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

Percentage Accurate: 72.8% → 82.1%

Time: 18.6s

Alternatives: 23

Speedup: 0.5×

• 57.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 72.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 82.1% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))) + (j * ((a * c) - (y * i)))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = z * (x * (y - (b * (c / x))))
	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(t * i) - Float64(z * c)))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(z * Float64(x * Float64(y - Float64(b * Float64(c / x)))));
	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 * ((t * i) - (z * c)))) + (j * ((a * c) - (y * i)));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = z * (x * (y - (b * (c / x))));
	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[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(z * N[(x * N[(y - N[(b * N[(c / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 89.1%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in z around inf 43.3%

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

      1. *-commutative 43.3%

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

      2. *-commutative 43.3%

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

   5. Simplified 43.3%

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

   6. Taylor expanded in x around inf 47.9%

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

      1. mul-1-neg 47.9%

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

      2. unsub-neg 47.9%

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

      3. associate-/l* 49.4%

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

   8. Simplified 49.4%

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

4. Final simplification 79.5%

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

Alternative 2: 52.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{+163}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-64}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-169}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-130}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+43}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+147}:\\ \;\;\;\;i \cdot \left(a \cdot \frac{c \cdot j}{i} - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c)))))
   (if (<= z -5.8e+163)
     t_1
     (if (<= z -2.8e-64)
       (+ (* y (- (* x z) (* i j))) (* t (* b i)))
       (if (<= z -9.5e-169)
         (* t (- (* b i) (* x a)))
         (if (<= z 2.55e-130)
           (* i (- (* t b) (* y j)))
           (if (<= z 6.8e+43)
             (- (* x (- (* y z) (* t a))) (* i (* y j)))
             (if (<= z 5.4e+147)
               (* i (- (* a (/ (* c j) i)) (* y j)))
               t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -5.8e+163) {
		tmp = t_1;
	} else if (z <= -2.8e-64) {
		tmp = (y * ((x * z) - (i * j))) + (t * (b * i));
	} else if (z <= -9.5e-169) {
		tmp = t * ((b * i) - (x * a));
	} else if (z <= 2.55e-130) {
		tmp = i * ((t * b) - (y * j));
	} else if (z <= 6.8e+43) {
		tmp = (x * ((y * z) - (t * a))) - (i * (y * j));
	} else if (z <= 5.4e+147) {
		tmp = i * ((a * ((c * j) / i)) - (y * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * ((x * y) - (b * c))
    if (z <= (-5.8d+163)) then
        tmp = t_1
    else if (z <= (-2.8d-64)) then
        tmp = (y * ((x * z) - (i * j))) + (t * (b * i))
    else if (z <= (-9.5d-169)) then
        tmp = t * ((b * i) - (x * a))
    else if (z <= 2.55d-130) then
        tmp = i * ((t * b) - (y * j))
    else if (z <= 6.8d+43) then
        tmp = (x * ((y * z) - (t * a))) - (i * (y * j))
    else if (z <= 5.4d+147) then
        tmp = i * ((a * ((c * j) / i)) - (y * j))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -5.8e+163) {
		tmp = t_1;
	} else if (z <= -2.8e-64) {
		tmp = (y * ((x * z) - (i * j))) + (t * (b * i));
	} else if (z <= -9.5e-169) {
		tmp = t * ((b * i) - (x * a));
	} else if (z <= 2.55e-130) {
		tmp = i * ((t * b) - (y * j));
	} else if (z <= 6.8e+43) {
		tmp = (x * ((y * z) - (t * a))) - (i * (y * j));
	} else if (z <= 5.4e+147) {
		tmp = i * ((a * ((c * j) / i)) - (y * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -5.8e+163:
		tmp = t_1
	elif z <= -2.8e-64:
		tmp = (y * ((x * z) - (i * j))) + (t * (b * i))
	elif z <= -9.5e-169:
		tmp = t * ((b * i) - (x * a))
	elif z <= 2.55e-130:
		tmp = i * ((t * b) - (y * j))
	elif z <= 6.8e+43:
		tmp = (x * ((y * z) - (t * a))) - (i * (y * j))
	elif z <= 5.4e+147:
		tmp = i * ((a * ((c * j) / i)) - (y * j))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (z <= -5.8e+163)
		tmp = t_1;
	elseif (z <= -2.8e-64)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(t * Float64(b * i)));
	elseif (z <= -9.5e-169)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (z <= 2.55e-130)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (z <= 6.8e+43)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(i * Float64(y * j)));
	elseif (z <= 5.4e+147)
		tmp = Float64(i * Float64(Float64(a * Float64(Float64(c * j) / i)) - Float64(y * j)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -5.8e+163)
		tmp = t_1;
	elseif (z <= -2.8e-64)
		tmp = (y * ((x * z) - (i * j))) + (t * (b * i));
	elseif (z <= -9.5e-169)
		tmp = t * ((b * i) - (x * a));
	elseif (z <= 2.55e-130)
		tmp = i * ((t * b) - (y * j));
	elseif (z <= 6.8e+43)
		tmp = (x * ((y * z) - (t * a))) - (i * (y * j));
	elseif (z <= 5.4e+147)
		tmp = i * ((a * ((c * j) / i)) - (y * j));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.8e+163], t$95$1, If[LessEqual[z, -2.8e-64], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9.5e-169], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.55e-130], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e+43], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.4e+147], N[(i * N[(N[(a * N[(N[(c * j), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -5.79999999999999996e163 or 5.39999999999999995e147 < z

   1. Initial program 48.2%

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

   3. Taylor expanded in z around inf 79.0%

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

      1. *-commutative 79.0%

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

      2. *-commutative 79.0%

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

   5. Simplified 79.0%

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

   if -5.79999999999999996e163 < z < -2.80000000000000004e-64

   1. Initial program 69.1%

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

   3. Taylor expanded in a around 0 66.6%

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

   5. Simplified 77.2%

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

   6. Taylor expanded in i around inf 66.5%

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

      1. associate-*r* 66.5%

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

      2. *-commutative 66.5%

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

   8. Simplified 66.5%

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

   if -2.80000000000000004e-64 < z < -9.5000000000000001e-169

   1. Initial program 83.3%

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

   3. Taylor expanded in t around inf 61.9%

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

      1. distribute-lft-out-- 61.9%

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

      2. *-commutative 61.9%

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

   5. Simplified 61.9%

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

   6. Taylor expanded in a around 0 61.9%

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

      1. +-commutative 61.9%

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

      2. *-commutative 61.9%

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

      3. mul-1-neg 61.9%

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

      4. *-commutative 61.9%

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

      5. unsub-neg 61.9%

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

   8. Simplified 61.9%

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

   if -9.5000000000000001e-169 < z < 2.5499999999999999e-130

   1. Initial program 72.3%

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

   3. Taylor expanded in a around 0 60.1%

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

   5. Simplified 61.4%

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

   6. Taylor expanded in i around -inf 61.9%

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

      1. mul-1-neg 61.9%

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

      2. *-commutative 61.9%

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

      3. distribute-rgt-neg-in 61.9%

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

      4. +-commutative 61.9%

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

      5. mul-1-neg 61.9%

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

      6. unsub-neg 61.9%

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

      7. *-commutative 61.9%

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

   8. Simplified 61.9%

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

   if 2.5499999999999999e-130 < z < 6.80000000000000024e43

   1. Initial program 74.6%

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

   3. Taylor expanded in b around 0 66.1%

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

   4. Taylor expanded in c around 0 61.7%

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

      1. +-commutative 61.7%

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

      2. sub-neg 61.7%

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

      3. sub-neg 61.7%

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

      4. *-commutative 61.7%

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

      5. mul-1-neg 61.7%

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

      6. unsub-neg 61.7%

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

      7. *-commutative 61.7%

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

      8. *-commutative 61.7%

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

   6. Simplified 61.7%

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

   if 6.80000000000000024e43 < z < 5.39999999999999995e147

   1. Initial program 72.1%

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

   3. Taylor expanded in j around inf 51.4%

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

   4. Taylor expanded in i around -inf 62.0%

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

      1. mul-1-neg 62.0%

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

      2. *-commutative 62.0%

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

      3. distribute-rgt-neg-in 62.0%

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

      4. +-commutative 62.0%

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

      5. *-commutative 62.0%

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

      6. mul-1-neg 62.0%

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

      7. unsub-neg 62.0%

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

      8. associate-/l* 67.4%

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

      9. *-commutative 67.4%

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

   6. Simplified 67.4%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+163}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-64}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-169}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-130}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+43}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+147}:\\ \;\;\;\;i \cdot \left(a \cdot \frac{c \cdot j}{i} - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{-57}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y - b \cdot \frac{c}{x}\right)\right)\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-173}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-7}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+43}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+147}:\\ \;\;\;\;i \cdot \left(a \cdot \frac{c \cdot j}{i} - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -1.22e-57)
   (* z (* x (- y (* b (/ c x)))))
   (if (<= z -1.7e-173)
     (* t (- (* b i) (* x a)))
     (if (<= z 3.2e-7)
       (* i (- (* t b) (* y j)))
       (if (<= z 2.2e+43)
         (* x (- (* y z) (* t a)))
         (if (<= z 5.4e+147)
           (* i (- (* a (/ (* c j) i)) (* y j)))
           (* z (- (* x y) (* b c)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -1.22e-57) {
		tmp = z * (x * (y - (b * (c / x))));
	} else if (z <= -1.7e-173) {
		tmp = t * ((b * i) - (x * a));
	} else if (z <= 3.2e-7) {
		tmp = i * ((t * b) - (y * j));
	} else if (z <= 2.2e+43) {
		tmp = x * ((y * z) - (t * a));
	} else if (z <= 5.4e+147) {
		tmp = i * ((a * ((c * j) / i)) - (y * j));
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-1.22d-57)) then
        tmp = z * (x * (y - (b * (c / x))))
    else if (z <= (-1.7d-173)) then
        tmp = t * ((b * i) - (x * a))
    else if (z <= 3.2d-7) then
        tmp = i * ((t * b) - (y * j))
    else if (z <= 2.2d+43) then
        tmp = x * ((y * z) - (t * a))
    else if (z <= 5.4d+147) then
        tmp = i * ((a * ((c * j) / i)) - (y * j))
    else
        tmp = z * ((x * y) - (b * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -1.22e-57) {
		tmp = z * (x * (y - (b * (c / x))));
	} else if (z <= -1.7e-173) {
		tmp = t * ((b * i) - (x * a));
	} else if (z <= 3.2e-7) {
		tmp = i * ((t * b) - (y * j));
	} else if (z <= 2.2e+43) {
		tmp = x * ((y * z) - (t * a));
	} else if (z <= 5.4e+147) {
		tmp = i * ((a * ((c * j) / i)) - (y * j));
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -1.22e-57:
		tmp = z * (x * (y - (b * (c / x))))
	elif z <= -1.7e-173:
		tmp = t * ((b * i) - (x * a))
	elif z <= 3.2e-7:
		tmp = i * ((t * b) - (y * j))
	elif z <= 2.2e+43:
		tmp = x * ((y * z) - (t * a))
	elif z <= 5.4e+147:
		tmp = i * ((a * ((c * j) / i)) - (y * j))
	else:
		tmp = z * ((x * y) - (b * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -1.22e-57)
		tmp = Float64(z * Float64(x * Float64(y - Float64(b * Float64(c / x)))));
	elseif (z <= -1.7e-173)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (z <= 3.2e-7)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (z <= 2.2e+43)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (z <= 5.4e+147)
		tmp = Float64(i * Float64(Float64(a * Float64(Float64(c * j) / i)) - Float64(y * j)));
	else
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -1.22e-57)
		tmp = z * (x * (y - (b * (c / x))));
	elseif (z <= -1.7e-173)
		tmp = t * ((b * i) - (x * a));
	elseif (z <= 3.2e-7)
		tmp = i * ((t * b) - (y * j));
	elseif (z <= 2.2e+43)
		tmp = x * ((y * z) - (t * a));
	elseif (z <= 5.4e+147)
		tmp = i * ((a * ((c * j) / i)) - (y * j));
	else
		tmp = z * ((x * y) - (b * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -1.22e-57], N[(z * N[(x * N[(y - N[(b * N[(c / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.7e-173], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e-7], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e+43], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.4e+147], N[(i * N[(N[(a * N[(N[(c * j), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.2200000000000001e-57

   1. Initial program 52.8%

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

   3. Taylor expanded in z around inf 57.3%

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

      1. *-commutative 57.3%

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

      2. *-commutative 57.3%

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

   5. Simplified 57.3%

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

   6. Taylor expanded in x around inf 60.4%

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

      1. mul-1-neg 60.4%

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

      2. unsub-neg 60.4%

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

      3. associate-/l* 59.0%

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

   8. Simplified 59.0%

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

   if -1.2200000000000001e-57 < z < -1.6999999999999999e-173

   1. Initial program 83.3%

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

   3. Taylor expanded in t around inf 61.9%

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

      1. distribute-lft-out-- 61.9%

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

      2. *-commutative 61.9%

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

   5. Simplified 61.9%

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

   6. Taylor expanded in a around 0 61.9%

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

      1. +-commutative 61.9%

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

      2. *-commutative 61.9%

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

      3. mul-1-neg 61.9%

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

      4. *-commutative 61.9%

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

      5. unsub-neg 61.9%

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

   8. Simplified 61.9%

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

   if -1.6999999999999999e-173 < z < 3.2000000000000001e-7

   1. Initial program 73.3%

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

   3. Taylor expanded in a around 0 59.9%

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

   5. Simplified 60.8%

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

   6. Taylor expanded in i around -inf 57.4%

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

      1. mul-1-neg 57.4%

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

      2. *-commutative 57.4%

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

      3. distribute-rgt-neg-in 57.4%

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

      4. +-commutative 57.4%

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

      5. mul-1-neg 57.4%

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

      6. unsub-neg 57.4%

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

      7. *-commutative 57.4%

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

   8. Simplified 57.4%

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

   if 3.2000000000000001e-7 < z < 2.20000000000000001e43

   1. Initial program 71.8%

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

   3. Taylor expanded in x around inf 79.0%

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

   if 2.20000000000000001e43 < z < 5.39999999999999995e147

   1. Initial program 72.1%

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

   3. Taylor expanded in j around inf 51.4%

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

   4. Taylor expanded in i around -inf 62.0%

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

      1. mul-1-neg 62.0%

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

      2. *-commutative 62.0%

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

      3. distribute-rgt-neg-in 62.0%

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

      4. +-commutative 62.0%

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

      5. *-commutative 62.0%

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

      6. mul-1-neg 62.0%

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

      7. unsub-neg 62.0%

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

      8. associate-/l* 67.4%

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

      9. *-commutative 67.4%

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

   6. Simplified 67.4%

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

   if 5.39999999999999995e147 < z

   1. Initial program 57.0%

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

   3. Taylor expanded in z around inf 90.2%

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

      1. *-commutative 90.2%

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

      2. *-commutative 90.2%

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

   5. Simplified 90.2%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{-57}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y - b \cdot \frac{c}{x}\right)\right)\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-173}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-7}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+43}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+147}:\\ \;\;\;\;i \cdot \left(a \cdot \frac{c \cdot j}{i} - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 70.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right) + t\_1\\ \mathbf{if}\;j \leq -1.28 \cdot 10^{+48}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 3.15 \cdot 10^{-176}:\\ \;\;\;\;\left(\left(t\_1 + i \cdot \left(t \cdot b\right)\right) + a \cdot \left(c \cdot j\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.75 \cdot 10^{+71}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - y \cdot \left(i \cdot j - x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (+ (* j (- (* a c) (* y i))) t_1)))
   (if (<= j -1.28e+48)
     t_2
     (if (<= j 3.15e-176)
       (- (+ (+ t_1 (* i (* t b))) (* a (* c j))) (* b (* z c)))
       (if (<= j 1.75e+71)
         (- (* b (- (* t i) (* z c))) (* y (- (* i j) (* x z))))
         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));
	double t_2 = (j * ((a * c) - (y * i))) + t_1;
	double tmp;
	if (j <= -1.28e+48) {
		tmp = t_2;
	} else if (j <= 3.15e-176) {
		tmp = ((t_1 + (i * (t * b))) + (a * (c * j))) - (b * (z * c));
	} else if (j <= 1.75e+71) {
		tmp = (b * ((t * i) - (z * c))) - (y * ((i * j) - (x * z)));
	} 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))
    t_2 = (j * ((a * c) - (y * i))) + t_1
    if (j <= (-1.28d+48)) then
        tmp = t_2
    else if (j <= 3.15d-176) then
        tmp = ((t_1 + (i * (t * b))) + (a * (c * j))) - (b * (z * c))
    else if (j <= 1.75d+71) then
        tmp = (b * ((t * i) - (z * c))) - (y * ((i * j) - (x * z)))
    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));
	double t_2 = (j * ((a * c) - (y * i))) + t_1;
	double tmp;
	if (j <= -1.28e+48) {
		tmp = t_2;
	} else if (j <= 3.15e-176) {
		tmp = ((t_1 + (i * (t * b))) + (a * (c * j))) - (b * (z * c));
	} else if (j <= 1.75e+71) {
		tmp = (b * ((t * i) - (z * c))) - (y * ((i * j) - (x * z)));
	} 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))
	t_2 = (j * ((a * c) - (y * i))) + t_1
	tmp = 0
	if j <= -1.28e+48:
		tmp = t_2
	elif j <= 3.15e-176:
		tmp = ((t_1 + (i * (t * b))) + (a * (c * j))) - (b * (z * c))
	elif j <= 1.75e+71:
		tmp = (b * ((t * i) - (z * c))) - (y * ((i * j) - (x * z)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + t_1)
	tmp = 0.0
	if (j <= -1.28e+48)
		tmp = t_2;
	elseif (j <= 3.15e-176)
		tmp = Float64(Float64(Float64(t_1 + Float64(i * Float64(t * b))) + Float64(a * Float64(c * j))) - Float64(b * Float64(z * c)));
	elseif (j <= 1.75e+71)
		tmp = Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) - Float64(y * Float64(Float64(i * j) - Float64(x * z))));
	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));
	t_2 = (j * ((a * c) - (y * i))) + t_1;
	tmp = 0.0;
	if (j <= -1.28e+48)
		tmp = t_2;
	elseif (j <= 3.15e-176)
		tmp = ((t_1 + (i * (t * b))) + (a * (c * j))) - (b * (z * c));
	elseif (j <= 1.75e+71)
		tmp = (b * ((t * i) - (z * c))) - (y * ((i * j) - (x * z)));
	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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[j, -1.28e+48], t$95$2, If[LessEqual[j, 3.15e-176], N[(N[(N[(t$95$1 + N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.75e+71], N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(i * j), $MachinePrecision] - N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.28e48 or 1.75e71 < j

   1. Initial program 62.0%

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

   3. Taylor expanded in b around 0 64.4%

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

   if -1.28e48 < j < 3.15000000000000006e-176

   1. Initial program 70.7%

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

   3. Taylor expanded in i around 0 83.3%

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

   4. Taylor expanded in j around 0 74.5%

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

      1. *-commutative 74.5%

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

   6. Simplified 74.5%

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

   if 3.15000000000000006e-176 < j < 1.75e71

   1. Initial program 72.1%

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

   3. Taylor expanded in a around 0 77.9%

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

   5. Simplified 85.2%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.28 \cdot 10^{+48}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 3.15 \cdot 10^{-176}:\\ \;\;\;\;\left(\left(x \cdot \left(y \cdot z - t \cdot a\right) + i \cdot \left(t \cdot b\right)\right) + a \cdot \left(c \cdot j\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.75 \cdot 10^{+71}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - y \cdot \left(i \cdot j - x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 28.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+118}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{+39}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-100}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+43}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+269}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x -1.25e+118)
   (* t (* x (- a)))
   (if (<= x -1.5e+39)
     (* z (* x y))
     (if (<= x 4.4e-100)
       (* b (* t i))
       (if (<= x 1.7e+43)
         (* (* y i) (- j))
         (if (<= x 9e+269) (* a (* x (- t))) (* y (* x z))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -1.25e+118) {
		tmp = t * (x * -a);
	} else if (x <= -1.5e+39) {
		tmp = z * (x * y);
	} else if (x <= 4.4e-100) {
		tmp = b * (t * i);
	} else if (x <= 1.7e+43) {
		tmp = (y * i) * -j;
	} else if (x <= 9e+269) {
		tmp = a * (x * -t);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (x <= (-1.25d+118)) then
        tmp = t * (x * -a)
    else if (x <= (-1.5d+39)) then
        tmp = z * (x * y)
    else if (x <= 4.4d-100) then
        tmp = b * (t * i)
    else if (x <= 1.7d+43) then
        tmp = (y * i) * -j
    else if (x <= 9d+269) then
        tmp = a * (x * -t)
    else
        tmp = y * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -1.25e+118) {
		tmp = t * (x * -a);
	} else if (x <= -1.5e+39) {
		tmp = z * (x * y);
	} else if (x <= 4.4e-100) {
		tmp = b * (t * i);
	} else if (x <= 1.7e+43) {
		tmp = (y * i) * -j;
	} else if (x <= 9e+269) {
		tmp = a * (x * -t);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if x <= -1.25e+118:
		tmp = t * (x * -a)
	elif x <= -1.5e+39:
		tmp = z * (x * y)
	elif x <= 4.4e-100:
		tmp = b * (t * i)
	elif x <= 1.7e+43:
		tmp = (y * i) * -j
	elif x <= 9e+269:
		tmp = a * (x * -t)
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= -1.25e+118)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (x <= -1.5e+39)
		tmp = Float64(z * Float64(x * y));
	elseif (x <= 4.4e-100)
		tmp = Float64(b * Float64(t * i));
	elseif (x <= 1.7e+43)
		tmp = Float64(Float64(y * i) * Float64(-j));
	elseif (x <= 9e+269)
		tmp = Float64(a * Float64(x * Float64(-t)));
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (x <= -1.25e+118)
		tmp = t * (x * -a);
	elseif (x <= -1.5e+39)
		tmp = z * (x * y);
	elseif (x <= 4.4e-100)
		tmp = b * (t * i);
	elseif (x <= 1.7e+43)
		tmp = (y * i) * -j;
	elseif (x <= 9e+269)
		tmp = a * (x * -t);
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, -1.25e+118], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.5e+39], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.4e-100], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.7e+43], N[(N[(y * i), $MachinePrecision] * (-j)), $MachinePrecision], If[LessEqual[x, 9e+269], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -1.24999999999999993e118

   1. Initial program 63.0%

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

   3. Taylor expanded in t around inf 56.6%

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

      1. distribute-lft-out-- 56.6%

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

      2. *-commutative 56.6%

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

   5. Simplified 56.6%

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

   6. Taylor expanded in a around inf 51.6%

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

      1. mul-1-neg 51.6%

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

      2. *-commutative 51.6%

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

      3. distribute-rgt-neg-in 51.6%

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

   8. Simplified 51.6%

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

   if -1.24999999999999993e118 < x < -1.5e39

   1. Initial program 66.6%

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

   3. Taylor expanded in z around inf 56.8%

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

      1. *-commutative 56.8%

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

      2. *-commutative 56.8%

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

   5. Simplified 56.8%

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

   6. Taylor expanded in y around inf 46.0%

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

   if -1.5e39 < x < 4.39999999999999978e-100

   1. Initial program 65.0%

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

   3. Taylor expanded in b around inf 51.0%

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

   4. Taylor expanded in i around inf 31.6%

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

   if 4.39999999999999978e-100 < x < 1.70000000000000006e43

   1. Initial program 84.1%

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

   3. Taylor expanded in j around inf 49.6%

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

   4. Taylor expanded in a around 0 37.3%

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

      1. mul-1-neg 37.3%

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

      2. distribute-lft-neg-out 37.3%

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

      3. *-commutative 37.3%

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

   6. Simplified 37.3%

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

   if 1.70000000000000006e43 < x < 9.0000000000000004e269

   1. Initial program 74.3%

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

   3. Taylor expanded in a around inf 54.8%

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

      1. +-commutative 54.8%

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

      2. mul-1-neg 54.8%

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

      3. unsub-neg 54.8%

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

      4. *-commutative 54.8%

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

   5. Simplified 54.8%

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

   6. Taylor expanded in j around 0 39.8%

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

      1. mul-1-neg 39.8%

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

      2. distribute-lft-neg-out 39.8%

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

      3. *-commutative 39.8%

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

   8. Simplified 39.8%

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

   if 9.0000000000000004e269 < x

   1. Initial program 50.0%

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

   3. Taylor expanded in z around inf 70.9%

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

      1. *-commutative 70.9%

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

      2. *-commutative 70.9%

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

   5. Simplified 70.9%

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

   6. Taylor expanded in y around inf 70.9%

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

   7. Taylor expanded in z around 0 80.2%

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

      1. associate-*r* 70.9%

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

      2. *-commutative 70.9%

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

      3. associate-*r* 80.2%

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

   9. Simplified 80.2%

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

4. Final simplification 39.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+118}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{+39}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-100}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+43}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+269}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 29.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{if}\;x \leq -6.2 \cdot 10^{+142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -8 \cdot 10^{+38}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-102}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;x \leq 10^{+46}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+269}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* x (- t)))))
   (if (<= x -6.2e+142)
     t_1
     (if (<= x -8e+38)
       (* z (* x y))
       (if (<= x 1.3e-102)
         (* b (* t i))
         (if (<= x 1e+46)
           (* (* y i) (- j))
           (if (<= x 5e+269) t_1 (* y (* x z)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (x * -t);
	double tmp;
	if (x <= -6.2e+142) {
		tmp = t_1;
	} else if (x <= -8e+38) {
		tmp = z * (x * y);
	} else if (x <= 1.3e-102) {
		tmp = b * (t * i);
	} else if (x <= 1e+46) {
		tmp = (y * i) * -j;
	} else if (x <= 5e+269) {
		tmp = t_1;
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (x * -t)
    if (x <= (-6.2d+142)) then
        tmp = t_1
    else if (x <= (-8d+38)) then
        tmp = z * (x * y)
    else if (x <= 1.3d-102) then
        tmp = b * (t * i)
    else if (x <= 1d+46) then
        tmp = (y * i) * -j
    else if (x <= 5d+269) then
        tmp = t_1
    else
        tmp = y * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (x * -t);
	double tmp;
	if (x <= -6.2e+142) {
		tmp = t_1;
	} else if (x <= -8e+38) {
		tmp = z * (x * y);
	} else if (x <= 1.3e-102) {
		tmp = b * (t * i);
	} else if (x <= 1e+46) {
		tmp = (y * i) * -j;
	} else if (x <= 5e+269) {
		tmp = t_1;
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (x * -t)
	tmp = 0
	if x <= -6.2e+142:
		tmp = t_1
	elif x <= -8e+38:
		tmp = z * (x * y)
	elif x <= 1.3e-102:
		tmp = b * (t * i)
	elif x <= 1e+46:
		tmp = (y * i) * -j
	elif x <= 5e+269:
		tmp = t_1
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(x * Float64(-t)))
	tmp = 0.0
	if (x <= -6.2e+142)
		tmp = t_1;
	elseif (x <= -8e+38)
		tmp = Float64(z * Float64(x * y));
	elseif (x <= 1.3e-102)
		tmp = Float64(b * Float64(t * i));
	elseif (x <= 1e+46)
		tmp = Float64(Float64(y * i) * Float64(-j));
	elseif (x <= 5e+269)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (x * -t);
	tmp = 0.0;
	if (x <= -6.2e+142)
		tmp = t_1;
	elseif (x <= -8e+38)
		tmp = z * (x * y);
	elseif (x <= 1.3e-102)
		tmp = b * (t * i);
	elseif (x <= 1e+46)
		tmp = (y * i) * -j;
	elseif (x <= 5e+269)
		tmp = t_1;
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.2e+142], t$95$1, If[LessEqual[x, -8e+38], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3e-102], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1e+46], N[(N[(y * i), $MachinePrecision] * (-j)), $MachinePrecision], If[LessEqual[x, 5e+269], t$95$1, N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -6.1999999999999998e142 or 9.9999999999999999e45 < x < 5.0000000000000002e269

   1. Initial program 66.6%

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

   3. Taylor expanded in a around inf 53.3%

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

      1. +-commutative 53.3%

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

      2. mul-1-neg 53.3%

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

      3. unsub-neg 53.3%

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

      4. *-commutative 53.3%

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

   5. Simplified 53.3%

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

   6. Taylor expanded in j around 0 46.3%

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

      1. mul-1-neg 46.3%

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

      2. distribute-lft-neg-out 46.3%

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

      3. *-commutative 46.3%

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

   8. Simplified 46.3%

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

   if -6.1999999999999998e142 < x < -7.99999999999999982e38

   1. Initial program 73.0%

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

   3. Taylor expanded in z around inf 51.2%

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

      1. *-commutative 51.2%

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

      2. *-commutative 51.2%

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

   5. Simplified 51.2%

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

   6. Taylor expanded in y around inf 43.7%

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

   if -7.99999999999999982e38 < x < 1.29999999999999993e-102

   1. Initial program 65.0%

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

   3. Taylor expanded in b around inf 51.0%

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

   4. Taylor expanded in i around inf 31.6%

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

   if 1.29999999999999993e-102 < x < 9.9999999999999999e45

   1. Initial program 84.1%

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

   3. Taylor expanded in j around inf 49.6%

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

   4. Taylor expanded in a around 0 37.3%

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

      1. mul-1-neg 37.3%

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

      2. distribute-lft-neg-out 37.3%

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

      3. *-commutative 37.3%

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

   6. Simplified 37.3%

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

   if 5.0000000000000002e269 < x

   1. Initial program 50.0%

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

   3. Taylor expanded in z around inf 70.9%

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

      1. *-commutative 70.9%

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

      2. *-commutative 70.9%

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

   5. Simplified 70.9%

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

   6. Taylor expanded in y around inf 70.9%

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

   7. Taylor expanded in z around 0 80.2%

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

      1. associate-*r* 70.9%

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

      2. *-commutative 70.9%

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

      3. associate-*r* 80.2%

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

   9. Simplified 80.2%

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

4. Final simplification 39.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+142}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;x \leq -8 \cdot 10^{+38}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-102}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;x \leq 10^{+46}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+269}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -1.22 \cdot 10^{-57}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-237}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-232}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+67}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* b i) (* x a)))) (t_2 (* z (- (* x y) (* b c)))))
   (if (<= z -1.22e-57)
     t_2
     (if (<= z -1.75e-237)
       t_1
       (if (<= z 2.1e-232)
         (* j (- (* a c) (* y i)))
         (if (<= z 1.15e+67) 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 = t * ((b * i) - (x * a));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -1.22e-57) {
		tmp = t_2;
	} else if (z <= -1.75e-237) {
		tmp = t_1;
	} else if (z <= 2.1e-232) {
		tmp = j * ((a * c) - (y * i));
	} else if (z <= 1.15e+67) {
		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 = t * ((b * i) - (x * a))
    t_2 = z * ((x * y) - (b * c))
    if (z <= (-1.22d-57)) then
        tmp = t_2
    else if (z <= (-1.75d-237)) then
        tmp = t_1
    else if (z <= 2.1d-232) then
        tmp = j * ((a * c) - (y * i))
    else if (z <= 1.15d+67) 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 = t * ((b * i) - (x * a));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -1.22e-57) {
		tmp = t_2;
	} else if (z <= -1.75e-237) {
		tmp = t_1;
	} else if (z <= 2.1e-232) {
		tmp = j * ((a * c) - (y * i));
	} else if (z <= 1.15e+67) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((b * i) - (x * a))
	t_2 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -1.22e-57:
		tmp = t_2
	elif z <= -1.75e-237:
		tmp = t_1
	elif z <= 2.1e-232:
		tmp = j * ((a * c) - (y * i))
	elif z <= 1.15e+67:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	t_2 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (z <= -1.22e-57)
		tmp = t_2;
	elseif (z <= -1.75e-237)
		tmp = t_1;
	elseif (z <= 2.1e-232)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (z <= 1.15e+67)
		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 = t * ((b * i) - (x * a));
	t_2 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -1.22e-57)
		tmp = t_2;
	elseif (z <= -1.75e-237)
		tmp = t_1;
	elseif (z <= 2.1e-232)
		tmp = j * ((a * c) - (y * i));
	elseif (z <= 1.15e+67)
		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[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.22e-57], t$95$2, If[LessEqual[z, -1.75e-237], t$95$1, If[LessEqual[z, 2.1e-232], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e+67], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.2200000000000001e-57 or 1.1499999999999999e67 < z

   1. Initial program 56.8%

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

   3. Taylor expanded in z around inf 65.4%

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

      1. *-commutative 65.4%

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

      2. *-commutative 65.4%

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

   5. Simplified 65.4%

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

   if -1.2200000000000001e-57 < z < -1.74999999999999992e-237 or 2.1e-232 < z < 1.1499999999999999e67

   1. Initial program 76.2%

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

   3. Taylor expanded in t around inf 51.7%

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

      1. distribute-lft-out-- 51.7%

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

      2. *-commutative 51.7%

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

   5. Simplified 51.7%

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

   6. Taylor expanded in a around 0 51.7%

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

      1. +-commutative 51.7%

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

      2. *-commutative 51.7%

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

      3. mul-1-neg 51.7%

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

      4. *-commutative 51.7%

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

      5. unsub-neg 51.7%

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

   8. Simplified 51.7%

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

   if -1.74999999999999992e-237 < z < 2.1e-232

   1. Initial program 71.1%

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

   3. Taylor expanded in j around inf 65.2%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{-57}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-237}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-232}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+67}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 42.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -4.2 \cdot 10^{+66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-193}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-303}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-102}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -4.2e+66)
     t_1
     (if (<= a -1.7e-193)
       (* b (* t i))
       (if (<= a 2.2e-303)
         (* z (* x y))
         (if (<= a 1.55e-102) (* b (* z (- c))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -4.2e+66) {
		tmp = t_1;
	} else if (a <= -1.7e-193) {
		tmp = b * (t * i);
	} else if (a <= 2.2e-303) {
		tmp = z * (x * y);
	} else if (a <= 1.55e-102) {
		tmp = b * (z * -c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (a <= (-4.2d+66)) then
        tmp = t_1
    else if (a <= (-1.7d-193)) then
        tmp = b * (t * i)
    else if (a <= 2.2d-303) then
        tmp = z * (x * y)
    else if (a <= 1.55d-102) then
        tmp = b * (z * -c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -4.2e+66) {
		tmp = t_1;
	} else if (a <= -1.7e-193) {
		tmp = b * (t * i);
	} else if (a <= 2.2e-303) {
		tmp = z * (x * y);
	} else if (a <= 1.55e-102) {
		tmp = b * (z * -c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -4.2e+66:
		tmp = t_1
	elif a <= -1.7e-193:
		tmp = b * (t * i)
	elif a <= 2.2e-303:
		tmp = z * (x * y)
	elif a <= 1.55e-102:
		tmp = b * (z * -c)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -4.2e+66)
		tmp = t_1;
	elseif (a <= -1.7e-193)
		tmp = Float64(b * Float64(t * i));
	elseif (a <= 2.2e-303)
		tmp = Float64(z * Float64(x * y));
	elseif (a <= 1.55e-102)
		tmp = Float64(b * Float64(z * Float64(-c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -4.2e+66)
		tmp = t_1;
	elseif (a <= -1.7e-193)
		tmp = b * (t * i);
	elseif (a <= 2.2e-303)
		tmp = z * (x * y);
	elseif (a <= 1.55e-102)
		tmp = b * (z * -c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.2e+66], t$95$1, If[LessEqual[a, -1.7e-193], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.2e-303], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.55e-102], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.20000000000000011e66 or 1.55000000000000006e-102 < a

   1. Initial program 58.6%

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

   3. Taylor expanded in a around inf 55.2%

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

      1. +-commutative 55.2%

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

      2. mul-1-neg 55.2%

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

      3. unsub-neg 55.2%

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

      4. *-commutative 55.2%

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

   5. Simplified 55.2%

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

   if -4.20000000000000011e66 < a < -1.7000000000000001e-193

   1. Initial program 72.6%

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

   3. Taylor expanded in b around inf 44.5%

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

   4. Taylor expanded in i around inf 34.5%

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

   if -1.7000000000000001e-193 < a < 2.20000000000000014e-303

   1. Initial program 88.0%

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

   3. Taylor expanded in z around inf 56.9%

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

      1. *-commutative 56.9%

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

      2. *-commutative 56.9%

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

   5. Simplified 56.9%

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

   6. Taylor expanded in y around inf 41.7%

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

   if 2.20000000000000014e-303 < a < 1.55000000000000006e-102

   1. Initial program 75.4%

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

   3. Taylor expanded in z around inf 49.4%

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

      1. *-commutative 49.4%

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

      2. *-commutative 49.4%

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

   5. Simplified 49.4%

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

   6. Taylor expanded in y around 0 40.3%

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

      1. associate-*r* 40.3%

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

      2. neg-mul-1 40.3%

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

      3. *-commutative 40.3%

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

   8. Simplified 40.3%

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

4. Final simplification 46.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{+66}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-193}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-303}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-102}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 62.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -2.25 \cdot 10^{-14} \lor \neg \left(i \leq 1.4 \cdot 10^{+88}\right):\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -2.25e-14) (not (<= i 1.4e+88)))
   (* i (- (* t b) (* y j)))
   (+ (* j (- (* a c) (* y i))) (* x (- (* y z) (* t a))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -2.25e-14) || !(i <= 1.4e+88)) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((i <= (-2.25d-14)) .or. (.not. (i <= 1.4d+88))) then
        tmp = i * ((t * b) - (y * j))
    else
        tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -2.25e-14) || !(i <= 1.4e+88)) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (i <= -2.25e-14) or not (i <= 1.4e+88):
		tmp = i * ((t * b) - (y * j))
	else:
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((i <= -2.25e-14) || !(i <= 1.4e+88))
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	else
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((i <= -2.25e-14) || ~((i <= 1.4e+88)))
		tmp = i * ((t * b) - (y * j));
	else
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[i, -2.25e-14], N[Not[LessEqual[i, 1.4e+88]], $MachinePrecision]], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -2.2499999999999999e-14 or 1.39999999999999994e88 < i

   1. Initial program 57.8%

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

   3. Taylor expanded in a around 0 63.5%

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

   5. Simplified 67.6%

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

   6. Taylor expanded in i around -inf 68.1%

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

      1. mul-1-neg 68.1%

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

      2. *-commutative 68.1%

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

      3. distribute-rgt-neg-in 68.1%

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

      4. +-commutative 68.1%

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

      5. mul-1-neg 68.1%

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

      6. unsub-neg 68.1%

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

      7. *-commutative 68.1%

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

   8. Simplified 68.1%

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

   if -2.2499999999999999e-14 < i < 1.39999999999999994e88

   1. Initial program 75.7%

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

   3. Taylor expanded in b around 0 63.7%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.25 \cdot 10^{-14} \lor \neg \left(i \leq 1.4 \cdot 10^{+88}\right):\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 64.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -6.4 \cdot 10^{+102}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+28}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - y \cdot \left(i \cdot j - x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= x -6.4e+102)
     t_1
     (if (<= x 3.5e+28)
       (- (* b (- (* t i) (* z c))) (* y (- (* i j) (* x z))))
       (+ (* j (- (* a 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 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -6.4e+102) {
		tmp = t_1;
	} else if (x <= 3.5e+28) {
		tmp = (b * ((t * i) - (z * c))) - (y * ((i * j) - (x * z)));
	} else {
		tmp = (j * ((a * c) - (y * i))) + 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 = x * ((y * z) - (t * a))
    if (x <= (-6.4d+102)) then
        tmp = t_1
    else if (x <= 3.5d+28) then
        tmp = (b * ((t * i) - (z * c))) - (y * ((i * j) - (x * z)))
    else
        tmp = (j * ((a * c) - (y * i))) + 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 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -6.4e+102) {
		tmp = t_1;
	} else if (x <= 3.5e+28) {
		tmp = (b * ((t * i) - (z * c))) - (y * ((i * j) - (x * z)));
	} else {
		tmp = (j * ((a * c) - (y * i))) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -6.4e+102:
		tmp = t_1
	elif x <= 3.5e+28:
		tmp = (b * ((t * i) - (z * c))) - (y * ((i * j) - (x * z)))
	else:
		tmp = (j * ((a * c) - (y * i))) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -6.4e+102)
		tmp = t_1;
	elseif (x <= 3.5e+28)
		tmp = Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) - Float64(y * Float64(Float64(i * j) - Float64(x * z))));
	else
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + t_1);
	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));
	tmp = 0.0;
	if (x <= -6.4e+102)
		tmp = t_1;
	elseif (x <= 3.5e+28)
		tmp = (b * ((t * i) - (z * c))) - (y * ((i * j) - (x * z)));
	else
		tmp = (j * ((a * c) - (y * i))) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.4e+102], t$95$1, If[LessEqual[x, 3.5e+28], N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(i * j), $MachinePrecision] - N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.3999999999999999e102

   1. Initial program 65.1%

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

   3. Taylor expanded in x around inf 70.0%

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

   if -6.3999999999999999e102 < x < 3.5e28

   1. Initial program 66.8%

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

   3. Taylor expanded in a around 0 66.2%

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

   5. Simplified 68.7%

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

   if 3.5e28 < x

   1. Initial program 71.7%

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

   3. Taylor expanded in b around 0 75.8%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{+102}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+28}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - y \cdot \left(i \cdot j - x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 59.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3.8 \cdot 10^{+68} \lor \neg \left(c \leq 7.5 \cdot 10^{+30}\right):\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + t \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -3.8e+68) (not (<= c 7.5e+30)))
   (* c (- (* a j) (* z b)))
   (+ (* y (- (* x z) (* i j))) (* t (* b i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -3.8e+68) || !(c <= 7.5e+30)) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = (y * ((x * z) - (i * j))) + (t * (b * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((c <= (-3.8d+68)) .or. (.not. (c <= 7.5d+30))) then
        tmp = c * ((a * j) - (z * b))
    else
        tmp = (y * ((x * z) - (i * j))) + (t * (b * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -3.8e+68) || !(c <= 7.5e+30)) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = (y * ((x * z) - (i * j))) + (t * (b * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -3.8e+68) or not (c <= 7.5e+30):
		tmp = c * ((a * j) - (z * b))
	else:
		tmp = (y * ((x * z) - (i * j))) + (t * (b * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -3.8e+68) || !(c <= 7.5e+30))
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	else
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(t * Float64(b * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -3.8e+68) || ~((c <= 7.5e+30)))
		tmp = c * ((a * j) - (z * b));
	else
		tmp = (y * ((x * z) - (i * j))) + (t * (b * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -3.8e+68], N[Not[LessEqual[c, 7.5e+30]], $MachinePrecision]], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -3.8000000000000001e68 or 7.49999999999999973e30 < c

   1. Initial program 55.7%

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

   3. Taylor expanded in c around inf 60.9%

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

      1. *-commutative 60.9%

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

   5. Simplified 60.9%

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

   if -3.8000000000000001e68 < c < 7.49999999999999973e30

   1. Initial program 75.7%

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

   3. Taylor expanded in a around 0 62.3%

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

   5. Simplified 66.2%

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

   6. Taylor expanded in i around inf 63.3%

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

      1. associate-*r* 59.7%

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

      2. *-commutative 59.7%

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

   8. Simplified 59.7%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.8 \cdot 10^{+68} \lor \neg \left(c \leq 7.5 \cdot 10^{+30}\right):\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + t \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 50.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -1.75 \cdot 10^{-37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{-130}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq 3.1 \cdot 10^{+85}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j)))))
   (if (<= i -1.75e-37)
     t_1
     (if (<= i 2.5e-130)
       (* x (- (* y z) (* t a)))
       (if (<= i 3.1e+85) (* j (- (* a 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 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -1.75e-37) {
		tmp = t_1;
	} else if (i <= 2.5e-130) {
		tmp = x * ((y * z) - (t * a));
	} else if (i <= 3.1e+85) {
		tmp = j * ((a * 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 = i * ((t * b) - (y * j))
    if (i <= (-1.75d-37)) then
        tmp = t_1
    else if (i <= 2.5d-130) then
        tmp = x * ((y * z) - (t * a))
    else if (i <= 3.1d+85) then
        tmp = j * ((a * 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 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -1.75e-37) {
		tmp = t_1;
	} else if (i <= 2.5e-130) {
		tmp = x * ((y * z) - (t * a));
	} else if (i <= 3.1e+85) {
		tmp = j * ((a * c) - (y * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -1.75e-37:
		tmp = t_1
	elif i <= 2.5e-130:
		tmp = x * ((y * z) - (t * a))
	elif i <= 3.1e+85:
		tmp = j * ((a * c) - (y * i))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -1.75e-37)
		tmp = t_1;
	elseif (i <= 2.5e-130)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (i <= 3.1e+85)
		tmp = Float64(j * Float64(Float64(a * 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 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -1.75e-37)
		tmp = t_1;
	elseif (i <= 2.5e-130)
		tmp = x * ((y * z) - (t * a));
	elseif (i <= 3.1e+85)
		tmp = j * ((a * 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[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.75e-37], t$95$1, If[LessEqual[i, 2.5e-130], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.1e+85], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if i < -1.7500000000000001e-37 or 3.10000000000000011e85 < i

   1. Initial program 60.4%

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

   3. Taylor expanded in a around 0 64.3%

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

   5. Simplified 68.2%

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

   6. Taylor expanded in i around -inf 67.0%

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

      1. mul-1-neg 67.0%

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

      2. *-commutative 67.0%

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

      3. distribute-rgt-neg-in 67.0%

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

      4. +-commutative 67.0%

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

      5. mul-1-neg 67.0%

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

      6. unsub-neg 67.0%

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

      7. *-commutative 67.0%

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

   8. Simplified 67.0%

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

   if -1.7500000000000001e-37 < i < 2.4999999999999998e-130

   1. Initial program 76.5%

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

   3. Taylor expanded in x around inf 58.2%

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

   if 2.4999999999999998e-130 < i < 3.10000000000000011e85

   1. Initial program 70.1%

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

   3. Taylor expanded in j around inf 48.6%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.75 \cdot 10^{-37}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{-130}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq 3.1 \cdot 10^{+85}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 29.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.9 \cdot 10^{-36}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 3.1 \cdot 10^{-307}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 1.9 \cdot 10^{+15}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -1.9e-36)
   (* t (* b i))
   (if (<= i 3.1e-307)
     (* y (* x z))
     (if (<= i 1.9e+15) (* z (* b (- c))) (* b (* t 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 (i <= -1.9e-36) {
		tmp = t * (b * i);
	} else if (i <= 3.1e-307) {
		tmp = y * (x * z);
	} else if (i <= 1.9e+15) {
		tmp = z * (b * -c);
	} else {
		tmp = b * (t * 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 (i <= (-1.9d-36)) then
        tmp = t * (b * i)
    else if (i <= 3.1d-307) then
        tmp = y * (x * z)
    else if (i <= 1.9d+15) then
        tmp = z * (b * -c)
    else
        tmp = b * (t * 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 (i <= -1.9e-36) {
		tmp = t * (b * i);
	} else if (i <= 3.1e-307) {
		tmp = y * (x * z);
	} else if (i <= 1.9e+15) {
		tmp = z * (b * -c);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -1.9e-36:
		tmp = t * (b * i)
	elif i <= 3.1e-307:
		tmp = y * (x * z)
	elif i <= 1.9e+15:
		tmp = z * (b * -c)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -1.9e-36)
		tmp = Float64(t * Float64(b * i));
	elseif (i <= 3.1e-307)
		tmp = Float64(y * Float64(x * z));
	elseif (i <= 1.9e+15)
		tmp = Float64(z * Float64(b * Float64(-c)));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -1.9e-36)
		tmp = t * (b * i);
	elseif (i <= 3.1e-307)
		tmp = y * (x * z);
	elseif (i <= 1.9e+15)
		tmp = z * (b * -c);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -1.9e-36], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.1e-307], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.9e+15], N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if i < -1.89999999999999985e-36

   1. Initial program 59.5%

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

   3. Taylor expanded in t around inf 47.1%

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

      1. distribute-lft-out-- 47.1%

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

      2. *-commutative 47.1%

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

   5. Simplified 47.1%

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

   6. Taylor expanded in a around 0 36.9%

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

      1. *-commutative 36.9%

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

   8. Simplified 36.9%

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

   if -1.89999999999999985e-36 < i < 3.0999999999999998e-307

   1. Initial program 70.8%

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

   3. Taylor expanded in z around inf 50.8%

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

      1. *-commutative 50.8%

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

      2. *-commutative 50.8%

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

   5. Simplified 50.8%

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

   6. Taylor expanded in y around inf 36.1%

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

   7. Taylor expanded in z around 0 39.7%

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

      1. associate-*r* 36.1%

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

      2. *-commutative 36.1%

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

      3. associate-*r* 45.1%

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

   9. Simplified 45.1%

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

   if 3.0999999999999998e-307 < i < 1.9e15

   1. Initial program 78.8%

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

   3. Taylor expanded in z around inf 42.6%

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

      1. *-commutative 42.6%

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

      2. *-commutative 42.6%

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

   5. Simplified 42.6%

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

   6. Taylor expanded in y around 0 29.1%

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

      1. mul-1-neg 29.1%

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

      2. associate-*r* 29.2%

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

      3. distribute-rgt-neg-in 29.2%

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

   8. Simplified 29.2%

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

   if 1.9e15 < i

   1. Initial program 62.7%

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

   3. Taylor expanded in b around inf 45.2%

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

   4. Taylor expanded in i around inf 37.4%

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

4. Final simplification 36.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.9 \cdot 10^{-36}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 3.1 \cdot 10^{-307}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 1.9 \cdot 10^{+15}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 29.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.25 \cdot 10^{-36}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -7.5 \cdot 10^{-308}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 4.1 \cdot 10^{+14}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -1.25e-36)
   (* t (* b i))
   (if (<= i -7.5e-308)
     (* y (* x z))
     (if (<= i 4.1e+14) (* b (* z (- c))) (* b (* t 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 (i <= -1.25e-36) {
		tmp = t * (b * i);
	} else if (i <= -7.5e-308) {
		tmp = y * (x * z);
	} else if (i <= 4.1e+14) {
		tmp = b * (z * -c);
	} else {
		tmp = b * (t * 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 (i <= (-1.25d-36)) then
        tmp = t * (b * i)
    else if (i <= (-7.5d-308)) then
        tmp = y * (x * z)
    else if (i <= 4.1d+14) then
        tmp = b * (z * -c)
    else
        tmp = b * (t * 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 (i <= -1.25e-36) {
		tmp = t * (b * i);
	} else if (i <= -7.5e-308) {
		tmp = y * (x * z);
	} else if (i <= 4.1e+14) {
		tmp = b * (z * -c);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -1.25e-36:
		tmp = t * (b * i)
	elif i <= -7.5e-308:
		tmp = y * (x * z)
	elif i <= 4.1e+14:
		tmp = b * (z * -c)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -1.25e-36)
		tmp = Float64(t * Float64(b * i));
	elseif (i <= -7.5e-308)
		tmp = Float64(y * Float64(x * z));
	elseif (i <= 4.1e+14)
		tmp = Float64(b * Float64(z * Float64(-c)));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -1.25e-36)
		tmp = t * (b * i);
	elseif (i <= -7.5e-308)
		tmp = y * (x * z);
	elseif (i <= 4.1e+14)
		tmp = b * (z * -c);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -1.25e-36], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -7.5e-308], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4.1e+14], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if i < -1.25000000000000001e-36

   1. Initial program 59.5%

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

   3. Taylor expanded in t around inf 47.1%

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

      1. distribute-lft-out-- 47.1%

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

      2. *-commutative 47.1%

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

   5. Simplified 47.1%

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

   6. Taylor expanded in a around 0 36.9%

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

      1. *-commutative 36.9%

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

   8. Simplified 36.9%

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

   if -1.25000000000000001e-36 < i < -7.4999999999999998e-308

   1. Initial program 70.8%

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

   3. Taylor expanded in z around inf 50.8%

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

      1. *-commutative 50.8%

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

      2. *-commutative 50.8%

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

   5. Simplified 50.8%

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

   6. Taylor expanded in y around inf 36.1%

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

   7. Taylor expanded in z around 0 39.7%

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

      1. associate-*r* 36.1%

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

      2. *-commutative 36.1%

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

      3. associate-*r* 45.1%

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

   9. Simplified 45.1%

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

   if -7.4999999999999998e-308 < i < 4.1e14

   1. Initial program 78.8%

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

   3. Taylor expanded in z around inf 42.6%

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

      1. *-commutative 42.6%

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

      2. *-commutative 42.6%

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

   5. Simplified 42.6%

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

   6. Taylor expanded in y around 0 29.1%

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

      1. associate-*r* 29.1%

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

      2. neg-mul-1 29.1%

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

      3. *-commutative 29.1%

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

   8. Simplified 29.1%

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

   if 4.1e14 < i

   1. Initial program 62.7%

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

   3. Taylor expanded in b around inf 45.2%

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

   4. Taylor expanded in i around inf 37.4%

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

4. Final simplification 36.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.25 \cdot 10^{-36}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -7.5 \cdot 10^{-308}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 4.1 \cdot 10^{+14}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 29.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.75 \cdot 10^{-37}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 2.8 \cdot 10^{-131}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 5.6 \cdot 10^{+85}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -1.75e-37)
   (* t (* b i))
   (if (<= i 2.8e-131)
     (* y (* x z))
     (if (<= i 5.6e+85) (* j (* a c)) (* b (* t 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 (i <= -1.75e-37) {
		tmp = t * (b * i);
	} else if (i <= 2.8e-131) {
		tmp = y * (x * z);
	} else if (i <= 5.6e+85) {
		tmp = j * (a * c);
	} else {
		tmp = b * (t * 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 (i <= (-1.75d-37)) then
        tmp = t * (b * i)
    else if (i <= 2.8d-131) then
        tmp = y * (x * z)
    else if (i <= 5.6d+85) then
        tmp = j * (a * c)
    else
        tmp = b * (t * 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 (i <= -1.75e-37) {
		tmp = t * (b * i);
	} else if (i <= 2.8e-131) {
		tmp = y * (x * z);
	} else if (i <= 5.6e+85) {
		tmp = j * (a * c);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -1.75e-37:
		tmp = t * (b * i)
	elif i <= 2.8e-131:
		tmp = y * (x * z)
	elif i <= 5.6e+85:
		tmp = j * (a * c)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -1.75e-37)
		tmp = Float64(t * Float64(b * i));
	elseif (i <= 2.8e-131)
		tmp = Float64(y * Float64(x * z));
	elseif (i <= 5.6e+85)
		tmp = Float64(j * Float64(a * c));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -1.75e-37)
		tmp = t * (b * i);
	elseif (i <= 2.8e-131)
		tmp = y * (x * z);
	elseif (i <= 5.6e+85)
		tmp = j * (a * c);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -1.75e-37], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.8e-131], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5.6e+85], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if i < -1.7500000000000001e-37

   1. Initial program 59.5%

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

   3. Taylor expanded in t around inf 47.1%

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

      1. distribute-lft-out-- 47.1%

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

      2. *-commutative 47.1%

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

   5. Simplified 47.1%

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

   6. Taylor expanded in a around 0 36.9%

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

      1. *-commutative 36.9%

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

   8. Simplified 36.9%

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

   if -1.7500000000000001e-37 < i < 2.8e-131

   1. Initial program 76.5%

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

   3. Taylor expanded in z around inf 48.7%

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

      1. *-commutative 48.7%

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

      2. *-commutative 48.7%

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

   5. Simplified 48.7%

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

   6. Taylor expanded in y around inf 29.5%

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

   7. Taylor expanded in z around 0 32.8%

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

      1. associate-*r* 29.5%

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

      2. *-commutative 29.5%

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

      3. associate-*r* 36.0%

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

   9. Simplified 36.0%

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

   if 2.8e-131 < i < 5.5999999999999998e85

   1. Initial program 70.1%

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

   3. Taylor expanded in j around inf 48.6%

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

   4. Taylor expanded in a around inf 29.3%

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

   if 5.5999999999999998e85 < i

   1. Initial program 61.9%

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

   3. Taylor expanded in b around inf 47.3%

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

   4. Taylor expanded in i around inf 41.5%

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

4. Final simplification 36.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.75 \cdot 10^{-37}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 2.8 \cdot 10^{-131}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 5.6 \cdot 10^{+85}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 29.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.16 \cdot 10^{+93}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;j \leq 4 \cdot 10^{-284}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;j \leq 1.55 \cdot 10^{+67}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -1.16e+93)
   (* j (* a c))
   (if (<= j 4e-284)
     (* b (* t i))
     (if (<= j 1.55e+67) (* x (* y z)) (* c (* a j))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -1.16e+93) {
		tmp = j * (a * c);
	} else if (j <= 4e-284) {
		tmp = b * (t * i);
	} else if (j <= 1.55e+67) {
		tmp = x * (y * z);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (j <= (-1.16d+93)) then
        tmp = j * (a * c)
    else if (j <= 4d-284) then
        tmp = b * (t * i)
    else if (j <= 1.55d+67) then
        tmp = x * (y * z)
    else
        tmp = c * (a * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -1.16e+93) {
		tmp = j * (a * c);
	} else if (j <= 4e-284) {
		tmp = b * (t * i);
	} else if (j <= 1.55e+67) {
		tmp = x * (y * z);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -1.16e+93:
		tmp = j * (a * c)
	elif j <= 4e-284:
		tmp = b * (t * i)
	elif j <= 1.55e+67:
		tmp = x * (y * z)
	else:
		tmp = c * (a * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -1.16e+93)
		tmp = Float64(j * Float64(a * c));
	elseif (j <= 4e-284)
		tmp = Float64(b * Float64(t * i));
	elseif (j <= 1.55e+67)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(c * Float64(a * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -1.16e+93)
		tmp = j * (a * c);
	elseif (j <= 4e-284)
		tmp = b * (t * i);
	elseif (j <= 1.55e+67)
		tmp = x * (y * z);
	else
		tmp = c * (a * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -1.16e+93], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4e-284], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.55e+67], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.16e93

   1. Initial program 62.9%

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

   3. Taylor expanded in j around inf 57.4%

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

   4. Taylor expanded in a around inf 40.3%

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

   if -1.16e93 < j < 4.00000000000000015e-284

   1. Initial program 73.7%

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

   3. Taylor expanded in b around inf 48.0%

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

   4. Taylor expanded in i around inf 32.7%

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

   if 4.00000000000000015e-284 < j < 1.54999999999999998e67

   1. Initial program 68.5%

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

   3. Taylor expanded in z around inf 50.1%

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

      1. *-commutative 50.1%

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

      2. *-commutative 50.1%

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

   5. Simplified 50.1%

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

   6. Taylor expanded in y around inf 29.0%

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

   7. Taylor expanded in z around 0 30.2%

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

   if 1.54999999999999998e67 < j

   1. Initial program 59.1%

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

   3. Taylor expanded in c around inf 45.8%

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

      1. *-commutative 45.8%

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

   5. Simplified 45.8%

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

   6. Taylor expanded in j around inf 42.0%

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

      1. *-commutative 42.0%

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

   8. Simplified 42.0%

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

4. Final simplification 35.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.16 \cdot 10^{+93}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;j \leq 4 \cdot 10^{-284}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;j \leq 1.55 \cdot 10^{+67}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 51.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+101} \lor \neg \left(x \leq 8 \cdot 10^{+42}\right):\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= x -5.5e+101) (not (<= x 8e+42)))
   (* x (- (* y z) (* t a)))
   (* b (- (* t i) (* z c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((x <= -5.5e+101) || !(x <= 8e+42)) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = b * ((t * i) - (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((x <= (-5.5d+101)) .or. (.not. (x <= 8d+42))) then
        tmp = x * ((y * z) - (t * a))
    else
        tmp = b * ((t * i) - (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((x <= -5.5e+101) || !(x <= 8e+42)) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = b * ((t * i) - (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (x <= -5.5e+101) or not (x <= 8e+42):
		tmp = x * ((y * z) - (t * a))
	else:
		tmp = b * ((t * i) - (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((x <= -5.5e+101) || !(x <= 8e+42))
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	else
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((x <= -5.5e+101) || ~((x <= 8e+42)))
		tmp = x * ((y * z) - (t * a));
	else
		tmp = b * ((t * i) - (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[x, -5.5e+101], N[Not[LessEqual[x, 8e+42]], $MachinePrecision]], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.50000000000000018e101 or 8.00000000000000036e42 < x

   1. Initial program 67.9%

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

   3. Taylor expanded in x around inf 64.7%

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

   if -5.50000000000000018e101 < x < 8.00000000000000036e42

   1. Initial program 67.2%

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

   3. Taylor expanded in b around inf 48.9%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+101} \lor \neg \left(x \leq 8 \cdot 10^{+42}\right):\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 51.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{+147} \lor \neg \left(a \leq 9.5 \cdot 10^{+17}\right):\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -1.1e+147) (not (<= a 9.5e+17)))
   (* a (- (* c j) (* x t)))
   (* b (- (* t i) (* z c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -1.1e+147) || !(a <= 9.5e+17)) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = b * ((t * i) - (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((a <= (-1.1d+147)) .or. (.not. (a <= 9.5d+17))) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = b * ((t * i) - (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -1.1e+147) || !(a <= 9.5e+17)) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = b * ((t * i) - (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (a <= -1.1e+147) or not (a <= 9.5e+17):
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = b * ((t * i) - (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -1.1e+147) || !(a <= 9.5e+17))
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((a <= -1.1e+147) || ~((a <= 9.5e+17)))
		tmp = a * ((c * j) - (x * t));
	else
		tmp = b * ((t * i) - (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -1.1e+147], N[Not[LessEqual[a, 9.5e+17]], $MachinePrecision]], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.1000000000000001e147 or 9.5e17 < a

   1. Initial program 57.2%

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

   3. Taylor expanded in a around inf 62.8%

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

      1. +-commutative 62.8%

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

      2. mul-1-neg 62.8%

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

      3. unsub-neg 62.8%

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

      4. *-commutative 62.8%

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

   5. Simplified 62.8%

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

   if -1.1000000000000001e147 < a < 9.5e17

   1. Initial program 73.1%

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

   3. Taylor expanded in b around inf 47.5%

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

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{+147} \lor \neg \left(a \leq 9.5 \cdot 10^{+17}\right):\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 29.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{+68} \lor \neg \left(a \leq 1.12 \cdot 10^{+74}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -1.55e+68) (not (<= a 1.12e+74))) (* a (* c j)) (* b (* t 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 ((a <= -1.55e+68) || !(a <= 1.12e+74)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * 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 ((a <= (-1.55d+68)) .or. (.not. (a <= 1.12d+74))) then
        tmp = a * (c * j)
    else
        tmp = b * (t * 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 ((a <= -1.55e+68) || !(a <= 1.12e+74)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (a <= -1.55e+68) or not (a <= 1.12e+74):
		tmp = a * (c * j)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -1.55e+68) || !(a <= 1.12e+74))
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((a <= -1.55e+68) || ~((a <= 1.12e+74)))
		tmp = a * (c * j);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -1.55e+68], N[Not[LessEqual[a, 1.12e+74]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.5499999999999999e68 or 1.12000000000000003e74 < a

   1. Initial program 53.2%

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

   3. Taylor expanded in a around inf 58.7%

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

      1. +-commutative 58.7%

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

      2. mul-1-neg 58.7%

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

      3. unsub-neg 58.7%

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

      4. *-commutative 58.7%

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

   5. Simplified 58.7%

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

   6. Taylor expanded in j around inf 35.8%

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

      1. *-commutative 35.8%

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

   8. Simplified 35.8%

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

   if -1.5499999999999999e68 < a < 1.12000000000000003e74

   1. Initial program 75.9%

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

   3. Taylor expanded in b around inf 47.1%

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

   4. Taylor expanded in i around inf 29.8%

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

4. Final simplification 32.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{+68} \lor \neg \left(a \leq 1.12 \cdot 10^{+74}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 28.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+139}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{+74}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -9.5e+139)
   (* j (* a c))
   (if (<= a 1.08e+74) (* t (* b i)) (* a (* c j)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -9.5e+139) {
		tmp = j * (a * c);
	} else if (a <= 1.08e+74) {
		tmp = t * (b * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (a <= (-9.5d+139)) then
        tmp = j * (a * c)
    else if (a <= 1.08d+74) then
        tmp = t * (b * i)
    else
        tmp = a * (c * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -9.5e+139) {
		tmp = j * (a * c);
	} else if (a <= 1.08e+74) {
		tmp = t * (b * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -9.5e+139:
		tmp = j * (a * c)
	elif a <= 1.08e+74:
		tmp = t * (b * i)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -9.5e+139)
		tmp = Float64(j * Float64(a * c));
	elseif (a <= 1.08e+74)
		tmp = Float64(t * Float64(b * i));
	else
		tmp = Float64(a * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -9.5e+139)
		tmp = j * (a * c);
	elseif (a <= 1.08e+74)
		tmp = t * (b * i);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -9.5e+139], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.08e+74], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.5000000000000002e139

   1. Initial program 62.8%

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

   3. Taylor expanded in j around inf 44.9%

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

   4. Taylor expanded in a around inf 38.4%

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

   if -9.5000000000000002e139 < a < 1.08e74

   1. Initial program 74.0%

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

   3. Taylor expanded in t around inf 39.7%

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

      1. distribute-lft-out-- 39.7%

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

      2. *-commutative 39.7%

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

   5. Simplified 39.7%

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

   6. Taylor expanded in a around 0 30.4%

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

      1. *-commutative 30.4%

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

   8. Simplified 30.4%

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

   if 1.08e74 < a

   1. Initial program 48.9%

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

   3. Taylor expanded in a around inf 65.6%

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

      1. +-commutative 65.6%

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

      2. mul-1-neg 65.6%

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

      3. unsub-neg 65.6%

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

      4. *-commutative 65.6%

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

   5. Simplified 65.6%

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

   6. Taylor expanded in j around inf 41.0%

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

      1. *-commutative 41.0%

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

   8. Simplified 41.0%

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

4. Final simplification 33.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+139}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{+74}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 28.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{+140}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;a \leq 9.7 \cdot 10^{+73}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -1.8e+140)
   (* j (* a c))
   (if (<= a 9.7e+73) (* b (* t i)) (* a (* c j)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -1.8e+140) {
		tmp = j * (a * c);
	} else if (a <= 9.7e+73) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (a <= (-1.8d+140)) then
        tmp = j * (a * c)
    else if (a <= 9.7d+73) then
        tmp = b * (t * i)
    else
        tmp = a * (c * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -1.8e+140) {
		tmp = j * (a * c);
	} else if (a <= 9.7e+73) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -1.8e+140:
		tmp = j * (a * c)
	elif a <= 9.7e+73:
		tmp = b * (t * i)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -1.8e+140)
		tmp = Float64(j * Float64(a * c));
	elseif (a <= 9.7e+73)
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(a * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -1.8e+140)
		tmp = j * (a * c);
	elseif (a <= 9.7e+73)
		tmp = b * (t * i);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -1.8e+140], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.7e+73], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.8e140

   1. Initial program 62.8%

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

   3. Taylor expanded in j around inf 44.9%

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

   4. Taylor expanded in a around inf 38.4%

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

   if -1.8e140 < a < 9.7000000000000006e73

   1. Initial program 74.0%

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

   3. Taylor expanded in b around inf 46.5%

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

   4. Taylor expanded in i around inf 29.2%

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

   if 9.7000000000000006e73 < a

   1. Initial program 48.9%

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

   3. Taylor expanded in a around inf 65.6%

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

      1. +-commutative 65.6%

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

      2. mul-1-neg 65.6%

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

      3. unsub-neg 65.6%

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

      4. *-commutative 65.6%

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

   5. Simplified 65.6%

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

   6. Taylor expanded in j around inf 41.0%

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

      1. *-commutative 41.0%

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

   8. Simplified 41.0%

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

4. Final simplification 32.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{+140}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;a \leq 9.7 \cdot 10^{+73}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 29.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -9.4 \cdot 10^{+92}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{+88}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -9.4e+92)
   (* a (* c j))
   (if (<= j 4.5e+88) (* b (* t i)) (* c (* a j)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -9.4e+92) {
		tmp = a * (c * j);
	} else if (j <= 4.5e+88) {
		tmp = b * (t * i);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (j <= (-9.4d+92)) then
        tmp = a * (c * j)
    else if (j <= 4.5d+88) then
        tmp = b * (t * i)
    else
        tmp = c * (a * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -9.4e+92) {
		tmp = a * (c * j);
	} else if (j <= 4.5e+88) {
		tmp = b * (t * i);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -9.4e+92:
		tmp = a * (c * j)
	elif j <= 4.5e+88:
		tmp = b * (t * i)
	else:
		tmp = c * (a * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -9.4e+92)
		tmp = Float64(a * Float64(c * j));
	elseif (j <= 4.5e+88)
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(c * Float64(a * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -9.4e+92)
		tmp = a * (c * j);
	elseif (j <= 4.5e+88)
		tmp = b * (t * i);
	else
		tmp = c * (a * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -9.4e+92], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.5e+88], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -9.4000000000000001e92

   1. Initial program 62.9%

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

   3. Taylor expanded in a around inf 46.5%

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

      1. +-commutative 46.5%

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

      2. mul-1-neg 46.5%

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

      3. unsub-neg 46.5%

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

      4. *-commutative 46.5%

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

   5. Simplified 46.5%

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

   6. Taylor expanded in j around inf 40.2%

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

      1. *-commutative 40.2%

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

   8. Simplified 40.2%

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

   if -9.4000000000000001e92 < j < 4.5e88

   1. Initial program 71.5%

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

   3. Taylor expanded in b around inf 43.6%

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

   4. Taylor expanded in i around inf 27.6%

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

   if 4.5e88 < j

   1. Initial program 57.7%

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

   3. Taylor expanded in c around inf 47.5%

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

      1. *-commutative 47.5%

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

   5. Simplified 47.5%

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

   6. Taylor expanded in j around inf 43.4%

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

      1. *-commutative 43.4%

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

   8. Simplified 43.4%

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

4. Final simplification 32.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -9.4 \cdot 10^{+92}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{+88}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 22.5% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(c \cdot j\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 67.5%

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

3. Taylor expanded in a around inf 34.7%

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

   1. +-commutative 34.7%

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

   2. mul-1-neg 34.7%

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

   3. unsub-neg 34.7%

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

   4. *-commutative 34.7%

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

5. Simplified 34.7%

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

6. Taylor expanded in j around inf 19.3%

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

   1. *-commutative 19.3%

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

8. Simplified 19.3%

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

9. Final simplification 19.3%

   \[\leadsto a \cdot \left(c \cdot j\right) \]
10. Add Preprocessing

Developer Target 1: 58.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right)\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + t\_1\\ \mathbf{if}\;x < -1.469694296777705 \cdot 10^{-64}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x < 3.2113527362226803 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* c a) (* y i))))
        (t_2
         (+
          (-
           (* x (- (* y z) (* t a)))
           (/
            (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0)))
            (+ (* c z) (* t i))))
          t_1)))
   (if (< x -1.469694296777705e-64)
     t_2
     (if (< x 3.2113527362226803e-147)
       (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) t_1))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (pow((c * z), 2.0) - pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((c * a) - (y * i))
    t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ** 2.0d0) - ((t * i) ** 2.0d0))) / ((c * z) + (t * i)))) + t_1
    if (x < (-1.469694296777705d-64)) then
        tmp = t_2
    else if (x < 3.2113527362226803d-147) then
        tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (Math.pow((c * z), 2.0) - Math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((c * a) - (y * i))
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (math.pow((c * z), 2.0) - math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1
	tmp = 0
	if x < -1.469694296777705e-64:
		tmp = t_2
	elif x < 3.2113527362226803e-147:
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(c * a) - Float64(y * i)))
	t_2 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(Float64(b * Float64((Float64(c * z) ^ 2.0) - (Float64(t * i) ^ 2.0))) / Float64(Float64(c * z) + Float64(t * i)))) + t_1)
	tmp = 0.0
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = Float64(Float64(Float64(Float64(b * i) - Float64(x * a)) * t) - Float64(Float64(z * Float64(c * b)) - t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((c * a) - (y * i));
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ^ 2.0) - ((t * i) ^ 2.0))) / ((c * z) + (t * i)))) + t_1;
	tmp = 0.0;
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[Power[N[(c * z), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(t * i), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * z), $MachinePrecision] + N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[Less[x, -1.469694296777705e-64], t$95$2, If[Less[x, 3.2113527362226803e-147], N[(N[(N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] - N[(N[(z * N[(c * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024116 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< x -293938859355541/2000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2) (pow (* t i) 2))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 32113527362226803/10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2) (pow (* t i) 2))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i)))))