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

Percentage Accurate: 72.9% → 81.8%

Time: 29.2s

Alternatives: 22

Speedup: 0.5×

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

Specification

Math

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

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: 72.9% 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: 81.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 89.7%

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

   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 52.7%

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

      1. *-commutative 52.7%

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

   5. Simplified 52.7%

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

4. Final simplification 83.3%

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

Alternative 2: 49.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t \cdot a\right) \cdot \left(j \cdot \frac{c}{t} - x\right)\\ t_2 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -9.5 \cdot 10^{+17}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -1.1 \cdot 10^{-126}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -2.6 \cdot 10^{-217}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq 1.4 \cdot 10^{-251}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 9.5 \cdot 10^{-185}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 2.6 \cdot 10^{-99}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 8.5 \cdot 10^{-25}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq 4.3 \cdot 10^{+192}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* t a) (- (* j (/ c t)) x))) (t_2 (* i (- (* t b) (* y j)))))
   (if (<= i -9.5e+17)
     t_2
     (if (<= i -1.1e-126)
       t_1
       (if (<= i -2.6e-217)
         (* x (- (* y z) (* t a)))
         (if (<= i 1.4e-251)
           t_1
           (if (<= i 9.5e-185)
             (* z (- (* x y) (* b c)))
             (if (<= i 2.6e-99)
               t_1
               (if (<= i 8.5e-25)
                 (* b (- (* t i) (* z c)))
                 (if (<= i 4.3e+192) (* y (- (* x z) (* i j))) 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 * a) * ((j * (c / t)) - x);
	double t_2 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -9.5e+17) {
		tmp = t_2;
	} else if (i <= -1.1e-126) {
		tmp = t_1;
	} else if (i <= -2.6e-217) {
		tmp = x * ((y * z) - (t * a));
	} else if (i <= 1.4e-251) {
		tmp = t_1;
	} else if (i <= 9.5e-185) {
		tmp = z * ((x * y) - (b * c));
	} else if (i <= 2.6e-99) {
		tmp = t_1;
	} else if (i <= 8.5e-25) {
		tmp = b * ((t * i) - (z * c));
	} else if (i <= 4.3e+192) {
		tmp = y * ((x * z) - (i * j));
	} 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 * a) * ((j * (c / t)) - x)
    t_2 = i * ((t * b) - (y * j))
    if (i <= (-9.5d+17)) then
        tmp = t_2
    else if (i <= (-1.1d-126)) then
        tmp = t_1
    else if (i <= (-2.6d-217)) then
        tmp = x * ((y * z) - (t * a))
    else if (i <= 1.4d-251) then
        tmp = t_1
    else if (i <= 9.5d-185) then
        tmp = z * ((x * y) - (b * c))
    else if (i <= 2.6d-99) then
        tmp = t_1
    else if (i <= 8.5d-25) then
        tmp = b * ((t * i) - (z * c))
    else if (i <= 4.3d+192) then
        tmp = y * ((x * z) - (i * j))
    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 * a) * ((j * (c / t)) - x);
	double t_2 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -9.5e+17) {
		tmp = t_2;
	} else if (i <= -1.1e-126) {
		tmp = t_1;
	} else if (i <= -2.6e-217) {
		tmp = x * ((y * z) - (t * a));
	} else if (i <= 1.4e-251) {
		tmp = t_1;
	} else if (i <= 9.5e-185) {
		tmp = z * ((x * y) - (b * c));
	} else if (i <= 2.6e-99) {
		tmp = t_1;
	} else if (i <= 8.5e-25) {
		tmp = b * ((t * i) - (z * c));
	} else if (i <= 4.3e+192) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (t * a) * ((j * (c / t)) - x)
	t_2 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -9.5e+17:
		tmp = t_2
	elif i <= -1.1e-126:
		tmp = t_1
	elif i <= -2.6e-217:
		tmp = x * ((y * z) - (t * a))
	elif i <= 1.4e-251:
		tmp = t_1
	elif i <= 9.5e-185:
		tmp = z * ((x * y) - (b * c))
	elif i <= 2.6e-99:
		tmp = t_1
	elif i <= 8.5e-25:
		tmp = b * ((t * i) - (z * c))
	elif i <= 4.3e+192:
		tmp = y * ((x * z) - (i * j))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(t * a) * Float64(Float64(j * Float64(c / t)) - x))
	t_2 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -9.5e+17)
		tmp = t_2;
	elseif (i <= -1.1e-126)
		tmp = t_1;
	elseif (i <= -2.6e-217)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (i <= 1.4e-251)
		tmp = t_1;
	elseif (i <= 9.5e-185)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (i <= 2.6e-99)
		tmp = t_1;
	elseif (i <= 8.5e-25)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (i <= 4.3e+192)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	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 * a) * ((j * (c / t)) - x);
	t_2 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -9.5e+17)
		tmp = t_2;
	elseif (i <= -1.1e-126)
		tmp = t_1;
	elseif (i <= -2.6e-217)
		tmp = x * ((y * z) - (t * a));
	elseif (i <= 1.4e-251)
		tmp = t_1;
	elseif (i <= 9.5e-185)
		tmp = z * ((x * y) - (b * c));
	elseif (i <= 2.6e-99)
		tmp = t_1;
	elseif (i <= 8.5e-25)
		tmp = b * ((t * i) - (z * c));
	elseif (i <= 4.3e+192)
		tmp = y * ((x * z) - (i * j));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(t * a), $MachinePrecision] * N[(N[(j * N[(c / t), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -9.5e+17], t$95$2, If[LessEqual[i, -1.1e-126], t$95$1, If[LessEqual[i, -2.6e-217], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.4e-251], t$95$1, If[LessEqual[i, 9.5e-185], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.6e-99], t$95$1, If[LessEqual[i, 8.5e-25], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4.3e+192], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -9.5e17 or 4.29999999999999976e192 < i

   1. Initial program 60.0%

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

   3. Taylor expanded in i around inf 72.3%

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

      1. distribute-lft-out-- 72.3%

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

      2. *-commutative 72.3%

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

      3. *-commutative 72.3%

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

   5. Simplified 72.3%

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

   if -9.5e17 < i < -1.10000000000000007e-126 or -2.59999999999999993e-217 < i < 1.39999999999999994e-251 or 9.50000000000000042e-185 < i < 2.60000000000000005e-99

   1. Initial program 84.3%

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

   3. Taylor expanded in a around inf 62.1%

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

      1. +-commutative 62.1%

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

      2. mul-1-neg 62.1%

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

      3. unsub-neg 62.1%

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

      4. *-commutative 62.1%

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

      5. *-commutative 62.1%

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

   5. Simplified 62.1%

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

   6. Taylor expanded in t around inf 63.3%

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

      1. +-commutative 63.3%

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

      2. mul-1-neg 63.3%

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

      3. unsub-neg 63.3%

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

      4. associate-/l* 64.5%

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

      5. associate-/l* 63.6%

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

   8. Simplified 63.6%

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

   9. Taylor expanded in t around inf 63.3%

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

       1. neg-mul-1 63.3%

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

       2. distribute-rgt-in 62.0%

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

       3. associate-*r* 63.2%

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

       4. *-commutative 63.2%

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

       5. associate-*r/ 58.8%

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

       6. distribute-rgt-in 60.0%

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

       7. +-commutative 60.0%

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

       8. distribute-lft-in 58.8%

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

       9. associate-*r/ 63.2%

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

       10. *-commutative 63.2%

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

       11. associate-*r* 62.0%

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

       12. associate-/l* 63.2%

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

       13. associate-*r/ 62.4%

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

       14. associate-*r* 52.5%

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

       15. *-commutative 52.5%

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

       16. distribute-rgt-neg-in 52.5%

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

   11. Simplified 68.1%

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

   if -1.10000000000000007e-126 < i < -2.59999999999999993e-217

   1. Initial program 87.9%

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

      1. sub-neg 87.9%

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

      2. distribute-rgt-in 83.9%

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

      3. *-commutative 83.9%

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

      4. distribute-rgt-neg-in 83.9%

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

   4. Applied egg-rr 83.9%

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

   5. Taylor expanded in x around inf 65.1%

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

      1. *-commutative 65.1%

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

      2. *-commutative 65.1%

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

   7. Simplified 65.1%

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

   if 1.39999999999999994e-251 < i < 9.50000000000000042e-185

   1. Initial program 70.6%

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

   3. Taylor expanded in z around inf 75.9%

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

      1. *-commutative 75.9%

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

   5. Simplified 75.9%

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

   if 2.60000000000000005e-99 < i < 8.49999999999999981e-25

   1. Initial program 92.2%

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

   3. Taylor expanded in b around inf 77.3%

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

      1. *-commutative 77.3%

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

      2. *-commutative 77.3%

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

   5. Simplified 77.3%

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

   if 8.49999999999999981e-25 < i < 4.29999999999999976e192

   1. Initial program 68.1%

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

   3. Taylor expanded in y around inf 63.6%

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

      1. +-commutative 63.6%

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

      2. mul-1-neg 63.6%

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

      3. unsub-neg 63.6%

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

      4. *-commutative 63.6%

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

   5. Simplified 63.6%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -9.5 \cdot 10^{+17}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -1.1 \cdot 10^{-126}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(j \cdot \frac{c}{t} - x\right)\\ \mathbf{elif}\;i \leq -2.6 \cdot 10^{-217}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq 1.4 \cdot 10^{-251}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(j \cdot \frac{c}{t} - x\right)\\ \mathbf{elif}\;i \leq 9.5 \cdot 10^{-185}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 2.6 \cdot 10^{-99}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(j \cdot \frac{c}{t} - x\right)\\ \mathbf{elif}\;i \leq 8.5 \cdot 10^{-25}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq 4.3 \cdot 10^{+192}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 49.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t \cdot a\right) \cdot \left(j \cdot \frac{c}{t} - x\right)\\ t_2 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -3.2 \cdot 10^{+14}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -7.2 \cdot 10^{-127}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -1.3 \cdot 10^{-227}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq 2.4 \cdot 10^{-250}:\\ \;\;\;\;t \cdot \left(a \cdot \left(c \cdot \frac{j}{t}\right) - x \cdot a\right)\\ \mathbf{elif}\;i \leq 3.8 \cdot 10^{-183}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 2.6 \cdot 10^{-99}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 2.2 \cdot 10^{-25}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq 4.4 \cdot 10^{+192}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* t a) (- (* j (/ c t)) x))) (t_2 (* i (- (* t b) (* y j)))))
   (if (<= i -3.2e+14)
     t_2
     (if (<= i -7.2e-127)
       t_1
       (if (<= i -1.3e-227)
         (* x (- (* y z) (* t a)))
         (if (<= i 2.4e-250)
           (* t (- (* a (* c (/ j t))) (* x a)))
           (if (<= i 3.8e-183)
             (* z (- (* x y) (* b c)))
             (if (<= i 2.6e-99)
               t_1
               (if (<= i 2.2e-25)
                 (* b (- (* t i) (* z c)))
                 (if (<= i 4.4e+192) (* y (- (* x z) (* i j))) 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 * a) * ((j * (c / t)) - x);
	double t_2 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -3.2e+14) {
		tmp = t_2;
	} else if (i <= -7.2e-127) {
		tmp = t_1;
	} else if (i <= -1.3e-227) {
		tmp = x * ((y * z) - (t * a));
	} else if (i <= 2.4e-250) {
		tmp = t * ((a * (c * (j / t))) - (x * a));
	} else if (i <= 3.8e-183) {
		tmp = z * ((x * y) - (b * c));
	} else if (i <= 2.6e-99) {
		tmp = t_1;
	} else if (i <= 2.2e-25) {
		tmp = b * ((t * i) - (z * c));
	} else if (i <= 4.4e+192) {
		tmp = y * ((x * z) - (i * j));
	} 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 * a) * ((j * (c / t)) - x)
    t_2 = i * ((t * b) - (y * j))
    if (i <= (-3.2d+14)) then
        tmp = t_2
    else if (i <= (-7.2d-127)) then
        tmp = t_1
    else if (i <= (-1.3d-227)) then
        tmp = x * ((y * z) - (t * a))
    else if (i <= 2.4d-250) then
        tmp = t * ((a * (c * (j / t))) - (x * a))
    else if (i <= 3.8d-183) then
        tmp = z * ((x * y) - (b * c))
    else if (i <= 2.6d-99) then
        tmp = t_1
    else if (i <= 2.2d-25) then
        tmp = b * ((t * i) - (z * c))
    else if (i <= 4.4d+192) then
        tmp = y * ((x * z) - (i * j))
    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 * a) * ((j * (c / t)) - x);
	double t_2 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -3.2e+14) {
		tmp = t_2;
	} else if (i <= -7.2e-127) {
		tmp = t_1;
	} else if (i <= -1.3e-227) {
		tmp = x * ((y * z) - (t * a));
	} else if (i <= 2.4e-250) {
		tmp = t * ((a * (c * (j / t))) - (x * a));
	} else if (i <= 3.8e-183) {
		tmp = z * ((x * y) - (b * c));
	} else if (i <= 2.6e-99) {
		tmp = t_1;
	} else if (i <= 2.2e-25) {
		tmp = b * ((t * i) - (z * c));
	} else if (i <= 4.4e+192) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (t * a) * ((j * (c / t)) - x)
	t_2 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -3.2e+14:
		tmp = t_2
	elif i <= -7.2e-127:
		tmp = t_1
	elif i <= -1.3e-227:
		tmp = x * ((y * z) - (t * a))
	elif i <= 2.4e-250:
		tmp = t * ((a * (c * (j / t))) - (x * a))
	elif i <= 3.8e-183:
		tmp = z * ((x * y) - (b * c))
	elif i <= 2.6e-99:
		tmp = t_1
	elif i <= 2.2e-25:
		tmp = b * ((t * i) - (z * c))
	elif i <= 4.4e+192:
		tmp = y * ((x * z) - (i * j))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(t * a) * Float64(Float64(j * Float64(c / t)) - x))
	t_2 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -3.2e+14)
		tmp = t_2;
	elseif (i <= -7.2e-127)
		tmp = t_1;
	elseif (i <= -1.3e-227)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (i <= 2.4e-250)
		tmp = Float64(t * Float64(Float64(a * Float64(c * Float64(j / t))) - Float64(x * a)));
	elseif (i <= 3.8e-183)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (i <= 2.6e-99)
		tmp = t_1;
	elseif (i <= 2.2e-25)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (i <= 4.4e+192)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	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 * a) * ((j * (c / t)) - x);
	t_2 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -3.2e+14)
		tmp = t_2;
	elseif (i <= -7.2e-127)
		tmp = t_1;
	elseif (i <= -1.3e-227)
		tmp = x * ((y * z) - (t * a));
	elseif (i <= 2.4e-250)
		tmp = t * ((a * (c * (j / t))) - (x * a));
	elseif (i <= 3.8e-183)
		tmp = z * ((x * y) - (b * c));
	elseif (i <= 2.6e-99)
		tmp = t_1;
	elseif (i <= 2.2e-25)
		tmp = b * ((t * i) - (z * c));
	elseif (i <= 4.4e+192)
		tmp = y * ((x * z) - (i * j));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(t * a), $MachinePrecision] * N[(N[(j * N[(c / t), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -3.2e+14], t$95$2, If[LessEqual[i, -7.2e-127], t$95$1, If[LessEqual[i, -1.3e-227], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.4e-250], N[(t * N[(N[(a * N[(c * N[(j / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.8e-183], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.6e-99], t$95$1, If[LessEqual[i, 2.2e-25], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4.4e+192], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if i < -3.2e14 or 4.4000000000000001e192 < i

   1. Initial program 60.0%

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

   3. Taylor expanded in i around inf 72.3%

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

      1. distribute-lft-out-- 72.3%

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

      2. *-commutative 72.3%

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

      3. *-commutative 72.3%

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

   5. Simplified 72.3%

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

   if -3.2e14 < i < -7.1999999999999999e-127 or 3.7999999999999996e-183 < i < 2.60000000000000005e-99

   1. Initial program 82.9%

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

   3. Taylor expanded in a around inf 65.1%

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

      1. +-commutative 65.1%

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

      2. mul-1-neg 65.1%

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

      3. unsub-neg 65.1%

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

      4. *-commutative 65.1%

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

      5. *-commutative 65.1%

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

   5. Simplified 65.1%

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

   6. Taylor expanded in t around inf 65.1%

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

      1. +-commutative 65.1%

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

      2. mul-1-neg 65.1%

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

      3. unsub-neg 65.1%

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

      4. associate-/l* 67.2%

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

      5. associate-/l* 65.1%

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

   8. Simplified 65.1%

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

   9. Taylor expanded in t around inf 65.1%

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

       1. neg-mul-1 65.1%

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

       2. distribute-rgt-in 65.1%

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

       3. associate-*r* 65.1%

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

       4. *-commutative 65.1%

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

       5. associate-*r/ 58.7%

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

       6. distribute-rgt-in 58.7%

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

       7. +-commutative 58.7%

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

       8. distribute-lft-in 58.7%

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

       9. associate-*r/ 65.1%

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

       10. *-commutative 65.1%

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

       11. associate-*r* 65.1%

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

       12. associate-/l* 67.2%

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

       13. associate-*r/ 65.1%

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

       14. associate-*r* 54.4%

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

       15. *-commutative 54.4%

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

       16. distribute-rgt-neg-in 54.4%

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

   11. Simplified 71.5%

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

   if -7.1999999999999999e-127 < i < -1.30000000000000006e-227

   1. Initial program 88.8%

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

      1. sub-neg 88.8%

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

      2. distribute-rgt-in 85.1%

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

      3. *-commutative 85.1%

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

      4. distribute-rgt-neg-in 85.1%

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

   4. Applied egg-rr 85.1%

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

   5. Taylor expanded in x around inf 64.2%

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

      1. *-commutative 64.2%

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

      2. *-commutative 64.2%

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

   7. Simplified 64.2%

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

   if -1.30000000000000006e-227 < i < 2.3999999999999999e-250

   1. Initial program 85.3%

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

   3. Taylor expanded in a around inf 58.6%

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

      1. +-commutative 58.6%

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

      2. mul-1-neg 58.6%

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

      3. unsub-neg 58.6%

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

      4. *-commutative 58.6%

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

      5. *-commutative 58.6%

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

   5. Simplified 58.6%

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

   6. Taylor expanded in t around inf 64.3%

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

      1. +-commutative 64.3%

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

      2. mul-1-neg 64.3%

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

      3. unsub-neg 64.3%

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

      4. associate-/l* 64.3%

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

      5. associate-/l* 65.2%

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

   8. Simplified 65.2%

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

   if 2.3999999999999999e-250 < i < 3.7999999999999996e-183

   1. Initial program 70.6%

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

   3. Taylor expanded in z around inf 75.9%

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

      1. *-commutative 75.9%

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

   5. Simplified 75.9%

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

   if 2.60000000000000005e-99 < i < 2.2000000000000002e-25

   1. Initial program 92.2%

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

   3. Taylor expanded in b around inf 77.3%

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

      1. *-commutative 77.3%

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

      2. *-commutative 77.3%

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

   5. Simplified 77.3%

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

   if 2.2000000000000002e-25 < i < 4.4000000000000001e192

   1. Initial program 68.1%

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

   3. Taylor expanded in y around inf 63.6%

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

      1. +-commutative 63.6%

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

      2. mul-1-neg 63.6%

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

      3. unsub-neg 63.6%

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

      4. *-commutative 63.6%

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

   5. Simplified 63.6%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z - j \cdot i\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.2 \cdot 10^{+14}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -7.2 \cdot 10^{-127}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(j \cdot \frac{c}{t} - x\right)\\ \mathbf{elif}\;i \leq -1.3 \cdot 10^{-227}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq 2.4 \cdot 10^{-250}:\\ \;\;\;\;t \cdot \left(a \cdot \left(c \cdot \frac{j}{t}\right) - x \cdot a\right)\\ \mathbf{elif}\;i \leq 3.8 \cdot 10^{-183}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 2.6 \cdot 10^{-99}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(j \cdot \frac{c}{t} - x\right)\\ \mathbf{elif}\;i \leq 2.2 \cdot 10^{-25}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq 4.4 \cdot 10^{+192}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 52.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_3 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;y \leq -2.16 \cdot 10^{+151}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{+126}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-304}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-185}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 3300000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+51}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j))))
        (t_2 (* a (- (* c j) (* x t))))
        (t_3 (* c (- (* a j) (* z b)))))
   (if (<= y -2.16e+151)
     t_1
     (if (<= y -1.2e+126)
       t_2
       (if (<= y -2.4e-37)
         t_1
         (if (<= y -6.2e-304)
           t_2
           (if (<= y 2.05e-185)
             t_3
             (if (<= y 3300000000000.0) t_2 (if (<= y 6.2e+51) t_3 t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double t_2 = a * ((c * j) - (x * t));
	double t_3 = c * ((a * j) - (z * b));
	double tmp;
	if (y <= -2.16e+151) {
		tmp = t_1;
	} else if (y <= -1.2e+126) {
		tmp = t_2;
	} else if (y <= -2.4e-37) {
		tmp = t_1;
	} else if (y <= -6.2e-304) {
		tmp = t_2;
	} else if (y <= 2.05e-185) {
		tmp = t_3;
	} else if (y <= 3300000000000.0) {
		tmp = t_2;
	} else if (y <= 6.2e+51) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y * ((x * z) - (i * j))
    t_2 = a * ((c * j) - (x * t))
    t_3 = c * ((a * j) - (z * b))
    if (y <= (-2.16d+151)) then
        tmp = t_1
    else if (y <= (-1.2d+126)) then
        tmp = t_2
    else if (y <= (-2.4d-37)) then
        tmp = t_1
    else if (y <= (-6.2d-304)) then
        tmp = t_2
    else if (y <= 2.05d-185) then
        tmp = t_3
    else if (y <= 3300000000000.0d0) then
        tmp = t_2
    else if (y <= 6.2d+51) then
        tmp = t_3
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double t_2 = a * ((c * j) - (x * t));
	double t_3 = c * ((a * j) - (z * b));
	double tmp;
	if (y <= -2.16e+151) {
		tmp = t_1;
	} else if (y <= -1.2e+126) {
		tmp = t_2;
	} else if (y <= -2.4e-37) {
		tmp = t_1;
	} else if (y <= -6.2e-304) {
		tmp = t_2;
	} else if (y <= 2.05e-185) {
		tmp = t_3;
	} else if (y <= 3300000000000.0) {
		tmp = t_2;
	} else if (y <= 6.2e+51) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	t_2 = a * ((c * j) - (x * t))
	t_3 = c * ((a * j) - (z * b))
	tmp = 0
	if y <= -2.16e+151:
		tmp = t_1
	elif y <= -1.2e+126:
		tmp = t_2
	elif y <= -2.4e-37:
		tmp = t_1
	elif y <= -6.2e-304:
		tmp = t_2
	elif y <= 2.05e-185:
		tmp = t_3
	elif y <= 3300000000000.0:
		tmp = t_2
	elif y <= 6.2e+51:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_3 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (y <= -2.16e+151)
		tmp = t_1;
	elseif (y <= -1.2e+126)
		tmp = t_2;
	elseif (y <= -2.4e-37)
		tmp = t_1;
	elseif (y <= -6.2e-304)
		tmp = t_2;
	elseif (y <= 2.05e-185)
		tmp = t_3;
	elseif (y <= 3300000000000.0)
		tmp = t_2;
	elseif (y <= 6.2e+51)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((x * z) - (i * j));
	t_2 = a * ((c * j) - (x * t));
	t_3 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (y <= -2.16e+151)
		tmp = t_1;
	elseif (y <= -1.2e+126)
		tmp = t_2;
	elseif (y <= -2.4e-37)
		tmp = t_1;
	elseif (y <= -6.2e-304)
		tmp = t_2;
	elseif (y <= 2.05e-185)
		tmp = t_3;
	elseif (y <= 3300000000000.0)
		tmp = t_2;
	elseif (y <= 6.2e+51)
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.16e+151], t$95$1, If[LessEqual[y, -1.2e+126], t$95$2, If[LessEqual[y, -2.4e-37], t$95$1, If[LessEqual[y, -6.2e-304], t$95$2, If[LessEqual[y, 2.05e-185], t$95$3, If[LessEqual[y, 3300000000000.0], t$95$2, If[LessEqual[y, 6.2e+51], t$95$3, t$95$1]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.16000000000000006e151 or -1.20000000000000006e126 < y < -2.39999999999999991e-37 or 6.20000000000000022e51 < y

   1. Initial program 68.1%

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

   3. Taylor expanded in y around inf 68.6%

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

      1. +-commutative 68.6%

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

      2. mul-1-neg 68.6%

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

      3. unsub-neg 68.6%

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

      4. *-commutative 68.6%

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

   5. Simplified 68.6%

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

   if -2.16000000000000006e151 < y < -1.20000000000000006e126 or -2.39999999999999991e-37 < y < -6.1999999999999997e-304 or 2.05e-185 < y < 3.3e12

   1. Initial program 81.8%

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

   3. Taylor expanded in a around inf 61.5%

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

      1. +-commutative 61.5%

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

      2. mul-1-neg 61.5%

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

      3. unsub-neg 61.5%

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

      4. *-commutative 61.5%

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

      5. *-commutative 61.5%

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

   5. Simplified 61.5%

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

   if -6.1999999999999997e-304 < y < 2.05e-185 or 3.3e12 < y < 6.20000000000000022e51

   1. Initial program 74.8%

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

   3. Taylor expanded in c around inf 69.8%

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

      1. *-commutative 69.8%

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

   5. Simplified 69.8%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.16 \cdot 10^{+151}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{+126}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-37}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-304}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-185}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 3300000000000:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+51}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_3 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;y \leq -1.85 \cdot 10^{+151}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{+122}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-35}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-266}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-187}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 2100000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+52}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t))))
        (t_2 (* y (- (* x z) (* i j))))
        (t_3 (* c (- (* a j) (* z b)))))
   (if (<= y -1.85e+151)
     t_2
     (if (<= y -5.5e+122)
       t_1
       (if (<= y -3.9e-35)
         t_2
         (if (<= y -3.9e-266)
           (* t (- (* b i) (* x a)))
           (if (<= y 3.1e-187)
             t_3
             (if (<= y 2100000000000.0) t_1 (if (<= y 3e+52) t_3 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = c * ((a * j) - (z * b));
	double tmp;
	if (y <= -1.85e+151) {
		tmp = t_2;
	} else if (y <= -5.5e+122) {
		tmp = t_1;
	} else if (y <= -3.9e-35) {
		tmp = t_2;
	} else if (y <= -3.9e-266) {
		tmp = t * ((b * i) - (x * a));
	} else if (y <= 3.1e-187) {
		tmp = t_3;
	} else if (y <= 2100000000000.0) {
		tmp = t_1;
	} else if (y <= 3e+52) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    t_2 = y * ((x * z) - (i * j))
    t_3 = c * ((a * j) - (z * b))
    if (y <= (-1.85d+151)) then
        tmp = t_2
    else if (y <= (-5.5d+122)) then
        tmp = t_1
    else if (y <= (-3.9d-35)) then
        tmp = t_2
    else if (y <= (-3.9d-266)) then
        tmp = t * ((b * i) - (x * a))
    else if (y <= 3.1d-187) then
        tmp = t_3
    else if (y <= 2100000000000.0d0) then
        tmp = t_1
    else if (y <= 3d+52) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = c * ((a * j) - (z * b));
	double tmp;
	if (y <= -1.85e+151) {
		tmp = t_2;
	} else if (y <= -5.5e+122) {
		tmp = t_1;
	} else if (y <= -3.9e-35) {
		tmp = t_2;
	} else if (y <= -3.9e-266) {
		tmp = t * ((b * i) - (x * a));
	} else if (y <= 3.1e-187) {
		tmp = t_3;
	} else if (y <= 2100000000000.0) {
		tmp = t_1;
	} else if (y <= 3e+52) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = y * ((x * z) - (i * j))
	t_3 = c * ((a * j) - (z * b))
	tmp = 0
	if y <= -1.85e+151:
		tmp = t_2
	elif y <= -5.5e+122:
		tmp = t_1
	elif y <= -3.9e-35:
		tmp = t_2
	elif y <= -3.9e-266:
		tmp = t * ((b * i) - (x * a))
	elif y <= 3.1e-187:
		tmp = t_3
	elif y <= 2100000000000.0:
		tmp = t_1
	elif y <= 3e+52:
		tmp = t_3
	else:
		tmp = t_2
	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)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_3 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (y <= -1.85e+151)
		tmp = t_2;
	elseif (y <= -5.5e+122)
		tmp = t_1;
	elseif (y <= -3.9e-35)
		tmp = t_2;
	elseif (y <= -3.9e-266)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (y <= 3.1e-187)
		tmp = t_3;
	elseif (y <= 2100000000000.0)
		tmp = t_1;
	elseif (y <= 3e+52)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	t_2 = y * ((x * z) - (i * j));
	t_3 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (y <= -1.85e+151)
		tmp = t_2;
	elseif (y <= -5.5e+122)
		tmp = t_1;
	elseif (y <= -3.9e-35)
		tmp = t_2;
	elseif (y <= -3.9e-266)
		tmp = t * ((b * i) - (x * a));
	elseif (y <= 3.1e-187)
		tmp = t_3;
	elseif (y <= 2100000000000.0)
		tmp = t_1;
	elseif (y <= 3e+52)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.85e+151], t$95$2, If[LessEqual[y, -5.5e+122], t$95$1, If[LessEqual[y, -3.9e-35], t$95$2, If[LessEqual[y, -3.9e-266], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.1e-187], t$95$3, If[LessEqual[y, 2100000000000.0], t$95$1, If[LessEqual[y, 3e+52], t$95$3, t$95$2]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.8499999999999999e151 or -5.4999999999999998e122 < y < -3.8999999999999998e-35 or 3e52 < y

   1. Initial program 67.8%

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

   3. Taylor expanded in y around inf 69.1%

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

      1. +-commutative 69.1%

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

      2. mul-1-neg 69.1%

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

      3. unsub-neg 69.1%

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

      4. *-commutative 69.1%

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

   5. Simplified 69.1%

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

   if -1.8499999999999999e151 < y < -5.4999999999999998e122 or 3.10000000000000019e-187 < y < 2.1e12

   1. Initial program 79.6%

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

   3. Taylor expanded in a around inf 62.3%

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

      1. +-commutative 62.3%

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

      2. mul-1-neg 62.3%

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

      3. unsub-neg 62.3%

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

      4. *-commutative 62.3%

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

      5. *-commutative 62.3%

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

   5. Simplified 62.3%

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

   if -3.8999999999999998e-35 < y < -3.90000000000000028e-266

   1. Initial program 83.1%

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

   3. Taylor expanded in t around -inf 66.8%

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

   if -3.90000000000000028e-266 < y < 3.10000000000000019e-187 or 2.1e12 < y < 3e52

   1. Initial program 77.4%

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

   3. Taylor expanded in c around inf 65.7%

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

      1. *-commutative 65.7%

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

   5. Simplified 65.7%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+151}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{+122}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-35}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-266}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-187}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 2100000000000:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+52}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 29.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(i \cdot j\right) \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -1.1 \cdot 10^{+205}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{+156}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-38}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-244}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-175}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-127}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+49}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* i j) (- y))))
   (if (<= y -1.1e+205)
     (* z (* x y))
     (if (<= y -4.1e+156)
       t_1
       (if (<= y -1.35e-38)
         (* x (* y z))
         (if (<= y -2.1e-244)
           (* x (* t (- a)))
           (if (<= y 1.25e-175)
             (* z (* b (- c)))
             (if (<= y 1.35e-127)
               (* a (* t (- x)))
               (if (<= y 2.05e+49) (* j (* a 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 = (i * j) * -y;
	double tmp;
	if (y <= -1.1e+205) {
		tmp = z * (x * y);
	} else if (y <= -4.1e+156) {
		tmp = t_1;
	} else if (y <= -1.35e-38) {
		tmp = x * (y * z);
	} else if (y <= -2.1e-244) {
		tmp = x * (t * -a);
	} else if (y <= 1.25e-175) {
		tmp = z * (b * -c);
	} else if (y <= 1.35e-127) {
		tmp = a * (t * -x);
	} else if (y <= 2.05e+49) {
		tmp = j * (a * 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 = (i * j) * -y
    if (y <= (-1.1d+205)) then
        tmp = z * (x * y)
    else if (y <= (-4.1d+156)) then
        tmp = t_1
    else if (y <= (-1.35d-38)) then
        tmp = x * (y * z)
    else if (y <= (-2.1d-244)) then
        tmp = x * (t * -a)
    else if (y <= 1.25d-175) then
        tmp = z * (b * -c)
    else if (y <= 1.35d-127) then
        tmp = a * (t * -x)
    else if (y <= 2.05d+49) then
        tmp = j * (a * 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 = (i * j) * -y;
	double tmp;
	if (y <= -1.1e+205) {
		tmp = z * (x * y);
	} else if (y <= -4.1e+156) {
		tmp = t_1;
	} else if (y <= -1.35e-38) {
		tmp = x * (y * z);
	} else if (y <= -2.1e-244) {
		tmp = x * (t * -a);
	} else if (y <= 1.25e-175) {
		tmp = z * (b * -c);
	} else if (y <= 1.35e-127) {
		tmp = a * (t * -x);
	} else if (y <= 2.05e+49) {
		tmp = j * (a * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (i * j) * -y
	tmp = 0
	if y <= -1.1e+205:
		tmp = z * (x * y)
	elif y <= -4.1e+156:
		tmp = t_1
	elif y <= -1.35e-38:
		tmp = x * (y * z)
	elif y <= -2.1e-244:
		tmp = x * (t * -a)
	elif y <= 1.25e-175:
		tmp = z * (b * -c)
	elif y <= 1.35e-127:
		tmp = a * (t * -x)
	elif y <= 2.05e+49:
		tmp = j * (a * c)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(i * j) * Float64(-y))
	tmp = 0.0
	if (y <= -1.1e+205)
		tmp = Float64(z * Float64(x * y));
	elseif (y <= -4.1e+156)
		tmp = t_1;
	elseif (y <= -1.35e-38)
		tmp = Float64(x * Float64(y * z));
	elseif (y <= -2.1e-244)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (y <= 1.25e-175)
		tmp = Float64(z * Float64(b * Float64(-c)));
	elseif (y <= 1.35e-127)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (y <= 2.05e+49)
		tmp = Float64(j * Float64(a * 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 = (i * j) * -y;
	tmp = 0.0;
	if (y <= -1.1e+205)
		tmp = z * (x * y);
	elseif (y <= -4.1e+156)
		tmp = t_1;
	elseif (y <= -1.35e-38)
		tmp = x * (y * z);
	elseif (y <= -2.1e-244)
		tmp = x * (t * -a);
	elseif (y <= 1.25e-175)
		tmp = z * (b * -c);
	elseif (y <= 1.35e-127)
		tmp = a * (t * -x);
	elseif (y <= 2.05e+49)
		tmp = j * (a * c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(i * j), $MachinePrecision] * (-y)), $MachinePrecision]}, If[LessEqual[y, -1.1e+205], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.1e+156], t$95$1, If[LessEqual[y, -1.35e-38], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.1e-244], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.25e-175], N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.35e-127], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.05e+49], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -1.0999999999999999e205

   1. Initial program 43.1%

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

      1. sub-neg 43.1%

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

      2. distribute-rgt-in 43.1%

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

      3. *-commutative 43.1%

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

      4. distribute-rgt-neg-in 43.1%

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

   4. Applied egg-rr 43.1%

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

   5. Taylor expanded in x around inf 56.3%

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

      1. *-commutative 56.3%

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

      2. *-commutative 56.3%

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

   7. Simplified 56.3%

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

   8. Taylor expanded in z around inf 48.2%

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

      1. associate-*r* 54.3%

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

   10. Simplified 54.3%

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

   if -1.0999999999999999e205 < y < -4.1000000000000002e156 or 2.05e49 < y

   1. Initial program 63.7%

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

      1. sub-neg 63.7%

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

      2. distribute-rgt-in 63.7%

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

      3. *-commutative 63.7%

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

      4. distribute-rgt-neg-in 63.7%

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

   4. Applied egg-rr 63.7%

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

   5. Taylor expanded in y around inf 71.9%

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

      1. mul-1-neg 71.9%

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

      2. +-commutative 71.9%

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

      3. *-commutative 71.9%

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

      4. sub-neg 71.9%

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

   7. Simplified 71.9%

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

   8. Taylor expanded in z around 0 54.9%

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

      1. mul-1-neg 54.9%

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

      2. distribute-lft-neg-out 54.9%

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

      3. *-commutative 54.9%

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

   10. Simplified 54.9%

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

   if -4.1000000000000002e156 < y < -1.35000000000000003e-38

   1. Initial program 88.2%

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

      1. sub-neg 88.2%

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

      2. distribute-rgt-in 88.2%

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

      3. *-commutative 88.2%

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

      4. distribute-rgt-neg-in 88.2%

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

   4. Applied egg-rr 88.2%

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

   5. Taylor expanded in y around inf 51.7%

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

      1. mul-1-neg 51.7%

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

      2. +-commutative 51.7%

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

      3. *-commutative 51.7%

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

      4. sub-neg 51.7%

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

   7. Simplified 51.7%

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

   8. Taylor expanded in z around inf 37.6%

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

   if -1.35000000000000003e-38 < y < -2.10000000000000002e-244

   1. Initial program 86.5%

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

      1. sub-neg 86.5%

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

      2. distribute-rgt-in 86.5%

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

      3. *-commutative 86.5%

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

      4. distribute-rgt-neg-in 86.5%

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

   4. Applied egg-rr 86.5%

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

   5. Taylor expanded in x around inf 52.9%

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

      1. *-commutative 52.9%

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

      2. *-commutative 52.9%

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

   7. Simplified 52.9%

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

   8. Taylor expanded in z around 0 45.2%

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

      1. neg-mul-1 45.2%

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

      2. distribute-rgt-neg-in 45.2%

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

   10. Simplified 45.2%

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

   if -2.10000000000000002e-244 < y < 1.25e-175

   1. Initial program 78.1%

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

   3. Taylor expanded in a around -inf 69.8%

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

   5. Simplified 67.5%

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

   6. Taylor expanded in c around inf 49.0%

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

   7. Taylor expanded in a around 0 33.4%

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

      1. mul-1-neg 33.4%

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

      2. associate-*r* 39.6%

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

      3. distribute-rgt-neg-in 39.6%

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

   9. Simplified 39.6%

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

   if 1.25e-175 < y < 1.35e-127

   1. Initial program 92.2%

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

   3. Taylor expanded in a around inf 65.0%

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

      1. +-commutative 65.0%

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

      2. mul-1-neg 65.0%

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

      3. unsub-neg 65.0%

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

      4. *-commutative 65.0%

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

      5. *-commutative 65.0%

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

   5. Simplified 65.0%

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

   6. Taylor expanded in j around 0 56.1%

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

      1. associate-*r* 56.1%

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

      2. neg-mul-1 56.1%

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

   8. Simplified 56.1%

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

   if 1.35e-127 < y < 2.05e49

   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 j around inf 50.4%

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

      1. *-commutative 50.4%

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

   5. Simplified 50.4%

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

   6. Taylor expanded in a around inf 44.3%

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

      1. *-commutative 44.3%

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

   8. Simplified 44.3%

      \[\leadsto j \cdot \color{blue}{\left(c \cdot a\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 46.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+205}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{+156}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-38}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-244}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-175}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-127}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+49}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t \cdot a - y \cdot z\right)\\ t_2 := \left(b \cdot \left(t \cdot i\right) - b \cdot \left(z \cdot c\right)\right) - t\_1\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.26 \cdot 10^{+94}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq -6.5 \cdot 10^{-8}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -1.75 \cdot 10^{-67}:\\ \;\;\;\;a \cdot \left(c \cdot j + \left(\frac{x \cdot \left(y \cdot z\right)}{a} - x \cdot t\right)\right)\\ \mathbf{elif}\;j \leq 1.28 \cdot 10^{+34}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3 - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* t a) (* y z))))
        (t_2 (- (- (* b (* t i)) (* b (* z c))) t_1))
        (t_3 (* j (- (* a c) (* y i)))))
   (if (<= j -1.26e+94)
     t_3
     (if (<= j -6.5e-8)
       t_2
       (if (<= j -1.75e-67)
         (* a (+ (* c j) (- (/ (* x (* y z)) a) (* x t))))
         (if (<= j 1.28e+34) t_2 (- t_3 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 * ((t * a) - (y * z));
	double t_2 = ((b * (t * i)) - (b * (z * c))) - t_1;
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -1.26e+94) {
		tmp = t_3;
	} else if (j <= -6.5e-8) {
		tmp = t_2;
	} else if (j <= -1.75e-67) {
		tmp = a * ((c * j) + (((x * (y * z)) / a) - (x * t)));
	} else if (j <= 1.28e+34) {
		tmp = t_2;
	} else {
		tmp = t_3 - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * ((t * a) - (y * z))
    t_2 = ((b * (t * i)) - (b * (z * c))) - t_1
    t_3 = j * ((a * c) - (y * i))
    if (j <= (-1.26d+94)) then
        tmp = t_3
    else if (j <= (-6.5d-8)) then
        tmp = t_2
    else if (j <= (-1.75d-67)) then
        tmp = a * ((c * j) + (((x * (y * z)) / a) - (x * t)))
    else if (j <= 1.28d+34) then
        tmp = t_2
    else
        tmp = t_3 - 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 * ((t * a) - (y * z));
	double t_2 = ((b * (t * i)) - (b * (z * c))) - t_1;
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -1.26e+94) {
		tmp = t_3;
	} else if (j <= -6.5e-8) {
		tmp = t_2;
	} else if (j <= -1.75e-67) {
		tmp = a * ((c * j) + (((x * (y * z)) / a) - (x * t)));
	} else if (j <= 1.28e+34) {
		tmp = t_2;
	} else {
		tmp = t_3 - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((t * a) - (y * z))
	t_2 = ((b * (t * i)) - (b * (z * c))) - t_1
	t_3 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -1.26e+94:
		tmp = t_3
	elif j <= -6.5e-8:
		tmp = t_2
	elif j <= -1.75e-67:
		tmp = a * ((c * j) + (((x * (y * z)) / a) - (x * t)))
	elif j <= 1.28e+34:
		tmp = t_2
	else:
		tmp = t_3 - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(t * a) - Float64(y * z)))
	t_2 = Float64(Float64(Float64(b * Float64(t * i)) - Float64(b * Float64(z * c))) - t_1)
	t_3 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -1.26e+94)
		tmp = t_3;
	elseif (j <= -6.5e-8)
		tmp = t_2;
	elseif (j <= -1.75e-67)
		tmp = Float64(a * Float64(Float64(c * j) + Float64(Float64(Float64(x * Float64(y * z)) / a) - Float64(x * t))));
	elseif (j <= 1.28e+34)
		tmp = t_2;
	else
		tmp = Float64(t_3 - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((t * a) - (y * z));
	t_2 = ((b * (t * i)) - (b * (z * c))) - t_1;
	t_3 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -1.26e+94)
		tmp = t_3;
	elseif (j <= -6.5e-8)
		tmp = t_2;
	elseif (j <= -1.75e-67)
		tmp = a * ((c * j) + (((x * (y * z)) / a) - (x * t)));
	elseif (j <= 1.28e+34)
		tmp = t_2;
	else
		tmp = t_3 - 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[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.26e+94], t$95$3, If[LessEqual[j, -6.5e-8], t$95$2, If[LessEqual[j, -1.75e-67], N[(a * N[(N[(c * j), $MachinePrecision] + N[(N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.28e+34], t$95$2, N[(t$95$3 - t$95$1), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.25999999999999997e94

   1. Initial program 71.3%

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

   3. Taylor expanded in j around inf 75.9%

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

      1. *-commutative 75.9%

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

   5. Simplified 75.9%

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

   if -1.25999999999999997e94 < j < -6.49999999999999997e-8 or -1.75e-67 < j < 1.28000000000000007e34

   1. Initial program 74.4%

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

      1. sub-neg 74.4%

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

      2. distribute-rgt-in 74.4%

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

      3. *-commutative 74.4%

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

      4. distribute-rgt-neg-in 74.4%

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

   4. Applied egg-rr 74.4%

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

   5. Taylor expanded in j around 0 72.9%

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

   if -6.49999999999999997e-8 < j < -1.75e-67

   1. Initial program 61.1%

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

   3. Taylor expanded in a around -inf 86.6%

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

   5. Simplified 86.5%

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

   6. Taylor expanded in x around inf 92.7%

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

   if 1.28000000000000007e34 < j

   1. Initial program 78.9%

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

   3. Taylor expanded in b around 0 82.1%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.26 \cdot 10^{+94}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -6.5 \cdot 10^{-8}:\\ \;\;\;\;\left(b \cdot \left(t \cdot i\right) - b \cdot \left(z \cdot c\right)\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;j \leq -1.75 \cdot 10^{-67}:\\ \;\;\;\;a \cdot \left(c \cdot j + \left(\frac{x \cdot \left(y \cdot z\right)}{a} - x \cdot t\right)\right)\\ \mathbf{elif}\;j \leq 1.28 \cdot 10^{+34}:\\ \;\;\;\;\left(b \cdot \left(t \cdot i\right) - b \cdot \left(z \cdot c\right)\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 54.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -175000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -8 \cdot 10^{-126}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq -1.12 \cdot 10^{-202}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 2.8 \cdot 10^{-99}:\\ \;\;\;\;a \cdot \left(c \cdot j + \left(\frac{x \cdot \left(y \cdot z\right)}{a} - x \cdot t\right)\right)\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{-24}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq 4.3 \cdot 10^{+192}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j)))))
   (if (<= i -175000000.0)
     t_1
     (if (<= i -8e-126)
       (* a (- (* c j) (* x t)))
       (if (<= i -1.12e-202)
         (* z (- (* x y) (* b c)))
         (if (<= i 2.8e-99)
           (* a (+ (* c j) (- (/ (* x (* y z)) a) (* x t))))
           (if (<= i 1.3e-24)
             (* b (- (* t i) (* z c)))
             (if (<= i 4.3e+192) (* y (- (* x z) (* i j))) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -175000000.0) {
		tmp = t_1;
	} else if (i <= -8e-126) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= -1.12e-202) {
		tmp = z * ((x * y) - (b * c));
	} else if (i <= 2.8e-99) {
		tmp = a * ((c * j) + (((x * (y * z)) / a) - (x * t)));
	} else if (i <= 1.3e-24) {
		tmp = b * ((t * i) - (z * c));
	} else if (i <= 4.3e+192) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * ((t * b) - (y * j))
    if (i <= (-175000000.0d0)) then
        tmp = t_1
    else if (i <= (-8d-126)) then
        tmp = a * ((c * j) - (x * t))
    else if (i <= (-1.12d-202)) then
        tmp = z * ((x * y) - (b * c))
    else if (i <= 2.8d-99) then
        tmp = a * ((c * j) + (((x * (y * z)) / a) - (x * t)))
    else if (i <= 1.3d-24) then
        tmp = b * ((t * i) - (z * c))
    else if (i <= 4.3d+192) then
        tmp = y * ((x * z) - (i * j))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -175000000.0) {
		tmp = t_1;
	} else if (i <= -8e-126) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= -1.12e-202) {
		tmp = z * ((x * y) - (b * c));
	} else if (i <= 2.8e-99) {
		tmp = a * ((c * j) + (((x * (y * z)) / a) - (x * t)));
	} else if (i <= 1.3e-24) {
		tmp = b * ((t * i) - (z * c));
	} else if (i <= 4.3e+192) {
		tmp = y * ((x * z) - (i * j));
	} 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 <= -175000000.0:
		tmp = t_1
	elif i <= -8e-126:
		tmp = a * ((c * j) - (x * t))
	elif i <= -1.12e-202:
		tmp = z * ((x * y) - (b * c))
	elif i <= 2.8e-99:
		tmp = a * ((c * j) + (((x * (y * z)) / a) - (x * t)))
	elif i <= 1.3e-24:
		tmp = b * ((t * i) - (z * c))
	elif i <= 4.3e+192:
		tmp = y * ((x * z) - (i * j))
	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 <= -175000000.0)
		tmp = t_1;
	elseif (i <= -8e-126)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (i <= -1.12e-202)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (i <= 2.8e-99)
		tmp = Float64(a * Float64(Float64(c * j) + Float64(Float64(Float64(x * Float64(y * z)) / a) - Float64(x * t))));
	elseif (i <= 1.3e-24)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (i <= 4.3e+192)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -175000000.0)
		tmp = t_1;
	elseif (i <= -8e-126)
		tmp = a * ((c * j) - (x * t));
	elseif (i <= -1.12e-202)
		tmp = z * ((x * y) - (b * c));
	elseif (i <= 2.8e-99)
		tmp = a * ((c * j) + (((x * (y * z)) / a) - (x * t)));
	elseif (i <= 1.3e-24)
		tmp = b * ((t * i) - (z * c));
	elseif (i <= 4.3e+192)
		tmp = y * ((x * z) - (i * j));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -175000000.0], t$95$1, If[LessEqual[i, -8e-126], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.12e-202], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.8e-99], N[(a * N[(N[(c * j), $MachinePrecision] + N[(N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.3e-24], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4.3e+192], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -1.75e8 or 4.29999999999999976e192 < i

   1. Initial program 60.0%

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

   3. Taylor expanded in i around inf 72.3%

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

      1. distribute-lft-out-- 72.3%

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

      2. *-commutative 72.3%

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

      3. *-commutative 72.3%

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

   5. Simplified 72.3%

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

   if -1.75e8 < i < -7.9999999999999996e-126

   1. Initial program 80.5%

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

   3. Taylor expanded in a around inf 71.2%

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

      1. +-commutative 71.2%

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

      2. mul-1-neg 71.2%

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

      3. unsub-neg 71.2%

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

      4. *-commutative 71.2%

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

      5. *-commutative 71.2%

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

   5. Simplified 71.2%

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

   if -7.9999999999999996e-126 < i < -1.12000000000000009e-202

   1. Initial program 85.6%

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

   3. Taylor expanded in z around inf 63.3%

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

      1. *-commutative 63.3%

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

   5. Simplified 63.3%

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

   if -1.12000000000000009e-202 < i < 2.8000000000000001e-99

   1. Initial program 83.0%

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

   3. Taylor expanded in a around -inf 72.5%

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

   5. Simplified 80.5%

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

   6. Taylor expanded in x around inf 72.9%

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

   if 2.8000000000000001e-99 < i < 1.3e-24

   1. Initial program 92.2%

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

   3. Taylor expanded in b around inf 77.3%

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

      1. *-commutative 77.3%

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

      2. *-commutative 77.3%

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

   5. Simplified 77.3%

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

   if 1.3e-24 < i < 4.29999999999999976e192

   1. Initial program 68.1%

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

   3. Taylor expanded in y around inf 63.6%

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

      1. +-commutative 63.6%

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

      2. mul-1-neg 63.6%

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

      3. unsub-neg 63.6%

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

      4. *-commutative 63.6%

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

   5. Simplified 63.6%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -175000000:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -8 \cdot 10^{-126}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq -1.12 \cdot 10^{-202}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 2.8 \cdot 10^{-99}:\\ \;\;\;\;a \cdot \left(c \cdot j + \left(\frac{x \cdot \left(y \cdot z\right)}{a} - x \cdot t\right)\right)\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{-24}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq 4.3 \cdot 10^{+192}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 43.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(b \cdot \left(-c\right)\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.05 \cdot 10^{-90}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.62 \cdot 10^{-283}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-293}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{-274}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-70}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* b (- c)))) (t_2 (* a (- (* c j) (* x t)))))
   (if (<= a -1.05e-90)
     t_2
     (if (<= a -1.62e-283)
       t_1
       (if (<= a 2.9e-293)
         (* t (* b i))
         (if (<= a 2.25e-274) t_1 (if (<= a 1.05e-70) (* x (* y 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 = z * (b * -c);
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.05e-90) {
		tmp = t_2;
	} else if (a <= -1.62e-283) {
		tmp = t_1;
	} else if (a <= 2.9e-293) {
		tmp = t * (b * i);
	} else if (a <= 2.25e-274) {
		tmp = t_1;
	} else if (a <= 1.05e-70) {
		tmp = x * (y * 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 = z * (b * -c)
    t_2 = a * ((c * j) - (x * t))
    if (a <= (-1.05d-90)) then
        tmp = t_2
    else if (a <= (-1.62d-283)) then
        tmp = t_1
    else if (a <= 2.9d-293) then
        tmp = t * (b * i)
    else if (a <= 2.25d-274) then
        tmp = t_1
    else if (a <= 1.05d-70) then
        tmp = x * (y * 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 = z * (b * -c);
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.05e-90) {
		tmp = t_2;
	} else if (a <= -1.62e-283) {
		tmp = t_1;
	} else if (a <= 2.9e-293) {
		tmp = t * (b * i);
	} else if (a <= 2.25e-274) {
		tmp = t_1;
	} else if (a <= 1.05e-70) {
		tmp = x * (y * z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (b * -c)
	t_2 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -1.05e-90:
		tmp = t_2
	elif a <= -1.62e-283:
		tmp = t_1
	elif a <= 2.9e-293:
		tmp = t * (b * i)
	elif a <= 2.25e-274:
		tmp = t_1
	elif a <= 1.05e-70:
		tmp = x * (y * z)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(b * Float64(-c)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -1.05e-90)
		tmp = t_2;
	elseif (a <= -1.62e-283)
		tmp = t_1;
	elseif (a <= 2.9e-293)
		tmp = Float64(t * Float64(b * i));
	elseif (a <= 2.25e-274)
		tmp = t_1;
	elseif (a <= 1.05e-70)
		tmp = Float64(x * Float64(y * 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 = z * (b * -c);
	t_2 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -1.05e-90)
		tmp = t_2;
	elseif (a <= -1.62e-283)
		tmp = t_1;
	elseif (a <= 2.9e-293)
		tmp = t * (b * i);
	elseif (a <= 2.25e-274)
		tmp = t_1;
	elseif (a <= 1.05e-70)
		tmp = x * (y * 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[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.05e-90], t$95$2, If[LessEqual[a, -1.62e-283], t$95$1, If[LessEqual[a, 2.9e-293], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.25e-274], t$95$1, If[LessEqual[a, 1.05e-70], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.05e-90 or 1.0500000000000001e-70 < a

   1. Initial program 73.6%

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

   3. Taylor expanded in a around inf 54.2%

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

      1. +-commutative 54.2%

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

      2. mul-1-neg 54.2%

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

      3. unsub-neg 54.2%

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

      4. *-commutative 54.2%

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

      5. *-commutative 54.2%

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

   5. Simplified 54.2%

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

   if -1.05e-90 < a < -1.62e-283 or 2.8999999999999999e-293 < a < 2.24999999999999996e-274

   1. Initial program 77.4%

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

   3. Taylor expanded in a around -inf 49.1%

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

   5. Simplified 58.0%

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

   6. Taylor expanded in c around inf 42.8%

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

   7. Taylor expanded in a around 0 46.2%

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

      1. mul-1-neg 46.2%

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

      2. associate-*r* 46.8%

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

      3. distribute-rgt-neg-in 46.8%

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

   9. Simplified 46.8%

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

   if -1.62e-283 < a < 2.8999999999999999e-293

   1. Initial program 87.3%

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

   3. Taylor expanded in t around -inf 63.1%

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

   4. Taylor expanded in a around 0 63.3%

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

      1. neg-mul-1 63.3%

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

      2. distribute-rgt-neg-in 63.3%

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

   6. Simplified 63.3%

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

   if 2.24999999999999996e-274 < a < 1.0500000000000001e-70

   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. Step-by-step derivation

      1. sub-neg 71.1%

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

      2. distribute-rgt-in 71.1%

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

      3. *-commutative 71.1%

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

      4. distribute-rgt-neg-in 71.1%

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

   4. Applied egg-rr 71.1%

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

   5. Taylor expanded in y around inf 71.3%

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

      1. mul-1-neg 71.3%

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

      2. +-commutative 71.3%

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

      3. *-commutative 71.3%

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

      4. sub-neg 71.3%

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

   7. Simplified 71.3%

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

   8. Taylor expanded in z around inf 44.7%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{-90}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.62 \cdot 10^{-283}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-293}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{-274}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-70}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 49.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_3 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -6.8 \cdot 10^{-25}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{-274}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-150}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{+14}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+135}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (* b (- (* t i) (* z c))))
        (t_3 (* a (- (* c j) (* x t)))))
   (if (<= a -6.8e-25)
     t_3
     (if (<= a 9.8e-274)
       t_2
       (if (<= a 4.6e-150)
         t_1
         (if (<= a 2.35e+14) t_2 (if (<= a 3.2e+135) t_1 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = b * ((t * i) - (z * c));
	double t_3 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -6.8e-25) {
		tmp = t_3;
	} else if (a <= 9.8e-274) {
		tmp = t_2;
	} else if (a <= 4.6e-150) {
		tmp = t_1;
	} else if (a <= 2.35e+14) {
		tmp = t_2;
	} else if (a <= 3.2e+135) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = b * ((t * i) - (z * c))
    t_3 = a * ((c * j) - (x * t))
    if (a <= (-6.8d-25)) then
        tmp = t_3
    else if (a <= 9.8d-274) then
        tmp = t_2
    else if (a <= 4.6d-150) then
        tmp = t_1
    else if (a <= 2.35d+14) then
        tmp = t_2
    else if (a <= 3.2d+135) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = b * ((t * i) - (z * c));
	double t_3 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -6.8e-25) {
		tmp = t_3;
	} else if (a <= 9.8e-274) {
		tmp = t_2;
	} else if (a <= 4.6e-150) {
		tmp = t_1;
	} else if (a <= 2.35e+14) {
		tmp = t_2;
	} else if (a <= 3.2e+135) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = b * ((t * i) - (z * c))
	t_3 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -6.8e-25:
		tmp = t_3
	elif a <= 9.8e-274:
		tmp = t_2
	elif a <= 4.6e-150:
		tmp = t_1
	elif a <= 2.35e+14:
		tmp = t_2
	elif a <= 3.2e+135:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_3 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -6.8e-25)
		tmp = t_3;
	elseif (a <= 9.8e-274)
		tmp = t_2;
	elseif (a <= 4.6e-150)
		tmp = t_1;
	elseif (a <= 2.35e+14)
		tmp = t_2;
	elseif (a <= 3.2e+135)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = b * ((t * i) - (z * c));
	t_3 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -6.8e-25)
		tmp = t_3;
	elseif (a <= 9.8e-274)
		tmp = t_2;
	elseif (a <= 4.6e-150)
		tmp = t_1;
	elseif (a <= 2.35e+14)
		tmp = t_2;
	elseif (a <= 3.2e+135)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.8e-25], t$95$3, If[LessEqual[a, 9.8e-274], t$95$2, If[LessEqual[a, 4.6e-150], t$95$1, If[LessEqual[a, 2.35e+14], t$95$2, If[LessEqual[a, 3.2e+135], t$95$1, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.80000000000000003e-25 or 3.19999999999999975e135 < a

   1. Initial program 70.2%

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

   3. Taylor expanded in a around inf 63.7%

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

      1. +-commutative 63.7%

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

      2. mul-1-neg 63.7%

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

      3. unsub-neg 63.7%

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

      4. *-commutative 63.7%

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

      5. *-commutative 63.7%

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

   5. Simplified 63.7%

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

   if -6.80000000000000003e-25 < a < 9.8000000000000009e-274 or 4.60000000000000006e-150 < a < 2.35e14

   1. Initial program 74.9%

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

   3. Taylor expanded in b around inf 54.6%

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

      1. *-commutative 54.6%

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

      2. *-commutative 54.6%

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

   5. Simplified 54.6%

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

   if 9.8000000000000009e-274 < a < 4.60000000000000006e-150 or 2.35e14 < a < 3.19999999999999975e135

   1. Initial program 80.5%

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

      1. sub-neg 80.5%

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

      2. distribute-rgt-in 80.5%

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

      3. *-commutative 80.5%

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

      4. distribute-rgt-neg-in 80.5%

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

   4. Applied egg-rr 80.5%

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

   5. Taylor expanded in x around inf 62.6%

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

      1. *-commutative 62.6%

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

      2. *-commutative 62.6%

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

   7. Simplified 62.6%

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

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{-25}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{-274}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-150}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{+14}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+135}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 30.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{+199}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{+156}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-37}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-269}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+48}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* y i) (- j))))
   (if (<= y -6.5e+199)
     (* z (* x y))
     (if (<= y -4.5e+156)
       t_1
       (if (<= y -2.5e-37)
         (* x (* y z))
         (if (<= y -1e-269)
           (* t (* x (- a)))
           (if (<= y 5.4e+48) (* j (* a 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 = (y * i) * -j;
	double tmp;
	if (y <= -6.5e+199) {
		tmp = z * (x * y);
	} else if (y <= -4.5e+156) {
		tmp = t_1;
	} else if (y <= -2.5e-37) {
		tmp = x * (y * z);
	} else if (y <= -1e-269) {
		tmp = t * (x * -a);
	} else if (y <= 5.4e+48) {
		tmp = j * (a * 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 = (y * i) * -j
    if (y <= (-6.5d+199)) then
        tmp = z * (x * y)
    else if (y <= (-4.5d+156)) then
        tmp = t_1
    else if (y <= (-2.5d-37)) then
        tmp = x * (y * z)
    else if (y <= (-1d-269)) then
        tmp = t * (x * -a)
    else if (y <= 5.4d+48) then
        tmp = j * (a * 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 = (y * i) * -j;
	double tmp;
	if (y <= -6.5e+199) {
		tmp = z * (x * y);
	} else if (y <= -4.5e+156) {
		tmp = t_1;
	} else if (y <= -2.5e-37) {
		tmp = x * (y * z);
	} else if (y <= -1e-269) {
		tmp = t * (x * -a);
	} else if (y <= 5.4e+48) {
		tmp = j * (a * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (y * i) * -j
	tmp = 0
	if y <= -6.5e+199:
		tmp = z * (x * y)
	elif y <= -4.5e+156:
		tmp = t_1
	elif y <= -2.5e-37:
		tmp = x * (y * z)
	elif y <= -1e-269:
		tmp = t * (x * -a)
	elif y <= 5.4e+48:
		tmp = j * (a * c)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(y * i) * Float64(-j))
	tmp = 0.0
	if (y <= -6.5e+199)
		tmp = Float64(z * Float64(x * y));
	elseif (y <= -4.5e+156)
		tmp = t_1;
	elseif (y <= -2.5e-37)
		tmp = Float64(x * Float64(y * z));
	elseif (y <= -1e-269)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (y <= 5.4e+48)
		tmp = Float64(j * Float64(a * 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 = (y * i) * -j;
	tmp = 0.0;
	if (y <= -6.5e+199)
		tmp = z * (x * y);
	elseif (y <= -4.5e+156)
		tmp = t_1;
	elseif (y <= -2.5e-37)
		tmp = x * (y * z);
	elseif (y <= -1e-269)
		tmp = t * (x * -a);
	elseif (y <= 5.4e+48)
		tmp = j * (a * c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(y * i), $MachinePrecision] * (-j)), $MachinePrecision]}, If[LessEqual[y, -6.5e+199], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.5e+156], t$95$1, If[LessEqual[y, -2.5e-37], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1e-269], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.4e+48], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -6.5000000000000003e199

   1. Initial program 43.1%

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

      1. sub-neg 43.1%

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

      2. distribute-rgt-in 43.1%

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

      3. *-commutative 43.1%

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

      4. distribute-rgt-neg-in 43.1%

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

   4. Applied egg-rr 43.1%

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

   5. Taylor expanded in x around inf 56.3%

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

      1. *-commutative 56.3%

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

      2. *-commutative 56.3%

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

   7. Simplified 56.3%

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

   8. Taylor expanded in z around inf 48.2%

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

      1. associate-*r* 54.3%

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

   10. Simplified 54.3%

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

   if -6.5000000000000003e199 < y < -4.50000000000000031e156 or 5.40000000000000007e48 < y

   1. Initial program 63.7%

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

   3. Taylor expanded in j around inf 58.3%

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

      1. *-commutative 58.3%

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

   5. Simplified 58.3%

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

   6. Taylor expanded in a around 0 50.4%

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

      1. neg-mul-1 50.4%

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

      2. distribute-rgt-neg-in 50.4%

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

   8. Simplified 50.4%

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

   if -4.50000000000000031e156 < y < -2.4999999999999999e-37

   1. Initial program 88.2%

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

      1. sub-neg 88.2%

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

      2. distribute-rgt-in 88.2%

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

      3. *-commutative 88.2%

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

      4. distribute-rgt-neg-in 88.2%

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

   4. Applied egg-rr 88.2%

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

   5. Taylor expanded in y around inf 51.7%

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

      1. mul-1-neg 51.7%

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

      2. +-commutative 51.7%

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

      3. *-commutative 51.7%

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

      4. sub-neg 51.7%

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

   7. Simplified 51.7%

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

   8. Taylor expanded in z around inf 37.6%

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

   if -2.4999999999999999e-37 < y < -9.9999999999999996e-270

   1. Initial program 83.1%

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

   3. Taylor expanded in a around inf 57.7%

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

      1. +-commutative 57.7%

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

      2. mul-1-neg 57.7%

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

      3. unsub-neg 57.7%

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

      4. *-commutative 57.7%

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

      5. *-commutative 57.7%

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

   5. Simplified 57.7%

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

   6. Taylor expanded in t around inf 53.1%

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

      1. +-commutative 53.1%

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

      2. mul-1-neg 53.1%

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

      3. unsub-neg 53.1%

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

      4. associate-/l* 53.1%

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

      5. associate-/l* 53.3%

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

   8. Simplified 53.3%

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

   9. Taylor expanded in t around inf 41.5%

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

       1. mul-1-neg 41.5%

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

       2. associate-*r* 43.5%

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

       3. distribute-rgt-neg-in 43.5%

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

       4. *-commutative 43.5%

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

       5. associate-*r* 41.4%

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

   11. Simplified 41.4%

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

   if -9.9999999999999996e-270 < y < 5.40000000000000007e48

   1. Initial program 79.7%

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

   3. Taylor expanded in j around inf 39.6%

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

      1. *-commutative 39.6%

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

   5. Simplified 39.6%

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

   6. Taylor expanded in a around inf 34.0%

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

      1. *-commutative 34.0%

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

   8. Simplified 34.0%

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

4. Final simplification 41.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+199}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{+156}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-37}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-269}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+48}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 30.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{if}\;y \leq -3 \cdot 10^{+199}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -5 \cdot 10^{+156}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-36}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-273}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 2.85 \cdot 10^{+48}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* y i) (- j))))
   (if (<= y -3e+199)
     (* z (* x y))
     (if (<= y -5e+156)
       t_1
       (if (<= y -2.5e-36)
         (* x (* y z))
         (if (<= y -3e-273)
           (* x (* t (- a)))
           (if (<= y 2.85e+48) (* j (* a 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 = (y * i) * -j;
	double tmp;
	if (y <= -3e+199) {
		tmp = z * (x * y);
	} else if (y <= -5e+156) {
		tmp = t_1;
	} else if (y <= -2.5e-36) {
		tmp = x * (y * z);
	} else if (y <= -3e-273) {
		tmp = x * (t * -a);
	} else if (y <= 2.85e+48) {
		tmp = j * (a * 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 = (y * i) * -j
    if (y <= (-3d+199)) then
        tmp = z * (x * y)
    else if (y <= (-5d+156)) then
        tmp = t_1
    else if (y <= (-2.5d-36)) then
        tmp = x * (y * z)
    else if (y <= (-3d-273)) then
        tmp = x * (t * -a)
    else if (y <= 2.85d+48) then
        tmp = j * (a * 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 = (y * i) * -j;
	double tmp;
	if (y <= -3e+199) {
		tmp = z * (x * y);
	} else if (y <= -5e+156) {
		tmp = t_1;
	} else if (y <= -2.5e-36) {
		tmp = x * (y * z);
	} else if (y <= -3e-273) {
		tmp = x * (t * -a);
	} else if (y <= 2.85e+48) {
		tmp = j * (a * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (y * i) * -j
	tmp = 0
	if y <= -3e+199:
		tmp = z * (x * y)
	elif y <= -5e+156:
		tmp = t_1
	elif y <= -2.5e-36:
		tmp = x * (y * z)
	elif y <= -3e-273:
		tmp = x * (t * -a)
	elif y <= 2.85e+48:
		tmp = j * (a * c)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(y * i) * Float64(-j))
	tmp = 0.0
	if (y <= -3e+199)
		tmp = Float64(z * Float64(x * y));
	elseif (y <= -5e+156)
		tmp = t_1;
	elseif (y <= -2.5e-36)
		tmp = Float64(x * Float64(y * z));
	elseif (y <= -3e-273)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (y <= 2.85e+48)
		tmp = Float64(j * Float64(a * 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 = (y * i) * -j;
	tmp = 0.0;
	if (y <= -3e+199)
		tmp = z * (x * y);
	elseif (y <= -5e+156)
		tmp = t_1;
	elseif (y <= -2.5e-36)
		tmp = x * (y * z);
	elseif (y <= -3e-273)
		tmp = x * (t * -a);
	elseif (y <= 2.85e+48)
		tmp = j * (a * c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(y * i), $MachinePrecision] * (-j)), $MachinePrecision]}, If[LessEqual[y, -3e+199], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5e+156], t$95$1, If[LessEqual[y, -2.5e-36], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3e-273], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.85e+48], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.0000000000000001e199

   1. Initial program 43.1%

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

      1. sub-neg 43.1%

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

      2. distribute-rgt-in 43.1%

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

      3. *-commutative 43.1%

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

      4. distribute-rgt-neg-in 43.1%

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

   4. Applied egg-rr 43.1%

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

   5. Taylor expanded in x around inf 56.3%

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

      1. *-commutative 56.3%

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

      2. *-commutative 56.3%

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

   7. Simplified 56.3%

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

   8. Taylor expanded in z around inf 48.2%

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

      1. associate-*r* 54.3%

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

   10. Simplified 54.3%

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

   if -3.0000000000000001e199 < y < -4.99999999999999992e156 or 2.84999999999999984e48 < y

   1. Initial program 63.7%

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

   3. Taylor expanded in j around inf 58.3%

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

      1. *-commutative 58.3%

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

   5. Simplified 58.3%

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

   6. Taylor expanded in a around 0 50.4%

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

      1. neg-mul-1 50.4%

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

      2. distribute-rgt-neg-in 50.4%

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

   8. Simplified 50.4%

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

   if -4.99999999999999992e156 < y < -2.50000000000000002e-36

   1. Initial program 88.2%

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

      1. sub-neg 88.2%

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

      2. distribute-rgt-in 88.2%

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

      3. *-commutative 88.2%

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

      4. distribute-rgt-neg-in 88.2%

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

   4. Applied egg-rr 88.2%

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

   5. Taylor expanded in y around inf 51.7%

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

      1. mul-1-neg 51.7%

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

      2. +-commutative 51.7%

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

      3. *-commutative 51.7%

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

      4. sub-neg 51.7%

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

   7. Simplified 51.7%

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

   8. Taylor expanded in z around inf 37.6%

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

   if -2.50000000000000002e-36 < y < -2.99999999999999987e-273

   1. Initial program 83.1%

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

      1. sub-neg 83.1%

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

      2. distribute-rgt-in 83.1%

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

      3. *-commutative 83.1%

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

      4. distribute-rgt-neg-in 83.1%

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

   4. Applied egg-rr 83.1%

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

   5. Taylor expanded in x around inf 50.4%

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

      1. *-commutative 50.4%

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

      2. *-commutative 50.4%

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

   7. Simplified 50.4%

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

   8. Taylor expanded in z around 0 43.5%

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

      1. neg-mul-1 43.5%

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

      2. distribute-rgt-neg-in 43.5%

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

   10. Simplified 43.5%

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

   if -2.99999999999999987e-273 < y < 2.84999999999999984e48

   1. Initial program 79.7%

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

   3. Taylor expanded in j around inf 39.6%

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

      1. *-commutative 39.6%

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

   5. Simplified 39.6%

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

   6. Taylor expanded in a around inf 34.0%

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

      1. *-commutative 34.0%

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

   8. Simplified 34.0%

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

4. Final simplification 42.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+199}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -5 \cdot 10^{+156}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-36}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-273}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 2.85 \cdot 10^{+48}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 30.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(i \cdot j\right) \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -2.25 \cdot 10^{+201}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{+156}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-39}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-273}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{+50}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* i j) (- y))))
   (if (<= y -2.25e+201)
     (* z (* x y))
     (if (<= y -2.3e+156)
       t_1
       (if (<= y -2.2e-39)
         (* x (* y z))
         (if (<= y -1.7e-273)
           (* x (* t (- a)))
           (if (<= y 5.1e+50) (* j (* a 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 = (i * j) * -y;
	double tmp;
	if (y <= -2.25e+201) {
		tmp = z * (x * y);
	} else if (y <= -2.3e+156) {
		tmp = t_1;
	} else if (y <= -2.2e-39) {
		tmp = x * (y * z);
	} else if (y <= -1.7e-273) {
		tmp = x * (t * -a);
	} else if (y <= 5.1e+50) {
		tmp = j * (a * 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 = (i * j) * -y
    if (y <= (-2.25d+201)) then
        tmp = z * (x * y)
    else if (y <= (-2.3d+156)) then
        tmp = t_1
    else if (y <= (-2.2d-39)) then
        tmp = x * (y * z)
    else if (y <= (-1.7d-273)) then
        tmp = x * (t * -a)
    else if (y <= 5.1d+50) then
        tmp = j * (a * 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 = (i * j) * -y;
	double tmp;
	if (y <= -2.25e+201) {
		tmp = z * (x * y);
	} else if (y <= -2.3e+156) {
		tmp = t_1;
	} else if (y <= -2.2e-39) {
		tmp = x * (y * z);
	} else if (y <= -1.7e-273) {
		tmp = x * (t * -a);
	} else if (y <= 5.1e+50) {
		tmp = j * (a * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (i * j) * -y
	tmp = 0
	if y <= -2.25e+201:
		tmp = z * (x * y)
	elif y <= -2.3e+156:
		tmp = t_1
	elif y <= -2.2e-39:
		tmp = x * (y * z)
	elif y <= -1.7e-273:
		tmp = x * (t * -a)
	elif y <= 5.1e+50:
		tmp = j * (a * c)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(i * j) * Float64(-y))
	tmp = 0.0
	if (y <= -2.25e+201)
		tmp = Float64(z * Float64(x * y));
	elseif (y <= -2.3e+156)
		tmp = t_1;
	elseif (y <= -2.2e-39)
		tmp = Float64(x * Float64(y * z));
	elseif (y <= -1.7e-273)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (y <= 5.1e+50)
		tmp = Float64(j * Float64(a * 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 = (i * j) * -y;
	tmp = 0.0;
	if (y <= -2.25e+201)
		tmp = z * (x * y);
	elseif (y <= -2.3e+156)
		tmp = t_1;
	elseif (y <= -2.2e-39)
		tmp = x * (y * z);
	elseif (y <= -1.7e-273)
		tmp = x * (t * -a);
	elseif (y <= 5.1e+50)
		tmp = j * (a * c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(i * j), $MachinePrecision] * (-y)), $MachinePrecision]}, If[LessEqual[y, -2.25e+201], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.3e+156], t$95$1, If[LessEqual[y, -2.2e-39], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.7e-273], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.1e+50], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.25000000000000005e201

   1. Initial program 43.1%

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

      1. sub-neg 43.1%

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

      2. distribute-rgt-in 43.1%

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

      3. *-commutative 43.1%

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

      4. distribute-rgt-neg-in 43.1%

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

   4. Applied egg-rr 43.1%

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

   5. Taylor expanded in x around inf 56.3%

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

      1. *-commutative 56.3%

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

      2. *-commutative 56.3%

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

   7. Simplified 56.3%

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

   8. Taylor expanded in z around inf 48.2%

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

      1. associate-*r* 54.3%

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

   10. Simplified 54.3%

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

   if -2.25000000000000005e201 < y < -2.2999999999999999e156 or 5.0999999999999998e50 < y

   1. Initial program 63.7%

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

      1. sub-neg 63.7%

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

      2. distribute-rgt-in 63.7%

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

      3. *-commutative 63.7%

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

      4. distribute-rgt-neg-in 63.7%

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

   4. Applied egg-rr 63.7%

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

   5. Taylor expanded in y around inf 71.9%

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

      1. mul-1-neg 71.9%

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

      2. +-commutative 71.9%

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

      3. *-commutative 71.9%

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

      4. sub-neg 71.9%

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

   7. Simplified 71.9%

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

   8. Taylor expanded in z around 0 54.9%

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

      1. mul-1-neg 54.9%

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

      2. distribute-lft-neg-out 54.9%

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

      3. *-commutative 54.9%

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

   10. Simplified 54.9%

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

   if -2.2999999999999999e156 < y < -2.20000000000000001e-39

   1. Initial program 88.2%

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

      1. sub-neg 88.2%

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

      2. distribute-rgt-in 88.2%

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

      3. *-commutative 88.2%

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

      4. distribute-rgt-neg-in 88.2%

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

   4. Applied egg-rr 88.2%

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

   5. Taylor expanded in y around inf 51.7%

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

      1. mul-1-neg 51.7%

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

      2. +-commutative 51.7%

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

      3. *-commutative 51.7%

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

      4. sub-neg 51.7%

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

   7. Simplified 51.7%

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

   8. Taylor expanded in z around inf 37.6%

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

   if -2.20000000000000001e-39 < y < -1.69999999999999996e-273

   1. Initial program 83.1%

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

      1. sub-neg 83.1%

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

      2. distribute-rgt-in 83.1%

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

      3. *-commutative 83.1%

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

      4. distribute-rgt-neg-in 83.1%

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

   4. Applied egg-rr 83.1%

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

   5. Taylor expanded in x around inf 50.4%

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

      1. *-commutative 50.4%

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

      2. *-commutative 50.4%

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

   7. Simplified 50.4%

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

   8. Taylor expanded in z around 0 43.5%

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

      1. neg-mul-1 43.5%

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

      2. distribute-rgt-neg-in 43.5%

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

   10. Simplified 43.5%

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

   if -1.69999999999999996e-273 < y < 5.0999999999999998e50

   1. Initial program 79.7%

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

   3. Taylor expanded in j around inf 39.6%

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

      1. *-commutative 39.6%

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

   5. Simplified 39.6%

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

   6. Taylor expanded in a around inf 34.0%

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

      1. *-commutative 34.0%

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

   8. Simplified 34.0%

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

4. Final simplification 43.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{+201}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{+156}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-39}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-273}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{+50}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 28.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.76 \cdot 10^{+183}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-101}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-285}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-148}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 85000000000000:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -1.76e+183)
   (* t (* x (- a)))
   (if (<= a -1.4e-101)
     (* c (* a j))
     (if (<= a -3.1e-285)
       (* z (* b (- c)))
       (if (<= a 1.5e-148)
         (* y (* x z))
         (if (<= a 85000000000000.0) (* t (* b i)) (* a (* t (- x)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -1.76e+183) {
		tmp = t * (x * -a);
	} else if (a <= -1.4e-101) {
		tmp = c * (a * j);
	} else if (a <= -3.1e-285) {
		tmp = z * (b * -c);
	} else if (a <= 1.5e-148) {
		tmp = y * (x * z);
	} else if (a <= 85000000000000.0) {
		tmp = t * (b * i);
	} else {
		tmp = a * (t * -x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (a <= (-1.76d+183)) then
        tmp = t * (x * -a)
    else if (a <= (-1.4d-101)) then
        tmp = c * (a * j)
    else if (a <= (-3.1d-285)) then
        tmp = z * (b * -c)
    else if (a <= 1.5d-148) then
        tmp = y * (x * z)
    else if (a <= 85000000000000.0d0) then
        tmp = t * (b * i)
    else
        tmp = a * (t * -x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -1.76e+183) {
		tmp = t * (x * -a);
	} else if (a <= -1.4e-101) {
		tmp = c * (a * j);
	} else if (a <= -3.1e-285) {
		tmp = z * (b * -c);
	} else if (a <= 1.5e-148) {
		tmp = y * (x * z);
	} else if (a <= 85000000000000.0) {
		tmp = t * (b * i);
	} else {
		tmp = a * (t * -x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -1.76e+183:
		tmp = t * (x * -a)
	elif a <= -1.4e-101:
		tmp = c * (a * j)
	elif a <= -3.1e-285:
		tmp = z * (b * -c)
	elif a <= 1.5e-148:
		tmp = y * (x * z)
	elif a <= 85000000000000.0:
		tmp = t * (b * i)
	else:
		tmp = a * (t * -x)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -1.76e+183)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (a <= -1.4e-101)
		tmp = Float64(c * Float64(a * j));
	elseif (a <= -3.1e-285)
		tmp = Float64(z * Float64(b * Float64(-c)));
	elseif (a <= 1.5e-148)
		tmp = Float64(y * Float64(x * z));
	elseif (a <= 85000000000000.0)
		tmp = Float64(t * Float64(b * i));
	else
		tmp = Float64(a * Float64(t * Float64(-x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -1.76e+183)
		tmp = t * (x * -a);
	elseif (a <= -1.4e-101)
		tmp = c * (a * j);
	elseif (a <= -3.1e-285)
		tmp = z * (b * -c);
	elseif (a <= 1.5e-148)
		tmp = y * (x * z);
	elseif (a <= 85000000000000.0)
		tmp = t * (b * i);
	else
		tmp = a * (t * -x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -1.76e+183], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.4e-101], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.1e-285], N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.5e-148], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 85000000000000.0], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -1.75999999999999997e183

   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 inf 72.2%

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

      1. +-commutative 72.2%

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

      2. mul-1-neg 72.2%

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

      3. unsub-neg 72.2%

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

      4. *-commutative 72.2%

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

      5. *-commutative 72.2%

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

   5. Simplified 72.2%

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

   6. Taylor expanded in t around inf 69.7%

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

      1. +-commutative 69.7%

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

      2. mul-1-neg 69.7%

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

      3. unsub-neg 69.7%

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

      4. associate-/l* 69.7%

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

      5. associate-/l* 73.5%

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

   8. Simplified 73.5%

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

   9. Taylor expanded in t around inf 54.7%

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

       1. mul-1-neg 54.7%

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

       2. associate-*r* 54.7%

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

       3. distribute-rgt-neg-in 54.7%

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

       4. *-commutative 54.7%

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

       5. associate-*r* 58.2%

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

   11. Simplified 58.2%

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

   if -1.75999999999999997e183 < a < -1.39999999999999995e-101

   1. Initial program 76.1%

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

   3. Taylor expanded in a around inf 49.4%

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

      1. +-commutative 49.4%

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

      2. mul-1-neg 49.4%

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

      3. unsub-neg 49.4%

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

      4. *-commutative 49.4%

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

      5. *-commutative 49.4%

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

   5. Simplified 49.4%

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

   6. Taylor expanded in t around inf 47.9%

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

      1. +-commutative 47.9%

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

      2. mul-1-neg 47.9%

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

      3. unsub-neg 47.9%

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

      4. associate-/l* 47.9%

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

      5. associate-/l* 45.1%

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

   8. Simplified 45.1%

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

   9. Taylor expanded in t around 0 35.4%

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

       1. *-commutative 35.4%

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

       2. associate-*r* 37.9%

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

       3. *-commutative 37.9%

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

   11. Simplified 37.9%

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

   if -1.39999999999999995e-101 < a < -3.1000000000000001e-285

   1. Initial program 79.4%

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

   3. Taylor expanded in a around -inf 51.0%

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

   5. Simplified 59.9%

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

   6. Taylor expanded in c around inf 42.9%

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

   7. Taylor expanded in a around 0 47.6%

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

      1. mul-1-neg 47.6%

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

      2. associate-*r* 48.4%

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

      3. distribute-rgt-neg-in 48.4%

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

   9. Simplified 48.4%

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

   if -3.1000000000000001e-285 < a < 1.49999999999999999e-148

   1. Initial program 79.9%

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

      1. sub-neg 79.9%

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

      2. distribute-rgt-in 79.9%

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

      3. *-commutative 79.9%

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

      4. distribute-rgt-neg-in 79.9%

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

   4. Applied egg-rr 79.9%

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

   5. Taylor expanded in y around inf 66.7%

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

      1. mul-1-neg 66.7%

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

      2. +-commutative 66.7%

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

      3. *-commutative 66.7%

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

      4. sub-neg 66.7%

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

   7. Simplified 66.7%

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

   8. Taylor expanded in z around inf 44.3%

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

   if 1.49999999999999999e-148 < a < 8.5e13

   1. Initial program 68.8%

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

   3. Taylor expanded in t around -inf 38.5%

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

   4. Taylor expanded in a around 0 35.8%

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

      1. neg-mul-1 35.8%

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

      2. distribute-rgt-neg-in 35.8%

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

   6. Simplified 35.8%

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

   if 8.5e13 < a

   1. Initial program 75.8%

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

   3. Taylor expanded in a around inf 58.0%

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

      1. +-commutative 58.0%

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

      2. mul-1-neg 58.0%

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

      3. unsub-neg 58.0%

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

      4. *-commutative 58.0%

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

      5. *-commutative 58.0%

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

   5. Simplified 58.0%

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

   6. Taylor expanded in j around 0 41.7%

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

      1. associate-*r* 41.7%

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

      2. neg-mul-1 41.7%

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

   8. Simplified 41.7%

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

4. Final simplification 43.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.76 \cdot 10^{+183}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-101}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-285}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-148}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 85000000000000:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 50.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.4 \cdot 10^{-23}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.96 \cdot 10^{-274}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-153}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{-11}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* a (- (* c j) (* x t)))))
   (if (<= a -1.4e-23)
     t_2
     (if (<= a 1.96e-274)
       t_1
       (if (<= a 6e-153) (* x (* y z)) (if (<= a 3.7e-11) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.4e-23) {
		tmp = t_2;
	} else if (a <= 1.96e-274) {
		tmp = t_1;
	} else if (a <= 6e-153) {
		tmp = x * (y * z);
	} else if (a <= 3.7e-11) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = a * ((c * j) - (x * t))
    if (a <= (-1.4d-23)) then
        tmp = t_2
    else if (a <= 1.96d-274) then
        tmp = t_1
    else if (a <= 6d-153) then
        tmp = x * (y * z)
    else if (a <= 3.7d-11) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.4e-23) {
		tmp = t_2;
	} else if (a <= 1.96e-274) {
		tmp = t_1;
	} else if (a <= 6e-153) {
		tmp = x * (y * z);
	} else if (a <= 3.7e-11) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -1.4e-23:
		tmp = t_2
	elif a <= 1.96e-274:
		tmp = t_1
	elif a <= 6e-153:
		tmp = x * (y * z)
	elif a <= 3.7e-11:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -1.4e-23)
		tmp = t_2;
	elseif (a <= 1.96e-274)
		tmp = t_1;
	elseif (a <= 6e-153)
		tmp = Float64(x * Float64(y * z));
	elseif (a <= 3.7e-11)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -1.4e-23)
		tmp = t_2;
	elseif (a <= 1.96e-274)
		tmp = t_1;
	elseif (a <= 6e-153)
		tmp = x * (y * z);
	elseif (a <= 3.7e-11)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.4e-23], t$95$2, If[LessEqual[a, 1.96e-274], t$95$1, If[LessEqual[a, 6e-153], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.7e-11], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.3999999999999999e-23 or 3.7000000000000001e-11 < a

   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 a around inf 59.4%

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

      1. +-commutative 59.4%

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

      2. mul-1-neg 59.4%

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

      3. unsub-neg 59.4%

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

      4. *-commutative 59.4%

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

      5. *-commutative 59.4%

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

   5. Simplified 59.4%

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

   if -1.3999999999999999e-23 < a < 1.95999999999999993e-274 or 6e-153 < a < 3.7000000000000001e-11

   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 b around inf 56.4%

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

      1. *-commutative 56.4%

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

      2. *-commutative 56.4%

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

   5. Simplified 56.4%

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

   if 1.95999999999999993e-274 < a < 6e-153

   1. Initial program 73.9%

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

      1. sub-neg 73.9%

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

      2. distribute-rgt-in 73.9%

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

      3. *-commutative 73.9%

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

      4. distribute-rgt-neg-in 73.9%

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

   4. Applied egg-rr 73.9%

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

   5. Taylor expanded in y around inf 76.7%

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

      1. mul-1-neg 76.7%

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

      2. +-commutative 76.7%

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

      3. *-commutative 76.7%

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

      4. sub-neg 76.7%

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

   7. Simplified 76.7%

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

   8. Taylor expanded in z around inf 53.7%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{-23}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq 1.96 \cdot 10^{-274}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-153}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{-11}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 63.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+146} \lor \neg \left(t \leq 10^{+53}\right):\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(b \cdot \frac{i}{a} - x\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -6.2e+146) (not (<= t 1e+53)))
   (* (* t a) (- (* b (/ i a)) x))
   (- (* j (- (* a c) (* y i))) (* x (- (* t a) (* y 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 ((t <= -6.2e+146) || !(t <= 1e+53)) {
		tmp = (t * a) * ((b * (i / a)) - x);
	} else {
		tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * 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 ((t <= (-6.2d+146)) .or. (.not. (t <= 1d+53))) then
        tmp = (t * a) * ((b * (i / a)) - x)
    else
        tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * 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 ((t <= -6.2e+146) || !(t <= 1e+53)) {
		tmp = (t * a) * ((b * (i / a)) - x);
	} else {
		tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -6.2e+146) or not (t <= 1e+53):
		tmp = (t * a) * ((b * (i / a)) - x)
	else:
		tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -6.2e+146) || !(t <= 1e+53))
		tmp = Float64(Float64(t * a) * Float64(Float64(b * Float64(i / a)) - x));
	else
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) - Float64(x * Float64(Float64(t * a) - Float64(y * z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -6.2e+146) || ~((t <= 1e+53)))
		tmp = (t * a) * ((b * (i / a)) - x);
	else
		tmp = (j * ((a * c) - (y * i))) - (x * ((t * a) - (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -6.2e+146], N[Not[LessEqual[t, 1e+53]], $MachinePrecision]], N[(N[(t * a), $MachinePrecision] * N[(N[(b * N[(i / a), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.2000000000000004e146 or 9.9999999999999999e52 < t

   1. Initial program 68.4%

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

   3. Taylor expanded in a around -inf 61.4%

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

   5. Simplified 64.9%

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

   6. Taylor expanded in t around inf 70.3%

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

      1. mul-1-neg 70.3%

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

      2. associate-*r* 72.6%

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

      3. distribute-rgt-neg-in 72.6%

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

      4. mul-1-neg 72.6%

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

      5. distribute-lft-out-- 72.6%

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

      6. *-commutative 72.6%

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

      7. sub-neg 72.6%

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

      8. mul-1-neg 72.6%

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

      9. remove-double-neg 72.6%

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

      10. +-commutative 72.6%

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

      11. neg-mul-1 72.6%

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

      12. unsub-neg 72.6%

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

      13. associate-/l* 73.8%

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

   8. Simplified 73.8%

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

   if -6.2000000000000004e146 < t < 9.9999999999999999e52

   1. Initial program 77.1%

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

   3. Taylor expanded in b around 0 66.5%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+146} \lor \neg \left(t \leq 10^{+53}\right):\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(b \cdot \frac{i}{a} - x\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 28.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{+197}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -4.9 \cdot 10^{+156}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -9.8 \cdot 10^{-213}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+48}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* y i) (- j))))
   (if (<= y -3.8e+197)
     (* z (* x y))
     (if (<= y -4.9e+156)
       t_1
       (if (<= y -9.8e-213)
         (* y (* x z))
         (if (<= y 9.5e+48) (* j (* a 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 = (y * i) * -j;
	double tmp;
	if (y <= -3.8e+197) {
		tmp = z * (x * y);
	} else if (y <= -4.9e+156) {
		tmp = t_1;
	} else if (y <= -9.8e-213) {
		tmp = y * (x * z);
	} else if (y <= 9.5e+48) {
		tmp = j * (a * 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 = (y * i) * -j
    if (y <= (-3.8d+197)) then
        tmp = z * (x * y)
    else if (y <= (-4.9d+156)) then
        tmp = t_1
    else if (y <= (-9.8d-213)) then
        tmp = y * (x * z)
    else if (y <= 9.5d+48) then
        tmp = j * (a * 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 = (y * i) * -j;
	double tmp;
	if (y <= -3.8e+197) {
		tmp = z * (x * y);
	} else if (y <= -4.9e+156) {
		tmp = t_1;
	} else if (y <= -9.8e-213) {
		tmp = y * (x * z);
	} else if (y <= 9.5e+48) {
		tmp = j * (a * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (y * i) * -j
	tmp = 0
	if y <= -3.8e+197:
		tmp = z * (x * y)
	elif y <= -4.9e+156:
		tmp = t_1
	elif y <= -9.8e-213:
		tmp = y * (x * z)
	elif y <= 9.5e+48:
		tmp = j * (a * c)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(y * i) * Float64(-j))
	tmp = 0.0
	if (y <= -3.8e+197)
		tmp = Float64(z * Float64(x * y));
	elseif (y <= -4.9e+156)
		tmp = t_1;
	elseif (y <= -9.8e-213)
		tmp = Float64(y * Float64(x * z));
	elseif (y <= 9.5e+48)
		tmp = Float64(j * Float64(a * 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 = (y * i) * -j;
	tmp = 0.0;
	if (y <= -3.8e+197)
		tmp = z * (x * y);
	elseif (y <= -4.9e+156)
		tmp = t_1;
	elseif (y <= -9.8e-213)
		tmp = y * (x * z);
	elseif (y <= 9.5e+48)
		tmp = j * (a * c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(y * i), $MachinePrecision] * (-j)), $MachinePrecision]}, If[LessEqual[y, -3.8e+197], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.9e+156], t$95$1, If[LessEqual[y, -9.8e-213], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.5e+48], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.8000000000000001e197

   1. Initial program 43.1%

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

      1. sub-neg 43.1%

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

      2. distribute-rgt-in 43.1%

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

      3. *-commutative 43.1%

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

      4. distribute-rgt-neg-in 43.1%

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

   4. Applied egg-rr 43.1%

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

   5. Taylor expanded in x around inf 56.3%

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

      1. *-commutative 56.3%

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

      2. *-commutative 56.3%

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

   7. Simplified 56.3%

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

   8. Taylor expanded in z around inf 48.2%

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

      1. associate-*r* 54.3%

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

   10. Simplified 54.3%

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

   if -3.8000000000000001e197 < y < -4.89999999999999969e156 or 9.4999999999999997e48 < y

   1. Initial program 63.7%

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

   3. Taylor expanded in j around inf 58.3%

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

      1. *-commutative 58.3%

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

   5. Simplified 58.3%

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

   6. Taylor expanded in a around 0 50.4%

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

      1. neg-mul-1 50.4%

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

      2. distribute-rgt-neg-in 50.4%

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

   8. Simplified 50.4%

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

   if -4.89999999999999969e156 < y < -9.7999999999999997e-213

   1. Initial program 85.8%

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

      1. sub-neg 85.8%

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

      2. distribute-rgt-in 85.8%

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

      3. *-commutative 85.8%

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

      4. distribute-rgt-neg-in 85.8%

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

   4. Applied egg-rr 85.8%

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

   5. Taylor expanded in y around inf 44.1%

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

      1. mul-1-neg 44.1%

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

      2. +-commutative 44.1%

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

      3. *-commutative 44.1%

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

      4. sub-neg 44.1%

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

   7. Simplified 44.1%

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

   8. Taylor expanded in z around inf 34.3%

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

   if -9.7999999999999997e-213 < y < 9.4999999999999997e48

   1. Initial program 80.3%

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

   3. Taylor expanded in j around inf 36.7%

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

      1. *-commutative 36.7%

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

   5. Simplified 36.7%

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

   6. Taylor expanded in a around inf 31.8%

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

      1. *-commutative 31.8%

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

   8. Simplified 31.8%

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

4. Final simplification 39.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+197}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -4.9 \cdot 10^{+156}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;y \leq -9.8 \cdot 10^{-213}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+48}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 30.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{-36} \lor \neg \left(y \leq 2.4 \cdot 10^{+48}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= y -4.3e-36) (not (<= y 2.4e+48))) (* x (* y z)) (* j (* a 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 ((y <= -4.3e-36) || !(y <= 2.4e+48)) {
		tmp = x * (y * z);
	} else {
		tmp = j * (a * 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 ((y <= (-4.3d-36)) .or. (.not. (y <= 2.4d+48))) then
        tmp = x * (y * z)
    else
        tmp = j * (a * 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 ((y <= -4.3e-36) || !(y <= 2.4e+48)) {
		tmp = x * (y * z);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (y <= -4.3e-36) or not (y <= 2.4e+48):
		tmp = x * (y * z)
	else:
		tmp = j * (a * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((y <= -4.3e-36) || !(y <= 2.4e+48))
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(j * Float64(a * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((y <= -4.3e-36) || ~((y <= 2.4e+48)))
		tmp = x * (y * z);
	else
		tmp = j * (a * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[y, -4.3e-36], N[Not[LessEqual[y, 2.4e+48]], $MachinePrecision]], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.3000000000000002e-36 or 2.4000000000000001e48 < y

   1. Initial program 67.6%

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

      1. sub-neg 67.6%

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

      2. distribute-rgt-in 67.6%

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

      3. *-commutative 67.6%

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

      4. distribute-rgt-neg-in 67.6%

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

   4. Applied egg-rr 67.6%

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

   5. Taylor expanded in y around inf 64.9%

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

      1. mul-1-neg 64.9%

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

      2. +-commutative 64.9%

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

      3. *-commutative 64.9%

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

      4. sub-neg 64.9%

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

   7. Simplified 64.9%

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

   8. Taylor expanded in z around inf 35.6%

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

   if -4.3000000000000002e-36 < y < 2.4000000000000001e48

   1. Initial program 80.9%

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

   3. Taylor expanded in j around inf 32.1%

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

      1. *-commutative 32.1%

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

   5. Simplified 32.1%

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

   6. Taylor expanded in a around inf 29.1%

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

      1. *-commutative 29.1%

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

   8. Simplified 29.1%

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

4. Final simplification 32.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{-36} \lor \neg \left(y \leq 2.4 \cdot 10^{+48}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 28.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-213}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+49}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -5.2e-213)
   (* y (* x z))
   (if (<= y 5e+49) (* j (* a c)) (* x (* y 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 (y <= -5.2e-213) {
		tmp = y * (x * z);
	} else if (y <= 5e+49) {
		tmp = j * (a * c);
	} else {
		tmp = x * (y * 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 (y <= (-5.2d-213)) then
        tmp = y * (x * z)
    else if (y <= 5d+49) then
        tmp = j * (a * c)
    else
        tmp = x * (y * 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 (y <= -5.2e-213) {
		tmp = y * (x * z);
	} else if (y <= 5e+49) {
		tmp = j * (a * c);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -5.2e-213:
		tmp = y * (x * z)
	elif y <= 5e+49:
		tmp = j * (a * c)
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -5.2e-213)
		tmp = Float64(y * Float64(x * z));
	elseif (y <= 5e+49)
		tmp = Float64(j * Float64(a * c));
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -5.2e-213)
		tmp = y * (x * z);
	elseif (y <= 5e+49)
		tmp = j * (a * c);
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -5.2e-213], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5e+49], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.2000000000000003e-213

   1. Initial program 74.2%

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

      1. sub-neg 74.2%

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

      2. distribute-rgt-in 74.2%

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

      3. *-commutative 74.2%

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

      4. distribute-rgt-neg-in 74.2%

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

   4. Applied egg-rr 74.2%

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

   5. Taylor expanded in y around inf 52.4%

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

      1. mul-1-neg 52.4%

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

      2. +-commutative 52.4%

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

      3. *-commutative 52.4%

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

      4. sub-neg 52.4%

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

   7. Simplified 52.4%

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

   8. Taylor expanded in z around inf 36.2%

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

   if -5.2000000000000003e-213 < y < 5.0000000000000004e49

   1. Initial program 80.3%

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

   3. Taylor expanded in j around inf 36.7%

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

      1. *-commutative 36.7%

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

   5. Simplified 36.7%

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

   6. Taylor expanded in a around inf 31.8%

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

      1. *-commutative 31.8%

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

   8. Simplified 31.8%

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

   if 5.0000000000000004e49 < y

   1. Initial program 63.1%

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

      1. sub-neg 63.1%

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

      2. distribute-rgt-in 63.1%

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

      3. *-commutative 63.1%

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

      4. distribute-rgt-neg-in 63.1%

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

   4. Applied egg-rr 63.1%

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

   5. Taylor expanded in y around inf 70.8%

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

      1. mul-1-neg 70.8%

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

      2. +-commutative 70.8%

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

      3. *-commutative 70.8%

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

      4. sub-neg 70.8%

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

   7. Simplified 70.8%

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

   8. Taylor expanded in z around inf 33.4%

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

4. Final simplification 33.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-213}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+49}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 28.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.04 \cdot 10^{-212}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+48}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -1.04e-212)
   (* y (* x z))
   (if (<= y 4.3e+48) (* j (* a c)) (* z (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -1.04e-212) {
		tmp = y * (x * z);
	} else if (y <= 4.3e+48) {
		tmp = j * (a * c);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-1.04d-212)) then
        tmp = y * (x * z)
    else if (y <= 4.3d+48) then
        tmp = j * (a * c)
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -1.04e-212) {
		tmp = y * (x * z);
	} else if (y <= 4.3e+48) {
		tmp = j * (a * c);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -1.04e-212:
		tmp = y * (x * z)
	elif y <= 4.3e+48:
		tmp = j * (a * c)
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -1.04e-212)
		tmp = Float64(y * Float64(x * z));
	elseif (y <= 4.3e+48)
		tmp = Float64(j * Float64(a * c));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -1.04e-212)
		tmp = y * (x * z);
	elseif (y <= 4.3e+48)
		tmp = j * (a * c);
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -1.04e-212], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.3e+48], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.0400000000000001e-212

   1. Initial program 74.2%

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

      1. sub-neg 74.2%

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

      2. distribute-rgt-in 74.2%

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

      3. *-commutative 74.2%

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

      4. distribute-rgt-neg-in 74.2%

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

   4. Applied egg-rr 74.2%

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

   5. Taylor expanded in y around inf 52.4%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 52.4%

         \[\leadsto y \cdot \left(\color{blue}{\left(-i \cdot j\right)} + x \cdot z\right) \]

      2. +-commutative 52.4%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + \left(-i \cdot j\right)\right)} \]

      3. *-commutative 52.4%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} + \left(-i \cdot j\right)\right) \]

      4. sub-neg 52.4%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   7. Simplified 52.4%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   8. Taylor expanded in z around inf 36.2%

      \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} \]

   if -1.0400000000000001e-212 < y < 4.29999999999999978e48

   1. Initial program 80.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 36.7%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-commutative 36.7%

         \[\leadsto j \cdot \left(a \cdot c - \color{blue}{y \cdot i}\right) \]

   5. Simplified 36.7%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - y \cdot i\right)} \]

   6. Taylor expanded in a around inf 31.8%

      \[\leadsto j \cdot \color{blue}{\left(a \cdot c\right)} \]
   7. Step-by-step derivation

      1. *-commutative 31.8%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot a\right)} \]

   8. Simplified 31.8%

      \[\leadsto j \cdot \color{blue}{\left(c \cdot a\right)} \]

   if 4.29999999999999978e48 < y

   1. Initial program 63.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg 63.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. distribute-rgt-in 63.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\left(c \cdot z\right) \cdot b + \left(-t \cdot i\right) \cdot b\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 63.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\color{blue}{\left(z \cdot c\right)} \cdot b + \left(-t \cdot i\right) \cdot b\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. distribute-rgt-neg-in 63.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(z \cdot c\right) \cdot b + \color{blue}{\left(t \cdot \left(-i\right)\right)} \cdot b\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 63.1%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\left(z \cdot c\right) \cdot b + \left(t \cdot \left(-i\right)\right) \cdot b\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in x around inf 45.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   6. Step-by-step derivation

      1. *-commutative 45.9%

         \[\leadsto x \cdot \left(\color{blue}{z \cdot y} - a \cdot t\right) \]

      2. *-commutative 45.9%

         \[\leadsto x \cdot \left(z \cdot y - \color{blue}{t \cdot a}\right) \]

   7. Simplified 45.9%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y - t \cdot a\right)} \]

   8. Taylor expanded in z around inf 33.4%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 36.8%

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot z} \]

   10. Simplified 36.8%

       \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 34.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.04 \cdot 10^{-212}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+48}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 22.4% 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 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 38.4%

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
4. Step-by-step derivation

   1. +-commutative 38.4%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

   2. mul-1-neg 38.4%

      \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

   3. unsub-neg 38.4%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. *-commutative 38.4%

      \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. *-commutative 38.4%

      \[\leadsto a \cdot \left(j \cdot c - \color{blue}{x \cdot t}\right) \]

5. Simplified 38.4%

   \[\leadsto \color{blue}{a \cdot \left(j \cdot c - x \cdot t\right)} \]

6. Taylor expanded in j around inf 20.0%

   \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

7. Final simplification 20.0%

   \[\leadsto a \cdot \left(c \cdot j\right) \]
8. Add Preprocessing

Alternative 22: 22.9% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ j \cdot \left(a \cdot c\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* j (* a c)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return j * (a * c);
}

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 = j * (a * c)
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 j * (a * c);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return j * (a * c)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(j * Float64(a * c))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = j * (a * c);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]

Derivation

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 j around inf 38.0%

   \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]
4. Step-by-step derivation

   1. *-commutative 38.0%

      \[\leadsto j \cdot \left(a \cdot c - \color{blue}{y \cdot i}\right) \]

5. Simplified 38.0%

   \[\leadsto \color{blue}{j \cdot \left(a \cdot c - y \cdot i\right)} \]

6. Taylor expanded in a around inf 20.9%

   \[\leadsto j \cdot \color{blue}{\left(a \cdot c\right)} \]
7. Step-by-step derivation

   1. *-commutative 20.9%

      \[\leadsto j \cdot \color{blue}{\left(c \cdot a\right)} \]

8. Simplified 20.9%

   \[\leadsto j \cdot \color{blue}{\left(c \cdot a\right)} \]

9. Final simplification 20.9%

   \[\leadsto j \cdot \left(a \cdot c\right) \]
10. Add Preprocessing

Developer target: 59.1% 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 2024073 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :alt
  (if (< x -1.469694296777705e-64) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 3.2113527362226803e-147) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i)))))