
    if (a <= (-2.05d-41)) then
        tmp = t_1
    else if (a <= 8d-304) then
        tmp = c * ((t * j) - (z * b))
    else if (a <= 6.5d-41) then
        tmp = j * ((t * c) - (y * i))
    else if (a <= 3.5d+129) then
        tmp = x * ((y * z) - (t * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -2.05e-41) {
		tmp = t_1;
	} else if (a <= 8e-304) {
		tmp = c * ((t * j) - (z * b));
	} else if (a <= 6.5e-41) {
		tmp = j * ((t * c) - (y * i));
	} else if (a <= 3.5e+129) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -2.05e-41:
		tmp = t_1
	elif a <= 8e-304:
		tmp = c * ((t * j) - (z * b))
	elif a <= 6.5e-41:
		tmp = j * ((t * c) - (y * i))
	elif a <= 3.5e+129:
		tmp = x * ((y * z) - (t * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -2.05e-41)
		tmp = t_1;
	elseif (a <= 8e-304)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (a <= 6.5e-41)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (a <= 3.5e+129)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -2.05e-41)
		tmp = t_1;
	elseif (a <= 8e-304)
		tmp = c * ((t * j) - (z * b));
	elseif (a <= 6.5e-41)
		tmp = j * ((t * c) - (y * i));
	elseif (a <= 3.5e+129)
		tmp = x * ((y * z) - (t * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.05e-41], t$95$1, If[LessEqual[a, 8e-304], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.5e-41], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.5e+129], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.05000000000000007e-41 or 3.4999999999999998e129 < a

   1. Initial program 57.6%

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

   3. Taylor expanded in c around 0 61.5%

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

   4. Taylor expanded in a around -inf 69.7%

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

      1. associate-*r* 69.7%

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

      2. neg-mul-1 69.7%

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

      3. *-commutative 69.7%

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

   6. Simplified 69.7%

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

   7. Taylor expanded in t around 0 64.0%

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

      1. +-commutative 64.0%

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

      2. mul-1-neg 64.0%

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

      3. unsub-neg 64.0%

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

      4. associate-*r* 60.1%

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

      5. *-commutative 60.1%

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

      6. associate-*r* 56.4%

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

      7. *-commutative 56.4%

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

   9. Simplified 56.4%

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

   10. Taylor expanded in b around 0 64.0%

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

       1. distribute-lft-out-- 69.7%

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

   12. Simplified 69.7%

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

   if -2.05000000000000007e-41 < a < 7.99999999999999977e-304

   1. Initial program 73.1%

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

      1. +-commutative 73.1%

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

      2. fma-define 74.9%

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

      3. *-commutative 74.9%

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

      4. *-commutative 74.9%

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

      5. cancel-sign-sub-inv 74.9%

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

      6. cancel-sign-sub 74.9%

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

      7. sub-neg 74.9%

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

      8. sub-neg 74.9%

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

      9. *-commutative 74.9%

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

      10. fmm-def 74.9%

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

      11. *-commutative 74.9%

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

      12. distribute-rgt-neg-out 74.9%

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

      13. remove-double-neg 74.9%

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

      14. *-commutative 74.9%

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

      15. *-commutative 74.9%

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

   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 c around inf 53.1%

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

      1. *-commutative 53.1%

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

      2. *-commutative 53.1%

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

   7. Simplified 53.1%

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

   if 7.99999999999999977e-304 < a < 6.5000000000000004e-41

   1. Initial program 89.2%

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

      1. +-commutative 89.2%

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

      2. fma-define 89.2%

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

      3. *-commutative 89.2%

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

      4. *-commutative 89.2%

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

      5. cancel-sign-sub-inv 89.2%

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

      6. cancel-sign-sub 89.2%

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

      7. sub-neg 89.2%

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

      8. sub-neg 89.2%

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

      9. *-commutative 89.2%

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

      10. fmm-def 89.2%

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

      11. *-commutative 89.2%

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

      12. distribute-rgt-neg-out 89.2%

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

      13. remove-double-neg 89.2%

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

      14. *-commutative 89.2%

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

      15. *-commutative 89.2%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in j around inf 58.3%

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

      1. *-commutative 58.3%

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

      2. *-commutative 58.3%

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

   7. Simplified 58.3%

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

   if 6.5000000000000004e-41 < a < 3.4999999999999998e129

   1. Initial program 87.4%

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

      1. +-commutative 87.4%

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

      2. fma-define 87.4%

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

      3. *-commutative 87.4%

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

      4. *-commutative 87.4%

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

      5. cancel-sign-sub-inv 87.4%

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

      6. cancel-sign-sub 87.4%

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

      7. sub-neg 87.4%

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

      8. sub-neg 87.4%

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

      9. *-commutative 87.4%

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

      10. fmm-def 87.4%

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

      11. *-commutative 87.4%

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

      12. distribute-rgt-neg-out 87.4%

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

      13. remove-double-neg 87.4%

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

      14. *-commutative 87.4%

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

      15. *-commutative 87.4%

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

   3. Simplified 87.4%

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

   5. Taylor expanded in x around inf 85.1%

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

      1. fma-define 85.1%

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

      2. fma-define 85.3%

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

      3. associate-/l* 82.9%

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

      4. *-commutative 82.9%

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

      5. *-commutative 82.9%

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

      6. fmm-def 82.9%

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

      7. associate-/l* 82.9%

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

      8. *-commutative 82.9%

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

   7. Simplified 82.9%

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

   8. Taylor expanded in x around inf 58.1%

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

      1. +-commutative 58.1%

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

      2. neg-mul-1 58.1%

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

      3. sub-neg 58.1%

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

      4. *-commutative 58.1%

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

   10. Simplified 58.1%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.05 \cdot 10^{-41}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-304}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-41}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+129}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;a \leq -1.2 \cdot 10^{-50}:\\ \;\;\;\;a \cdot \left(t \cdot \left(b \cdot \frac{i}{t} - x\right)\right)\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+36}:\\ \;\;\;\;t\_1 + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))))
   (if (<= a -1.2e-50)
     (* a (* t (- (* b (/ i t)) x)))
     (if (<= a 1.85e+36)
       (+ t_1 (* z (- (* x y) (* b c))))
       (+ t_1 (* a (- (* b i) (* x t))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double tmp;
	if (a <= -1.2e-50) {
		tmp = a * (t * ((b * (i / t)) - x));
	} else if (a <= 1.85e+36) {
		tmp = t_1 + (z * ((x * y) - (b * c)));
	} else {
		tmp = t_1 + (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) :: t_1
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    if (a <= (-1.2d-50)) then
        tmp = a * (t * ((b * (i / t)) - x))
    else if (a <= 1.85d+36) then
        tmp = t_1 + (z * ((x * y) - (b * c)))
    else
        tmp = t_1 + (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 t_1 = j * ((t * c) - (y * i));
	double tmp;
	if (a <= -1.2e-50) {
		tmp = a * (t * ((b * (i / t)) - x));
	} else if (a <= 1.85e+36) {
		tmp = t_1 + (z * ((x * y) - (b * c)));
	} else {
		tmp = t_1 + (a * ((b * i) - (x * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	tmp = 0
	if a <= -1.2e-50:
		tmp = a * (t * ((b * (i / t)) - x))
	elif a <= 1.85e+36:
		tmp = t_1 + (z * ((x * y) - (b * c)))
	else:
		tmp = t_1 + (a * ((b * i) - (x * t)))
	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)))
	tmp = 0.0
	if (a <= -1.2e-50)
		tmp = Float64(a * Float64(t * Float64(Float64(b * Float64(i / t)) - x)));
	elseif (a <= 1.85e+36)
		tmp = Float64(t_1 + Float64(z * Float64(Float64(x * y) - Float64(b * c))));
	else
		tmp = Float64(t_1 + Float64(a * Float64(Float64(b * i) - Float64(x * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (a <= -1.2e-50)
		tmp = a * (t * ((b * (i / t)) - x));
	elseif (a <= 1.85e+36)
		tmp = t_1 + (z * ((x * y) - (b * c)));
	else
		tmp = t_1 + (a * ((b * i) - (x * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.2e-50], N[(a * N[(t * N[(N[(b * N[(i / t), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.85e+36], N[(t$95$1 + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.20000000000000001e-50

   1. Initial program 56.6%

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

   3. Taylor expanded in c around 0 59.6%

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

   4. Taylor expanded in a around -inf 65.8%

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

      1. associate-*r* 65.8%

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

      2. neg-mul-1 65.8%

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

      3. *-commutative 65.8%

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

   6. Simplified 65.8%

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

   7. Taylor expanded in t around inf 71.4%

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

      1. mul-1-neg 71.4%

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

      2. unsub-neg 71.4%

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

      3. associate-/l* 68.8%

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

   9. Simplified 68.8%

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

   if -1.20000000000000001e-50 < a < 1.85000000000000014e36

   1. Initial program 82.3%

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

      1. cancel-sign-sub-inv 82.3%

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

      2. cancel-sign-sub 82.3%

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

      3. fmm-def 82.3%

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

      4. distribute-lft-neg-out 82.3%

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

      5. *-commutative 82.3%

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

      6. remove-double-neg 82.3%

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

      7. *-commutative 82.3%

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

      8. *-commutative 82.3%

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

      9. *-commutative 82.3%

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

      10. *-commutative 82.3%

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

   3. Simplified 82.3%

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

   5. Taylor expanded in z around inf 75.9%

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

   if 1.85000000000000014e36 < a

   1. Initial program 70.3%

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

      1. cancel-sign-sub-inv 70.3%

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

      2. cancel-sign-sub 70.3%

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

      3. fmm-def 70.3%

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

      4. distribute-lft-neg-out 70.3%

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

      5. *-commutative 70.3%

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

      6. remove-double-neg 70.3%

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

      7. *-commutative 70.3%

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

      8. *-commutative 70.3%

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

      9. *-commutative 70.3%

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

      10. *-commutative 70.3%

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

   3. Simplified 70.3%

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

   5. Taylor expanded in a around -inf 79.7%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{-50}:\\ \;\;\;\;a \cdot \left(t \cdot \left(b \cdot \frac{i}{t} - x\right)\right)\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+36}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.12 \cdot 10^{-50}:\\ \;\;\;\;a \cdot \left(t \cdot \left(b \cdot \frac{i}{t} - x\right)\right)\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+141}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -1.12e-50)
   (* a (* t (- (* b (/ i t)) x)))
   (if (<= a 2e+141)
     (+ (* j (- (* t c) (* y i))) (* z (- (* x y) (* b 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 (a <= -1.12e-50) {
		tmp = a * (t * ((b * (i / t)) - x));
	} else if (a <= 2e+141) {
		tmp = (j * ((t * c) - (y * i))) + (z * ((x * y) - (b * 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 (a <= (-1.12d-50)) then
        tmp = a * (t * ((b * (i / t)) - x))
    else if (a <= 2d+141) then
        tmp = (j * ((t * c) - (y * i))) + (z * ((x * y) - (b * 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 (a <= -1.12e-50) {
		tmp = a * (t * ((b * (i / t)) - x));
	} else if (a <= 2e+141) {
		tmp = (j * ((t * c) - (y * i))) + (z * ((x * y) - (b * 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 a <= -1.12e-50:
		tmp = a * (t * ((b * (i / t)) - x))
	elif a <= 2e+141:
		tmp = (j * ((t * c) - (y * i))) + (z * ((x * y) - (b * 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 (a <= -1.12e-50)
		tmp = Float64(a * Float64(t * Float64(Float64(b * Float64(i / t)) - x)));
	elseif (a <= 2e+141)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(z * Float64(Float64(x * y) - Float64(b * 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 (a <= -1.12e-50)
		tmp = a * (t * ((b * (i / t)) - x));
	elseif (a <= 2e+141)
		tmp = (j * ((t * c) - (y * i))) + (z * ((x * y) - (b * 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[LessEqual[a, -1.12e-50], N[(a * N[(t * N[(N[(b * N[(i / t), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2e+141], 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], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.12e-50

   1. Initial program 56.6%

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

   3. Taylor expanded in c around 0 59.6%

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

   4. Taylor expanded in a around -inf 65.8%

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

      1. associate-*r* 65.8%

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

      2. neg-mul-1 65.8%

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

      3. *-commutative 65.8%

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

   6. Simplified 65.8%

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

   7. Taylor expanded in t around inf 71.4%

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

      1. mul-1-neg 71.4%

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

      2. unsub-neg 71.4%

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

      3. associate-/l* 68.8%

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

   9. Simplified 68.8%

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

   if -1.12e-50 < a < 2.00000000000000003e141

   1. Initial program 82.4%

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

      1. cancel-sign-sub-inv 82.4%

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

      2. cancel-sign-sub 82.4%

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

      3. fmm-def 82.4%

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

      4. distribute-lft-neg-out 82.4%

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

      5. *-commutative 82.4%

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

      6. remove-double-neg 82.4%

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

      7. *-commutative 82.4%

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

      8. *-commutative 82.4%

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

      9. *-commutative 82.4%

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

      10. *-commutative 82.4%

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

   3. Simplified 82.4%

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

   5. Taylor expanded in z around inf 73.2%

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

   if 2.00000000000000003e141 < a

   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 c around 0 62.9%

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

   4. Taylor expanded in a around -inf 81.1%

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

      1. associate-*r* 81.1%

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

      2. neg-mul-1 81.1%

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

      3. *-commutative 81.1%

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

   6. Simplified 81.1%

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

   7. Taylor expanded in t around 0 66.8%

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

      1. +-commutative 66.8%

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

      2. mul-1-neg 66.8%

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

      3. unsub-neg 66.8%

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

      4. associate-*r* 63.3%

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

      5. *-commutative 63.3%

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

      6. associate-*r* 57.8%

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

      7. *-commutative 57.8%

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

   9. Simplified 57.8%

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

   10. Taylor expanded in b around 0 66.8%

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

       1. distribute-lft-out-- 81.1%

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

   12. Simplified 81.1%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.12 \cdot 10^{-50}:\\ \;\;\;\;a \cdot \left(t \cdot \left(b \cdot \frac{i}{t} - x\right)\right)\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+141}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 29.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -320000000:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{-250}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;i \leq 75000000000000:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;i \leq 2.05 \cdot 10^{+154}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -320000000.0)
   (* b (* a i))
   (if (<= i 4.8e-250)
     (* a (* x (- t)))
     (if (<= i 75000000000000.0)
       (* z (* b (- c)))
       (if (<= i 2.05e+154) (* i (* a b)) (* (* i j) (- y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -320000000.0) {
		tmp = b * (a * i);
	} else if (i <= 4.8e-250) {
		tmp = a * (x * -t);
	} else if (i <= 75000000000000.0) {
		tmp = z * (b * -c);
	} else if (i <= 2.05e+154) {
		tmp = i * (a * b);
	} else {
		tmp = (i * j) * -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (i <= (-320000000.0d0)) then
        tmp = b * (a * i)
    else if (i <= 4.8d-250) then
        tmp = a * (x * -t)
    else if (i <= 75000000000000.0d0) then
        tmp = z * (b * -c)
    else if (i <= 2.05d+154) then
        tmp = i * (a * b)
    else
        tmp = (i * j) * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -320000000.0) {
		tmp = b * (a * i);
	} else if (i <= 4.8e-250) {
		tmp = a * (x * -t);
	} else if (i <= 75000000000000.0) {
		tmp = z * (b * -c);
	} else if (i <= 2.05e+154) {
		tmp = i * (a * b);
	} else {
		tmp = (i * j) * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -320000000.0:
		tmp = b * (a * i)
	elif i <= 4.8e-250:
		tmp = a * (x * -t)
	elif i <= 75000000000000.0:
		tmp = z * (b * -c)
	elif i <= 2.05e+154:
		tmp = i * (a * b)
	else:
		tmp = (i * j) * -y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -320000000.0)
		tmp = Float64(b * Float64(a * i));
	elseif (i <= 4.8e-250)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (i <= 75000000000000.0)
		tmp = Float64(z * Float64(b * Float64(-c)));
	elseif (i <= 2.05e+154)
		tmp = Float64(i * Float64(a * b));
	else
		tmp = Float64(Float64(i * j) * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -320000000.0)
		tmp = b * (a * i);
	elseif (i <= 4.8e-250)
		tmp = a * (x * -t);
	elseif (i <= 75000000000000.0)
		tmp = z * (b * -c);
	elseif (i <= 2.05e+154)
		tmp = i * (a * b);
	else
		tmp = (i * j) * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -320000000.0], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4.8e-250], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 75000000000000.0], N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.05e+154], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(N[(i * j), $MachinePrecision] * (-y)), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -3.2e8

   1. Initial program 69.2%

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

      1. +-commutative 69.2%

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

      2. fma-define 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. sub-neg 69.2%

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

      8. sub-neg 69.2%

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

      9. *-commutative 69.2%

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

      10. fmm-def 69.2%

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

      11. *-commutative 69.2%

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

      12. distribute-rgt-neg-out 69.2%

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

      13. remove-double-neg 69.2%

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

      14. *-commutative 69.2%

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

      15. *-commutative 69.2%

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

   3. Simplified 69.2%

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

   5. Taylor expanded in i around inf 65.6%

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

      1. distribute-lft-out-- 65.6%

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

      2. *-commutative 65.6%

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

   7. Simplified 65.6%

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

   8. Taylor expanded in y around 0 46.0%

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

      1. *-commutative 46.0%

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

      2. associate-*r* 46.2%

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

      3. *-commutative 46.2%

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

   10. Simplified 46.2%

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

   if -3.2e8 < i < 4.7999999999999998e-250

   1. Initial program 82.0%

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

   3. Taylor expanded in c around 0 48.5%

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

   4. Taylor expanded in a around -inf 39.5%

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

      1. associate-*r* 39.5%

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

      2. neg-mul-1 39.5%

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

      3. *-commutative 39.5%

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

   6. Simplified 39.5%

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

   7. Taylor expanded in t around inf 35.3%

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

      1. associate-*r* 35.3%

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

      2. mul-1-neg 35.3%

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

   9. Simplified 35.3%

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

   if 4.7999999999999998e-250 < i < 7.5e13

   1. Initial program 72.9%

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

      1. +-commutative 72.9%

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

      2. fma-define 74.5%

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

      3. *-commutative 74.5%

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

      4. *-commutative 74.5%

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

      5. cancel-sign-sub-inv 74.5%

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

      6. cancel-sign-sub 74.5%

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

      7. sub-neg 74.5%

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

      8. sub-neg 74.5%

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

      9. *-commutative 74.5%

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

      10. fmm-def 74.5%

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

      11. *-commutative 74.5%

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

      12. distribute-rgt-neg-out 74.5%

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

      13. remove-double-neg 74.5%

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

      14. *-commutative 74.5%

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

      15. *-commutative 74.5%

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

   3. Simplified 74.5%

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

   5. Taylor expanded in c around inf 46.9%

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

      1. *-commutative 46.9%

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

      2. *-commutative 46.9%

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

   7. Simplified 46.9%

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

   8. Taylor expanded in t around 0 35.9%

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

      1. associate-*r* 35.9%

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

      2. neg-mul-1 35.9%

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

      3. *-commutative 35.9%

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

   10. Simplified 35.9%

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

   11. Taylor expanded in b around 0 35.9%

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

       1. mul-1-neg 35.9%

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

       2. associate-*r* 41.6%

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

       3. distribute-lft-neg-in 41.6%

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

   13. Simplified 41.6%

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

   if 7.5e13 < i < 2.05e154

   1. Initial program 63.5%

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

      1. +-commutative 63.5%

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

      2. fma-define 63.5%

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

      3. *-commutative 63.5%

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

      4. *-commutative 63.5%

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

      5. cancel-sign-sub-inv 63.5%

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

      6. cancel-sign-sub 63.5%

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

      7. sub-neg 63.5%

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

      8. sub-neg 63.5%

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

      9. *-commutative 63.5%

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

      10. fmm-def 63.5%

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

      11. *-commutative 63.5%

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

      12. distribute-rgt-neg-out 63.5%

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

      13. remove-double-neg 63.5%

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

      14. *-commutative 63.5%

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

      15. *-commutative 63.5%

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

   3. Simplified 63.5%

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

   5. Taylor expanded in i around inf 57.8%

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

      1. distribute-lft-out-- 57.8%

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

      2. *-commutative 57.8%

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

   7. Simplified 57.8%

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

   8. Taylor expanded in y around 0 39.5%

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

   if 2.05e154 < i

   1. Initial program 63.8%

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

   3. Taylor expanded in b around 0 60.1%

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

   4. Taylor expanded in y around inf 57.5%

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

      1. associate-*r* 54.7%

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

      2. *-commutative 54.7%

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

   6. Simplified 54.7%

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

   7. Taylor expanded in y around -inf 62.9%

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

      1. mul-1-neg 62.9%

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

      2. distribute-rgt-neg-in 62.9%

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

      3. +-commutative 62.9%

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

      4. mul-1-neg 62.9%

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

      5. unsub-neg 62.9%

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

   9. Simplified 62.9%

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

   10. Taylor expanded in i around inf 55.1%

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

       1. *-commutative 55.1%

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

   12. Simplified 55.1%

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

4. Final simplification 42.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -320000000:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{-250}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;i \leq 75000000000000:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;i \leq 2.05 \cdot 10^{+154}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 29.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i\right)\\ t_2 := t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{if}\;a \leq -7.5 \cdot 10^{+132}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-35}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+132}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* a i))) (t_2 (* t (* x (- a)))))
   (if (<= a -7.5e+132)
     t_2
     (if (<= a -6e-36)
       t_1
       (if (<= a 9.2e-35) (* t (* c j)) (if (<= a 1.6e+132) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (a * i);
	double t_2 = t * (x * -a);
	double tmp;
	if (a <= -7.5e+132) {
		tmp = t_2;
	} else if (a <= -6e-36) {
		tmp = t_1;
	} else if (a <= 9.2e-35) {
		tmp = t * (c * j);
	} else if (a <= 1.6e+132) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (a * i)
    t_2 = t * (x * -a)
    if (a <= (-7.5d+132)) then
        tmp = t_2
    else if (a <= (-6d-36)) then
        tmp = t_1
    else if (a <= 9.2d-35) then
        tmp = t * (c * j)
    else if (a <= 1.6d+132) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (a * i);
	double t_2 = t * (x * -a);
	double tmp;
	if (a <= -7.5e+132) {
		tmp = t_2;
	} else if (a <= -6e-36) {
		tmp = t_1;
	} else if (a <= 9.2e-35) {
		tmp = t * (c * j);
	} else if (a <= 1.6e+132) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (a * i)
	t_2 = t * (x * -a)
	tmp = 0
	if a <= -7.5e+132:
		tmp = t_2
	elif a <= -6e-36:
		tmp = t_1
	elif a <= 9.2e-35:
		tmp = t * (c * j)
	elif a <= 1.6e+132:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(a * i))
	t_2 = Float64(t * Float64(x * Float64(-a)))
	tmp = 0.0
	if (a <= -7.5e+132)
		tmp = t_2;
	elseif (a <= -6e-36)
		tmp = t_1;
	elseif (a <= 9.2e-35)
		tmp = Float64(t * Float64(c * j));
	elseif (a <= 1.6e+132)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (a * i);
	t_2 = t * (x * -a);
	tmp = 0.0;
	if (a <= -7.5e+132)
		tmp = t_2;
	elseif (a <= -6e-36)
		tmp = t_1;
	elseif (a <= 9.2e-35)
		tmp = t * (c * j);
	elseif (a <= 1.6e+132)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.5e+132], t$95$2, If[LessEqual[a, -6e-36], t$95$1, If[LessEqual[a, 9.2e-35], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.6e+132], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.50000000000000017e132 or 9.1999999999999996e-35 < a < 1.5999999999999999e132

   1. Initial program 68.5%

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

   3. Taylor expanded in c around 0 62.0%

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

   4. Taylor expanded in a around -inf 55.1%

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

      1. associate-*r* 55.1%

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

      2. neg-mul-1 55.1%

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

      3. *-commutative 55.1%

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

   6. Simplified 55.1%

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

   7. Taylor expanded in t around 0 53.8%

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

      1. +-commutative 53.8%

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

      2. mul-1-neg 53.8%

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

      3. unsub-neg 53.8%

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

      4. associate-*r* 51.2%

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

      5. *-commutative 51.2%

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

      6. associate-*r* 49.8%

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

      7. *-commutative 49.8%

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

   9. Simplified 49.8%

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

   10. Taylor expanded in b around 0 41.0%

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

       1. mul-1-neg 41.0%

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

       2. associate-*r* 39.6%

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

       3. *-commutative 39.6%

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

       4. associate-*r* 47.3%

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

       5. distribute-rgt-neg-in 47.3%

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

       6. distribute-rgt-neg-in 47.3%

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

   12. Simplified 47.3%

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

   if -7.50000000000000017e132 < a < -6.0000000000000003e-36 or 1.5999999999999999e132 < a

   1. Initial program 62.6%

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

      1. +-commutative 62.6%

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

      2. fma-define 65.6%

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

      3. *-commutative 65.6%

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

      4. *-commutative 65.6%

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

      5. cancel-sign-sub-inv 65.6%

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

      6. cancel-sign-sub 65.6%

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

      7. sub-neg 65.6%

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

      8. sub-neg 65.6%

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

      9. *-commutative 65.6%

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

      10. fmm-def 65.6%

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

      11. *-commutative 65.6%

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

      12. distribute-rgt-neg-out 65.6%

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

      13. remove-double-neg 65.6%

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

      14. *-commutative 65.6%

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

      15. *-commutative 65.6%

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

   3. Simplified 65.6%

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

   5. Taylor expanded in i around inf 62.4%

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

      1. distribute-lft-out-- 62.4%

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

      2. *-commutative 62.4%

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

   7. Simplified 62.4%

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

   8. Taylor expanded in y around 0 51.2%

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

      1. *-commutative 51.2%

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

      2. associate-*r* 52.7%

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

      3. *-commutative 52.7%

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

   10. Simplified 52.7%

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

   if -6.0000000000000003e-36 < a < 9.1999999999999996e-35

   1. Initial program 80.8%

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

      1. +-commutative 80.8%

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

      2. fma-define 81.7%

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

      3. *-commutative 81.7%

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

      4. *-commutative 81.7%

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

      5. cancel-sign-sub-inv 81.7%

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

      6. cancel-sign-sub 81.7%

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

      7. sub-neg 81.7%

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

      8. sub-neg 81.7%

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

      9. *-commutative 81.7%

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

      10. fmm-def 81.7%

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

      11. *-commutative 81.7%

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

      12. distribute-rgt-neg-out 81.7%

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

      13. remove-double-neg 81.7%

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

      14. *-commutative 81.7%

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

      15. *-commutative 81.7%

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

   3. Simplified 81.7%

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

   5. Taylor expanded in c around inf 46.2%

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

      1. *-commutative 46.2%

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

      2. *-commutative 46.2%

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

   7. Simplified 46.2%

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

   8. Taylor expanded in t around inf 29.1%

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

      1. associate-*r* 31.1%

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

      2. *-commutative 31.1%

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

   10. Simplified 31.1%

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

4. Final simplification 41.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{+132}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-36}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-35}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+132}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 57.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{-50} \lor \neg \left(a \leq 2.8 \cdot 10^{+49}\right):\\ \;\;\;\;a \cdot \left(t \cdot \left(b \cdot \frac{i}{t} - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -1.2e-50) (not (<= a 2.8e+49)))
   (* a (* t (- (* b (/ i t)) x)))
   (+ (* j (- (* t c) (* y i))) (* z (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -1.2e-50) || !(a <= 2.8e+49)) {
		tmp = a * (t * ((b * (i / t)) - x));
	} else {
		tmp = (j * ((t * c) - (y * i))) + (z * (x * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((a <= (-1.2d-50)) .or. (.not. (a <= 2.8d+49))) then
        tmp = a * (t * ((b * (i / t)) - x))
    else
        tmp = (j * ((t * c) - (y * i))) + (z * (x * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -1.2e-50) || !(a <= 2.8e+49)) {
		tmp = a * (t * ((b * (i / t)) - x));
	} else {
		tmp = (j * ((t * c) - (y * i))) + (z * (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (a <= -1.2e-50) or not (a <= 2.8e+49):
		tmp = a * (t * ((b * (i / t)) - x))
	else:
		tmp = (j * ((t * c) - (y * i))) + (z * (x * y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -1.2e-50) || !(a <= 2.8e+49))
		tmp = Float64(a * Float64(t * Float64(Float64(b * Float64(i / t)) - x)));
	else
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(z * Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((a <= -1.2e-50) || ~((a <= 2.8e+49)))
		tmp = a * (t * ((b * (i / t)) - x));
	else
		tmp = (j * ((t * c) - (y * i))) + (z * (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -1.2e-50], N[Not[LessEqual[a, 2.8e+49]], $MachinePrecision]], N[(a * N[(t * N[(N[(b * N[(i / t), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.20000000000000001e-50 or 2.7999999999999998e49 < a

   1. Initial program 61.5%

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

   3. Taylor expanded in c around 0 63.1%

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

   4. Taylor expanded in a around -inf 67.9%

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

      1. associate-*r* 67.9%

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

      2. neg-mul-1 67.9%

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

      3. *-commutative 67.9%

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

   6. Simplified 67.9%

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

   7. Taylor expanded in t around inf 70.7%

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

      1. mul-1-neg 70.7%

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

      2. unsub-neg 70.7%

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

      3. associate-/l* 70.0%

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

   9. Simplified 70.0%

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

   if -1.20000000000000001e-50 < a < 2.7999999999999998e49

   1. Initial program 83.1%

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

   3. Taylor expanded in b around 0 66.0%

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

   4. Taylor expanded in y around inf 62.1%

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

      1. associate-*r* 62.1%

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

      2. *-commutative 62.1%

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

   6. Simplified 62.1%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{-50} \lor \neg \left(a \leq 2.8 \cdot 10^{+49}\right):\\ \;\;\;\;a \cdot \left(t \cdot \left(b \cdot \frac{i}{t} - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 53.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{-14}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(z - i \cdot \frac{j}{x}\right)\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-92}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 3600000000000:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -5.4e-14)
   (* (* x y) (- z (* i (/ j x))))
   (if (<= y -1.4e-92)
     (* c (- (* t j) (* z b)))
     (if (<= y 3600000000000.0)
       (* a (- (* b i) (* x t)))
       (* y (- (* x z) (* i j)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -5.4e-14) {
		tmp = (x * y) * (z - (i * (j / x)));
	} else if (y <= -1.4e-92) {
		tmp = c * ((t * j) - (z * b));
	} else if (y <= 3600000000000.0) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = y * ((x * z) - (i * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-5.4d-14)) then
        tmp = (x * y) * (z - (i * (j / x)))
    else if (y <= (-1.4d-92)) then
        tmp = c * ((t * j) - (z * b))
    else if (y <= 3600000000000.0d0) then
        tmp = a * ((b * i) - (x * t))
    else
        tmp = y * ((x * z) - (i * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -5.4e-14) {
		tmp = (x * y) * (z - (i * (j / x)));
	} else if (y <= -1.4e-92) {
		tmp = c * ((t * j) - (z * b));
	} else if (y <= 3600000000000.0) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = y * ((x * z) - (i * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -5.4e-14:
		tmp = (x * y) * (z - (i * (j / x)))
	elif y <= -1.4e-92:
		tmp = c * ((t * j) - (z * b))
	elif y <= 3600000000000.0:
		tmp = a * ((b * i) - (x * t))
	else:
		tmp = y * ((x * z) - (i * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -5.4e-14)
		tmp = Float64(Float64(x * y) * Float64(z - Float64(i * Float64(j / x))));
	elseif (y <= -1.4e-92)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (y <= 3600000000000.0)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	else
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -5.4e-14)
		tmp = (x * y) * (z - (i * (j / x)));
	elseif (y <= -1.4e-92)
		tmp = c * ((t * j) - (z * b));
	elseif (y <= 3600000000000.0)
		tmp = a * ((b * i) - (x * t));
	else
		tmp = y * ((x * z) - (i * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -5.4e-14], N[(N[(x * y), $MachinePrecision] * N[(z - N[(i * N[(j / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.4e-92], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3600000000000.0], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.3999999999999997e-14

   1. Initial program 70.1%

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

      1. +-commutative 70.1%

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

      2. fma-define 71.8%

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

      3. *-commutative 71.8%

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

      4. *-commutative 71.8%

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

      5. cancel-sign-sub-inv 71.8%

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

      6. cancel-sign-sub 71.8%

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

      7. sub-neg 71.8%

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

      8. sub-neg 71.8%

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

      9. *-commutative 71.8%

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

      10. fmm-def 71.8%

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

      11. *-commutative 71.8%

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

      12. distribute-rgt-neg-out 71.8%

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

      13. remove-double-neg 71.8%

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

      14. *-commutative 71.8%

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

      15. *-commutative 71.8%

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

   3. Simplified 71.8%

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

   5. Taylor expanded in x around inf 65.0%

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

      1. fma-define 65.0%

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

      2. fma-define 70.0%

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

      3. associate-/l* 66.8%

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

      4. *-commutative 66.8%

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

      5. *-commutative 66.8%

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

      6. fmm-def 66.8%

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

      7. associate-/l* 63.6%

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

      8. *-commutative 63.6%

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

   7. Simplified 63.6%

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

   8. Taylor expanded in y around inf 74.1%

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

      1. associate-*r* 75.6%

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

      2. *-commutative 75.6%

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

      3. mul-1-neg 75.6%

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

      4. unsub-neg 75.6%

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

      5. associate-/l* 75.6%

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

   10. Simplified 75.6%

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

   if -5.3999999999999997e-14 < y < -1.4e-92

   1. Initial program 82.4%

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

      1. +-commutative 82.4%

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

      2. fma-define 82.4%

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

      3. *-commutative 82.4%

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

      4. *-commutative 82.4%

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

      5. cancel-sign-sub-inv 82.4%

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

      6. cancel-sign-sub 82.4%

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

      7. sub-neg 82.4%

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

      8. sub-neg 82.4%

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

      9. *-commutative 82.4%

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

      10. fmm-def 82.4%

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

      11. *-commutative 82.4%

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

      12. distribute-rgt-neg-out 82.4%

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

      13. remove-double-neg 82.4%

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

      14. *-commutative 82.4%

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

      15. *-commutative 82.4%

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

   3. Simplified 82.4%

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

   5. Taylor expanded in 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%

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

   if -1.4e-92 < y < 3.6e12

   1. Initial program 77.1%

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

   3. Taylor expanded in c around 0 59.0%

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

   4. Taylor expanded in a around -inf 58.2%

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

      1. associate-*r* 58.2%

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

      2. neg-mul-1 58.2%

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

      3. *-commutative 58.2%

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

   6. Simplified 58.2%

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

   7. Taylor expanded in t around 0 53.9%

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

      1. +-commutative 53.9%

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

      2. mul-1-neg 53.9%

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

      3. unsub-neg 53.9%

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

      4. associate-*r* 52.3%

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

      5. *-commutative 52.3%

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

      6. associate-*r* 49.9%

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

      7. *-commutative 49.9%

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

   9. Simplified 49.9%

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

   10. Taylor expanded in b around 0 53.9%

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

       1. distribute-lft-out-- 58.2%

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

   12. Simplified 58.2%

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

   if 3.6e12 < y

   1. Initial program 60.8%

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

      1. +-commutative 60.8%

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

      2. fma-define 60.8%

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

      3. *-commutative 60.8%

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

      4. *-commutative 60.8%

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

      5. cancel-sign-sub-inv 60.8%

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

      6. cancel-sign-sub 60.8%

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

      7. sub-neg 60.8%

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

      8. sub-neg 60.8%

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

      9. *-commutative 60.8%

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

      10. fmm-def 62.6%

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

      11. *-commutative 62.6%

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

      12. distribute-rgt-neg-out 62.6%

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

      13. remove-double-neg 62.6%

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

      14. *-commutative 62.6%

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

      15. *-commutative 62.6%

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

   3. Simplified 62.6%

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

   5. Taylor expanded in y around inf 63.5%

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

      1. +-commutative 63.5%

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

      2. mul-1-neg 63.5%

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

      3. unsub-neg 63.5%

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

   7. Simplified 63.5%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{-14}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(z - i \cdot \frac{j}{x}\right)\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-92}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 3600000000000:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 53.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-92}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 72000000000000:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j)))))
   (if (<= y -6.5e-14)
     t_1
     (if (<= y -1.45e-92)
       (* c (- (* t j) (* z b)))
       (if (<= y 72000000000000.0) (* a (- (* b i) (* x t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -6.5e-14) {
		tmp = t_1;
	} else if (y <= -1.45e-92) {
		tmp = c * ((t * j) - (z * b));
	} else if (y <= 72000000000000.0) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((x * z) - (i * j))
    if (y <= (-6.5d-14)) then
        tmp = t_1
    else if (y <= (-1.45d-92)) then
        tmp = c * ((t * j) - (z * b))
    else if (y <= 72000000000000.0d0) then
        tmp = a * ((b * i) - (x * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -6.5e-14) {
		tmp = t_1;
	} else if (y <= -1.45e-92) {
		tmp = c * ((t * j) - (z * b));
	} else if (y <= 72000000000000.0) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -6.5e-14:
		tmp = t_1
	elif y <= -1.45e-92:
		tmp = c * ((t * j) - (z * b))
	elif y <= 72000000000000.0:
		tmp = a * ((b * i) - (x * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -6.5e-14)
		tmp = t_1;
	elseif (y <= -1.45e-92)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (y <= 72000000000000.0)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -6.5e-14)
		tmp = t_1;
	elseif (y <= -1.45e-92)
		tmp = c * ((t * j) - (z * b));
	elseif (y <= 72000000000000.0)
		tmp = a * ((b * i) - (x * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.5e-14], t$95$1, If[LessEqual[y, -1.45e-92], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 72000000000000.0], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.5000000000000001e-14 or 7.2e13 < y

   1. Initial program 65.6%

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

      1. +-commutative 65.6%

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

      2. fma-define 66.5%

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

      3. *-commutative 66.5%

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

      4. *-commutative 66.5%

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

      5. cancel-sign-sub-inv 66.5%

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

      6. cancel-sign-sub 66.5%

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

      7. sub-neg 66.5%

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

      8. sub-neg 66.5%

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

      9. *-commutative 66.5%

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

      10. fmm-def 67.3%

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

      11. *-commutative 67.3%

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

      12. distribute-rgt-neg-out 67.3%

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

      13. remove-double-neg 67.3%

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

      14. *-commutative 67.3%

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

      15. *-commutative 67.3%

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

   3. Simplified 67.3%

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

   5. Taylor expanded in y around inf 67.3%

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

      1. +-commutative 67.3%

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

      2. mul-1-neg 67.3%

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

      3. unsub-neg 67.3%

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

   7. Simplified 67.3%

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

   if -6.5000000000000001e-14 < y < -1.44999999999999992e-92

   1. Initial program 82.4%

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

      1. +-commutative 82.4%

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

      2. fma-define 82.4%

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

      3. *-commutative 82.4%

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

      4. *-commutative 82.4%

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

      5. cancel-sign-sub-inv 82.4%

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

      6. cancel-sign-sub 82.4%

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

      7. sub-neg 82.4%

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

      8. sub-neg 82.4%

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

      9. *-commutative 82.4%

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

      10. fmm-def 82.4%

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

      11. *-commutative 82.4%

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

      12. distribute-rgt-neg-out 82.4%

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

      13. remove-double-neg 82.4%

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

      14. *-commutative 82.4%

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

      15. *-commutative 82.4%

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

   3. Simplified 82.4%

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

   5. Taylor expanded in 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%

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

   if -1.44999999999999992e-92 < y < 7.2e13

   1. Initial program 77.1%

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

   3. Taylor expanded in c around 0 59.0%

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

   4. Taylor expanded in a around -inf 58.2%

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

      1. associate-*r* 58.2%

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

      2. neg-mul-1 58.2%

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

      3. *-commutative 58.2%

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

   6. Simplified 58.2%

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

   7. Taylor expanded in t around 0 53.9%

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

      1. +-commutative 53.9%

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

      2. mul-1-neg 53.9%

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

      3. unsub-neg 53.9%

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

      4. associate-*r* 52.3%

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

      5. *-commutative 52.3%

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

      6. associate-*r* 49.9%

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

      7. *-commutative 49.9%

         \[\leadsto \left(b \cdot a\right) \cdot i - \color{blue}{\left(t \cdot a\right)} \cdot x \]

   9. Simplified 49.9%

      \[\leadsto \color{blue}{\left(b \cdot a\right) \cdot i - \left(t \cdot a\right) \cdot x} \]

   10. Taylor expanded in b around 0 53.9%

       \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right) - a \cdot \left(t \cdot x\right)} \]
   11. Step-by-step derivation

       1. distribute-lft-out-- 58.2%

          \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   12. Simplified 58.2%

       \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-14}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-92}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 72000000000000:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 51.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -2.3 \cdot 10^{-40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-304}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-39}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))))
   (if (<= a -2.3e-40)
     t_1
     (if (<= a 5.4e-304)
       (* c (- (* t j) (* z b)))
       (if (<= a 9e-39) (* 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 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -2.3e-40) {
		tmp = t_1;
	} else if (a <= 5.4e-304) {
		tmp = c * ((t * j) - (z * b));
	} else if (a <= 9e-39) {
		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 = a * ((b * i) - (x * t))
    if (a <= (-2.3d-40)) then
        tmp = t_1
    else if (a <= 5.4d-304) then
        tmp = c * ((t * j) - (z * b))
    else if (a <= 9d-39) 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 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -2.3e-40) {
		tmp = t_1;
	} else if (a <= 5.4e-304) {
		tmp = c * ((t * j) - (z * b));
	} else if (a <= 9e-39) {
		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 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -2.3e-40:
		tmp = t_1
	elif a <= 5.4e-304:
		tmp = c * ((t * j) - (z * b))
	elif a <= 9e-39:
		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(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -2.3e-40)
		tmp = t_1;
	elseif (a <= 5.4e-304)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (a <= 9e-39)
		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 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -2.3e-40)
		tmp = t_1;
	elseif (a <= 5.4e-304)
		tmp = c * ((t * j) - (z * b));
	elseif (a <= 9e-39)
		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[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.3e-40], t$95$1, If[LessEqual[a, 5.4e-304], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9e-39], 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 a < -2.3e-40 or 9.0000000000000002e-39 < a

   1. Initial program 65.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0 64.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) - -1 \cdot \left(a \cdot \left(b \cdot i\right)\right)} \]

   4. Taylor expanded in a around -inf 63.8%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 63.8%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x - b \cdot i\right)} \]

      2. neg-mul-1 63.8%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(t \cdot x - b \cdot i\right) \]

      3. *-commutative 63.8%

         \[\leadsto \left(-a\right) \cdot \left(t \cdot x - \color{blue}{i \cdot b}\right) \]

   6. Simplified 63.8%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(t \cdot x - i \cdot b\right)} \]

   7. Taylor expanded in t around 0 59.7%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(b \cdot i\right)} \]
   8. Step-by-step derivation

      1. +-commutative 59.7%

         \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 59.7%

         \[\leadsto a \cdot \left(b \cdot i\right) + \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} \]

      3. unsub-neg 59.7%

         \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right) - a \cdot \left(t \cdot x\right)} \]

      4. associate-*r* 56.8%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot i} - a \cdot \left(t \cdot x\right) \]

      5. *-commutative 56.8%

         \[\leadsto \color{blue}{\left(b \cdot a\right)} \cdot i - a \cdot \left(t \cdot x\right) \]

      6. associate-*r* 54.1%

         \[\leadsto \left(b \cdot a\right) \cdot i - \color{blue}{\left(a \cdot t\right) \cdot x} \]

      7. *-commutative 54.1%

         \[\leadsto \left(b \cdot a\right) \cdot i - \color{blue}{\left(t \cdot a\right)} \cdot x \]

   9. Simplified 54.1%

      \[\leadsto \color{blue}{\left(b \cdot a\right) \cdot i - \left(t \cdot a\right) \cdot x} \]

   10. Taylor expanded in b around 0 59.7%

       \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right) - a \cdot \left(t \cdot x\right)} \]
   11. Step-by-step derivation

       1. distribute-lft-out-- 63.8%

          \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   12. Simplified 63.8%

       \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   if -2.3e-40 < a < 5.40000000000000021e-304

   1. Initial program 73.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 73.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 74.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 74.9%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 74.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 74.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 74.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 74.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 74.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 74.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fmm-def 74.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 74.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 74.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 74.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 74.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      15. *-commutative 74.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   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 c around inf 53.1%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 53.1%

         \[\leadsto c \cdot \left(\color{blue}{t \cdot j} - b \cdot z\right) \]

      2. *-commutative 53.1%

         \[\leadsto c \cdot \left(t \cdot j - \color{blue}{z \cdot b}\right) \]

   7. Simplified 53.1%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   if 5.40000000000000021e-304 < a < 9.0000000000000002e-39

   1. Initial program 89.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 89.4%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 89.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 89.4%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 89.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 89.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 89.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 89.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 89.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 89.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fmm-def 89.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 89.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 89.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 89.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 89.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      15. *-commutative 89.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 89.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in j around inf 57.4%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]
   6. Step-by-step derivation

      1. *-commutative 57.4%

         \[\leadsto j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      2. *-commutative 57.4%

         \[\leadsto j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   7. Simplified 57.4%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot c - y \cdot i\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{-40}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-304}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-39}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 29.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i\right)\\ \mathbf{if}\;a \leq -5.6 \cdot 10^{-34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-51}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{+60}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* a i))))
   (if (<= a -5.6e-34)
     t_1
     (if (<= a 1.8e-51)
       (* t (* c j))
       (if (<= a 7.8e+60) (* c (* z (- b))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (a * i);
	double tmp;
	if (a <= -5.6e-34) {
		tmp = t_1;
	} else if (a <= 1.8e-51) {
		tmp = t * (c * j);
	} else if (a <= 7.8e+60) {
		tmp = c * (z * -b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a * i)
    if (a <= (-5.6d-34)) then
        tmp = t_1
    else if (a <= 1.8d-51) then
        tmp = t * (c * j)
    else if (a <= 7.8d+60) then
        tmp = c * (z * -b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (a * i);
	double tmp;
	if (a <= -5.6e-34) {
		tmp = t_1;
	} else if (a <= 1.8e-51) {
		tmp = t * (c * j);
	} else if (a <= 7.8e+60) {
		tmp = c * (z * -b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (a * i)
	tmp = 0
	if a <= -5.6e-34:
		tmp = t_1
	elif a <= 1.8e-51:
		tmp = t * (c * j)
	elif a <= 7.8e+60:
		tmp = c * (z * -b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(a * i))
	tmp = 0.0
	if (a <= -5.6e-34)
		tmp = t_1;
	elseif (a <= 1.8e-51)
		tmp = Float64(t * Float64(c * j));
	elseif (a <= 7.8e+60)
		tmp = Float64(c * Float64(z * Float64(-b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (a * i);
	tmp = 0.0;
	if (a <= -5.6e-34)
		tmp = t_1;
	elseif (a <= 1.8e-51)
		tmp = t * (c * j);
	elseif (a <= 7.8e+60)
		tmp = c * (z * -b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.6e-34], t$95$1, If[LessEqual[a, 1.8e-51], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.8e+60], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.59999999999999994e-34 or 7.8000000000000006e60 < a

   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. Step-by-step derivation

      1. +-commutative 61.9%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 63.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 63.5%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 63.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 63.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 63.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 63.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 63.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 63.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fmm-def 64.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 64.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 64.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 64.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 64.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      15. *-commutative 64.3%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 64.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around inf 51.3%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. distribute-lft-out-- 51.3%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. *-commutative 51.3%

         \[\leadsto i \cdot \left(-1 \cdot \left(\color{blue}{y \cdot j} - a \cdot b\right)\right) \]

   7. Simplified 51.3%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j - a \cdot b\right)\right)} \]

   8. Taylor expanded in y around 0 40.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   9. Step-by-step derivation

      1. *-commutative 40.0%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b\right)} \]

      2. associate-*r* 42.4%

         \[\leadsto \color{blue}{\left(a \cdot i\right) \cdot b} \]

      3. *-commutative 42.4%

         \[\leadsto \color{blue}{\left(i \cdot a\right)} \cdot b \]

   10. Simplified 42.4%

       \[\leadsto \color{blue}{\left(i \cdot a\right) \cdot b} \]

   if -5.59999999999999994e-34 < a < 1.8e-51

   1. Initial program 81.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 81.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 82.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 82.2%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 82.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 82.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 82.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 82.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 82.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 82.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fmm-def 82.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 82.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 82.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 82.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 82.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      15. *-commutative 82.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 82.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 45.2%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 45.2%

         \[\leadsto c \cdot \left(\color{blue}{t \cdot j} - b \cdot z\right) \]

      2. *-commutative 45.2%

         \[\leadsto c \cdot \left(t \cdot j - \color{blue}{z \cdot b}\right) \]

   7. Simplified 45.2%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   8. Taylor expanded in t around inf 29.5%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 31.6%

         \[\leadsto \color{blue}{\left(c \cdot j\right) \cdot t} \]

      2. *-commutative 31.6%

         \[\leadsto \color{blue}{\left(j \cdot c\right)} \cdot t \]

   10. Simplified 31.6%

       \[\leadsto \color{blue}{\left(j \cdot c\right) \cdot t} \]

   if 1.8e-51 < a < 7.8000000000000006e60

   1. Initial program 86.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 86.4%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 86.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 86.4%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 86.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 86.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 86.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 86.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 86.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 86.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fmm-def 86.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 86.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 86.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 86.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 86.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      15. *-commutative 86.4%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 86.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 38.0%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 38.0%

         \[\leadsto c \cdot \left(\color{blue}{t \cdot j} - b \cdot z\right) \]

      2. *-commutative 38.0%

         \[\leadsto c \cdot \left(t \cdot j - \color{blue}{z \cdot b}\right) \]

   7. Simplified 38.0%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   8. Taylor expanded in t around 0 37.7%

      \[\leadsto c \cdot \color{blue}{\left(-1 \cdot \left(b \cdot z\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 37.7%

         \[\leadsto c \cdot \color{blue}{\left(-b \cdot z\right)} \]

      2. *-commutative 37.7%

         \[\leadsto c \cdot \left(-\color{blue}{z \cdot b}\right) \]

      3. distribute-rgt-neg-in 37.7%

         \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(-b\right)\right)} \]

   10. Simplified 37.7%

       \[\leadsto c \cdot \color{blue}{\left(z \cdot \left(-b\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 37.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{-34}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-51}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{+60}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 28.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i\right)\\ \mathbf{if}\;a \leq -4.6 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-98}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{+131}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* a i))))
   (if (<= a -4.6e-28)
     t_1
     (if (<= a 4.5e-98)
       (* t (* c j))
       (if (<= a 4.4e+131) (* x (* y z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (a * i);
	double tmp;
	if (a <= -4.6e-28) {
		tmp = t_1;
	} else if (a <= 4.5e-98) {
		tmp = t * (c * j);
	} else if (a <= 4.4e+131) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a * i)
    if (a <= (-4.6d-28)) then
        tmp = t_1
    else if (a <= 4.5d-98) then
        tmp = t * (c * j)
    else if (a <= 4.4d+131) then
        tmp = x * (y * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (a * i);
	double tmp;
	if (a <= -4.6e-28) {
		tmp = t_1;
	} else if (a <= 4.5e-98) {
		tmp = t * (c * j);
	} else if (a <= 4.4e+131) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (a * i)
	tmp = 0
	if a <= -4.6e-28:
		tmp = t_1
	elif a <= 4.5e-98:
		tmp = t * (c * j)
	elif a <= 4.4e+131:
		tmp = x * (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(a * i))
	tmp = 0.0
	if (a <= -4.6e-28)
		tmp = t_1;
	elseif (a <= 4.5e-98)
		tmp = Float64(t * Float64(c * j));
	elseif (a <= 4.4e+131)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (a * i);
	tmp = 0.0;
	if (a <= -4.6e-28)
		tmp = t_1;
	elseif (a <= 4.5e-98)
		tmp = t * (c * j);
	elseif (a <= 4.4e+131)
		tmp = x * (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.6e-28], t$95$1, If[LessEqual[a, 4.5e-98], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.4e+131], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.59999999999999971e-28 or 4.3999999999999998e131 < a

   1. Initial program 57.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 57.8%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 59.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 59.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 59.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 59.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 59.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 59.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 59.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 59.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fmm-def 60.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 60.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 60.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 60.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 60.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      15. *-commutative 60.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 60.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around inf 54.1%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. distribute-lft-out-- 54.1%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. *-commutative 54.1%

         \[\leadsto i \cdot \left(-1 \cdot \left(\color{blue}{y \cdot j} - a \cdot b\right)\right) \]

   7. Simplified 54.1%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j - a \cdot b\right)\right)} \]

   8. Taylor expanded in y around 0 43.1%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   9. Step-by-step derivation

      1. *-commutative 43.1%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b\right)} \]

      2. associate-*r* 45.9%

         \[\leadsto \color{blue}{\left(a \cdot i\right) \cdot b} \]

      3. *-commutative 45.9%

         \[\leadsto \color{blue}{\left(i \cdot a\right)} \cdot b \]

   10. Simplified 45.9%

       \[\leadsto \color{blue}{\left(i \cdot a\right) \cdot b} \]

   if -4.59999999999999971e-28 < a < 4.49999999999999997e-98

   1. Initial program 80.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 80.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 81.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 81.2%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 81.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 81.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 81.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 81.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 81.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 81.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fmm-def 81.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 81.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 81.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 81.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 81.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      15. *-commutative 81.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 81.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 47.0%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 47.0%

         \[\leadsto c \cdot \left(\color{blue}{t \cdot j} - b \cdot z\right) \]

      2. *-commutative 47.0%

         \[\leadsto c \cdot \left(t \cdot j - \color{blue}{z \cdot b}\right) \]

   7. Simplified 47.0%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   8. Taylor expanded in t around inf 28.6%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 31.0%

         \[\leadsto \color{blue}{\left(c \cdot j\right) \cdot t} \]

      2. *-commutative 31.0%

         \[\leadsto \color{blue}{\left(j \cdot c\right)} \cdot t \]

   10. Simplified 31.0%

       \[\leadsto \color{blue}{\left(j \cdot c\right) \cdot t} \]

   if 4.49999999999999997e-98 < a < 4.3999999999999998e131

   1. Initial program 86.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 74.1%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   4. Taylor expanded in y around inf 57.6%

      \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \color{blue}{x \cdot \left(y \cdot z\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 57.8%

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \color{blue}{\left(x \cdot y\right) \cdot z} \]

      2. *-commutative 57.8%

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \color{blue}{\left(y \cdot x\right)} \cdot z \]

   6. Simplified 57.8%

      \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \color{blue}{\left(y \cdot x\right) \cdot z} \]

   7. Taylor expanded in y around -inf 52.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + \left(-1 \cdot \frac{c \cdot \left(j \cdot t\right)}{y} + i \cdot j\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 52.0%

         \[\leadsto \color{blue}{-y \cdot \left(-1 \cdot \left(x \cdot z\right) + \left(-1 \cdot \frac{c \cdot \left(j \cdot t\right)}{y} + i \cdot j\right)\right)} \]

      2. distribute-rgt-neg-in 52.0%

         \[\leadsto \color{blue}{y \cdot \left(-\left(-1 \cdot \left(x \cdot z\right) + \left(-1 \cdot \frac{c \cdot \left(j \cdot t\right)}{y} + i \cdot j\right)\right)\right)} \]

      3. +-commutative 52.0%

         \[\leadsto y \cdot \left(-\color{blue}{\left(\left(-1 \cdot \frac{c \cdot \left(j \cdot t\right)}{y} + i \cdot j\right) + -1 \cdot \left(x \cdot z\right)\right)}\right) \]

      4. mul-1-neg 52.0%

         \[\leadsto y \cdot \left(-\left(\left(-1 \cdot \frac{c \cdot \left(j \cdot t\right)}{y} + i \cdot j\right) + \color{blue}{\left(-x \cdot z\right)}\right)\right) \]

      5. unsub-neg 52.0%

         \[\leadsto y \cdot \left(-\color{blue}{\left(\left(-1 \cdot \frac{c \cdot \left(j \cdot t\right)}{y} + i \cdot j\right) - x \cdot z\right)}\right) \]

   9. Simplified 55.7%

      \[\leadsto \color{blue}{y \cdot \left(-\left(\left(i \cdot j - c \cdot \left(j \cdot \frac{t}{y}\right)\right) - z \cdot x\right)\right)} \]

   10. Taylor expanded in j around 0 32.3%

       \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 37.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.6 \cdot 10^{-28}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-98}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{+131}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 28.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i\right)\\ \mathbf{if}\;a \leq -1.9 \cdot 10^{-29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-98}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+130}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* a i))))
   (if (<= a -1.9e-29)
     t_1
     (if (<= a 2.2e-98)
       (* c (* t j))
       (if (<= a 3.8e+130) (* x (* y z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (a * i);
	double tmp;
	if (a <= -1.9e-29) {
		tmp = t_1;
	} else if (a <= 2.2e-98) {
		tmp = c * (t * j);
	} else if (a <= 3.8e+130) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a * i)
    if (a <= (-1.9d-29)) then
        tmp = t_1
    else if (a <= 2.2d-98) then
        tmp = c * (t * j)
    else if (a <= 3.8d+130) then
        tmp = x * (y * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (a * i);
	double tmp;
	if (a <= -1.9e-29) {
		tmp = t_1;
	} else if (a <= 2.2e-98) {
		tmp = c * (t * j);
	} else if (a <= 3.8e+130) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (a * i)
	tmp = 0
	if a <= -1.9e-29:
		tmp = t_1
	elif a <= 2.2e-98:
		tmp = c * (t * j)
	elif a <= 3.8e+130:
		tmp = x * (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(a * i))
	tmp = 0.0
	if (a <= -1.9e-29)
		tmp = t_1;
	elseif (a <= 2.2e-98)
		tmp = Float64(c * Float64(t * j));
	elseif (a <= 3.8e+130)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (a * i);
	tmp = 0.0;
	if (a <= -1.9e-29)
		tmp = t_1;
	elseif (a <= 2.2e-98)
		tmp = c * (t * j);
	elseif (a <= 3.8e+130)
		tmp = x * (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.9e-29], t$95$1, If[LessEqual[a, 2.2e-98], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.8e+130], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.89999999999999988e-29 or 3.8000000000000002e130 < a

   1. Initial program 57.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 57.8%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 59.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 59.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 59.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 59.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 59.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 59.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 59.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 59.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fmm-def 60.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 60.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 60.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 60.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 60.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      15. *-commutative 60.7%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 60.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around inf 54.1%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. distribute-lft-out-- 54.1%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. *-commutative 54.1%

         \[\leadsto i \cdot \left(-1 \cdot \left(\color{blue}{y \cdot j} - a \cdot b\right)\right) \]

   7. Simplified 54.1%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j - a \cdot b\right)\right)} \]

   8. Taylor expanded in y around 0 43.1%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   9. Step-by-step derivation

      1. *-commutative 43.1%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b\right)} \]

      2. associate-*r* 45.9%

         \[\leadsto \color{blue}{\left(a \cdot i\right) \cdot b} \]

      3. *-commutative 45.9%

         \[\leadsto \color{blue}{\left(i \cdot a\right)} \cdot b \]

   10. Simplified 45.9%

       \[\leadsto \color{blue}{\left(i \cdot a\right) \cdot b} \]

   if -1.89999999999999988e-29 < a < 2.19999999999999996e-98

   1. Initial program 80.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 80.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 81.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 81.2%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 81.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 81.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 81.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 81.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 81.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 81.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fmm-def 81.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 81.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 81.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 81.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 81.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      15. *-commutative 81.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 81.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 47.0%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 47.0%

         \[\leadsto c \cdot \left(\color{blue}{t \cdot j} - b \cdot z\right) \]

      2. *-commutative 47.0%

         \[\leadsto c \cdot \left(t \cdot j - \color{blue}{z \cdot b}\right) \]

   7. Simplified 47.0%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   8. Taylor expanded in t around inf 28.6%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]

   if 2.19999999999999996e-98 < a < 3.8000000000000002e130

   1. Initial program 86.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 74.1%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   4. Taylor expanded in y around inf 57.6%

      \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \color{blue}{x \cdot \left(y \cdot z\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 57.8%

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \color{blue}{\left(x \cdot y\right) \cdot z} \]

      2. *-commutative 57.8%

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \color{blue}{\left(y \cdot x\right)} \cdot z \]

   6. Simplified 57.8%

      \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \color{blue}{\left(y \cdot x\right) \cdot z} \]

   7. Taylor expanded in y around -inf 52.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + \left(-1 \cdot \frac{c \cdot \left(j \cdot t\right)}{y} + i \cdot j\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 52.0%

         \[\leadsto \color{blue}{-y \cdot \left(-1 \cdot \left(x \cdot z\right) + \left(-1 \cdot \frac{c \cdot \left(j \cdot t\right)}{y} + i \cdot j\right)\right)} \]

      2. distribute-rgt-neg-in 52.0%

         \[\leadsto \color{blue}{y \cdot \left(-\left(-1 \cdot \left(x \cdot z\right) + \left(-1 \cdot \frac{c \cdot \left(j \cdot t\right)}{y} + i \cdot j\right)\right)\right)} \]

      3. +-commutative 52.0%

         \[\leadsto y \cdot \left(-\color{blue}{\left(\left(-1 \cdot \frac{c \cdot \left(j \cdot t\right)}{y} + i \cdot j\right) + -1 \cdot \left(x \cdot z\right)\right)}\right) \]

      4. mul-1-neg 52.0%

         \[\leadsto y \cdot \left(-\left(\left(-1 \cdot \frac{c \cdot \left(j \cdot t\right)}{y} + i \cdot j\right) + \color{blue}{\left(-x \cdot z\right)}\right)\right) \]

      5. unsub-neg 52.0%

         \[\leadsto y \cdot \left(-\color{blue}{\left(\left(-1 \cdot \frac{c \cdot \left(j \cdot t\right)}{y} + i \cdot j\right) - x \cdot z\right)}\right) \]

   9. Simplified 55.7%

      \[\leadsto \color{blue}{y \cdot \left(-\left(\left(i \cdot j - c \cdot \left(j \cdot \frac{t}{y}\right)\right) - z \cdot x\right)\right)} \]

   10. Taylor expanded in j around 0 32.3%

       \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 36.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{-29}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-98}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+130}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 51.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.05 \cdot 10^{-42} \lor \neg \left(a \leq 2.65 \cdot 10^{+39}\right):\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -2.05e-42) (not (<= a 2.65e+39)))
   (* 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 <= -2.05e-42) || !(a <= 2.65e+39)) {
		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 <= (-2.05d-42)) .or. (.not. (a <= 2.65d+39))) 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 <= -2.05e-42) || !(a <= 2.65e+39)) {
		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 <= -2.05e-42) or not (a <= 2.65e+39):
		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 <= -2.05e-42) || !(a <= 2.65e+39))
		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 <= -2.05e-42) || ~((a <= 2.65e+39)))
		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, -2.05e-42], N[Not[LessEqual[a, 2.65e+39]], $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 < -2.0500000000000001e-42 or 2.64999999999999989e39 < a

   1. Initial program 63.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0 64.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) - -1 \cdot \left(a \cdot \left(b \cdot i\right)\right)} \]

   4. Taylor expanded in a around -inf 66.6%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 66.6%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x - b \cdot i\right)} \]

      2. neg-mul-1 66.6%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(t \cdot x - b \cdot i\right) \]

      3. *-commutative 66.6%

         \[\leadsto \left(-a\right) \cdot \left(t \cdot x - \color{blue}{i \cdot b}\right) \]

   6. Simplified 66.6%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(t \cdot x - i \cdot b\right)} \]

   7. Taylor expanded in t around 0 62.0%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(b \cdot i\right)} \]
   8. Step-by-step derivation

      1. +-commutative 62.0%

         \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 62.0%

         \[\leadsto a \cdot \left(b \cdot i\right) + \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} \]

      3. unsub-neg 62.0%

         \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right) - a \cdot \left(t \cdot x\right)} \]

      4. associate-*r* 58.9%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot i} - a \cdot \left(t \cdot x\right) \]

      5. *-commutative 58.9%

         \[\leadsto \color{blue}{\left(b \cdot a\right)} \cdot i - a \cdot \left(t \cdot x\right) \]

      6. associate-*r* 55.9%

         \[\leadsto \left(b \cdot a\right) \cdot i - \color{blue}{\left(a \cdot t\right) \cdot x} \]

      7. *-commutative 55.9%

         \[\leadsto \left(b \cdot a\right) \cdot i - \color{blue}{\left(t \cdot a\right)} \cdot x \]

   9. Simplified 55.9%

      \[\leadsto \color{blue}{\left(b \cdot a\right) \cdot i - \left(t \cdot a\right) \cdot x} \]

   10. Taylor expanded in b around 0 62.0%

       \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right) - a \cdot \left(t \cdot x\right)} \]
   11. Step-by-step derivation

       1. distribute-lft-out-- 66.6%

          \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   12. Simplified 66.6%

       \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   if -2.0500000000000001e-42 < a < 2.64999999999999989e39

   1. Initial program 81.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 81.8%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 82.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 82.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 82.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 82.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 82.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 82.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 82.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 82.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fmm-def 82.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 82.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 82.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 82.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 82.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      15. *-commutative 82.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 82.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 46.6%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 46.6%

         \[\leadsto c \cdot \left(\color{blue}{t \cdot j} - b \cdot z\right) \]

      2. *-commutative 46.6%

         \[\leadsto c \cdot \left(t \cdot j - \color{blue}{z \cdot b}\right) \]

   7. Simplified 46.6%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.05 \cdot 10^{-42} \lor \neg \left(a \leq 2.65 \cdot 10^{+39}\right):\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 42.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -9.5 \cdot 10^{+172}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq 1.12 \cdot 10^{+141}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -9.5e+172)
   (* t (* c j))
   (if (<= j 1.12e+141) (* a (- (* b i) (* x t))) (* i (* y (- j))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -9.5e+172) {
		tmp = t * (c * j);
	} else if (j <= 1.12e+141) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = i * (y * -j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (j <= (-9.5d+172)) then
        tmp = t * (c * j)
    else if (j <= 1.12d+141) then
        tmp = a * ((b * i) - (x * t))
    else
        tmp = i * (y * -j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -9.5e+172) {
		tmp = t * (c * j);
	} else if (j <= 1.12e+141) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = i * (y * -j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -9.5e+172:
		tmp = t * (c * j)
	elif j <= 1.12e+141:
		tmp = a * ((b * i) - (x * t))
	else:
		tmp = i * (y * -j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -9.5e+172)
		tmp = Float64(t * Float64(c * j));
	elseif (j <= 1.12e+141)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	else
		tmp = Float64(i * Float64(y * Float64(-j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -9.5e+172)
		tmp = t * (c * j);
	elseif (j <= 1.12e+141)
		tmp = a * ((b * i) - (x * t));
	else
		tmp = i * (y * -j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -9.5e+172], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.12e+141], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -9.50000000000000027e172

   1. Initial program 64.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 64.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 75.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 75.0%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 75.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 75.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 75.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 75.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 75.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 75.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fmm-def 75.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 75.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 75.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 75.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 75.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      15. *-commutative 75.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 75.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in 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 40.6%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 47.0%

         \[\leadsto \color{blue}{\left(c \cdot j\right) \cdot t} \]

      2. *-commutative 47.0%

         \[\leadsto \color{blue}{\left(j \cdot c\right)} \cdot t \]

   10. Simplified 47.0%

       \[\leadsto \color{blue}{\left(j \cdot c\right) \cdot t} \]

   if -9.50000000000000027e172 < j < 1.11999999999999993e141

   1. Initial program 75.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0 63.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) - -1 \cdot \left(a \cdot \left(b \cdot i\right)\right)} \]

   4. Taylor expanded in a around -inf 50.2%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 50.2%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x - b \cdot i\right)} \]

      2. neg-mul-1 50.2%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(t \cdot x - b \cdot i\right) \]

      3. *-commutative 50.2%

         \[\leadsto \left(-a\right) \cdot \left(t \cdot x - \color{blue}{i \cdot b}\right) \]

   6. Simplified 50.2%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(t \cdot x - i \cdot b\right)} \]

   7. Taylor expanded in t around 0 47.1%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(b \cdot i\right)} \]
   8. Step-by-step derivation

      1. +-commutative 47.1%

         \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 47.1%

         \[\leadsto a \cdot \left(b \cdot i\right) + \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} \]

      3. unsub-neg 47.1%

         \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right) - a \cdot \left(t \cdot x\right)} \]

      4. associate-*r* 44.5%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot i} - a \cdot \left(t \cdot x\right) \]

      5. *-commutative 44.5%

         \[\leadsto \color{blue}{\left(b \cdot a\right)} \cdot i - a \cdot \left(t \cdot x\right) \]

      6. associate-*r* 42.1%

         \[\leadsto \left(b \cdot a\right) \cdot i - \color{blue}{\left(a \cdot t\right) \cdot x} \]

      7. *-commutative 42.1%

         \[\leadsto \left(b \cdot a\right) \cdot i - \color{blue}{\left(t \cdot a\right)} \cdot x \]

   9. Simplified 42.1%

      \[\leadsto \color{blue}{\left(b \cdot a\right) \cdot i - \left(t \cdot a\right) \cdot x} \]

   10. Taylor expanded in b around 0 47.1%

       \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right) - a \cdot \left(t \cdot x\right)} \]
   11. Step-by-step derivation

       1. distribute-lft-out-- 50.2%

          \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   12. Simplified 50.2%

       \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   if 1.11999999999999993e141 < j

   1. Initial program 60.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 60.5%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 60.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 60.5%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 60.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 60.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 60.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 60.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 60.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 60.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fmm-def 60.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 60.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 60.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 60.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 60.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      15. *-commutative 60.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 60.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around inf 54.5%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. distribute-lft-out-- 54.5%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. *-commutative 54.5%

         \[\leadsto i \cdot \left(-1 \cdot \left(\color{blue}{y \cdot j} - a \cdot b\right)\right) \]

   7. Simplified 54.5%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j - a \cdot b\right)\right)} \]

   8. Taylor expanded in y around inf 54.3%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 54.3%

         \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(j \cdot y\right)} \]

      2. *-commutative 54.3%

         \[\leadsto \left(-1 \cdot i\right) \cdot \color{blue}{\left(y \cdot j\right)} \]

      3. mul-1-neg 54.3%

         \[\leadsto \color{blue}{\left(-i\right)} \cdot \left(y \cdot j\right) \]

   10. Simplified 54.3%

       \[\leadsto \color{blue}{\left(-i\right) \cdot \left(y \cdot j\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 50.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -9.5 \cdot 10^{+172}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq 1.12 \cdot 10^{+141}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 28.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+219} \lor \neg \left(z \leq 2.5 \cdot 10^{+45}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= z -3.4e+219) (not (<= z 2.5e+45))) (* x (* y z)) (* a (* b i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((z <= -3.4e+219) || !(z <= 2.5e+45)) {
		tmp = x * (y * z);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((z <= (-3.4d+219)) .or. (.not. (z <= 2.5d+45))) then
        tmp = x * (y * z)
    else
        tmp = a * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((z <= -3.4e+219) || !(z <= 2.5e+45)) {
		tmp = x * (y * z);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (z <= -3.4e+219) or not (z <= 2.5e+45):
		tmp = x * (y * z)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((z <= -3.4e+219) || !(z <= 2.5e+45))
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((z <= -3.4e+219) || ~((z <= 2.5e+45)))
		tmp = x * (y * z);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[z, -3.4e+219], N[Not[LessEqual[z, 2.5e+45]], $MachinePrecision]], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.40000000000000016e219 or 2.5e45 < z

   1. Initial program 64.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 57.4%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   4. Taylor expanded in y around inf 54.6%

      \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \color{blue}{x \cdot \left(y \cdot z\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 59.3%

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \color{blue}{\left(x \cdot y\right) \cdot z} \]

      2. *-commutative 59.3%

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \color{blue}{\left(y \cdot x\right)} \cdot z \]

   6. Simplified 59.3%

      \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \color{blue}{\left(y \cdot x\right) \cdot z} \]

   7. Taylor expanded in y around -inf 58.5%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + \left(-1 \cdot \frac{c \cdot \left(j \cdot t\right)}{y} + i \cdot j\right)\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 58.5%

         \[\leadsto \color{blue}{-y \cdot \left(-1 \cdot \left(x \cdot z\right) + \left(-1 \cdot \frac{c \cdot \left(j \cdot t\right)}{y} + i \cdot j\right)\right)} \]

      2. distribute-rgt-neg-in 58.5%

         \[\leadsto \color{blue}{y \cdot \left(-\left(-1 \cdot \left(x \cdot z\right) + \left(-1 \cdot \frac{c \cdot \left(j \cdot t\right)}{y} + i \cdot j\right)\right)\right)} \]

      3. +-commutative 58.5%

         \[\leadsto y \cdot \left(-\color{blue}{\left(\left(-1 \cdot \frac{c \cdot \left(j \cdot t\right)}{y} + i \cdot j\right) + -1 \cdot \left(x \cdot z\right)\right)}\right) \]

      4. mul-1-neg 58.5%

         \[\leadsto y \cdot \left(-\left(\left(-1 \cdot \frac{c \cdot \left(j \cdot t\right)}{y} + i \cdot j\right) + \color{blue}{\left(-x \cdot z\right)}\right)\right) \]

      5. unsub-neg 58.5%

         \[\leadsto y \cdot \left(-\color{blue}{\left(\left(-1 \cdot \frac{c \cdot \left(j \cdot t\right)}{y} + i \cdot j\right) - x \cdot z\right)}\right) \]

   9. Simplified 57.2%

      \[\leadsto \color{blue}{y \cdot \left(-\left(\left(i \cdot j - c \cdot \left(j \cdot \frac{t}{y}\right)\right) - z \cdot x\right)\right)} \]

   10. Taylor expanded in j around 0 42.9%

       \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   if -3.40000000000000016e219 < z < 2.5e45

   1. Initial program 76.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 76.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 78.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 78.0%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 78.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 78.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 78.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 78.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 78.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 78.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fmm-def 78.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 78.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 78.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 78.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 78.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      15. *-commutative 78.0%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 78.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around inf 47.7%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. distribute-lft-out-- 47.7%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. *-commutative 47.7%

         \[\leadsto i \cdot \left(-1 \cdot \left(\color{blue}{y \cdot j} - a \cdot b\right)\right) \]

   7. Simplified 47.7%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j - a \cdot b\right)\right)} \]

   8. Taylor expanded in y around 0 29.7%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 34.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+219} \lor \neg \left(z \leq 2.5 \cdot 10^{+45}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 29.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.25 \cdot 10^{+175} \lor \neg \left(j \leq 1.35 \cdot 10^{+29}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -1.25e+175) (not (<= j 1.35e+29))) (* c (* t 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 ((j <= -1.25e+175) || !(j <= 1.35e+29)) {
		tmp = c * (t * 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 ((j <= (-1.25d+175)) .or. (.not. (j <= 1.35d+29))) then
        tmp = c * (t * 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 ((j <= -1.25e+175) || !(j <= 1.35e+29)) {
		tmp = c * (t * j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -1.25e+175) or not (j <= 1.35e+29):
		tmp = c * (t * j)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -1.25e+175) || !(j <= 1.35e+29))
		tmp = Float64(c * Float64(t * 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 ((j <= -1.25e+175) || ~((j <= 1.35e+29)))
		tmp = c * (t * 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[j, -1.25e+175], N[Not[LessEqual[j, 1.35e+29]], $MachinePrecision]], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -1.25e175 or 1.35e29 < j

   1. Initial program 69.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 69.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 72.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 72.5%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 72.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 72.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 72.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 72.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 72.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 72.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fmm-def 72.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 72.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 72.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 72.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 72.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      15. *-commutative 72.5%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 72.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in c around inf 47.1%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 47.1%

         \[\leadsto c \cdot \left(\color{blue}{t \cdot j} - b \cdot z\right) \]

      2. *-commutative 47.1%

         \[\leadsto c \cdot \left(t \cdot j - \color{blue}{z \cdot b}\right) \]

   7. Simplified 47.1%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   8. Taylor expanded in t around inf 38.5%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]

   if -1.25e175 < j < 1.35e29

   1. Initial program 74.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 74.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-define 74.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 74.2%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 74.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 74.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 74.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. sub-neg 74.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. sub-neg 74.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      9. *-commutative 74.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      10. fmm-def 74.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      11. *-commutative 74.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      12. distribute-rgt-neg-out 74.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      13. remove-double-neg 74.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      14. *-commutative 74.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      15. *-commutative 74.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 74.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in i around inf 38.6%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. distribute-lft-out-- 38.6%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. *-commutative 38.6%

         \[\leadsto i \cdot \left(-1 \cdot \left(\color{blue}{y \cdot j} - a \cdot b\right)\right) \]

   7. Simplified 38.6%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j - a \cdot b\right)\right)} \]

   8. Taylor expanded in y around 0 29.7%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 32.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.25 \cdot 10^{+175} \lor \neg \left(j \leq 1.35 \cdot 10^{+29}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 22.2% 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 72.4%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
2. Step-by-step derivation

   1. +-commutative 72.4%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

   2. fma-define 73.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

   3. *-commutative 73.6%

      \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

   4. *-commutative 73.6%

      \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

   5. cancel-sign-sub-inv 73.6%

      \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

   6. cancel-sign-sub 73.6%

      \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

   7. sub-neg 73.6%

      \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

   8. sub-neg 73.6%

      \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

   9. *-commutative 73.6%

      \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - \color{blue}{a \cdot t}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

   10. fmm-def 74.0%

       \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \color{blue}{\mathsf{fma}\left(y, z, -a \cdot t\right)} - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

   11. *-commutative 74.0%

       \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, -\color{blue}{t \cdot a}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

   12. distribute-rgt-neg-out 74.0%

       \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, \color{blue}{t \cdot \left(-a\right)}\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)\right) \]

   13. remove-double-neg 74.0%

       \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

   14. *-commutative 74.0%

       \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

   15. *-commutative 74.0%

       \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

3. Simplified 74.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]
4. Add Preprocessing

5. Taylor expanded in i around inf 40.8%

   \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
6. Step-by-step derivation

   1. distribute-lft-out-- 40.8%

      \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

   2. *-commutative 40.8%

      \[\leadsto i \cdot \left(-1 \cdot \left(\color{blue}{y \cdot j} - a \cdot b\right)\right) \]

7. Simplified 40.8%

   \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j - a \cdot b\right)\right)} \]

8. Taylor expanded in y around 0 24.8%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
9. Add Preprocessing

Developer Target 1: 69.5% 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 2024149 
(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)))))