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

Percentage Accurate: 73.2% → 81.7%

Time: 34.8s

Alternatives: 28

Speedup: 0.5×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.2% 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: 81.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $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 90.9%

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

   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 t around inf 58.4%

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

      1. distribute-lft-out-- 58.4%

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

      2. *-commutative 58.4%

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

   5. Simplified 58.4%

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

   6. Taylor expanded in t around 0 58.4%

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

      1. mul-1-neg 58.4%

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

      2. distribute-rgt-neg-out 58.4%

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

   8. Simplified 58.4%

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

4. Final simplification 84.3%

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

Alternative 2: 64.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := a \cdot c - y \cdot i\\ t_3 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_4 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_5 := j \cdot \left(t\_2 + \frac{t\_4}{j}\right)\\ t_6 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;t \leq -3.8 \cdot 10^{+267}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -4.25 \cdot 10^{+18}:\\ \;\;\;\;t\_1 + t\_6\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-18}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-83}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + t\_6\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-126}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;t \leq 10^{-189}:\\ \;\;\;\;i \cdot \left(\frac{a \cdot \left(c \cdot j\right) + t\_4}{i} - y \cdot j\right)\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-5}:\\ \;\;\;\;t\_1 + j \cdot t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (- (* a c) (* y i)))
        (t_3 (* t (- (* b i) (* x a))))
        (t_4 (* z (- (* x y) (* b c))))
        (t_5 (* j (+ t_2 (/ t_4 j))))
        (t_6 (* b (- (* t i) (* z c)))))
   (if (<= t -3.8e+267)
     t_3
     (if (<= t -4.25e+18)
       (+ t_1 t_6)
       (if (<= t -5.4e-18)
         t_5
         (if (<= t -2.2e-83)
           (+ (* a (- (* c j) (* x t))) t_6)
           (if (<= t -1.8e-126)
             t_5
             (if (<= t 1e-189)
               (* i (- (/ (+ (* a (* c j)) t_4) i) (* y j)))
               (if (<= t 1.02e-5) (+ t_1 (* j t_2)) 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 = (a * c) - (y * i);
	double t_3 = t * ((b * i) - (x * a));
	double t_4 = z * ((x * y) - (b * c));
	double t_5 = j * (t_2 + (t_4 / j));
	double t_6 = b * ((t * i) - (z * c));
	double tmp;
	if (t <= -3.8e+267) {
		tmp = t_3;
	} else if (t <= -4.25e+18) {
		tmp = t_1 + t_6;
	} else if (t <= -5.4e-18) {
		tmp = t_5;
	} else if (t <= -2.2e-83) {
		tmp = (a * ((c * j) - (x * t))) + t_6;
	} else if (t <= -1.8e-126) {
		tmp = t_5;
	} else if (t <= 1e-189) {
		tmp = i * ((((a * (c * j)) + t_4) / i) - (y * j));
	} else if (t <= 1.02e-5) {
		tmp = t_1 + (j * t_2);
	} 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) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = (a * c) - (y * i)
    t_3 = t * ((b * i) - (x * a))
    t_4 = z * ((x * y) - (b * c))
    t_5 = j * (t_2 + (t_4 / j))
    t_6 = b * ((t * i) - (z * c))
    if (t <= (-3.8d+267)) then
        tmp = t_3
    else if (t <= (-4.25d+18)) then
        tmp = t_1 + t_6
    else if (t <= (-5.4d-18)) then
        tmp = t_5
    else if (t <= (-2.2d-83)) then
        tmp = (a * ((c * j) - (x * t))) + t_6
    else if (t <= (-1.8d-126)) then
        tmp = t_5
    else if (t <= 1d-189) then
        tmp = i * ((((a * (c * j)) + t_4) / i) - (y * j))
    else if (t <= 1.02d-5) then
        tmp = t_1 + (j * t_2)
    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 = (a * c) - (y * i);
	double t_3 = t * ((b * i) - (x * a));
	double t_4 = z * ((x * y) - (b * c));
	double t_5 = j * (t_2 + (t_4 / j));
	double t_6 = b * ((t * i) - (z * c));
	double tmp;
	if (t <= -3.8e+267) {
		tmp = t_3;
	} else if (t <= -4.25e+18) {
		tmp = t_1 + t_6;
	} else if (t <= -5.4e-18) {
		tmp = t_5;
	} else if (t <= -2.2e-83) {
		tmp = (a * ((c * j) - (x * t))) + t_6;
	} else if (t <= -1.8e-126) {
		tmp = t_5;
	} else if (t <= 1e-189) {
		tmp = i * ((((a * (c * j)) + t_4) / i) - (y * j));
	} else if (t <= 1.02e-5) {
		tmp = t_1 + (j * t_2);
	} 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 = (a * c) - (y * i)
	t_3 = t * ((b * i) - (x * a))
	t_4 = z * ((x * y) - (b * c))
	t_5 = j * (t_2 + (t_4 / j))
	t_6 = b * ((t * i) - (z * c))
	tmp = 0
	if t <= -3.8e+267:
		tmp = t_3
	elif t <= -4.25e+18:
		tmp = t_1 + t_6
	elif t <= -5.4e-18:
		tmp = t_5
	elif t <= -2.2e-83:
		tmp = (a * ((c * j) - (x * t))) + t_6
	elif t <= -1.8e-126:
		tmp = t_5
	elif t <= 1e-189:
		tmp = i * ((((a * (c * j)) + t_4) / i) - (y * j))
	elif t <= 1.02e-5:
		tmp = t_1 + (j * t_2)
	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(Float64(a * c) - Float64(y * i))
	t_3 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	t_4 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	t_5 = Float64(j * Float64(t_2 + Float64(t_4 / j)))
	t_6 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (t <= -3.8e+267)
		tmp = t_3;
	elseif (t <= -4.25e+18)
		tmp = Float64(t_1 + t_6);
	elseif (t <= -5.4e-18)
		tmp = t_5;
	elseif (t <= -2.2e-83)
		tmp = Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) + t_6);
	elseif (t <= -1.8e-126)
		tmp = t_5;
	elseif (t <= 1e-189)
		tmp = Float64(i * Float64(Float64(Float64(Float64(a * Float64(c * j)) + t_4) / i) - Float64(y * j)));
	elseif (t <= 1.02e-5)
		tmp = Float64(t_1 + Float64(j * t_2));
	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 = (a * c) - (y * i);
	t_3 = t * ((b * i) - (x * a));
	t_4 = z * ((x * y) - (b * c));
	t_5 = j * (t_2 + (t_4 / j));
	t_6 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (t <= -3.8e+267)
		tmp = t_3;
	elseif (t <= -4.25e+18)
		tmp = t_1 + t_6;
	elseif (t <= -5.4e-18)
		tmp = t_5;
	elseif (t <= -2.2e-83)
		tmp = (a * ((c * j) - (x * t))) + t_6;
	elseif (t <= -1.8e-126)
		tmp = t_5;
	elseif (t <= 1e-189)
		tmp = i * ((((a * (c * j)) + t_4) / i) - (y * j));
	elseif (t <= 1.02e-5)
		tmp = t_1 + (j * t_2);
	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[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(j * N[(t$95$2 + N[(t$95$4 / j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.8e+267], t$95$3, If[LessEqual[t, -4.25e+18], N[(t$95$1 + t$95$6), $MachinePrecision], If[LessEqual[t, -5.4e-18], t$95$5, If[LessEqual[t, -2.2e-83], N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$6), $MachinePrecision], If[LessEqual[t, -1.8e-126], t$95$5, If[LessEqual[t, 1e-189], N[(i * N[(N[(N[(N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision] / i), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.02e-5], N[(t$95$1 + N[(j * t$95$2), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -3.80000000000000017e267 or 1.0200000000000001e-5 < t

   1. Initial program 50.8%

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

   3. Taylor expanded in t around inf 78.8%

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

      1. distribute-lft-out-- 78.8%

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

      2. *-commutative 78.8%

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

   5. Simplified 78.8%

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

   6. Taylor expanded in t around 0 78.8%

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

      1. mul-1-neg 78.8%

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

      2. distribute-rgt-neg-out 78.8%

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

   8. Simplified 78.8%

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

   if -3.80000000000000017e267 < t < -4.25e18

   1. Initial program 75.3%

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

   3. Taylor expanded in j around 0 78.8%

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

   if -4.25e18 < t < -5.39999999999999977e-18 or -2.20000000000000008e-83 < t < -1.8e-126

   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 t around 0 80.4%

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

   4. Taylor expanded in j around -inf 80.4%

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

      1. associate-*r* 80.4%

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

      2. mul-1-neg 80.4%

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

      3. mul-1-neg 80.4%

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

      4. unsub-neg 80.4%

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

      5. mul-1-neg 80.4%

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

      6. *-commutative 80.4%

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

      7. associate-*r* 81.0%

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

      8. cancel-sign-sub-inv 81.0%

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

      9. associate-*r* 85.7%

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

      10. mul-1-neg 85.7%

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

      11. distribute-rgt-in 90.7%

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

      12. mul-1-neg 90.7%

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

      13. sub-neg 90.7%

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

   6. Simplified 90.7%

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

   if -5.39999999999999977e-18 < t < -2.20000000000000008e-83

   1. Initial program 94.4%

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

   3. Taylor expanded in y around 0 88.8%

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

      1. cancel-sign-sub-inv 88.8%

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

      2. *-commutative 88.8%

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

      3. associate-*r* 88.8%

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

      4. *-commutative 88.8%

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

      5. distribute-rgt-in 88.8%

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

      6. +-commutative 88.8%

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

      7. mul-1-neg 88.8%

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

      8. unsub-neg 88.8%

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

      9. *-commutative 88.8%

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

      10. distribute-lft-neg-in 88.8%

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

      11. sub-neg 88.8%

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

      12. distribute-rgt-neg-out 88.8%

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

      13. distribute-lft-out 88.8%

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

      14. +-commutative 88.8%

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

      15. distribute-rgt-neg-out 88.8%

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

      16. distribute-rgt-neg-in 88.8%

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

      17. mul-1-neg 88.8%

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

   5. Simplified 88.8%

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

   if -1.8e-126 < t < 1.00000000000000007e-189

   1. Initial program 76.0%

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

   3. Taylor expanded in t around 0 68.0%

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

   4. Taylor expanded in i around -inf 66.9%

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

      1. mul-1-neg 66.9%

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

      2. distribute-rgt-neg-in 66.9%

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

      3. +-commutative 66.9%

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

      4. mul-1-neg 66.9%

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

      5. unsub-neg 66.9%

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

      6. *-commutative 66.9%

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

   6. Simplified 75.8%

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

   if 1.00000000000000007e-189 < t < 1.0200000000000001e-5

   1. Initial program 86.2%

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

   3. Taylor expanded in b around 0 78.3%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+267}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -4.25 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-18}:\\ \;\;\;\;j \cdot \left(\left(a \cdot c - y \cdot i\right) + \frac{z \cdot \left(x \cdot y - b \cdot c\right)}{j}\right)\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-83}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-126}:\\ \;\;\;\;j \cdot \left(\left(a \cdot c - y \cdot i\right) + \frac{z \cdot \left(x \cdot y - b \cdot c\right)}{j}\right)\\ \mathbf{elif}\;t \leq 10^{-189}:\\ \;\;\;\;i \cdot \left(\frac{a \cdot \left(c \cdot j\right) + z \cdot \left(x \cdot y - b \cdot c\right)}{i} - y \cdot j\right)\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -4.2 \cdot 10^{+152}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{+46}:\\ \;\;\;\;x \cdot \left(y \cdot \left(z - \frac{t \cdot a}{y}\right)\right)\\ \mathbf{elif}\;t \leq -82000:\\ \;\;\;\;b \cdot \left(z \cdot \left(i \cdot \frac{t}{z} - c\right)\right)\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-186}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-225}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-200}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))) (t_2 (* t (- (* b i) (* x a)))))
   (if (<= t -4.2e+152)
     t_2
     (if (<= t -5.5e+46)
       (* x (* y (- z (/ (* t a) y))))
       (if (<= t -82000.0)
         (* b (* z (- (* i (/ t z)) c)))
         (if (<= t -3.2e-66)
           t_1
           (if (<= t -1.5e-186)
             (* i (- (* t b) (* y j)))
             (if (<= t -5.4e-225)
               (* z (- (* x y) (* b c)))
               (if (<= t 6e-200)
                 (- (* z (* x y)) (* i (* y j)))
                 (if (<= t 7e-22) 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 * ((a * c) - (y * i));
	double t_2 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -4.2e+152) {
		tmp = t_2;
	} else if (t <= -5.5e+46) {
		tmp = x * (y * (z - ((t * a) / y)));
	} else if (t <= -82000.0) {
		tmp = b * (z * ((i * (t / z)) - c));
	} else if (t <= -3.2e-66) {
		tmp = t_1;
	} else if (t <= -1.5e-186) {
		tmp = i * ((t * b) - (y * j));
	} else if (t <= -5.4e-225) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 6e-200) {
		tmp = (z * (x * y)) - (i * (y * j));
	} else if (t <= 7e-22) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = t * ((b * i) - (x * a))
    if (t <= (-4.2d+152)) then
        tmp = t_2
    else if (t <= (-5.5d+46)) then
        tmp = x * (y * (z - ((t * a) / y)))
    else if (t <= (-82000.0d0)) then
        tmp = b * (z * ((i * (t / z)) - c))
    else if (t <= (-3.2d-66)) then
        tmp = t_1
    else if (t <= (-1.5d-186)) then
        tmp = i * ((t * b) - (y * j))
    else if (t <= (-5.4d-225)) then
        tmp = z * ((x * y) - (b * c))
    else if (t <= 6d-200) then
        tmp = (z * (x * y)) - (i * (y * j))
    else if (t <= 7d-22) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -4.2e+152) {
		tmp = t_2;
	} else if (t <= -5.5e+46) {
		tmp = x * (y * (z - ((t * a) / y)));
	} else if (t <= -82000.0) {
		tmp = b * (z * ((i * (t / z)) - c));
	} else if (t <= -3.2e-66) {
		tmp = t_1;
	} else if (t <= -1.5e-186) {
		tmp = i * ((t * b) - (y * j));
	} else if (t <= -5.4e-225) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 6e-200) {
		tmp = (z * (x * y)) - (i * (y * j));
	} else if (t <= 7e-22) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = t * ((b * i) - (x * a))
	tmp = 0
	if t <= -4.2e+152:
		tmp = t_2
	elif t <= -5.5e+46:
		tmp = x * (y * (z - ((t * a) / y)))
	elif t <= -82000.0:
		tmp = b * (z * ((i * (t / z)) - c))
	elif t <= -3.2e-66:
		tmp = t_1
	elif t <= -1.5e-186:
		tmp = i * ((t * b) - (y * j))
	elif t <= -5.4e-225:
		tmp = z * ((x * y) - (b * c))
	elif t <= 6e-200:
		tmp = (z * (x * y)) - (i * (y * j))
	elif t <= 7e-22:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	tmp = 0.0
	if (t <= -4.2e+152)
		tmp = t_2;
	elseif (t <= -5.5e+46)
		tmp = Float64(x * Float64(y * Float64(z - Float64(Float64(t * a) / y))));
	elseif (t <= -82000.0)
		tmp = Float64(b * Float64(z * Float64(Float64(i * Float64(t / z)) - c)));
	elseif (t <= -3.2e-66)
		tmp = t_1;
	elseif (t <= -1.5e-186)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (t <= -5.4e-225)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (t <= 6e-200)
		tmp = Float64(Float64(z * Float64(x * y)) - Float64(i * Float64(y * j)));
	elseif (t <= 7e-22)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -4.2e+152)
		tmp = t_2;
	elseif (t <= -5.5e+46)
		tmp = x * (y * (z - ((t * a) / y)));
	elseif (t <= -82000.0)
		tmp = b * (z * ((i * (t / z)) - c));
	elseif (t <= -3.2e-66)
		tmp = t_1;
	elseif (t <= -1.5e-186)
		tmp = i * ((t * b) - (y * j));
	elseif (t <= -5.4e-225)
		tmp = z * ((x * y) - (b * c));
	elseif (t <= 6e-200)
		tmp = (z * (x * y)) - (i * (y * j));
	elseif (t <= 7e-22)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.2e+152], t$95$2, If[LessEqual[t, -5.5e+46], N[(x * N[(y * N[(z - N[(N[(t * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -82000.0], N[(b * N[(z * N[(N[(i * N[(t / z), $MachinePrecision]), $MachinePrecision] - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.2e-66], t$95$1, If[LessEqual[t, -1.5e-186], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.4e-225], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e-200], N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e-22], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -4.2000000000000003e152 or 7.00000000000000011e-22 < t

   1. Initial program 57.5%

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

   3. Taylor expanded in t around inf 72.2%

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

      1. distribute-lft-out-- 72.2%

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

      2. *-commutative 72.2%

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

   5. Simplified 72.2%

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

   6. Taylor expanded in t around 0 72.2%

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

      1. mul-1-neg 72.2%

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

      2. distribute-rgt-neg-out 72.2%

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

   8. Simplified 72.2%

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

   if -4.2000000000000003e152 < t < -5.4999999999999998e46

   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 y around -inf 73.4%

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

   5. Simplified 77.3%

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

   6. Taylor expanded in x around inf 73.8%

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

      1. associate-*r/ 73.8%

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

      2. associate-*r* 73.8%

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

      3. neg-mul-1 73.8%

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

   8. Simplified 73.8%

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

   if -5.4999999999999998e46 < t < -82000

   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

   3. Taylor expanded in b around inf 70.4%

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

   4. Taylor expanded in z around inf 80.0%

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

      1. associate-/l* 80.0%

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

   6. Simplified 80.0%

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

   if -82000 < t < -3.19999999999999982e-66 or 5.99999999999999989e-200 < t < 7.00000000000000011e-22

   1. Initial program 86.4%

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

   3. Taylor expanded in t around 0 76.8%

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

   4. Taylor expanded in j around inf 67.2%

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

      1. sub-neg 67.2%

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

      2. *-commutative 67.2%

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

      3. sub-neg 67.2%

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

   6. Simplified 67.2%

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

   if -3.19999999999999982e-66 < t < -1.5000000000000001e-186

   1. Initial program 81.5%

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

   3. Taylor expanded in i around inf 57.9%

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

      1. distribute-lft-out-- 57.9%

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

   5. Simplified 57.9%

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

   6. Taylor expanded in i around 0 57.9%

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

      1. mul-1-neg 57.9%

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

      2. *-commutative 57.9%

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

      3. *-commutative 57.9%

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

      4. *-commutative 57.9%

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

      5. fma-neg 57.9%

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

      6. distribute-rgt-neg-in 57.9%

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

      7. fma-neg 57.9%

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

   8. Simplified 57.9%

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

   if -1.5000000000000001e-186 < t < -5.39999999999999984e-225

   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 z around inf 95.3%

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

      1. *-commutative 95.3%

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

      2. *-commutative 95.3%

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

   5. Simplified 95.3%

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

   if -5.39999999999999984e-225 < t < 5.99999999999999989e-200

   1. Initial program 74.7%

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

   3. Taylor expanded in t around 0 69.3%

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

   4. Taylor expanded in c around 0 55.5%

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

      1. +-commutative 55.5%

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

      2. mul-1-neg 55.5%

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

      3. unsub-neg 55.5%

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

      4. associate-*r* 61.4%

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

      5. *-commutative 61.4%

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

      6. *-commutative 61.4%

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

   6. Simplified 61.4%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+152}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{+46}:\\ \;\;\;\;x \cdot \left(y \cdot \left(z - \frac{t \cdot a}{y}\right)\right)\\ \mathbf{elif}\;t \leq -82000:\\ \;\;\;\;b \cdot \left(z \cdot \left(i \cdot \frac{t}{z} - c\right)\right)\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-66}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-186}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-225}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-200}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-22}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 63.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.3 \cdot 10^{-51}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -1.7 \cdot 10^{-208}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq -3.55 \cdot 10^{-236}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;j \leq -1.35 \cdot 10^{-282}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 1.2 \cdot 10^{-284}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(z - a \cdot \frac{t}{y}\right)\\ \mathbf{elif}\;j \leq 1.15 \cdot 10^{+54}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* a (- (* c j) (* x t))) (* b (- (* t i) (* z c)))))
        (t_2 (+ (* x (- (* y z) (* t a))) (* j (- (* a c) (* y i))))))
   (if (<= j -1.3e-51)
     t_2
     (if (<= j -1.7e-208)
       (* t (- (* b i) (* x a)))
       (if (<= j -3.55e-236)
         (- (* z (* x y)) (* i (* y j)))
         (if (<= j -1.35e-282)
           t_1
           (if (<= j 1.2e-284)
             (* (* x y) (- z (* a (/ t y))))
             (if (<= j 1.15e+54) 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 = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	double t_2 = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	double tmp;
	if (j <= -1.3e-51) {
		tmp = t_2;
	} else if (j <= -1.7e-208) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= -3.55e-236) {
		tmp = (z * (x * y)) - (i * (y * j));
	} else if (j <= -1.35e-282) {
		tmp = t_1;
	} else if (j <= 1.2e-284) {
		tmp = (x * y) * (z - (a * (t / y)));
	} else if (j <= 1.15e+54) {
		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 = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)))
    t_2 = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)))
    if (j <= (-1.3d-51)) then
        tmp = t_2
    else if (j <= (-1.7d-208)) then
        tmp = t * ((b * i) - (x * a))
    else if (j <= (-3.55d-236)) then
        tmp = (z * (x * y)) - (i * (y * j))
    else if (j <= (-1.35d-282)) then
        tmp = t_1
    else if (j <= 1.2d-284) then
        tmp = (x * y) * (z - (a * (t / y)))
    else if (j <= 1.15d+54) 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 = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	double t_2 = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	double tmp;
	if (j <= -1.3e-51) {
		tmp = t_2;
	} else if (j <= -1.7e-208) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= -3.55e-236) {
		tmp = (z * (x * y)) - (i * (y * j));
	} else if (j <= -1.35e-282) {
		tmp = t_1;
	} else if (j <= 1.2e-284) {
		tmp = (x * y) * (z - (a * (t / y)));
	} else if (j <= 1.15e+54) {
		tmp = t_1;
	} 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))) + (b * ((t * i) - (z * c)))
	t_2 = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)))
	tmp = 0
	if j <= -1.3e-51:
		tmp = t_2
	elif j <= -1.7e-208:
		tmp = t * ((b * i) - (x * a))
	elif j <= -3.55e-236:
		tmp = (z * (x * y)) - (i * (y * j))
	elif j <= -1.35e-282:
		tmp = t_1
	elif j <= 1.2e-284:
		tmp = (x * y) * (z - (a * (t / y)))
	elif j <= 1.15e+54:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))))
	t_2 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))))
	tmp = 0.0
	if (j <= -1.3e-51)
		tmp = t_2;
	elseif (j <= -1.7e-208)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (j <= -3.55e-236)
		tmp = Float64(Float64(z * Float64(x * y)) - Float64(i * Float64(y * j)));
	elseif (j <= -1.35e-282)
		tmp = t_1;
	elseif (j <= 1.2e-284)
		tmp = Float64(Float64(x * y) * Float64(z - Float64(a * Float64(t / y))));
	elseif (j <= 1.15e+54)
		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 = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	t_2 = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	tmp = 0.0;
	if (j <= -1.3e-51)
		tmp = t_2;
	elseif (j <= -1.7e-208)
		tmp = t * ((b * i) - (x * a));
	elseif (j <= -3.55e-236)
		tmp = (z * (x * y)) - (i * (y * j));
	elseif (j <= -1.35e-282)
		tmp = t_1;
	elseif (j <= 1.2e-284)
		tmp = (x * y) * (z - (a * (t / y)));
	elseif (j <= 1.15e+54)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.3e-51], t$95$2, If[LessEqual[j, -1.7e-208], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3.55e-236], N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.35e-282], t$95$1, If[LessEqual[j, 1.2e-284], N[(N[(x * y), $MachinePrecision] * N[(z - N[(a * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.15e+54], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -1.3e-51 or 1.14999999999999997e54 < j

   1. Initial program 75.9%

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

   3. Taylor expanded in b around 0 70.6%

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

   if -1.3e-51 < j < -1.7e-208

   1. Initial program 55.4%

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

   3. Taylor expanded in t around inf 73.0%

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

      1. distribute-lft-out-- 73.0%

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

      2. *-commutative 73.0%

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

   5. Simplified 73.0%

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

   6. Taylor expanded in t around 0 73.0%

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

      1. mul-1-neg 73.0%

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

      2. distribute-rgt-neg-out 73.0%

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

   8. Simplified 73.0%

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

   if -1.7e-208 < j < -3.55000000000000001e-236

   1. Initial program 51.5%

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

   3. Taylor expanded in t around 0 63.8%

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

   4. Taylor expanded in c around 0 75.3%

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

      1. +-commutative 75.3%

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

      2. mul-1-neg 75.3%

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

      3. unsub-neg 75.3%

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

      4. associate-*r* 75.4%

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

      5. *-commutative 75.4%

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

      6. *-commutative 75.4%

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

   6. Simplified 75.4%

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

   if -3.55000000000000001e-236 < j < -1.34999999999999991e-282 or 1.20000000000000001e-284 < j < 1.14999999999999997e54

   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 y around 0 79.5%

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

      1. cancel-sign-sub-inv 79.5%

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

      2. *-commutative 79.5%

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

      3. associate-*r* 79.5%

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

      4. *-commutative 79.5%

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

      5. distribute-rgt-in 79.5%

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

      6. +-commutative 79.5%

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

      7. mul-1-neg 79.5%

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

      8. unsub-neg 79.5%

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

      9. *-commutative 79.5%

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

      10. distribute-lft-neg-in 79.5%

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

      11. sub-neg 79.5%

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

      12. distribute-rgt-neg-out 79.5%

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

      13. distribute-lft-out 78.2%

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

      14. +-commutative 78.2%

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

      15. distribute-rgt-neg-out 78.2%

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

      16. distribute-rgt-neg-in 78.2%

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

      17. mul-1-neg 78.2%

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

   5. Simplified 79.5%

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

   if -1.34999999999999991e-282 < j < 1.20000000000000001e-284

   1. Initial program 59.1%

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

   3. Taylor expanded in y around -inf 70.4%

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

   5. Simplified 70.4%

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

   6. Taylor expanded in x around inf 88.8%

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

      1. associate-*r* 88.9%

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

      2. *-commutative 88.9%

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

      3. mul-1-neg 88.9%

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

      4. unsub-neg 88.9%

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

      5. associate-/l* 88.9%

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

   8. Simplified 88.9%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.3 \cdot 10^{-51}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -1.7 \cdot 10^{-208}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq -3.55 \cdot 10^{-236}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;j \leq -1.35 \cdot 10^{-282}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.2 \cdot 10^{-284}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(z - a \cdot \frac{t}{y}\right)\\ \mathbf{elif}\;j \leq 1.15 \cdot 10^{+54}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot c - y \cdot i\\ t_2 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_3 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;t \leq -1.4 \cdot 10^{+267}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + t\_3\\ \mathbf{elif}\;t \leq -1.76 \cdot 10^{-19}:\\ \;\;\;\;j \cdot \left(t\_1 + \frac{z \cdot \left(x \cdot y - b \cdot c\right)}{j}\right)\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-83}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + t\_3\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-6}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z\right) + j \cdot t\_1\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* a c) (* y i)))
        (t_2 (* t (- (* b i) (* x a))))
        (t_3 (* b (- (* t i) (* z c)))))
   (if (<= t -1.4e+267)
     t_2
     (if (<= t -5.8e+18)
       (+ (* x (- (* y z) (* t a))) t_3)
       (if (<= t -1.76e-19)
         (* j (+ t_1 (/ (* z (- (* x y) (* b c))) j)))
         (if (<= t -1.35e-83)
           (+ (* a (- (* c j) (* x t))) t_3)
           (if (<= t 1.5e-6)
             (- (+ (* x (* y z)) (* j t_1)) (* b (* z c)))
             t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (a * c) - (y * i);
	double t_2 = t * ((b * i) - (x * a));
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if (t <= -1.4e+267) {
		tmp = t_2;
	} else if (t <= -5.8e+18) {
		tmp = (x * ((y * z) - (t * a))) + t_3;
	} else if (t <= -1.76e-19) {
		tmp = j * (t_1 + ((z * ((x * y) - (b * c))) / j));
	} else if (t <= -1.35e-83) {
		tmp = (a * ((c * j) - (x * t))) + t_3;
	} else if (t <= 1.5e-6) {
		tmp = ((x * (y * z)) + (j * t_1)) - (b * (z * c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (a * c) - (y * i)
    t_2 = t * ((b * i) - (x * a))
    t_3 = b * ((t * i) - (z * c))
    if (t <= (-1.4d+267)) then
        tmp = t_2
    else if (t <= (-5.8d+18)) then
        tmp = (x * ((y * z) - (t * a))) + t_3
    else if (t <= (-1.76d-19)) then
        tmp = j * (t_1 + ((z * ((x * y) - (b * c))) / j))
    else if (t <= (-1.35d-83)) then
        tmp = (a * ((c * j) - (x * t))) + t_3
    else if (t <= 1.5d-6) then
        tmp = ((x * (y * z)) + (j * t_1)) - (b * (z * c))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (a * c) - (y * i);
	double t_2 = t * ((b * i) - (x * a));
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if (t <= -1.4e+267) {
		tmp = t_2;
	} else if (t <= -5.8e+18) {
		tmp = (x * ((y * z) - (t * a))) + t_3;
	} else if (t <= -1.76e-19) {
		tmp = j * (t_1 + ((z * ((x * y) - (b * c))) / j));
	} else if (t <= -1.35e-83) {
		tmp = (a * ((c * j) - (x * t))) + t_3;
	} else if (t <= 1.5e-6) {
		tmp = ((x * (y * z)) + (j * t_1)) - (b * (z * c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (a * c) - (y * i)
	t_2 = t * ((b * i) - (x * a))
	t_3 = b * ((t * i) - (z * c))
	tmp = 0
	if t <= -1.4e+267:
		tmp = t_2
	elif t <= -5.8e+18:
		tmp = (x * ((y * z) - (t * a))) + t_3
	elif t <= -1.76e-19:
		tmp = j * (t_1 + ((z * ((x * y) - (b * c))) / j))
	elif t <= -1.35e-83:
		tmp = (a * ((c * j) - (x * t))) + t_3
	elif t <= 1.5e-6:
		tmp = ((x * (y * z)) + (j * t_1)) - (b * (z * c))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(a * c) - Float64(y * i))
	t_2 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	t_3 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (t <= -1.4e+267)
		tmp = t_2;
	elseif (t <= -5.8e+18)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_3);
	elseif (t <= -1.76e-19)
		tmp = Float64(j * Float64(t_1 + Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) / j)));
	elseif (t <= -1.35e-83)
		tmp = Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) + t_3);
	elseif (t <= 1.5e-6)
		tmp = Float64(Float64(Float64(x * Float64(y * z)) + Float64(j * t_1)) - Float64(b * Float64(z * c)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (a * c) - (y * i);
	t_2 = t * ((b * i) - (x * a));
	t_3 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (t <= -1.4e+267)
		tmp = t_2;
	elseif (t <= -5.8e+18)
		tmp = (x * ((y * z) - (t * a))) + t_3;
	elseif (t <= -1.76e-19)
		tmp = j * (t_1 + ((z * ((x * y) - (b * c))) / j));
	elseif (t <= -1.35e-83)
		tmp = (a * ((c * j) - (x * t))) + t_3;
	elseif (t <= 1.5e-6)
		tmp = ((x * (y * z)) + (j * t_1)) - (b * (z * c));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.4e+267], t$95$2, If[LessEqual[t, -5.8e+18], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision], If[LessEqual[t, -1.76e-19], N[(j * N[(t$95$1 + N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.35e-83], N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision], If[LessEqual[t, 1.5e-6], N[(N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(j * t$95$1), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.4000000000000001e267 or 1.5e-6 < t

   1. Initial program 50.8%

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

   3. Taylor expanded in t around inf 78.8%

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

      1. distribute-lft-out-- 78.8%

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

      2. *-commutative 78.8%

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

   5. Simplified 78.8%

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

   6. Taylor expanded in t around 0 78.8%

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

      1. mul-1-neg 78.8%

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

      2. distribute-rgt-neg-out 78.8%

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

   8. Simplified 78.8%

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

   if -1.4000000000000001e267 < t < -5.8e18

   1. Initial program 75.3%

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

   3. Taylor expanded in j around 0 78.8%

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

   if -5.8e18 < t < -1.75999999999999993e-19

   1. Initial program 78.8%

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

   3. Taylor expanded in t around 0 78.9%

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

   4. Taylor expanded in j around -inf 78.9%

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

      1. associate-*r* 78.9%

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

      2. mul-1-neg 78.9%

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

      3. mul-1-neg 78.9%

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

      4. unsub-neg 78.9%

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

      5. mul-1-neg 78.9%

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

      6. *-commutative 78.9%

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

      7. associate-*r* 79.7%

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

      8. cancel-sign-sub-inv 79.7%

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

      9. associate-*r* 86.4%

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

      10. mul-1-neg 86.4%

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

      11. distribute-rgt-in 93.5%

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

      12. mul-1-neg 93.5%

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

      13. sub-neg 93.5%

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

   6. Simplified 93.5%

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

   if -1.75999999999999993e-19 < t < -1.34999999999999996e-83

   1. Initial program 94.4%

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

   3. Taylor expanded in y around 0 88.8%

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

      1. cancel-sign-sub-inv 88.8%

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

      2. *-commutative 88.8%

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

      3. associate-*r* 88.8%

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

      4. *-commutative 88.8%

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

      5. distribute-rgt-in 88.8%

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

      6. +-commutative 88.8%

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

      7. mul-1-neg 88.8%

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

      8. unsub-neg 88.8%

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

      9. *-commutative 88.8%

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

      10. distribute-lft-neg-in 88.8%

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

      11. sub-neg 88.8%

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

      12. distribute-rgt-neg-out 88.8%

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

      13. distribute-lft-out 88.8%

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

      14. +-commutative 88.8%

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

      15. distribute-rgt-neg-out 88.8%

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

      16. distribute-rgt-neg-in 88.8%

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

      17. mul-1-neg 88.8%

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

   5. Simplified 88.8%

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

   if -1.34999999999999996e-83 < t < 1.5e-6

   1. Initial program 80.4%

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

   3. Taylor expanded in t around 0 71.0%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+267}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq -1.76 \cdot 10^{-19}:\\ \;\;\;\;j \cdot \left(\left(a \cdot c - y \cdot i\right) + \frac{z \cdot \left(x \cdot y - b \cdot c\right)}{j}\right)\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-83}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-6}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z\right) + j \cdot \left(a \cdot c - y \cdot i\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -8 \cdot 10^{+18}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.35 \cdot 10^{-66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-187}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-224}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-200}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-198}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-21}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))) (t_2 (* t (- (* b i) (* x a)))))
   (if (<= t -8e+18)
     t_2
     (if (<= t -2.35e-66)
       t_1
       (if (<= t -9.2e-187)
         (* i (- (* t b) (* y j)))
         (if (<= t -3e-224)
           (* z (- (* x y) (* b c)))
           (if (<= t 9.5e-200)
             (* y (- (* x z) (* i j)))
             (if (<= t 7e-198)
               (* c (- (* a j) (* z b)))
               (if (<= t 1.25e-21) 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 * ((a * c) - (y * i));
	double t_2 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -8e+18) {
		tmp = t_2;
	} else if (t <= -2.35e-66) {
		tmp = t_1;
	} else if (t <= -9.2e-187) {
		tmp = i * ((t * b) - (y * j));
	} else if (t <= -3e-224) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 9.5e-200) {
		tmp = y * ((x * z) - (i * j));
	} else if (t <= 7e-198) {
		tmp = c * ((a * j) - (z * b));
	} else if (t <= 1.25e-21) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = t * ((b * i) - (x * a))
    if (t <= (-8d+18)) then
        tmp = t_2
    else if (t <= (-2.35d-66)) then
        tmp = t_1
    else if (t <= (-9.2d-187)) then
        tmp = i * ((t * b) - (y * j))
    else if (t <= (-3d-224)) then
        tmp = z * ((x * y) - (b * c))
    else if (t <= 9.5d-200) then
        tmp = y * ((x * z) - (i * j))
    else if (t <= 7d-198) then
        tmp = c * ((a * j) - (z * b))
    else if (t <= 1.25d-21) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -8e+18) {
		tmp = t_2;
	} else if (t <= -2.35e-66) {
		tmp = t_1;
	} else if (t <= -9.2e-187) {
		tmp = i * ((t * b) - (y * j));
	} else if (t <= -3e-224) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 9.5e-200) {
		tmp = y * ((x * z) - (i * j));
	} else if (t <= 7e-198) {
		tmp = c * ((a * j) - (z * b));
	} else if (t <= 1.25e-21) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = t * ((b * i) - (x * a))
	tmp = 0
	if t <= -8e+18:
		tmp = t_2
	elif t <= -2.35e-66:
		tmp = t_1
	elif t <= -9.2e-187:
		tmp = i * ((t * b) - (y * j))
	elif t <= -3e-224:
		tmp = z * ((x * y) - (b * c))
	elif t <= 9.5e-200:
		tmp = y * ((x * z) - (i * j))
	elif t <= 7e-198:
		tmp = c * ((a * j) - (z * b))
	elif t <= 1.25e-21:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	tmp = 0.0
	if (t <= -8e+18)
		tmp = t_2;
	elseif (t <= -2.35e-66)
		tmp = t_1;
	elseif (t <= -9.2e-187)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (t <= -3e-224)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (t <= 9.5e-200)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (t <= 7e-198)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (t <= 1.25e-21)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -8e+18)
		tmp = t_2;
	elseif (t <= -2.35e-66)
		tmp = t_1;
	elseif (t <= -9.2e-187)
		tmp = i * ((t * b) - (y * j));
	elseif (t <= -3e-224)
		tmp = z * ((x * y) - (b * c));
	elseif (t <= 9.5e-200)
		tmp = y * ((x * z) - (i * j));
	elseif (t <= 7e-198)
		tmp = c * ((a * j) - (z * b));
	elseif (t <= 1.25e-21)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8e+18], t$95$2, If[LessEqual[t, -2.35e-66], t$95$1, If[LessEqual[t, -9.2e-187], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3e-224], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e-200], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e-198], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.25e-21], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -8e18 or 1.24999999999999993e-21 < t

   1. Initial program 63.6%

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

   3. Taylor expanded in t around inf 70.2%

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

      1. distribute-lft-out-- 70.2%

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

      2. *-commutative 70.2%

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

   5. Simplified 70.2%

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

   6. Taylor expanded in t around 0 70.2%

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

      1. mul-1-neg 70.2%

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

      2. distribute-rgt-neg-out 70.2%

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

   8. Simplified 70.2%

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

   if -8e18 < t < -2.35e-66 or 7.0000000000000005e-198 < t < 1.24999999999999993e-21

   1. Initial program 86.9%

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

   3. Taylor expanded in t around 0 77.6%

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

   4. Taylor expanded in j around inf 66.6%

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

      1. sub-neg 66.6%

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

      2. *-commutative 66.6%

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

      3. sub-neg 66.6%

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

   6. Simplified 66.6%

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

   if -2.35e-66 < t < -9.19999999999999991e-187

   1. Initial program 81.5%

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

   3. Taylor expanded in i around inf 57.9%

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

      1. distribute-lft-out-- 57.9%

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

   5. Simplified 57.9%

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

   6. Taylor expanded in i around 0 57.9%

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

      1. mul-1-neg 57.9%

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

      2. *-commutative 57.9%

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

      3. *-commutative 57.9%

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

      4. *-commutative 57.9%

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

      5. fma-neg 57.9%

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

      6. distribute-rgt-neg-in 57.9%

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

      7. fma-neg 57.9%

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

   8. Simplified 57.9%

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

   if -9.19999999999999991e-187 < t < -2.99999999999999982e-224

   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 z around inf 95.3%

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

      1. *-commutative 95.3%

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

      2. *-commutative 95.3%

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

   5. Simplified 95.3%

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

   if -2.99999999999999982e-224 < t < 9.4999999999999995e-200

   1. Initial program 74.7%

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

   3. Taylor expanded in y around inf 61.2%

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

      1. +-commutative 61.2%

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

      2. mul-1-neg 61.2%

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

      3. unsub-neg 61.2%

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

      4. *-commutative 61.2%

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

      5. *-commutative 61.2%

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

   5. Simplified 61.2%

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

   if 9.4999999999999995e-200 < t < 7.0000000000000005e-198

   1. Initial program 98.4%

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

   3. Taylor expanded in c around inf 100.0%

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

      1. *-commutative 100.0%

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

   5. Simplified 100.0%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+18}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -2.35 \cdot 10^{-66}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-187}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-224}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-200}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-198}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-21}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_3 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -1.36 \cdot 10^{+19}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-186}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq -4.7 \cdot 10^{-210}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-210}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-185}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-23}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i))))
        (t_2 (* z (- (* x y) (* b c))))
        (t_3 (* t (- (* b i) (* x a)))))
   (if (<= t -1.36e+19)
     t_3
     (if (<= t -2.4e-66)
       t_1
       (if (<= t -5.5e-186)
         (* i (- (* t b) (* y j)))
         (if (<= t -4.7e-210)
           t_2
           (if (<= t 9e-210)
             (- (* x (* y z)) (* b (* z c)))
             (if (<= t 6.2e-185) t_2 (if (<= t 2.6e-23) 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 = j * ((a * c) - (y * i));
	double t_2 = z * ((x * y) - (b * c));
	double t_3 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -1.36e+19) {
		tmp = t_3;
	} else if (t <= -2.4e-66) {
		tmp = t_1;
	} else if (t <= -5.5e-186) {
		tmp = i * ((t * b) - (y * j));
	} else if (t <= -4.7e-210) {
		tmp = t_2;
	} else if (t <= 9e-210) {
		tmp = (x * (y * z)) - (b * (z * c));
	} else if (t <= 6.2e-185) {
		tmp = t_2;
	} else if (t <= 2.6e-23) {
		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 = j * ((a * c) - (y * i))
    t_2 = z * ((x * y) - (b * c))
    t_3 = t * ((b * i) - (x * a))
    if (t <= (-1.36d+19)) then
        tmp = t_3
    else if (t <= (-2.4d-66)) then
        tmp = t_1
    else if (t <= (-5.5d-186)) then
        tmp = i * ((t * b) - (y * j))
    else if (t <= (-4.7d-210)) then
        tmp = t_2
    else if (t <= 9d-210) then
        tmp = (x * (y * z)) - (b * (z * c))
    else if (t <= 6.2d-185) then
        tmp = t_2
    else if (t <= 2.6d-23) 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 = j * ((a * c) - (y * i));
	double t_2 = z * ((x * y) - (b * c));
	double t_3 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -1.36e+19) {
		tmp = t_3;
	} else if (t <= -2.4e-66) {
		tmp = t_1;
	} else if (t <= -5.5e-186) {
		tmp = i * ((t * b) - (y * j));
	} else if (t <= -4.7e-210) {
		tmp = t_2;
	} else if (t <= 9e-210) {
		tmp = (x * (y * z)) - (b * (z * c));
	} else if (t <= 6.2e-185) {
		tmp = t_2;
	} else if (t <= 2.6e-23) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = z * ((x * y) - (b * c))
	t_3 = t * ((b * i) - (x * a))
	tmp = 0
	if t <= -1.36e+19:
		tmp = t_3
	elif t <= -2.4e-66:
		tmp = t_1
	elif t <= -5.5e-186:
		tmp = i * ((t * b) - (y * j))
	elif t <= -4.7e-210:
		tmp = t_2
	elif t <= 9e-210:
		tmp = (x * (y * z)) - (b * (z * c))
	elif t <= 6.2e-185:
		tmp = t_2
	elif t <= 2.6e-23:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	t_3 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	tmp = 0.0
	if (t <= -1.36e+19)
		tmp = t_3;
	elseif (t <= -2.4e-66)
		tmp = t_1;
	elseif (t <= -5.5e-186)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (t <= -4.7e-210)
		tmp = t_2;
	elseif (t <= 9e-210)
		tmp = Float64(Float64(x * Float64(y * z)) - Float64(b * Float64(z * c)));
	elseif (t <= 6.2e-185)
		tmp = t_2;
	elseif (t <= 2.6e-23)
		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 = j * ((a * c) - (y * i));
	t_2 = z * ((x * y) - (b * c));
	t_3 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -1.36e+19)
		tmp = t_3;
	elseif (t <= -2.4e-66)
		tmp = t_1;
	elseif (t <= -5.5e-186)
		tmp = i * ((t * b) - (y * j));
	elseif (t <= -4.7e-210)
		tmp = t_2;
	elseif (t <= 9e-210)
		tmp = (x * (y * z)) - (b * (z * c));
	elseif (t <= 6.2e-185)
		tmp = t_2;
	elseif (t <= 2.6e-23)
		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[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.36e+19], t$95$3, If[LessEqual[t, -2.4e-66], t$95$1, If[LessEqual[t, -5.5e-186], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.7e-210], t$95$2, If[LessEqual[t, 9e-210], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.2e-185], t$95$2, If[LessEqual[t, 2.6e-23], t$95$1, t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.36e19 or 2.6e-23 < t

   1. Initial program 63.6%

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

   3. Taylor expanded in t around inf 70.2%

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

      1. distribute-lft-out-- 70.2%

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

      2. *-commutative 70.2%

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

   5. Simplified 70.2%

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

   6. Taylor expanded in t around 0 70.2%

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

      1. mul-1-neg 70.2%

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

      2. distribute-rgt-neg-out 70.2%

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

   8. Simplified 70.2%

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

   if -1.36e19 < t < -2.40000000000000026e-66 or 6.1999999999999994e-185 < t < 2.6e-23

   1. Initial program 86.7%

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

   3. Taylor expanded in t around 0 78.8%

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

   4. Taylor expanded in j around inf 67.6%

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

      1. sub-neg 67.6%

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

      2. *-commutative 67.6%

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

      3. sub-neg 67.6%

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

   6. Simplified 67.6%

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

   if -2.40000000000000026e-66 < t < -5.5000000000000001e-186

   1. Initial program 81.5%

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

   3. Taylor expanded in i around inf 57.9%

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

      1. distribute-lft-out-- 57.9%

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

   5. Simplified 57.9%

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

   6. Taylor expanded in i around 0 57.9%

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

      1. mul-1-neg 57.9%

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

      2. *-commutative 57.9%

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

      3. *-commutative 57.9%

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

      4. *-commutative 57.9%

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

      5. fma-neg 57.9%

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

      6. distribute-rgt-neg-in 57.9%

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

      7. fma-neg 57.9%

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

   8. Simplified 57.9%

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

   if -5.5000000000000001e-186 < t < -4.69999999999999967e-210 or 9.00000000000000039e-210 < t < 6.1999999999999994e-185

   1. Initial program 65.2%

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

   3. Taylor expanded in z around inf 79.8%

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

      1. *-commutative 79.8%

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

      2. *-commutative 79.8%

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

   5. Simplified 79.8%

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

   if -4.69999999999999967e-210 < t < 9.00000000000000039e-210

   1. Initial program 78.4%

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

   3. Taylor expanded in t around 0 75.5%

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

   4. Taylor expanded in j around 0 62.9%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.36 \cdot 10^{+19}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-66}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-186}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq -4.7 \cdot 10^{-210}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-210}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-185}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-23}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 38.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;y \leq -1.85 \cdot 10^{+189}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-262}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-263}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-188}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+43}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+163}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= y -1.85e+189)
     (* x (* y z))
     (if (<= y -2.15e-262)
       t_1
       (if (<= y 3.6e-263)
         (* i (* t b))
         (if (<= y 1.05e-188)
           t_1
           (if (<= y 6.8e+43)
             (* b (* t i))
             (if (<= y 1.12e+163) t_1 (* i (* y (- j)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (y <= -1.85e+189) {
		tmp = x * (y * z);
	} else if (y <= -2.15e-262) {
		tmp = t_1;
	} else if (y <= 3.6e-263) {
		tmp = i * (t * b);
	} else if (y <= 1.05e-188) {
		tmp = t_1;
	} else if (y <= 6.8e+43) {
		tmp = b * (t * i);
	} else if (y <= 1.12e+163) {
		tmp = t_1;
	} else {
		tmp = i * (y * -j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (y <= (-1.85d+189)) then
        tmp = x * (y * z)
    else if (y <= (-2.15d-262)) then
        tmp = t_1
    else if (y <= 3.6d-263) then
        tmp = i * (t * b)
    else if (y <= 1.05d-188) then
        tmp = t_1
    else if (y <= 6.8d+43) then
        tmp = b * (t * i)
    else if (y <= 1.12d+163) then
        tmp = t_1
    else
        tmp = i * (y * -j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (y <= -1.85e+189) {
		tmp = x * (y * z);
	} else if (y <= -2.15e-262) {
		tmp = t_1;
	} else if (y <= 3.6e-263) {
		tmp = i * (t * b);
	} else if (y <= 1.05e-188) {
		tmp = t_1;
	} else if (y <= 6.8e+43) {
		tmp = b * (t * i);
	} else if (y <= 1.12e+163) {
		tmp = t_1;
	} else {
		tmp = i * (y * -j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if y <= -1.85e+189:
		tmp = x * (y * z)
	elif y <= -2.15e-262:
		tmp = t_1
	elif y <= 3.6e-263:
		tmp = i * (t * b)
	elif y <= 1.05e-188:
		tmp = t_1
	elif y <= 6.8e+43:
		tmp = b * (t * i)
	elif y <= 1.12e+163:
		tmp = t_1
	else:
		tmp = i * (y * -j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (y <= -1.85e+189)
		tmp = Float64(x * Float64(y * z));
	elseif (y <= -2.15e-262)
		tmp = t_1;
	elseif (y <= 3.6e-263)
		tmp = Float64(i * Float64(t * b));
	elseif (y <= 1.05e-188)
		tmp = t_1;
	elseif (y <= 6.8e+43)
		tmp = Float64(b * Float64(t * i));
	elseif (y <= 1.12e+163)
		tmp = t_1;
	else
		tmp = Float64(i * Float64(y * Float64(-j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (y <= -1.85e+189)
		tmp = x * (y * z);
	elseif (y <= -2.15e-262)
		tmp = t_1;
	elseif (y <= 3.6e-263)
		tmp = i * (t * b);
	elseif (y <= 1.05e-188)
		tmp = t_1;
	elseif (y <= 6.8e+43)
		tmp = b * (t * i);
	elseif (y <= 1.12e+163)
		tmp = t_1;
	else
		tmp = i * (y * -j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.85e+189], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.15e-262], t$95$1, If[LessEqual[y, 3.6e-263], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.05e-188], t$95$1, If[LessEqual[y, 6.8e+43], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.12e+163], t$95$1, N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.8500000000000001e189

   1. Initial program 67.0%

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

   3. Taylor expanded in y around -inf 79.1%

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

   5. Simplified 79.1%

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

   6. Taylor expanded in x around inf 67.3%

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

      1. associate-*r/ 67.3%

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

      2. associate-*r* 67.3%

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

      3. neg-mul-1 67.3%

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

   8. Simplified 67.3%

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

   9. Taylor expanded in y around inf 63.2%

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

       1. *-commutative 63.2%

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

   11. Simplified 63.2%

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

   if -1.8500000000000001e189 < y < -2.1500000000000001e-262 or 3.6e-263 < y < 1.05e-188 or 6.80000000000000024e43 < y < 1.11999999999999996e163

   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. Taylor expanded in a around inf 46.1%

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

      1. +-commutative 46.1%

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

      2. mul-1-neg 46.1%

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

      3. unsub-neg 46.1%

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

      4. *-commutative 46.1%

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

   5. Simplified 46.1%

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

   if -2.1500000000000001e-262 < y < 3.6e-263

   1. Initial program 87.6%

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

   3. Taylor expanded in i around inf 55.6%

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

      1. distribute-lft-out-- 55.6%

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

   5. Simplified 55.6%

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

   6. Taylor expanded in j around 0 49.7%

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

      1. *-commutative 49.7%

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

   8. Simplified 49.7%

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

   9. Taylor expanded in b around 0 49.7%

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

       1. associate-*r* 49.7%

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

       2. *-commutative 49.7%

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

       3. associate-*r* 55.6%

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

   11. Simplified 55.6%

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

   if 1.05e-188 < y < 6.80000000000000024e43

   1. Initial program 71.0%

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

   3. Taylor expanded in i around inf 55.3%

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

      1. distribute-lft-out-- 55.3%

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

   5. Simplified 55.3%

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

   6. Taylor expanded in j around 0 48.1%

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

      1. *-commutative 48.1%

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

   8. Simplified 48.1%

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

   if 1.11999999999999996e163 < y

   1. Initial program 60.9%

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

   3. Taylor expanded in i around inf 54.6%

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

      1. distribute-lft-out-- 54.6%

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

   5. Simplified 54.6%

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

   6. Taylor expanded in j around inf 54.3%

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

      1. mul-1-neg 54.3%

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

      2. *-commutative 54.3%

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

      3. distribute-rgt-neg-in 54.3%

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

      4. *-commutative 54.3%

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

   8. Simplified 54.3%

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

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+189}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-262}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-263}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-188}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+43}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+163}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 50.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -2.7 \cdot 10^{+76}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-63}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{+14}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+81}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 -2.7e+76)
     t_2
     (if (<= a -2.5e-18)
       t_1
       (if (<= a -3e-63)
         (* i (* y (- j)))
         (if (<= a 2.9e-31)
           t_1
           (if (<= a 1.08e+14) (* y (* x z)) (if (<= a 4e+81) 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 <= -2.7e+76) {
		tmp = t_2;
	} else if (a <= -2.5e-18) {
		tmp = t_1;
	} else if (a <= -3e-63) {
		tmp = i * (y * -j);
	} else if (a <= 2.9e-31) {
		tmp = t_1;
	} else if (a <= 1.08e+14) {
		tmp = y * (x * z);
	} else if (a <= 4e+81) {
		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 <= (-2.7d+76)) then
        tmp = t_2
    else if (a <= (-2.5d-18)) then
        tmp = t_1
    else if (a <= (-3d-63)) then
        tmp = i * (y * -j)
    else if (a <= 2.9d-31) then
        tmp = t_1
    else if (a <= 1.08d+14) then
        tmp = y * (x * z)
    else if (a <= 4d+81) 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 <= -2.7e+76) {
		tmp = t_2;
	} else if (a <= -2.5e-18) {
		tmp = t_1;
	} else if (a <= -3e-63) {
		tmp = i * (y * -j);
	} else if (a <= 2.9e-31) {
		tmp = t_1;
	} else if (a <= 1.08e+14) {
		tmp = y * (x * z);
	} else if (a <= 4e+81) {
		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 <= -2.7e+76:
		tmp = t_2
	elif a <= -2.5e-18:
		tmp = t_1
	elif a <= -3e-63:
		tmp = i * (y * -j)
	elif a <= 2.9e-31:
		tmp = t_1
	elif a <= 1.08e+14:
		tmp = y * (x * z)
	elif a <= 4e+81:
		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 <= -2.7e+76)
		tmp = t_2;
	elseif (a <= -2.5e-18)
		tmp = t_1;
	elseif (a <= -3e-63)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (a <= 2.9e-31)
		tmp = t_1;
	elseif (a <= 1.08e+14)
		tmp = Float64(y * Float64(x * z));
	elseif (a <= 4e+81)
		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 <= -2.7e+76)
		tmp = t_2;
	elseif (a <= -2.5e-18)
		tmp = t_1;
	elseif (a <= -3e-63)
		tmp = i * (y * -j);
	elseif (a <= 2.9e-31)
		tmp = t_1;
	elseif (a <= 1.08e+14)
		tmp = y * (x * z);
	elseif (a <= 4e+81)
		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, -2.7e+76], t$95$2, If[LessEqual[a, -2.5e-18], t$95$1, If[LessEqual[a, -3e-63], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.9e-31], t$95$1, If[LessEqual[a, 1.08e+14], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4e+81], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.6999999999999999e76 or 3.99999999999999969e81 < a

   1. Initial program 59.5%

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

   3. Taylor expanded in a around inf 68.4%

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

      1. +-commutative 68.4%

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

      2. mul-1-neg 68.4%

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

      3. unsub-neg 68.4%

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

      4. *-commutative 68.4%

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

   5. Simplified 68.4%

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

   if -2.6999999999999999e76 < a < -2.50000000000000018e-18 or -2.99999999999999979e-63 < a < 2.9000000000000001e-31 or 1.08e14 < a < 3.99999999999999969e81

   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. Taylor expanded in b around inf 56.5%

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

   if -2.50000000000000018e-18 < a < -2.99999999999999979e-63

   1. Initial program 77.3%

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

   3. Taylor expanded in i around inf 47.9%

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

      1. distribute-lft-out-- 47.9%

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

   5. Simplified 47.9%

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

   6. Taylor expanded in j around inf 48.1%

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

      1. mul-1-neg 48.1%

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

      2. *-commutative 48.1%

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

      3. distribute-rgt-neg-in 48.1%

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

      4. *-commutative 48.1%

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

   8. Simplified 48.1%

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

   if 2.9000000000000001e-31 < a < 1.08e14

   1. Initial program 66.5%

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

   3. Taylor expanded in y around -inf 66.5%

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

   5. Simplified 66.5%

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

   6. Taylor expanded in x around inf 89.0%

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

      1. associate-*r/ 89.0%

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

      2. associate-*r* 89.0%

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

      3. neg-mul-1 89.0%

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

   8. Simplified 89.0%

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

   9. Taylor expanded in y around inf 89.0%

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

       1. *-commutative 89.0%

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

       2. associate-*l* 89.0%

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

   11. Simplified 89.0%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{+76}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-18}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-63}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-31}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{+14}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+81}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 53.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{+71}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-249}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+99}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{+107}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* y (- (* x z) (* i j)))))
   (if (<= y -6.5e+71)
     t_2
     (if (<= y -4.4e-75)
       t_1
       (if (<= y -2.15e-249)
         (* a (- (* c j) (* x t)))
         (if (<= y 3.2e+43)
           t_1
           (if (<= y 6e+99)
             (* j (- (* a c) (* y i)))
             (if (<= y 2.95e+107) (* c (- (* a j) (* z b))) 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 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -6.5e+71) {
		tmp = t_2;
	} else if (y <= -4.4e-75) {
		tmp = t_1;
	} else if (y <= -2.15e-249) {
		tmp = a * ((c * j) - (x * t));
	} else if (y <= 3.2e+43) {
		tmp = t_1;
	} else if (y <= 6e+99) {
		tmp = j * ((a * c) - (y * i));
	} else if (y <= 2.95e+107) {
		tmp = c * ((a * j) - (z * b));
	} 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 = y * ((x * z) - (i * j))
    if (y <= (-6.5d+71)) then
        tmp = t_2
    else if (y <= (-4.4d-75)) then
        tmp = t_1
    else if (y <= (-2.15d-249)) then
        tmp = a * ((c * j) - (x * t))
    else if (y <= 3.2d+43) then
        tmp = t_1
    else if (y <= 6d+99) then
        tmp = j * ((a * c) - (y * i))
    else if (y <= 2.95d+107) then
        tmp = c * ((a * j) - (z * b))
    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 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -6.5e+71) {
		tmp = t_2;
	} else if (y <= -4.4e-75) {
		tmp = t_1;
	} else if (y <= -2.15e-249) {
		tmp = a * ((c * j) - (x * t));
	} else if (y <= 3.2e+43) {
		tmp = t_1;
	} else if (y <= 6e+99) {
		tmp = j * ((a * c) - (y * i));
	} else if (y <= 2.95e+107) {
		tmp = c * ((a * j) - (z * b));
	} 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 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -6.5e+71:
		tmp = t_2
	elif y <= -4.4e-75:
		tmp = t_1
	elif y <= -2.15e-249:
		tmp = a * ((c * j) - (x * t))
	elif y <= 3.2e+43:
		tmp = t_1
	elif y <= 6e+99:
		tmp = j * ((a * c) - (y * i))
	elif y <= 2.95e+107:
		tmp = c * ((a * j) - (z * b))
	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(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -6.5e+71)
		tmp = t_2;
	elseif (y <= -4.4e-75)
		tmp = t_1;
	elseif (y <= -2.15e-249)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (y <= 3.2e+43)
		tmp = t_1;
	elseif (y <= 6e+99)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (y <= 2.95e+107)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	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 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -6.5e+71)
		tmp = t_2;
	elseif (y <= -4.4e-75)
		tmp = t_1;
	elseif (y <= -2.15e-249)
		tmp = a * ((c * j) - (x * t));
	elseif (y <= 3.2e+43)
		tmp = t_1;
	elseif (y <= 6e+99)
		tmp = j * ((a * c) - (y * i));
	elseif (y <= 2.95e+107)
		tmp = c * ((a * j) - (z * b));
	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[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.5e+71], t$95$2, If[LessEqual[y, -4.4e-75], t$95$1, If[LessEqual[y, -2.15e-249], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e+43], t$95$1, If[LessEqual[y, 6e+99], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.95e+107], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -6.49999999999999954e71 or 2.9500000000000002e107 < y

   1. Initial program 63.3%

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

   3. Taylor expanded in y around inf 71.3%

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

      1. +-commutative 71.3%

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

      2. mul-1-neg 71.3%

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

      3. unsub-neg 71.3%

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

      4. *-commutative 71.3%

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

      5. *-commutative 71.3%

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

   5. Simplified 71.3%

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

   if -6.49999999999999954e71 < y < -4.40000000000000011e-75 or -2.1500000000000001e-249 < y < 3.20000000000000014e43

   1. Initial program 75.6%

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

   3. Taylor expanded in b around inf 52.2%

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

   if -4.40000000000000011e-75 < y < -2.1500000000000001e-249

   1. Initial program 82.2%

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

   3. Taylor expanded in a around inf 65.7%

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

      1. +-commutative 65.7%

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

      2. mul-1-neg 65.7%

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

      3. unsub-neg 65.7%

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

      4. *-commutative 65.7%

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

   5. Simplified 65.7%

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

   if 3.20000000000000014e43 < y < 6.00000000000000029e99

   1. Initial program 80.0%

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

   3. Taylor expanded in t around 0 67.0%

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

   4. Taylor expanded in j around inf 73.8%

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

      1. sub-neg 73.8%

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

      2. *-commutative 73.8%

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

      3. sub-neg 73.8%

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

   6. Simplified 73.8%

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

   if 6.00000000000000029e99 < y < 2.9500000000000002e107

   1. Initial program 74.6%

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

   3. Taylor expanded in c around inf 75.8%

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

      1. *-commutative 75.8%

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

   5. Simplified 75.8%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+71}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-75}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-249}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+43}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+99}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{+107}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{+19}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-186}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-232}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-200}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;t \leq 3.95 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))) (t_2 (* t (- (* b i) (* x a)))))
   (if (<= t -1.15e+19)
     t_2
     (if (<= t -4e-66)
       t_1
       (if (<= t -3e-186)
         (* i (- (* t b) (* y j)))
         (if (<= t -2.5e-232)
           (* z (- (* x y) (* b c)))
           (if (<= t 8e-200)
             (- (* z (* x y)) (* i (* y j)))
             (if (<= t 3.95e-22) 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 * ((a * c) - (y * i));
	double t_2 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -1.15e+19) {
		tmp = t_2;
	} else if (t <= -4e-66) {
		tmp = t_1;
	} else if (t <= -3e-186) {
		tmp = i * ((t * b) - (y * j));
	} else if (t <= -2.5e-232) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 8e-200) {
		tmp = (z * (x * y)) - (i * (y * j));
	} else if (t <= 3.95e-22) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = t * ((b * i) - (x * a))
    if (t <= (-1.15d+19)) then
        tmp = t_2
    else if (t <= (-4d-66)) then
        tmp = t_1
    else if (t <= (-3d-186)) then
        tmp = i * ((t * b) - (y * j))
    else if (t <= (-2.5d-232)) then
        tmp = z * ((x * y) - (b * c))
    else if (t <= 8d-200) then
        tmp = (z * (x * y)) - (i * (y * j))
    else if (t <= 3.95d-22) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -1.15e+19) {
		tmp = t_2;
	} else if (t <= -4e-66) {
		tmp = t_1;
	} else if (t <= -3e-186) {
		tmp = i * ((t * b) - (y * j));
	} else if (t <= -2.5e-232) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 8e-200) {
		tmp = (z * (x * y)) - (i * (y * j));
	} else if (t <= 3.95e-22) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = t * ((b * i) - (x * a))
	tmp = 0
	if t <= -1.15e+19:
		tmp = t_2
	elif t <= -4e-66:
		tmp = t_1
	elif t <= -3e-186:
		tmp = i * ((t * b) - (y * j))
	elif t <= -2.5e-232:
		tmp = z * ((x * y) - (b * c))
	elif t <= 8e-200:
		tmp = (z * (x * y)) - (i * (y * j))
	elif t <= 3.95e-22:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	tmp = 0.0
	if (t <= -1.15e+19)
		tmp = t_2;
	elseif (t <= -4e-66)
		tmp = t_1;
	elseif (t <= -3e-186)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (t <= -2.5e-232)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (t <= 8e-200)
		tmp = Float64(Float64(z * Float64(x * y)) - Float64(i * Float64(y * j)));
	elseif (t <= 3.95e-22)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -1.15e+19)
		tmp = t_2;
	elseif (t <= -4e-66)
		tmp = t_1;
	elseif (t <= -3e-186)
		tmp = i * ((t * b) - (y * j));
	elseif (t <= -2.5e-232)
		tmp = z * ((x * y) - (b * c));
	elseif (t <= 8e-200)
		tmp = (z * (x * y)) - (i * (y * j));
	elseif (t <= 3.95e-22)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.15e+19], t$95$2, If[LessEqual[t, -4e-66], t$95$1, If[LessEqual[t, -3e-186], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.5e-232], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8e-200], N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.95e-22], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.15e19 or 3.9499999999999999e-22 < t

   1. Initial program 63.6%

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

   3. Taylor expanded in t around inf 70.2%

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

      1. distribute-lft-out-- 70.2%

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

      2. *-commutative 70.2%

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

   5. Simplified 70.2%

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

   6. Taylor expanded in t around 0 70.2%

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

      1. mul-1-neg 70.2%

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

      2. distribute-rgt-neg-out 70.2%

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

   8. Simplified 70.2%

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

   if -1.15e19 < t < -3.9999999999999999e-66 or 7.9999999999999999e-200 < t < 3.9499999999999999e-22

   1. Initial program 87.1%

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

   3. Taylor expanded in t around 0 77.9%

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

   4. Taylor expanded in j around inf 65.6%

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

      1. sub-neg 65.6%

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

      2. *-commutative 65.6%

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

      3. sub-neg 65.6%

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

   6. Simplified 65.6%

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

   if -3.9999999999999999e-66 < t < -3.0000000000000001e-186

   1. Initial program 81.5%

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

   3. Taylor expanded in i around inf 57.9%

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

      1. distribute-lft-out-- 57.9%

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

   5. Simplified 57.9%

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

   6. Taylor expanded in i around 0 57.9%

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

      1. mul-1-neg 57.9%

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

      2. *-commutative 57.9%

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

      3. *-commutative 57.9%

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

      4. *-commutative 57.9%

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

      5. fma-neg 57.9%

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

      6. distribute-rgt-neg-in 57.9%

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

      7. fma-neg 57.9%

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

   8. Simplified 57.9%

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

   if -3.0000000000000001e-186 < t < -2.5e-232

   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 z around inf 95.3%

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

      1. *-commutative 95.3%

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

      2. *-commutative 95.3%

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

   5. Simplified 95.3%

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

   if -2.5e-232 < t < 7.9999999999999999e-200

   1. Initial program 74.7%

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

   3. Taylor expanded in t around 0 69.3%

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

   4. Taylor expanded in c around 0 55.5%

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

      1. +-commutative 55.5%

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

      2. mul-1-neg 55.5%

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

      3. unsub-neg 55.5%

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

      4. associate-*r* 61.4%

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

      5. *-commutative 61.4%

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

      6. *-commutative 61.4%

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

   6. Simplified 61.4%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+19}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-66}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-186}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-232}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-200}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;t \leq 3.95 \cdot 10^{-22}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 66.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -9.6 \cdot 10^{+73}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+34}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+163}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* a (- (* c j) (* x t))) (* b (- (* t i) (* z c)))))
        (t_2 (* y (- (* x z) (* i j)))))
   (if (<= y -9.6e+73)
     t_2
     (if (<= y 1.02e-49)
       t_1
       (if (<= y 7.5e+34)
         (* t (- (* b i) (* x a)))
         (if (<= y 1.12e+163) 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 = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -9.6e+73) {
		tmp = t_2;
	} else if (y <= 1.02e-49) {
		tmp = t_1;
	} else if (y <= 7.5e+34) {
		tmp = t * ((b * i) - (x * a));
	} else if (y <= 1.12e+163) {
		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 = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)))
    t_2 = y * ((x * z) - (i * j))
    if (y <= (-9.6d+73)) then
        tmp = t_2
    else if (y <= 1.02d-49) then
        tmp = t_1
    else if (y <= 7.5d+34) then
        tmp = t * ((b * i) - (x * a))
    else if (y <= 1.12d+163) 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 = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -9.6e+73) {
		tmp = t_2;
	} else if (y <= 1.02e-49) {
		tmp = t_1;
	} else if (y <= 7.5e+34) {
		tmp = t * ((b * i) - (x * a));
	} else if (y <= 1.12e+163) {
		tmp = t_1;
	} 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))) + (b * ((t * i) - (z * c)))
	t_2 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -9.6e+73:
		tmp = t_2
	elif y <= 1.02e-49:
		tmp = t_1
	elif y <= 7.5e+34:
		tmp = t * ((b * i) - (x * a))
	elif y <= 1.12e+163:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -9.6e+73)
		tmp = t_2;
	elseif (y <= 1.02e-49)
		tmp = t_1;
	elseif (y <= 7.5e+34)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (y <= 1.12e+163)
		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 = (a * ((c * j) - (x * t))) + (b * ((t * i) - (z * c)));
	t_2 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -9.6e+73)
		tmp = t_2;
	elseif (y <= 1.02e-49)
		tmp = t_1;
	elseif (y <= 7.5e+34)
		tmp = t * ((b * i) - (x * a));
	elseif (y <= 1.12e+163)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.6e+73], t$95$2, If[LessEqual[y, 1.02e-49], t$95$1, If[LessEqual[y, 7.5e+34], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.12e+163], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.60000000000000009e73 or 1.11999999999999996e163 < y

   1. Initial program 64.1%

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

   3. Taylor expanded in y around inf 74.2%

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

      1. +-commutative 74.2%

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

      2. mul-1-neg 74.2%

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

      3. unsub-neg 74.2%

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

      4. *-commutative 74.2%

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

      5. *-commutative 74.2%

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

   5. Simplified 74.2%

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

   if -9.60000000000000009e73 < y < 1.02000000000000009e-49 or 7.49999999999999976e34 < y < 1.11999999999999996e163

   1. Initial program 79.1%

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

   3. Taylor expanded in y around 0 69.8%

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

      1. cancel-sign-sub-inv 69.8%

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

      2. *-commutative 69.8%

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

      3. associate-*r* 69.8%

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

      4. *-commutative 69.8%

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

      5. distribute-rgt-in 70.4%

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

      6. +-commutative 70.4%

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

      7. mul-1-neg 70.4%

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

      8. unsub-neg 70.4%

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

      9. *-commutative 70.4%

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

      10. distribute-lft-neg-in 70.4%

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

      11. sub-neg 70.4%

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

      12. distribute-rgt-neg-out 70.4%

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

      13. distribute-lft-out 69.8%

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

      14. +-commutative 69.8%

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

      15. distribute-rgt-neg-out 69.8%

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

      16. distribute-rgt-neg-in 69.8%

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

      17. mul-1-neg 69.8%

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

   5. Simplified 70.4%

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

   if 1.02000000000000009e-49 < y < 7.49999999999999976e34

   1. Initial program 50.8%

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

   3. Taylor expanded in t around inf 72.6%

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

      1. distribute-lft-out-- 72.6%

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

      2. *-commutative 72.6%

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

   5. Simplified 72.6%

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

   6. Taylor expanded in t around 0 72.6%

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

      1. mul-1-neg 72.6%

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

      2. distribute-rgt-neg-out 72.6%

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

   8. Simplified 72.6%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.6 \cdot 10^{+73}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-49}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+34}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+163}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 31.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{if}\;t \leq -2.35 \cdot 10^{+148}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4.7 \cdot 10^{+18}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-162}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-200}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-13}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* x (- t)))))
   (if (<= t -2.35e+148)
     (* b (* t i))
     (if (<= t -6.5e+52)
       t_1
       (if (<= t -4.7e+18)
         (* i (* t b))
         (if (<= t -5.5e-162)
           (* a (* c j))
           (if (<= t 7e-200)
             (* y (* x z))
             (if (<= t 2.9e-13) (* (* y i) (- j)) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (x * -t);
	double tmp;
	if (t <= -2.35e+148) {
		tmp = b * (t * i);
	} else if (t <= -6.5e+52) {
		tmp = t_1;
	} else if (t <= -4.7e+18) {
		tmp = i * (t * b);
	} else if (t <= -5.5e-162) {
		tmp = a * (c * j);
	} else if (t <= 7e-200) {
		tmp = y * (x * z);
	} else if (t <= 2.9e-13) {
		tmp = (y * i) * -j;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (x * -t)
    if (t <= (-2.35d+148)) then
        tmp = b * (t * i)
    else if (t <= (-6.5d+52)) then
        tmp = t_1
    else if (t <= (-4.7d+18)) then
        tmp = i * (t * b)
    else if (t <= (-5.5d-162)) then
        tmp = a * (c * j)
    else if (t <= 7d-200) then
        tmp = y * (x * z)
    else if (t <= 2.9d-13) then
        tmp = (y * i) * -j
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (x * -t);
	double tmp;
	if (t <= -2.35e+148) {
		tmp = b * (t * i);
	} else if (t <= -6.5e+52) {
		tmp = t_1;
	} else if (t <= -4.7e+18) {
		tmp = i * (t * b);
	} else if (t <= -5.5e-162) {
		tmp = a * (c * j);
	} else if (t <= 7e-200) {
		tmp = y * (x * z);
	} else if (t <= 2.9e-13) {
		tmp = (y * i) * -j;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (x * -t)
	tmp = 0
	if t <= -2.35e+148:
		tmp = b * (t * i)
	elif t <= -6.5e+52:
		tmp = t_1
	elif t <= -4.7e+18:
		tmp = i * (t * b)
	elif t <= -5.5e-162:
		tmp = a * (c * j)
	elif t <= 7e-200:
		tmp = y * (x * z)
	elif t <= 2.9e-13:
		tmp = (y * i) * -j
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(x * Float64(-t)))
	tmp = 0.0
	if (t <= -2.35e+148)
		tmp = Float64(b * Float64(t * i));
	elseif (t <= -6.5e+52)
		tmp = t_1;
	elseif (t <= -4.7e+18)
		tmp = Float64(i * Float64(t * b));
	elseif (t <= -5.5e-162)
		tmp = Float64(a * Float64(c * j));
	elseif (t <= 7e-200)
		tmp = Float64(y * Float64(x * z));
	elseif (t <= 2.9e-13)
		tmp = Float64(Float64(y * i) * Float64(-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 = a * (x * -t);
	tmp = 0.0;
	if (t <= -2.35e+148)
		tmp = b * (t * i);
	elseif (t <= -6.5e+52)
		tmp = t_1;
	elseif (t <= -4.7e+18)
		tmp = i * (t * b);
	elseif (t <= -5.5e-162)
		tmp = a * (c * j);
	elseif (t <= 7e-200)
		tmp = y * (x * z);
	elseif (t <= 2.9e-13)
		tmp = (y * i) * -j;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.35e+148], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6.5e+52], t$95$1, If[LessEqual[t, -4.7e+18], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.5e-162], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e-200], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.9e-13], N[(N[(y * i), $MachinePrecision] * (-j)), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -2.3499999999999999e148

   1. Initial program 52.2%

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

   3. Taylor expanded in i around inf 50.7%

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

      1. distribute-lft-out-- 50.7%

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

   5. Simplified 50.7%

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

   6. Taylor expanded in j around 0 46.5%

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

      1. *-commutative 46.5%

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

   8. Simplified 46.5%

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

   if -2.3499999999999999e148 < t < -6.49999999999999996e52 or 2.8999999999999998e-13 < t

   1. Initial program 66.7%

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

   3. Taylor expanded in a around inf 52.9%

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

      1. +-commutative 52.9%

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

      2. mul-1-neg 52.9%

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

      3. unsub-neg 52.9%

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

      4. *-commutative 52.9%

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

   5. Simplified 52.9%

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

   6. Taylor expanded in j around 0 45.3%

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

      1. mul-1-neg 45.3%

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

      2. distribute-lft-neg-out 45.3%

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

      3. *-commutative 45.3%

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

   8. Simplified 45.3%

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

   if -6.49999999999999996e52 < t < -4.7e18

   1. Initial program 88.5%

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

   3. Taylor expanded in i around inf 67.1%

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

      1. distribute-lft-out-- 67.1%

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

   5. Simplified 67.1%

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

   6. Taylor expanded in j around 0 56.3%

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

      1. *-commutative 56.3%

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

   8. Simplified 56.3%

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

   9. Taylor expanded in b around 0 56.3%

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

       1. associate-*r* 56.5%

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

       2. *-commutative 56.5%

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

       3. associate-*r* 56.5%

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

   11. Simplified 56.5%

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

   if -4.7e18 < t < -5.50000000000000006e-162

   1. Initial program 85.4%

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

   3. Taylor expanded in a around inf 41.0%

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

      1. +-commutative 41.0%

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

      2. mul-1-neg 41.0%

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

      3. unsub-neg 41.0%

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

      4. *-commutative 41.0%

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

   5. Simplified 41.0%

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

   6. Taylor expanded in j around inf 34.2%

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

   if -5.50000000000000006e-162 < t < 7.00000000000000045e-200

   1. Initial program 76.0%

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

   3. Taylor expanded in y around -inf 82.2%

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

   5. Simplified 82.2%

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

   6. Taylor expanded in x around inf 38.0%

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

      1. associate-*r/ 38.0%

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

      2. associate-*r* 38.0%

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

      3. neg-mul-1 38.0%

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

   8. Simplified 38.0%

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

   9. Taylor expanded in y around inf 34.2%

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

       1. *-commutative 34.2%

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

       2. associate-*l* 39.4%

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

   11. Simplified 39.4%

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

   if 7.00000000000000045e-200 < t < 2.8999999999999998e-13

   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. Taylor expanded in i around inf 50.4%

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

      1. distribute-lft-out-- 50.4%

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

   5. Simplified 50.4%

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

   6. Taylor expanded in i around 0 50.4%

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

      1. mul-1-neg 50.4%

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

      2. *-commutative 50.4%

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

      3. *-commutative 50.4%

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

      4. *-commutative 50.4%

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

      5. fma-neg 50.4%

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

      6. distribute-rgt-neg-in 50.4%

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

      7. fma-neg 50.4%

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

   8. Simplified 50.4%

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

   9. Taylor expanded in y around inf 42.5%

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

       1. *-commutative 42.5%

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

       2. associate-*r* 42.4%

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

       3. associate-*l* 42.4%

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

       4. *-commutative 42.4%

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

       5. mul-1-neg 42.4%

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

       6. distribute-rgt-neg-in 42.4%

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

   11. Simplified 42.4%

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

4. Final simplification 42.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.35 \cdot 10^{+148}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{+52}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;t \leq -4.7 \cdot 10^{+18}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-162}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-200}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-13}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 30.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+148}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq -2 \cdot 10^{+50}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;t \leq -6.9 \cdot 10^{+18}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-161}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-200}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-9}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -1.7e+148)
   (* b (* t i))
   (if (<= t -2e+50)
     (* t (* x (- a)))
     (if (<= t -6.9e+18)
       (* i (* t b))
       (if (<= t -5.6e-161)
         (* a (* c j))
         (if (<= t 9.2e-200)
           (* y (* x z))
           (if (<= t 2.8e-9) (* (* y i) (- j)) (* a (* x (- t))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -1.7e+148) {
		tmp = b * (t * i);
	} else if (t <= -2e+50) {
		tmp = t * (x * -a);
	} else if (t <= -6.9e+18) {
		tmp = i * (t * b);
	} else if (t <= -5.6e-161) {
		tmp = a * (c * j);
	} else if (t <= 9.2e-200) {
		tmp = y * (x * z);
	} else if (t <= 2.8e-9) {
		tmp = (y * i) * -j;
	} else {
		tmp = a * (x * -t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (t <= (-1.7d+148)) then
        tmp = b * (t * i)
    else if (t <= (-2d+50)) then
        tmp = t * (x * -a)
    else if (t <= (-6.9d+18)) then
        tmp = i * (t * b)
    else if (t <= (-5.6d-161)) then
        tmp = a * (c * j)
    else if (t <= 9.2d-200) then
        tmp = y * (x * z)
    else if (t <= 2.8d-9) then
        tmp = (y * i) * -j
    else
        tmp = a * (x * -t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -1.7e+148) {
		tmp = b * (t * i);
	} else if (t <= -2e+50) {
		tmp = t * (x * -a);
	} else if (t <= -6.9e+18) {
		tmp = i * (t * b);
	} else if (t <= -5.6e-161) {
		tmp = a * (c * j);
	} else if (t <= 9.2e-200) {
		tmp = y * (x * z);
	} else if (t <= 2.8e-9) {
		tmp = (y * i) * -j;
	} else {
		tmp = a * (x * -t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -1.7e+148:
		tmp = b * (t * i)
	elif t <= -2e+50:
		tmp = t * (x * -a)
	elif t <= -6.9e+18:
		tmp = i * (t * b)
	elif t <= -5.6e-161:
		tmp = a * (c * j)
	elif t <= 9.2e-200:
		tmp = y * (x * z)
	elif t <= 2.8e-9:
		tmp = (y * i) * -j
	else:
		tmp = a * (x * -t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -1.7e+148)
		tmp = Float64(b * Float64(t * i));
	elseif (t <= -2e+50)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (t <= -6.9e+18)
		tmp = Float64(i * Float64(t * b));
	elseif (t <= -5.6e-161)
		tmp = Float64(a * Float64(c * j));
	elseif (t <= 9.2e-200)
		tmp = Float64(y * Float64(x * z));
	elseif (t <= 2.8e-9)
		tmp = Float64(Float64(y * i) * Float64(-j));
	else
		tmp = Float64(a * Float64(x * Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -1.7e+148)
		tmp = b * (t * i);
	elseif (t <= -2e+50)
		tmp = t * (x * -a);
	elseif (t <= -6.9e+18)
		tmp = i * (t * b);
	elseif (t <= -5.6e-161)
		tmp = a * (c * j);
	elseif (t <= 9.2e-200)
		tmp = y * (x * z);
	elseif (t <= 2.8e-9)
		tmp = (y * i) * -j;
	else
		tmp = a * (x * -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -1.7e+148], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2e+50], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6.9e+18], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.6e-161], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.2e-200], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.8e-9], N[(N[(y * i), $MachinePrecision] * (-j)), $MachinePrecision], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -1.7000000000000001e148

   1. Initial program 52.2%

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

   3. Taylor expanded in i around inf 50.7%

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

      1. distribute-lft-out-- 50.7%

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

   5. Simplified 50.7%

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

   6. Taylor expanded in j around 0 46.5%

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

      1. *-commutative 46.5%

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

   8. Simplified 46.5%

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

   if -1.7000000000000001e148 < t < -2.0000000000000002e50

   1. Initial program 85.9%

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

   3. Taylor expanded in a around inf 58.2%

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

      1. +-commutative 58.2%

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

      2. mul-1-neg 58.2%

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

      3. unsub-neg 58.2%

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

      4. *-commutative 58.2%

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

   5. Simplified 58.2%

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

   6. Taylor expanded in t around inf 67.4%

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

      1. +-commutative 67.4%

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

      2. mul-1-neg 67.4%

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

      3. unsub-neg 67.4%

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

      4. associate-/l* 67.4%

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

      5. associate-/l* 58.7%

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

      6. *-commutative 58.7%

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

   8. Simplified 58.7%

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

   9. Taylor expanded in c around 0 44.3%

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

       1. neg-mul-1 44.3%

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

       2. distribute-rgt-neg-in 44.3%

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

   11. Simplified 44.3%

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

   if -2.0000000000000002e50 < t < -6.9e18

   1. Initial program 88.5%

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

   3. Taylor expanded in i around inf 67.1%

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

      1. distribute-lft-out-- 67.1%

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

   5. Simplified 67.1%

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

   6. Taylor expanded in j around 0 56.3%

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

      1. *-commutative 56.3%

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

   8. Simplified 56.3%

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

   9. Taylor expanded in b around 0 56.3%

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

       1. associate-*r* 56.5%

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

       2. *-commutative 56.5%

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

       3. associate-*r* 56.5%

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

   11. Simplified 56.5%

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

   if -6.9e18 < t < -5.59999999999999984e-161

   1. Initial program 85.4%

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

   3. Taylor expanded in a around inf 41.0%

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

      1. +-commutative 41.0%

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

      2. mul-1-neg 41.0%

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

      3. unsub-neg 41.0%

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

      4. *-commutative 41.0%

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

   5. Simplified 41.0%

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

   6. Taylor expanded in j around inf 34.2%

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

   if -5.59999999999999984e-161 < t < 9.2000000000000003e-200

   1. Initial program 76.0%

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

   3. Taylor expanded in y around -inf 82.2%

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

   5. Simplified 82.2%

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

   6. Taylor expanded in x around inf 38.0%

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

      1. associate-*r/ 38.0%

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

      2. associate-*r* 38.0%

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

      3. neg-mul-1 38.0%

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

   8. Simplified 38.0%

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

   9. Taylor expanded in y around inf 34.2%

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

       1. *-commutative 34.2%

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

       2. associate-*l* 39.4%

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

   11. Simplified 39.4%

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

   if 9.2000000000000003e-200 < t < 2.79999999999999984e-9

   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. Taylor expanded in i around inf 50.4%

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

      1. distribute-lft-out-- 50.4%

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

   5. Simplified 50.4%

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

   6. Taylor expanded in i around 0 50.4%

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

      1. mul-1-neg 50.4%

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

      2. *-commutative 50.4%

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

      3. *-commutative 50.4%

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

      4. *-commutative 50.4%

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

      5. fma-neg 50.4%

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

      6. distribute-rgt-neg-in 50.4%

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

      7. fma-neg 50.4%

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

   8. Simplified 50.4%

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

   9. Taylor expanded in y around inf 42.5%

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

       1. *-commutative 42.5%

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

       2. associate-*r* 42.4%

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

       3. associate-*l* 42.4%

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

       4. *-commutative 42.4%

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

       5. mul-1-neg 42.4%

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

       6. distribute-rgt-neg-in 42.4%

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

   11. Simplified 42.4%

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

   if 2.79999999999999984e-9 < t

   1. Initial program 59.2%

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

   3. Taylor expanded in a around inf 50.9%

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

      1. +-commutative 50.9%

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

      2. mul-1-neg 50.9%

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

      3. unsub-neg 50.9%

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

      4. *-commutative 50.9%

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

   5. Simplified 50.9%

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

   6. Taylor expanded in j around 0 47.5%

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

      1. mul-1-neg 47.5%

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

      2. distribute-lft-neg-out 47.5%

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

      3. *-commutative 47.5%

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

   8. Simplified 47.5%

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

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+148}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq -2 \cdot 10^{+50}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;t \leq -6.9 \cdot 10^{+18}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-161}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-200}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-9}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 30.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+148}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq -1.02 \cdot 10^{+55}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;t \leq -3.55 \cdot 10^{+18}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-281}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-200}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-12}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -1.55e+148)
   (* b (* t i))
   (if (<= t -1.02e+55)
     (* t (* x (- a)))
     (if (<= t -3.55e+18)
       (* i (* t b))
       (if (<= t -4.6e-281)
         (* z (* c (- b)))
         (if (<= t 5.2e-200)
           (* y (* x z))
           (if (<= t 3.7e-12) (* (* y i) (- j)) (* a (* x (- t))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -1.55e+148) {
		tmp = b * (t * i);
	} else if (t <= -1.02e+55) {
		tmp = t * (x * -a);
	} else if (t <= -3.55e+18) {
		tmp = i * (t * b);
	} else if (t <= -4.6e-281) {
		tmp = z * (c * -b);
	} else if (t <= 5.2e-200) {
		tmp = y * (x * z);
	} else if (t <= 3.7e-12) {
		tmp = (y * i) * -j;
	} else {
		tmp = a * (x * -t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (t <= (-1.55d+148)) then
        tmp = b * (t * i)
    else if (t <= (-1.02d+55)) then
        tmp = t * (x * -a)
    else if (t <= (-3.55d+18)) then
        tmp = i * (t * b)
    else if (t <= (-4.6d-281)) then
        tmp = z * (c * -b)
    else if (t <= 5.2d-200) then
        tmp = y * (x * z)
    else if (t <= 3.7d-12) then
        tmp = (y * i) * -j
    else
        tmp = a * (x * -t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -1.55e+148) {
		tmp = b * (t * i);
	} else if (t <= -1.02e+55) {
		tmp = t * (x * -a);
	} else if (t <= -3.55e+18) {
		tmp = i * (t * b);
	} else if (t <= -4.6e-281) {
		tmp = z * (c * -b);
	} else if (t <= 5.2e-200) {
		tmp = y * (x * z);
	} else if (t <= 3.7e-12) {
		tmp = (y * i) * -j;
	} else {
		tmp = a * (x * -t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -1.55e+148:
		tmp = b * (t * i)
	elif t <= -1.02e+55:
		tmp = t * (x * -a)
	elif t <= -3.55e+18:
		tmp = i * (t * b)
	elif t <= -4.6e-281:
		tmp = z * (c * -b)
	elif t <= 5.2e-200:
		tmp = y * (x * z)
	elif t <= 3.7e-12:
		tmp = (y * i) * -j
	else:
		tmp = a * (x * -t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -1.55e+148)
		tmp = Float64(b * Float64(t * i));
	elseif (t <= -1.02e+55)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (t <= -3.55e+18)
		tmp = Float64(i * Float64(t * b));
	elseif (t <= -4.6e-281)
		tmp = Float64(z * Float64(c * Float64(-b)));
	elseif (t <= 5.2e-200)
		tmp = Float64(y * Float64(x * z));
	elseif (t <= 3.7e-12)
		tmp = Float64(Float64(y * i) * Float64(-j));
	else
		tmp = Float64(a * Float64(x * Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -1.55e+148)
		tmp = b * (t * i);
	elseif (t <= -1.02e+55)
		tmp = t * (x * -a);
	elseif (t <= -3.55e+18)
		tmp = i * (t * b);
	elseif (t <= -4.6e-281)
		tmp = z * (c * -b);
	elseif (t <= 5.2e-200)
		tmp = y * (x * z);
	elseif (t <= 3.7e-12)
		tmp = (y * i) * -j;
	else
		tmp = a * (x * -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -1.55e+148], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.02e+55], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.55e+18], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.6e-281], N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.2e-200], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.7e-12], N[(N[(y * i), $MachinePrecision] * (-j)), $MachinePrecision], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -1.54999999999999988e148

   1. Initial program 52.2%

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

   3. Taylor expanded in i around inf 50.7%

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

      1. distribute-lft-out-- 50.7%

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

   5. Simplified 50.7%

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

   6. Taylor expanded in j around 0 46.5%

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

      1. *-commutative 46.5%

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

   8. Simplified 46.5%

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

   if -1.54999999999999988e148 < t < -1.02000000000000002e55

   1. Initial program 85.9%

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

   3. Taylor expanded in a around inf 58.2%

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

      1. +-commutative 58.2%

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

      2. mul-1-neg 58.2%

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

      3. unsub-neg 58.2%

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

      4. *-commutative 58.2%

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

   5. Simplified 58.2%

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

   6. Taylor expanded in t around inf 67.4%

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

      1. +-commutative 67.4%

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

      2. mul-1-neg 67.4%

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

      3. unsub-neg 67.4%

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

      4. associate-/l* 67.4%

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

      5. associate-/l* 58.7%

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

      6. *-commutative 58.7%

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

   8. Simplified 58.7%

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

   9. Taylor expanded in c around 0 44.3%

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

       1. neg-mul-1 44.3%

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

       2. distribute-rgt-neg-in 44.3%

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

   11. Simplified 44.3%

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

   if -1.02000000000000002e55 < t < -3.55e18

   1. Initial program 88.5%

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

   3. Taylor expanded in i around inf 67.1%

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

      1. distribute-lft-out-- 67.1%

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

   5. Simplified 67.1%

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

   6. Taylor expanded in j around 0 56.3%

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

      1. *-commutative 56.3%

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

   8. Simplified 56.3%

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

   9. Taylor expanded in b around 0 56.3%

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

       1. associate-*r* 56.5%

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

       2. *-commutative 56.5%

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

       3. associate-*r* 56.5%

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

   11. Simplified 56.5%

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

   if -3.55e18 < t < -4.59999999999999978e-281

   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 t around 0 74.7%

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

   4. Taylor expanded in b around inf 33.2%

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

      1. associate-*r* 31.8%

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

      2. neg-mul-1 31.8%

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

      3. *-commutative 31.8%

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

      4. distribute-rgt-neg-in 31.8%

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

      5. distribute-lft-neg-in 31.8%

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

   6. Simplified 31.8%

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

   if -4.59999999999999978e-281 < t < 5.19999999999999979e-200

   1. Initial program 73.4%

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

   3. Taylor expanded in y around -inf 81.2%

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

   5. Simplified 81.2%

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

   6. Taylor expanded in x around inf 51.2%

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

      1. associate-*r/ 51.2%

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

      2. associate-*r* 51.2%

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

      3. neg-mul-1 51.2%

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

   8. Simplified 51.2%

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

   9. Taylor expanded in y around inf 43.9%

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

       1. *-commutative 43.9%

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

       2. associate-*l* 51.1%

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

   11. Simplified 51.1%

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

   if 5.19999999999999979e-200 < t < 3.69999999999999999e-12

   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. Taylor expanded in i around inf 50.4%

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

      1. distribute-lft-out-- 50.4%

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

   5. Simplified 50.4%

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

   6. Taylor expanded in i around 0 50.4%

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

      1. mul-1-neg 50.4%

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

      2. *-commutative 50.4%

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

      3. *-commutative 50.4%

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

      4. *-commutative 50.4%

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

      5. fma-neg 50.4%

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

      6. distribute-rgt-neg-in 50.4%

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

      7. fma-neg 50.4%

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

   8. Simplified 50.4%

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

   9. Taylor expanded in y around inf 42.5%

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

       1. *-commutative 42.5%

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

       2. associate-*r* 42.4%

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

       3. associate-*l* 42.4%

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

       4. *-commutative 42.4%

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

       5. mul-1-neg 42.4%

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

       6. distribute-rgt-neg-in 42.4%

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

   11. Simplified 42.4%

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

   if 3.69999999999999999e-12 < t

   1. Initial program 59.2%

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

   3. Taylor expanded in a around inf 50.9%

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

      1. +-commutative 50.9%

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

      2. mul-1-neg 50.9%

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

      3. unsub-neg 50.9%

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

      4. *-commutative 50.9%

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

   5. Simplified 50.9%

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

   6. Taylor expanded in j around 0 47.5%

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

      1. mul-1-neg 47.5%

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

      2. distribute-lft-neg-out 47.5%

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

      3. *-commutative 47.5%

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

   8. Simplified 47.5%

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

4. Final simplification 43.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+148}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq -1.02 \cdot 10^{+55}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;t \leq -3.55 \cdot 10^{+18}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-281}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-200}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-12}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 66.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -1.75 \cdot 10^{+267}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{-6}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z\right) + j \cdot \left(a \cdot c - y \cdot i\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* b i) (* x a)))))
   (if (<= t -1.75e+267)
     t_1
     (if (<= t -4.8e+18)
       (+ (* x (- (* y z) (* t a))) (* b (- (* t i) (* z c))))
       (if (<= t 7.6e-6)
         (- (+ (* x (* y z)) (* j (- (* a c) (* y i)))) (* b (* z c)))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -1.75e+267) {
		tmp = t_1;
	} else if (t <= -4.8e+18) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	} else if (t <= 7.6e-6) {
		tmp = ((x * (y * z)) + (j * ((a * c) - (y * i)))) - (b * (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((b * i) - (x * a))
    if (t <= (-1.75d+267)) then
        tmp = t_1
    else if (t <= (-4.8d+18)) then
        tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))
    else if (t <= 7.6d-6) then
        tmp = ((x * (y * z)) + (j * ((a * c) - (y * i)))) - (b * (z * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -1.75e+267) {
		tmp = t_1;
	} else if (t <= -4.8e+18) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	} else if (t <= 7.6e-6) {
		tmp = ((x * (y * z)) + (j * ((a * c) - (y * i)))) - (b * (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((b * i) - (x * a))
	tmp = 0
	if t <= -1.75e+267:
		tmp = t_1
	elif t <= -4.8e+18:
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))
	elif t <= 7.6e-6:
		tmp = ((x * (y * z)) + (j * ((a * c) - (y * i)))) - (b * (z * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	tmp = 0.0
	if (t <= -1.75e+267)
		tmp = t_1;
	elseif (t <= -4.8e+18)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	elseif (t <= 7.6e-6)
		tmp = Float64(Float64(Float64(x * Float64(y * z)) + Float64(j * Float64(Float64(a * c) - Float64(y * i)))) - Float64(b * Float64(z * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -1.75e+267)
		tmp = t_1;
	elseif (t <= -4.8e+18)
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	elseif (t <= 7.6e-6)
		tmp = ((x * (y * z)) + (j * ((a * c) - (y * i)))) - (b * (z * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.75e+267], t$95$1, If[LessEqual[t, -4.8e+18], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.6e-6], N[(N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.75e267 or 7.6000000000000001e-6 < t

   1. Initial program 50.8%

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

   3. Taylor expanded in t around inf 78.8%

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

      1. distribute-lft-out-- 78.8%

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

      2. *-commutative 78.8%

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

   5. Simplified 78.8%

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

   6. Taylor expanded in t around 0 78.8%

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

      1. mul-1-neg 78.8%

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

      2. distribute-rgt-neg-out 78.8%

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

   8. Simplified 78.8%

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

   if -1.75e267 < t < -4.8e18

   1. Initial program 75.3%

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

   3. Taylor expanded in j around 0 78.8%

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

   if -4.8e18 < t < 7.6000000000000001e-6

   1. Initial program 82.1%

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

   3. Taylor expanded in t around 0 72.7%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+267}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{-6}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z\right) + j \cdot \left(a \cdot c - y \cdot i\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 29.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c\right)\\ \mathbf{if}\;i \leq -5 \cdot 10^{-114}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -6.6 \cdot 10^{-221}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;i \leq -2.2 \cdot 10^{-269}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 3.5 \cdot 10^{-247}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 3.7 \cdot 10^{-94}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 10^{+49}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (* a c))))
   (if (<= i -5e-114)
     (* t (* b i))
     (if (<= i -6.6e-221)
       (* a (* x (- t)))
       (if (<= i -2.2e-269)
         t_1
         (if (<= i 3.5e-247)
           (* y (* x z))
           (if (<= i 3.7e-94)
             t_1
             (if (<= i 1e+49) (* x (* y z)) (* b (* t i))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (a * c);
	double tmp;
	if (i <= -5e-114) {
		tmp = t * (b * i);
	} else if (i <= -6.6e-221) {
		tmp = a * (x * -t);
	} else if (i <= -2.2e-269) {
		tmp = t_1;
	} else if (i <= 3.5e-247) {
		tmp = y * (x * z);
	} else if (i <= 3.7e-94) {
		tmp = t_1;
	} else if (i <= 1e+49) {
		tmp = x * (y * z);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * (a * c)
    if (i <= (-5d-114)) then
        tmp = t * (b * i)
    else if (i <= (-6.6d-221)) then
        tmp = a * (x * -t)
    else if (i <= (-2.2d-269)) then
        tmp = t_1
    else if (i <= 3.5d-247) then
        tmp = y * (x * z)
    else if (i <= 3.7d-94) then
        tmp = t_1
    else if (i <= 1d+49) then
        tmp = x * (y * z)
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (a * c);
	double tmp;
	if (i <= -5e-114) {
		tmp = t * (b * i);
	} else if (i <= -6.6e-221) {
		tmp = a * (x * -t);
	} else if (i <= -2.2e-269) {
		tmp = t_1;
	} else if (i <= 3.5e-247) {
		tmp = y * (x * z);
	} else if (i <= 3.7e-94) {
		tmp = t_1;
	} else if (i <= 1e+49) {
		tmp = x * (y * z);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * (a * c)
	tmp = 0
	if i <= -5e-114:
		tmp = t * (b * i)
	elif i <= -6.6e-221:
		tmp = a * (x * -t)
	elif i <= -2.2e-269:
		tmp = t_1
	elif i <= 3.5e-247:
		tmp = y * (x * z)
	elif i <= 3.7e-94:
		tmp = t_1
	elif i <= 1e+49:
		tmp = x * (y * z)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(a * c))
	tmp = 0.0
	if (i <= -5e-114)
		tmp = Float64(t * Float64(b * i));
	elseif (i <= -6.6e-221)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (i <= -2.2e-269)
		tmp = t_1;
	elseif (i <= 3.5e-247)
		tmp = Float64(y * Float64(x * z));
	elseif (i <= 3.7e-94)
		tmp = t_1;
	elseif (i <= 1e+49)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * (a * c);
	tmp = 0.0;
	if (i <= -5e-114)
		tmp = t * (b * i);
	elseif (i <= -6.6e-221)
		tmp = a * (x * -t);
	elseif (i <= -2.2e-269)
		tmp = t_1;
	elseif (i <= 3.5e-247)
		tmp = y * (x * z);
	elseif (i <= 3.7e-94)
		tmp = t_1;
	elseif (i <= 1e+49)
		tmp = x * (y * z);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -5e-114], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -6.6e-221], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -2.2e-269], t$95$1, If[LessEqual[i, 3.5e-247], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.7e-94], t$95$1, If[LessEqual[i, 1e+49], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -4.99999999999999989e-114

   1. Initial program 71.8%

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

   3. Taylor expanded in i around inf 61.0%

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

      1. distribute-lft-out-- 61.0%

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

   5. Simplified 61.0%

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

   6. Taylor expanded in j around 0 39.8%

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

      1. *-commutative 39.8%

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

   8. Simplified 39.8%

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

   9. Taylor expanded in b around 0 39.8%

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

       1. associate-*r* 40.7%

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

       2. *-commutative 40.7%

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

   11. Simplified 40.7%

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

   if -4.99999999999999989e-114 < i < -6.59999999999999979e-221

   1. Initial program 84.6%

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

   3. Taylor expanded in a around inf 51.3%

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

      1. +-commutative 51.3%

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

      2. mul-1-neg 51.3%

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

      3. unsub-neg 51.3%

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

      4. *-commutative 51.3%

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

   5. Simplified 51.3%

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

   6. Taylor expanded in j around 0 43.8%

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

      1. mul-1-neg 43.8%

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

      2. distribute-lft-neg-out 43.8%

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

      3. *-commutative 43.8%

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

   8. Simplified 43.8%

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

   if -6.59999999999999979e-221 < i < -2.19999999999999984e-269 or 3.4999999999999999e-247 < i < 3.6999999999999998e-94

   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 46.9%

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

      1. +-commutative 46.9%

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

      2. mul-1-neg 46.9%

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

      3. unsub-neg 46.9%

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

      4. *-commutative 46.9%

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

   5. Simplified 46.9%

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

   6. Taylor expanded in t around inf 42.6%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + \frac{a \cdot \left(c \cdot j\right)}{t}\right)} \]
   7. Step-by-step derivation

      1. +-commutative 42.6%

         \[\leadsto t \cdot \color{blue}{\left(\frac{a \cdot \left(c \cdot j\right)}{t} + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 42.6%

         \[\leadsto t \cdot \left(\frac{a \cdot \left(c \cdot j\right)}{t} + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 42.6%

         \[\leadsto t \cdot \color{blue}{\left(\frac{a \cdot \left(c \cdot j\right)}{t} - a \cdot x\right)} \]

      4. associate-/l* 42.6%

         \[\leadsto t \cdot \left(\color{blue}{a \cdot \frac{c \cdot j}{t}} - a \cdot x\right) \]

      5. associate-/l* 46.8%

         \[\leadsto t \cdot \left(a \cdot \color{blue}{\left(c \cdot \frac{j}{t}\right)} - a \cdot x\right) \]

      6. *-commutative 46.8%

         \[\leadsto t \cdot \left(a \cdot \left(c \cdot \frac{j}{t}\right) - \color{blue}{x \cdot a}\right) \]

   8. Simplified 46.8%

      \[\leadsto \color{blue}{t \cdot \left(a \cdot \left(c \cdot \frac{j}{t}\right) - x \cdot a\right)} \]

   9. Taylor expanded in t around 0 34.6%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 45.0%

          \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]

       2. *-commutative 45.0%

          \[\leadsto \color{blue}{\left(c \cdot a\right)} \cdot j \]

   11. Simplified 45.0%

       \[\leadsto \color{blue}{\left(c \cdot a\right) \cdot j} \]

   if -2.19999999999999984e-269 < i < 3.4999999999999999e-247

   1. Initial program 82.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 76.7%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + \left(-1 \cdot \frac{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(c \cdot j\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}{y} + i \cdot j\right)\right)\right)} \]

   5. Simplified 76.7%

      \[\leadsto \color{blue}{\left(\left(j \cdot i - \frac{a \cdot \left(j \cdot c - t \cdot x\right) + b \cdot \left(i \cdot t - c \cdot z\right)}{y}\right) - z \cdot x\right) \cdot \left(-y\right)} \]

   6. Taylor expanded in x around inf 52.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(z + -1 \cdot \frac{a \cdot t}{y}\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r/ 52.8%

         \[\leadsto x \cdot \left(y \cdot \left(z + \color{blue}{\frac{-1 \cdot \left(a \cdot t\right)}{y}}\right)\right) \]

      2. associate-*r* 52.8%

         \[\leadsto x \cdot \left(y \cdot \left(z + \frac{\color{blue}{\left(-1 \cdot a\right) \cdot t}}{y}\right)\right) \]

      3. neg-mul-1 52.8%

         \[\leadsto x \cdot \left(y \cdot \left(z + \frac{\color{blue}{\left(-a\right)} \cdot t}{y}\right)\right) \]

   8. Simplified 52.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(z + \frac{\left(-a\right) \cdot t}{y}\right)\right)} \]

   9. Taylor expanded in y around inf 39.5%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   10. Step-by-step derivation

       1. *-commutative 39.5%

          \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

       2. associate-*l* 45.3%

          \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   11. Simplified 45.3%

       \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if 3.6999999999999998e-94 < i < 9.99999999999999946e48

   1. Initial program 66.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 67.4%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + \left(-1 \cdot \frac{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(c \cdot j\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}{y} + i \cdot j\right)\right)\right)} \]

   5. Simplified 67.4%

      \[\leadsto \color{blue}{\left(\left(j \cdot i - \frac{a \cdot \left(j \cdot c - t \cdot x\right) + b \cdot \left(i \cdot t - c \cdot z\right)}{y}\right) - z \cdot x\right) \cdot \left(-y\right)} \]

   6. Taylor expanded in x around inf 54.0%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(z + -1 \cdot \frac{a \cdot t}{y}\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r/ 54.0%

         \[\leadsto x \cdot \left(y \cdot \left(z + \color{blue}{\frac{-1 \cdot \left(a \cdot t\right)}{y}}\right)\right) \]

      2. associate-*r* 54.0%

         \[\leadsto x \cdot \left(y \cdot \left(z + \frac{\color{blue}{\left(-1 \cdot a\right) \cdot t}}{y}\right)\right) \]

      3. neg-mul-1 54.0%

         \[\leadsto x \cdot \left(y \cdot \left(z + \frac{\color{blue}{\left(-a\right)} \cdot t}{y}\right)\right) \]

   8. Simplified 54.0%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(z + \frac{\left(-a\right) \cdot t}{y}\right)\right)} \]

   9. Taylor expanded in y around inf 34.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   10. Step-by-step derivation

       1. *-commutative 34.9%

          \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

   11. Simplified 34.9%

       \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

   if 9.99999999999999946e48 < i

   1. Initial program 63.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 63.2%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 63.2%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   5. Simplified 63.2%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   6. Taylor expanded in j around 0 40.2%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 40.2%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   8. Simplified 40.2%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -5 \cdot 10^{-114}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -6.6 \cdot 10^{-221}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;i \leq -2.2 \cdot 10^{-269}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;i \leq 3.5 \cdot 10^{-247}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 3.7 \cdot 10^{-94}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;i \leq 10^{+49}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 52.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.9 \cdot 10^{-36}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -1.6 \cdot 10^{-282}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 4.8 \cdot 10^{-300}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 7 \cdot 10^{-72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 7.2 \cdot 10^{+25}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* j (- (* a c) (* y i)))))
   (if (<= j -1.9e-36)
     t_2
     (if (<= j -1.6e-282)
       t_1
       (if (<= j 4.8e-300)
         (* y (* x z))
         (if (<= j 7e-72)
           t_1
           (if (<= j 7.2e+25) (* a (- (* c j) (* x t))) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -1.9e-36) {
		tmp = t_2;
	} else if (j <= -1.6e-282) {
		tmp = t_1;
	} else if (j <= 4.8e-300) {
		tmp = y * (x * z);
	} else if (j <= 7e-72) {
		tmp = t_1;
	} else if (j <= 7.2e+25) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = j * ((a * c) - (y * i))
    if (j <= (-1.9d-36)) then
        tmp = t_2
    else if (j <= (-1.6d-282)) then
        tmp = t_1
    else if (j <= 4.8d-300) then
        tmp = y * (x * z)
    else if (j <= 7d-72) then
        tmp = t_1
    else if (j <= 7.2d+25) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -1.9e-36) {
		tmp = t_2;
	} else if (j <= -1.6e-282) {
		tmp = t_1;
	} else if (j <= 4.8e-300) {
		tmp = y * (x * z);
	} else if (j <= 7e-72) {
		tmp = t_1;
	} else if (j <= 7.2e+25) {
		tmp = a * ((c * j) - (x * t));
	} 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 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -1.9e-36:
		tmp = t_2
	elif j <= -1.6e-282:
		tmp = t_1
	elif j <= 4.8e-300:
		tmp = y * (x * z)
	elif j <= 7e-72:
		tmp = t_1
	elif j <= 7.2e+25:
		tmp = a * ((c * j) - (x * t))
	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(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -1.9e-36)
		tmp = t_2;
	elseif (j <= -1.6e-282)
		tmp = t_1;
	elseif (j <= 4.8e-300)
		tmp = Float64(y * Float64(x * z));
	elseif (j <= 7e-72)
		tmp = t_1;
	elseif (j <= 7.2e+25)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -1.9e-36)
		tmp = t_2;
	elseif (j <= -1.6e-282)
		tmp = t_1;
	elseif (j <= 4.8e-300)
		tmp = y * (x * z);
	elseif (j <= 7e-72)
		tmp = t_1;
	elseif (j <= 7.2e+25)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.9e-36], t$95$2, If[LessEqual[j, -1.6e-282], t$95$1, If[LessEqual[j, 4.8e-300], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7e-72], t$95$1, If[LessEqual[j, 7.2e+25], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.89999999999999985e-36 or 7.20000000000000031e25 < j

   1. Initial program 75.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 66.5%

      \[\leadsto \color{blue}{\left(j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z\right)} \]

   4. Taylor expanded in j around inf 59.0%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]
   5. Step-by-step derivation

      1. sub-neg 59.0%

         \[\leadsto j \cdot \color{blue}{\left(a \cdot c + \left(-i \cdot y\right)\right)} \]

      2. *-commutative 59.0%

         \[\leadsto j \cdot \left(a \cdot c + \left(-\color{blue}{y \cdot i}\right)\right) \]

      3. sub-neg 59.0%

         \[\leadsto j \cdot \color{blue}{\left(a \cdot c - y \cdot i\right)} \]

   6. Simplified 59.0%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - y \cdot i\right)} \]

   if -1.89999999999999985e-36 < j < -1.59999999999999991e-282 or 4.79999999999999999e-300 < j < 7.00000000000000001e-72

   1. Initial program 69.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 58.3%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]

   if -1.59999999999999991e-282 < j < 4.79999999999999999e-300

   1. Initial program 61.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 76.7%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + \left(-1 \cdot \frac{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(c \cdot j\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}{y} + i \cdot j\right)\right)\right)} \]

   5. Simplified 76.7%

      \[\leadsto \color{blue}{\left(\left(j \cdot i - \frac{a \cdot \left(j \cdot c - t \cdot x\right) + b \cdot \left(i \cdot t - c \cdot z\right)}{y}\right) - z \cdot x\right) \cdot \left(-y\right)} \]

   6. Taylor expanded in x around inf 92.7%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(z + -1 \cdot \frac{a \cdot t}{y}\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r/ 92.7%

         \[\leadsto x \cdot \left(y \cdot \left(z + \color{blue}{\frac{-1 \cdot \left(a \cdot t\right)}{y}}\right)\right) \]

      2. associate-*r* 92.7%

         \[\leadsto x \cdot \left(y \cdot \left(z + \frac{\color{blue}{\left(-1 \cdot a\right) \cdot t}}{y}\right)\right) \]

      3. neg-mul-1 92.7%

         \[\leadsto x \cdot \left(y \cdot \left(z + \frac{\color{blue}{\left(-a\right)} \cdot t}{y}\right)\right) \]

   8. Simplified 92.7%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(z + \frac{\left(-a\right) \cdot t}{y}\right)\right)} \]

   9. Taylor expanded in y around inf 69.7%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   10. Step-by-step derivation

       1. *-commutative 69.7%

          \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

       2. associate-*l* 76.7%

          \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   11. Simplified 76.7%

       \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if 7.00000000000000001e-72 < j < 7.20000000000000031e25

   1. Initial program 70.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 55.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 55.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 55.5%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 55.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 55.5%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 55.5%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.9 \cdot 10^{-36}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -1.6 \cdot 10^{-282}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 4.8 \cdot 10^{-300}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 7 \cdot 10^{-72}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 7.2 \cdot 10^{+25}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 69.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := t\_2 + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.25 \cdot 10^{-52}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{-122}:\\ \;\;\;\;t\_2 + t\_1\\ \mathbf{elif}\;j \leq 1.25 \cdot 10^{+50}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c))))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (+ t_2 (* j (- (* a c) (* y i))))))
   (if (<= j -1.25e-52)
     t_3
     (if (<= j 1.5e-122)
       (+ t_2 t_1)
       (if (<= j 1.25e+50) (+ (* a (- (* c j) (* x t))) 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 = b * ((t * i) - (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = t_2 + (j * ((a * c) - (y * i)));
	double tmp;
	if (j <= -1.25e-52) {
		tmp = t_3;
	} else if (j <= 1.5e-122) {
		tmp = t_2 + t_1;
	} else if (j <= 1.25e+50) {
		tmp = (a * ((c * j) - (x * t))) + 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 = b * ((t * i) - (z * c))
    t_2 = x * ((y * z) - (t * a))
    t_3 = t_2 + (j * ((a * c) - (y * i)))
    if (j <= (-1.25d-52)) then
        tmp = t_3
    else if (j <= 1.5d-122) then
        tmp = t_2 + t_1
    else if (j <= 1.25d+50) then
        tmp = (a * ((c * j) - (x * t))) + 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 = b * ((t * i) - (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = t_2 + (j * ((a * c) - (y * i)));
	double tmp;
	if (j <= -1.25e-52) {
		tmp = t_3;
	} else if (j <= 1.5e-122) {
		tmp = t_2 + t_1;
	} else if (j <= 1.25e+50) {
		tmp = (a * ((c * j) - (x * t))) + t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = x * ((y * z) - (t * a))
	t_3 = t_2 + (j * ((a * c) - (y * i)))
	tmp = 0
	if j <= -1.25e-52:
		tmp = t_3
	elif j <= 1.5e-122:
		tmp = t_2 + t_1
	elif j <= 1.25e+50:
		tmp = (a * ((c * j) - (x * t))) + t_1
	else:
		tmp = t_3
	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(x * Float64(Float64(y * z) - Float64(t * a)))
	t_3 = Float64(t_2 + Float64(j * Float64(Float64(a * c) - Float64(y * i))))
	tmp = 0.0
	if (j <= -1.25e-52)
		tmp = t_3;
	elseif (j <= 1.5e-122)
		tmp = Float64(t_2 + t_1);
	elseif (j <= 1.25e+50)
		tmp = Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) + 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 = b * ((t * i) - (z * c));
	t_2 = x * ((y * z) - (t * a));
	t_3 = t_2 + (j * ((a * c) - (y * i)));
	tmp = 0.0;
	if (j <= -1.25e-52)
		tmp = t_3;
	elseif (j <= 1.5e-122)
		tmp = t_2 + t_1;
	elseif (j <= 1.25e+50)
		tmp = (a * ((c * j) - (x * t))) + 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[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.25e-52], t$95$3, If[LessEqual[j, 1.5e-122], N[(t$95$2 + t$95$1), $MachinePrecision], If[LessEqual[j, 1.25e+50], N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], t$95$3]]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.25e-52 or 1.25e50 < j

   1. Initial program 75.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 70.8%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   if -1.25e-52 < j < 1.50000000000000002e-122

   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 j around 0 75.6%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   if 1.50000000000000002e-122 < j < 1.25e50

   1. Initial program 72.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 78.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(c \cdot j\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   4. Step-by-step derivation

      1. cancel-sign-sub-inv 78.7%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(c \cdot j\right)\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot t\right)} \]

      2. *-commutative 78.7%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(t \cdot x\right) \cdot a\right)} + a \cdot \left(c \cdot j\right)\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot t\right) \]

      3. associate-*r* 78.7%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right) \cdot a} + a \cdot \left(c \cdot j\right)\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot t\right) \]

      4. *-commutative 78.7%

         \[\leadsto \left(\left(-1 \cdot \left(t \cdot x\right)\right) \cdot a + \color{blue}{\left(c \cdot j\right) \cdot a}\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot t\right) \]

      5. distribute-rgt-in 78.7%

         \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} + \left(-b\right) \cdot \left(c \cdot z - i \cdot t\right) \]

      6. +-commutative 78.7%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} + \left(-b\right) \cdot \left(c \cdot z - i \cdot t\right) \]

      7. mul-1-neg 78.7%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot t\right) \]

      8. unsub-neg 78.7%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} + \left(-b\right) \cdot \left(c \cdot z - i \cdot t\right) \]

      9. *-commutative 78.7%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot t\right) \]

      10. distribute-lft-neg-in 78.7%

          \[\leadsto a \cdot \left(j \cdot c - t \cdot x\right) + \color{blue}{\left(-b \cdot \left(c \cdot z - i \cdot t\right)\right)} \]

      11. sub-neg 78.7%

          \[\leadsto a \cdot \left(j \cdot c - t \cdot x\right) + \left(-b \cdot \color{blue}{\left(c \cdot z + \left(-i \cdot t\right)\right)}\right) \]

      12. distribute-rgt-neg-out 78.7%

          \[\leadsto a \cdot \left(j \cdot c - t \cdot x\right) + \left(-b \cdot \left(c \cdot z + \color{blue}{i \cdot \left(-t\right)}\right)\right) \]

      13. distribute-lft-out 75.6%

          \[\leadsto a \cdot \left(j \cdot c - t \cdot x\right) + \left(-\color{blue}{\left(b \cdot \left(c \cdot z\right) + b \cdot \left(i \cdot \left(-t\right)\right)\right)}\right) \]

      14. +-commutative 75.6%

          \[\leadsto a \cdot \left(j \cdot c - t \cdot x\right) + \left(-\color{blue}{\left(b \cdot \left(i \cdot \left(-t\right)\right) + b \cdot \left(c \cdot z\right)\right)}\right) \]

      15. distribute-rgt-neg-out 75.6%

          \[\leadsto a \cdot \left(j \cdot c - t \cdot x\right) + \left(-\left(b \cdot \color{blue}{\left(-i \cdot t\right)} + b \cdot \left(c \cdot z\right)\right)\right) \]

      16. distribute-rgt-neg-in 75.6%

          \[\leadsto a \cdot \left(j \cdot c - t \cdot x\right) + \left(-\left(\color{blue}{\left(-b \cdot \left(i \cdot t\right)\right)} + b \cdot \left(c \cdot z\right)\right)\right) \]

      17. mul-1-neg 75.6%

          \[\leadsto a \cdot \left(j \cdot c - t \cdot x\right) + \left(-\left(\color{blue}{-1 \cdot \left(b \cdot \left(i \cdot t\right)\right)} + b \cdot \left(c \cdot z\right)\right)\right) \]

   5. Simplified 78.7%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right) + b \cdot \left(i \cdot t - c \cdot z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.25 \cdot 10^{-52}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{-122}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.25 \cdot 10^{+50}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 29.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+70}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-201}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+43}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;y \leq 10^{+163}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+213}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -2.7e+70)
   (* y (* x z))
   (if (<= y 6.8e-201)
     (* b (* z (- c)))
     (if (<= y 1.35e+43)
       (* b (* t i))
       (if (<= y 1e+163)
         (* j (* a c))
         (if (<= y 1.4e+213) (* (* y i) (- j)) (* 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 <= -2.7e+70) {
		tmp = y * (x * z);
	} else if (y <= 6.8e-201) {
		tmp = b * (z * -c);
	} else if (y <= 1.35e+43) {
		tmp = b * (t * i);
	} else if (y <= 1e+163) {
		tmp = j * (a * c);
	} else if (y <= 1.4e+213) {
		tmp = (y * i) * -j;
	} 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 <= (-2.7d+70)) then
        tmp = y * (x * z)
    else if (y <= 6.8d-201) then
        tmp = b * (z * -c)
    else if (y <= 1.35d+43) then
        tmp = b * (t * i)
    else if (y <= 1d+163) then
        tmp = j * (a * c)
    else if (y <= 1.4d+213) then
        tmp = (y * i) * -j
    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 <= -2.7e+70) {
		tmp = y * (x * z);
	} else if (y <= 6.8e-201) {
		tmp = b * (z * -c);
	} else if (y <= 1.35e+43) {
		tmp = b * (t * i);
	} else if (y <= 1e+163) {
		tmp = j * (a * c);
	} else if (y <= 1.4e+213) {
		tmp = (y * i) * -j;
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -2.7e+70:
		tmp = y * (x * z)
	elif y <= 6.8e-201:
		tmp = b * (z * -c)
	elif y <= 1.35e+43:
		tmp = b * (t * i)
	elif y <= 1e+163:
		tmp = j * (a * c)
	elif y <= 1.4e+213:
		tmp = (y * i) * -j
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -2.7e+70)
		tmp = Float64(y * Float64(x * z));
	elseif (y <= 6.8e-201)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (y <= 1.35e+43)
		tmp = Float64(b * Float64(t * i));
	elseif (y <= 1e+163)
		tmp = Float64(j * Float64(a * c));
	elseif (y <= 1.4e+213)
		tmp = Float64(Float64(y * i) * Float64(-j));
	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 <= -2.7e+70)
		tmp = y * (x * z);
	elseif (y <= 6.8e-201)
		tmp = b * (z * -c);
	elseif (y <= 1.35e+43)
		tmp = b * (t * i);
	elseif (y <= 1e+163)
		tmp = j * (a * c);
	elseif (y <= 1.4e+213)
		tmp = (y * i) * -j;
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -2.7e+70], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.8e-201], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.35e+43], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e+163], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.4e+213], N[(N[(y * i), $MachinePrecision] * (-j)), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -2.7e70

   1. Initial program 65.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 80.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + \left(-1 \cdot \frac{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(c \cdot j\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}{y} + i \cdot j\right)\right)\right)} \]

   5. Simplified 80.8%

      \[\leadsto \color{blue}{\left(\left(j \cdot i - \frac{a \cdot \left(j \cdot c - t \cdot x\right) + b \cdot \left(i \cdot t - c \cdot z\right)}{y}\right) - z \cdot x\right) \cdot \left(-y\right)} \]

   6. Taylor expanded in x around inf 53.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(z + -1 \cdot \frac{a \cdot t}{y}\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r/ 53.1%

         \[\leadsto x \cdot \left(y \cdot \left(z + \color{blue}{\frac{-1 \cdot \left(a \cdot t\right)}{y}}\right)\right) \]

      2. associate-*r* 53.1%

         \[\leadsto x \cdot \left(y \cdot \left(z + \frac{\color{blue}{\left(-1 \cdot a\right) \cdot t}}{y}\right)\right) \]

      3. neg-mul-1 53.1%

         \[\leadsto x \cdot \left(y \cdot \left(z + \frac{\color{blue}{\left(-a\right)} \cdot t}{y}\right)\right) \]

   8. Simplified 53.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(z + \frac{\left(-a\right) \cdot t}{y}\right)\right)} \]

   9. Taylor expanded in y around inf 45.4%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   10. Step-by-step derivation

       1. *-commutative 45.4%

          \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

       2. associate-*l* 47.0%

          \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   11. Simplified 47.0%

       \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if -2.7e70 < y < 6.7999999999999997e-201

   1. Initial program 79.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 48.3%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]

   4. Taylor expanded in i around 0 34.2%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 34.2%

         \[\leadsto \color{blue}{-b \cdot \left(c \cdot z\right)} \]

      2. *-commutative 34.2%

         \[\leadsto -\color{blue}{\left(c \cdot z\right) \cdot b} \]

      3. distribute-rgt-neg-in 34.2%

         \[\leadsto \color{blue}{\left(c \cdot z\right) \cdot \left(-b\right)} \]

   6. Simplified 34.2%

      \[\leadsto \color{blue}{\left(c \cdot z\right) \cdot \left(-b\right)} \]

   if 6.7999999999999997e-201 < y < 1.3500000000000001e43

   1. Initial program 71.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 54.1%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 54.1%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   5. Simplified 54.1%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   6. Taylor expanded in j around 0 47.1%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 47.1%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   8. Simplified 47.1%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]

   if 1.3500000000000001e43 < y < 9.9999999999999994e162

   1. Initial program 71.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 52.9%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 52.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 52.9%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 52.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 52.9%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 52.9%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in t around inf 37.9%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + \frac{a \cdot \left(c \cdot j\right)}{t}\right)} \]
   7. Step-by-step derivation

      1. +-commutative 37.9%

         \[\leadsto t \cdot \color{blue}{\left(\frac{a \cdot \left(c \cdot j\right)}{t} + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 37.9%

         \[\leadsto t \cdot \left(\frac{a \cdot \left(c \cdot j\right)}{t} + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 37.9%

         \[\leadsto t \cdot \color{blue}{\left(\frac{a \cdot \left(c \cdot j\right)}{t} - a \cdot x\right)} \]

      4. associate-/l* 41.4%

         \[\leadsto t \cdot \left(\color{blue}{a \cdot \frac{c \cdot j}{t}} - a \cdot x\right) \]

      5. associate-/l* 39.4%

         \[\leadsto t \cdot \left(a \cdot \color{blue}{\left(c \cdot \frac{j}{t}\right)} - a \cdot x\right) \]

      6. *-commutative 39.4%

         \[\leadsto t \cdot \left(a \cdot \left(c \cdot \frac{j}{t}\right) - \color{blue}{x \cdot a}\right) \]

   8. Simplified 39.4%

      \[\leadsto \color{blue}{t \cdot \left(a \cdot \left(c \cdot \frac{j}{t}\right) - x \cdot a\right)} \]

   9. Taylor expanded in t around 0 34.9%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 41.7%

          \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]

       2. *-commutative 41.7%

          \[\leadsto \color{blue}{\left(c \cdot a\right)} \cdot j \]

   11. Simplified 41.7%

       \[\leadsto \color{blue}{\left(c \cdot a\right) \cdot j} \]

   if 9.9999999999999994e162 < y < 1.39999999999999995e213

   1. Initial program 1.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 80.2%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 80.2%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   5. Simplified 80.2%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   6. Taylor expanded in i around 0 80.2%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y - b \cdot t\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 80.2%

         \[\leadsto \color{blue}{-i \cdot \left(j \cdot y - b \cdot t\right)} \]

      2. *-commutative 80.2%

         \[\leadsto -\color{blue}{\left(j \cdot y - b \cdot t\right) \cdot i} \]

      3. *-commutative 80.2%

         \[\leadsto -\left(\color{blue}{y \cdot j} - b \cdot t\right) \cdot i \]

      4. *-commutative 80.2%

         \[\leadsto -\left(y \cdot j - \color{blue}{t \cdot b}\right) \cdot i \]

      5. fma-neg 80.2%

         \[\leadsto -\color{blue}{\mathsf{fma}\left(y, j, -t \cdot b\right)} \cdot i \]

      6. distribute-rgt-neg-in 80.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, j, -t \cdot b\right) \cdot \left(-i\right)} \]

      7. fma-neg 80.2%

         \[\leadsto \color{blue}{\left(y \cdot j - t \cdot b\right)} \cdot \left(-i\right) \]

   8. Simplified 80.2%

      \[\leadsto \color{blue}{\left(y \cdot j - t \cdot b\right) \cdot \left(-i\right)} \]

   9. Taylor expanded in y around inf 80.2%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 80.2%

          \[\leadsto -1 \cdot \left(i \cdot \color{blue}{\left(y \cdot j\right)}\right) \]

       2. associate-*r* 80.2%

          \[\leadsto -1 \cdot \color{blue}{\left(\left(i \cdot y\right) \cdot j\right)} \]

       3. associate-*l* 80.2%

          \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot y\right)\right) \cdot j} \]

       4. *-commutative 80.2%

          \[\leadsto \color{blue}{j \cdot \left(-1 \cdot \left(i \cdot y\right)\right)} \]

       5. mul-1-neg 80.2%

          \[\leadsto j \cdot \color{blue}{\left(-i \cdot y\right)} \]

       6. distribute-rgt-neg-in 80.2%

          \[\leadsto j \cdot \color{blue}{\left(i \cdot \left(-y\right)\right)} \]

   11. Simplified 80.2%

       \[\leadsto \color{blue}{j \cdot \left(i \cdot \left(-y\right)\right)} \]

   if 1.39999999999999995e213 < y

   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. Taylor expanded in y around -inf 78.1%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + \left(-1 \cdot \frac{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(c \cdot j\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}{y} + i \cdot j\right)\right)\right)} \]

   5. Simplified 78.1%

      \[\leadsto \color{blue}{\left(\left(j \cdot i - \frac{a \cdot \left(j \cdot c - t \cdot x\right) + b \cdot \left(i \cdot t - c \cdot z\right)}{y}\right) - z \cdot x\right) \cdot \left(-y\right)} \]

   6. Taylor expanded in x around inf 57.2%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(z + -1 \cdot \frac{a \cdot t}{y}\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r/ 57.2%

         \[\leadsto x \cdot \left(y \cdot \left(z + \color{blue}{\frac{-1 \cdot \left(a \cdot t\right)}{y}}\right)\right) \]

      2. associate-*r* 57.2%

         \[\leadsto x \cdot \left(y \cdot \left(z + \frac{\color{blue}{\left(-1 \cdot a\right) \cdot t}}{y}\right)\right) \]

      3. neg-mul-1 57.2%

         \[\leadsto x \cdot \left(y \cdot \left(z + \frac{\color{blue}{\left(-a\right)} \cdot t}{y}\right)\right) \]

   8. Simplified 57.2%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(z + \frac{\left(-a\right) \cdot t}{y}\right)\right)} \]

   9. Taylor expanded in y around inf 48.5%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   10. Step-by-step derivation

       1. *-commutative 48.5%

          \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

   11. Simplified 48.5%

       \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]
3. Recombined 6 regimes into one program.

4. Final simplification 41.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+70}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-201}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+43}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;y \leq 10^{+163}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+213}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 52.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -1.4 \cdot 10^{+19}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-150}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-185}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))) (t_2 (* t (- (* b i) (* x a)))))
   (if (<= t -1.4e+19)
     t_2
     (if (<= t -9.2e-150)
       t_1
       (if (<= t 6.2e-185)
         (* z (- (* x y) (* b c)))
         (if (<= t 6.4e-22) 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 * ((a * c) - (y * i));
	double t_2 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -1.4e+19) {
		tmp = t_2;
	} else if (t <= -9.2e-150) {
		tmp = t_1;
	} else if (t <= 6.2e-185) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 6.4e-22) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = t * ((b * i) - (x * a))
    if (t <= (-1.4d+19)) then
        tmp = t_2
    else if (t <= (-9.2d-150)) then
        tmp = t_1
    else if (t <= 6.2d-185) then
        tmp = z * ((x * y) - (b * c))
    else if (t <= 6.4d-22) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -1.4e+19) {
		tmp = t_2;
	} else if (t <= -9.2e-150) {
		tmp = t_1;
	} else if (t <= 6.2e-185) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 6.4e-22) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = t * ((b * i) - (x * a))
	tmp = 0
	if t <= -1.4e+19:
		tmp = t_2
	elif t <= -9.2e-150:
		tmp = t_1
	elif t <= 6.2e-185:
		tmp = z * ((x * y) - (b * c))
	elif t <= 6.4e-22:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	tmp = 0.0
	if (t <= -1.4e+19)
		tmp = t_2;
	elseif (t <= -9.2e-150)
		tmp = t_1;
	elseif (t <= 6.2e-185)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (t <= 6.4e-22)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -1.4e+19)
		tmp = t_2;
	elseif (t <= -9.2e-150)
		tmp = t_1;
	elseif (t <= 6.2e-185)
		tmp = z * ((x * y) - (b * c));
	elseif (t <= 6.4e-22)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.4e+19], t$95$2, If[LessEqual[t, -9.2e-150], t$95$1, If[LessEqual[t, 6.2e-185], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.4e-22], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.4e19 or 6.39999999999999975e-22 < t

   1. Initial program 63.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 70.2%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 70.2%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x - b \cdot i\right)\right)} \]

      2. *-commutative 70.2%

         \[\leadsto t \cdot \left(-1 \cdot \left(a \cdot x - \color{blue}{i \cdot b}\right)\right) \]

   5. Simplified 70.2%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x - i \cdot b\right)\right)} \]

   6. Taylor expanded in t around 0 70.2%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(a \cdot x - b \cdot i\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 70.2%

         \[\leadsto \color{blue}{-t \cdot \left(a \cdot x - b \cdot i\right)} \]

      2. distribute-rgt-neg-out 70.2%

         \[\leadsto \color{blue}{t \cdot \left(-\left(a \cdot x - b \cdot i\right)\right)} \]

   8. Simplified 70.2%

      \[\leadsto \color{blue}{t \cdot \left(-\left(a \cdot x - b \cdot i\right)\right)} \]

   if -1.4e19 < t < -9.20000000000000011e-150 or 6.1999999999999994e-185 < t < 6.39999999999999975e-22

   1. Initial program 85.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 77.0%

      \[\leadsto \color{blue}{\left(j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z\right)} \]

   4. Taylor expanded in j around inf 63.5%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]
   5. Step-by-step derivation

      1. sub-neg 63.5%

         \[\leadsto j \cdot \color{blue}{\left(a \cdot c + \left(-i \cdot y\right)\right)} \]

      2. *-commutative 63.5%

         \[\leadsto j \cdot \left(a \cdot c + \left(-\color{blue}{y \cdot i}\right)\right) \]

      3. sub-neg 63.5%

         \[\leadsto j \cdot \color{blue}{\left(a \cdot c - y \cdot i\right)} \]

   6. Simplified 63.5%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - y \cdot i\right)} \]

   if -9.20000000000000011e-150 < t < 6.1999999999999994e-185

   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 z around inf 58.2%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 58.2%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

      2. *-commutative 58.2%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) \]

   5. Simplified 58.2%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+19}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-150}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-185}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{-22}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 29.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+70}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-202}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+44}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+163}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -3.1e+70)
   (* y (* x z))
   (if (<= y 3.1e-202)
     (* b (* z (- c)))
     (if (<= y 1.75e+44)
       (* b (* t i))
       (if (<= y 1.12e+163) (* j (* a c)) (* i (* y (- j))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -3.1e+70) {
		tmp = y * (x * z);
	} else if (y <= 3.1e-202) {
		tmp = b * (z * -c);
	} else if (y <= 1.75e+44) {
		tmp = b * (t * i);
	} else if (y <= 1.12e+163) {
		tmp = j * (a * c);
	} else {
		tmp = i * (y * -j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-3.1d+70)) then
        tmp = y * (x * z)
    else if (y <= 3.1d-202) then
        tmp = b * (z * -c)
    else if (y <= 1.75d+44) then
        tmp = b * (t * i)
    else if (y <= 1.12d+163) then
        tmp = j * (a * c)
    else
        tmp = i * (y * -j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -3.1e+70) {
		tmp = y * (x * z);
	} else if (y <= 3.1e-202) {
		tmp = b * (z * -c);
	} else if (y <= 1.75e+44) {
		tmp = b * (t * i);
	} else if (y <= 1.12e+163) {
		tmp = j * (a * c);
	} else {
		tmp = i * (y * -j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -3.1e+70:
		tmp = y * (x * z)
	elif y <= 3.1e-202:
		tmp = b * (z * -c)
	elif y <= 1.75e+44:
		tmp = b * (t * i)
	elif y <= 1.12e+163:
		tmp = j * (a * c)
	else:
		tmp = i * (y * -j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -3.1e+70)
		tmp = Float64(y * Float64(x * z));
	elseif (y <= 3.1e-202)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (y <= 1.75e+44)
		tmp = Float64(b * Float64(t * i));
	elseif (y <= 1.12e+163)
		tmp = Float64(j * Float64(a * c));
	else
		tmp = Float64(i * Float64(y * Float64(-j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -3.1e+70)
		tmp = y * (x * z);
	elseif (y <= 3.1e-202)
		tmp = b * (z * -c);
	elseif (y <= 1.75e+44)
		tmp = b * (t * i);
	elseif (y <= 1.12e+163)
		tmp = j * (a * c);
	else
		tmp = i * (y * -j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -3.1e+70], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.1e-202], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.75e+44], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.12e+163], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.1000000000000003e70

   1. Initial program 65.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 80.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + \left(-1 \cdot \frac{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(c \cdot j\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}{y} + i \cdot j\right)\right)\right)} \]

   5. Simplified 80.8%

      \[\leadsto \color{blue}{\left(\left(j \cdot i - \frac{a \cdot \left(j \cdot c - t \cdot x\right) + b \cdot \left(i \cdot t - c \cdot z\right)}{y}\right) - z \cdot x\right) \cdot \left(-y\right)} \]

   6. Taylor expanded in x around inf 53.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(z + -1 \cdot \frac{a \cdot t}{y}\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r/ 53.1%

         \[\leadsto x \cdot \left(y \cdot \left(z + \color{blue}{\frac{-1 \cdot \left(a \cdot t\right)}{y}}\right)\right) \]

      2. associate-*r* 53.1%

         \[\leadsto x \cdot \left(y \cdot \left(z + \frac{\color{blue}{\left(-1 \cdot a\right) \cdot t}}{y}\right)\right) \]

      3. neg-mul-1 53.1%

         \[\leadsto x \cdot \left(y \cdot \left(z + \frac{\color{blue}{\left(-a\right)} \cdot t}{y}\right)\right) \]

   8. Simplified 53.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(z + \frac{\left(-a\right) \cdot t}{y}\right)\right)} \]

   9. Taylor expanded in y around inf 45.4%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   10. Step-by-step derivation

       1. *-commutative 45.4%

          \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

       2. associate-*l* 47.0%

          \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   11. Simplified 47.0%

       \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if -3.1000000000000003e70 < y < 3.1e-202

   1. Initial program 79.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 48.3%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]

   4. Taylor expanded in i around 0 34.2%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 34.2%

         \[\leadsto \color{blue}{-b \cdot \left(c \cdot z\right)} \]

      2. *-commutative 34.2%

         \[\leadsto -\color{blue}{\left(c \cdot z\right) \cdot b} \]

      3. distribute-rgt-neg-in 34.2%

         \[\leadsto \color{blue}{\left(c \cdot z\right) \cdot \left(-b\right)} \]

   6. Simplified 34.2%

      \[\leadsto \color{blue}{\left(c \cdot z\right) \cdot \left(-b\right)} \]

   if 3.1e-202 < y < 1.75e44

   1. Initial program 71.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 54.1%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 54.1%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   5. Simplified 54.1%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   6. Taylor expanded in j around 0 47.1%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 47.1%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   8. Simplified 47.1%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]

   if 1.75e44 < y < 1.11999999999999996e163

   1. Initial program 71.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 52.9%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 52.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 52.9%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 52.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 52.9%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 52.9%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in t around inf 37.9%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + \frac{a \cdot \left(c \cdot j\right)}{t}\right)} \]
   7. Step-by-step derivation

      1. +-commutative 37.9%

         \[\leadsto t \cdot \color{blue}{\left(\frac{a \cdot \left(c \cdot j\right)}{t} + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 37.9%

         \[\leadsto t \cdot \left(\frac{a \cdot \left(c \cdot j\right)}{t} + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 37.9%

         \[\leadsto t \cdot \color{blue}{\left(\frac{a \cdot \left(c \cdot j\right)}{t} - a \cdot x\right)} \]

      4. associate-/l* 41.4%

         \[\leadsto t \cdot \left(\color{blue}{a \cdot \frac{c \cdot j}{t}} - a \cdot x\right) \]

      5. associate-/l* 39.4%

         \[\leadsto t \cdot \left(a \cdot \color{blue}{\left(c \cdot \frac{j}{t}\right)} - a \cdot x\right) \]

      6. *-commutative 39.4%

         \[\leadsto t \cdot \left(a \cdot \left(c \cdot \frac{j}{t}\right) - \color{blue}{x \cdot a}\right) \]

   8. Simplified 39.4%

      \[\leadsto \color{blue}{t \cdot \left(a \cdot \left(c \cdot \frac{j}{t}\right) - x \cdot a\right)} \]

   9. Taylor expanded in t around 0 34.9%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 41.7%

          \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]

       2. *-commutative 41.7%

          \[\leadsto \color{blue}{\left(c \cdot a\right)} \cdot j \]

   11. Simplified 41.7%

       \[\leadsto \color{blue}{\left(c \cdot a\right) \cdot j} \]

   if 1.11999999999999996e163 < y

   1. Initial program 60.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 54.6%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 54.6%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   5. Simplified 54.6%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   6. Taylor expanded in j around inf 54.3%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 54.3%

         \[\leadsto \color{blue}{-i \cdot \left(j \cdot y\right)} \]

      2. *-commutative 54.3%

         \[\leadsto -\color{blue}{\left(j \cdot y\right) \cdot i} \]

      3. distribute-rgt-neg-in 54.3%

         \[\leadsto \color{blue}{\left(j \cdot y\right) \cdot \left(-i\right)} \]

      4. *-commutative 54.3%

         \[\leadsto \color{blue}{\left(y \cdot j\right)} \cdot \left(-i\right) \]

   8. Simplified 54.3%

      \[\leadsto \color{blue}{\left(y \cdot j\right) \cdot \left(-i\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 42.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+70}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-202}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+44}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+163}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 30.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;i \leq -4.5 \cdot 10^{-114}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 5 \cdot 10^{-248}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 6.2 \cdot 10^{-94}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 5.5 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* x z))))
   (if (<= i -4.5e-114)
     (* t (* b i))
     (if (<= i 5e-248)
       t_1
       (if (<= i 6.2e-94)
         (* a (* c j))
         (if (<= i 5.5e+50) t_1 (* b (* t i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (x * z);
	double tmp;
	if (i <= -4.5e-114) {
		tmp = t * (b * i);
	} else if (i <= 5e-248) {
		tmp = t_1;
	} else if (i <= 6.2e-94) {
		tmp = a * (c * j);
	} else if (i <= 5.5e+50) {
		tmp = t_1;
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (x * z)
    if (i <= (-4.5d-114)) then
        tmp = t * (b * i)
    else if (i <= 5d-248) then
        tmp = t_1
    else if (i <= 6.2d-94) then
        tmp = a * (c * j)
    else if (i <= 5.5d+50) then
        tmp = t_1
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (x * z);
	double tmp;
	if (i <= -4.5e-114) {
		tmp = t * (b * i);
	} else if (i <= 5e-248) {
		tmp = t_1;
	} else if (i <= 6.2e-94) {
		tmp = a * (c * j);
	} else if (i <= 5.5e+50) {
		tmp = t_1;
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (x * z)
	tmp = 0
	if i <= -4.5e-114:
		tmp = t * (b * i)
	elif i <= 5e-248:
		tmp = t_1
	elif i <= 6.2e-94:
		tmp = a * (c * j)
	elif i <= 5.5e+50:
		tmp = t_1
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(x * z))
	tmp = 0.0
	if (i <= -4.5e-114)
		tmp = Float64(t * Float64(b * i));
	elseif (i <= 5e-248)
		tmp = t_1;
	elseif (i <= 6.2e-94)
		tmp = Float64(a * Float64(c * j));
	elseif (i <= 5.5e+50)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * (x * z);
	tmp = 0.0;
	if (i <= -4.5e-114)
		tmp = t * (b * i);
	elseif (i <= 5e-248)
		tmp = t_1;
	elseif (i <= 6.2e-94)
		tmp = a * (c * j);
	elseif (i <= 5.5e+50)
		tmp = t_1;
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -4.5e-114], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5e-248], t$95$1, If[LessEqual[i, 6.2e-94], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5.5e+50], t$95$1, N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -4.49999999999999969e-114

   1. Initial program 71.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 61.0%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 61.0%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   5. Simplified 61.0%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   6. Taylor expanded in j around 0 39.8%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 39.8%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   8. Simplified 39.8%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]

   9. Taylor expanded in b around 0 39.8%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 40.7%

          \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot t} \]

       2. *-commutative 40.7%

          \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]

   11. Simplified 40.7%

       \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]

   if -4.49999999999999969e-114 < i < 5.0000000000000001e-248 or 6.1999999999999996e-94 < i < 5.4999999999999998e50

   1. Initial program 75.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 71.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + \left(-1 \cdot \frac{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(c \cdot j\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}{y} + i \cdot j\right)\right)\right)} \]

   5. Simplified 71.9%

      \[\leadsto \color{blue}{\left(\left(j \cdot i - \frac{a \cdot \left(j \cdot c - t \cdot x\right) + b \cdot \left(i \cdot t - c \cdot z\right)}{y}\right) - z \cdot x\right) \cdot \left(-y\right)} \]

   6. Taylor expanded in x around inf 55.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(z + -1 \cdot \frac{a \cdot t}{y}\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r/ 55.3%

         \[\leadsto x \cdot \left(y \cdot \left(z + \color{blue}{\frac{-1 \cdot \left(a \cdot t\right)}{y}}\right)\right) \]

      2. associate-*r* 55.3%

         \[\leadsto x \cdot \left(y \cdot \left(z + \frac{\color{blue}{\left(-1 \cdot a\right) \cdot t}}{y}\right)\right) \]

      3. neg-mul-1 55.3%

         \[\leadsto x \cdot \left(y \cdot \left(z + \frac{\color{blue}{\left(-a\right)} \cdot t}{y}\right)\right) \]

   8. Simplified 55.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(z + \frac{\left(-a\right) \cdot t}{y}\right)\right)} \]

   9. Taylor expanded in y around inf 35.0%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   10. Step-by-step derivation

       1. *-commutative 35.0%

          \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

       2. associate-*l* 37.9%

          \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   11. Simplified 37.9%

       \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if 5.0000000000000001e-248 < i < 6.1999999999999996e-94

   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 43.4%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 43.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 43.4%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 43.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 43.4%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 43.4%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around inf 25.0%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

   if 5.4999999999999998e50 < i

   1. Initial program 63.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 63.2%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 63.2%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   5. Simplified 63.2%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   6. Taylor expanded in j around 0 40.2%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 40.2%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   8. Simplified 40.2%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 37.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4.5 \cdot 10^{-114}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 5 \cdot 10^{-248}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 6.2 \cdot 10^{-94}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 5.5 \cdot 10^{+50}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 30.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;i \leq -2.55 \cdot 10^{-114}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 1.06 \cdot 10^{-246}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 5.4 \cdot 10^{-94}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;i \leq 1.8 \cdot 10^{+54}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* x z))))
   (if (<= i -2.55e-114)
     (* t (* b i))
     (if (<= i 1.06e-246)
       t_1
       (if (<= i 5.4e-94)
         (* j (* a c))
         (if (<= i 1.8e+54) t_1 (* b (* t i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (x * z);
	double tmp;
	if (i <= -2.55e-114) {
		tmp = t * (b * i);
	} else if (i <= 1.06e-246) {
		tmp = t_1;
	} else if (i <= 5.4e-94) {
		tmp = j * (a * c);
	} else if (i <= 1.8e+54) {
		tmp = t_1;
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (x * z)
    if (i <= (-2.55d-114)) then
        tmp = t * (b * i)
    else if (i <= 1.06d-246) then
        tmp = t_1
    else if (i <= 5.4d-94) then
        tmp = j * (a * c)
    else if (i <= 1.8d+54) then
        tmp = t_1
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (x * z);
	double tmp;
	if (i <= -2.55e-114) {
		tmp = t * (b * i);
	} else if (i <= 1.06e-246) {
		tmp = t_1;
	} else if (i <= 5.4e-94) {
		tmp = j * (a * c);
	} else if (i <= 1.8e+54) {
		tmp = t_1;
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (x * z)
	tmp = 0
	if i <= -2.55e-114:
		tmp = t * (b * i)
	elif i <= 1.06e-246:
		tmp = t_1
	elif i <= 5.4e-94:
		tmp = j * (a * c)
	elif i <= 1.8e+54:
		tmp = t_1
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(x * z))
	tmp = 0.0
	if (i <= -2.55e-114)
		tmp = Float64(t * Float64(b * i));
	elseif (i <= 1.06e-246)
		tmp = t_1;
	elseif (i <= 5.4e-94)
		tmp = Float64(j * Float64(a * c));
	elseif (i <= 1.8e+54)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * (x * z);
	tmp = 0.0;
	if (i <= -2.55e-114)
		tmp = t * (b * i);
	elseif (i <= 1.06e-246)
		tmp = t_1;
	elseif (i <= 5.4e-94)
		tmp = j * (a * c);
	elseif (i <= 1.8e+54)
		tmp = t_1;
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.55e-114], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.06e-246], t$95$1, If[LessEqual[i, 5.4e-94], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.8e+54], t$95$1, N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -2.55e-114

   1. Initial program 71.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 61.0%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 61.0%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   5. Simplified 61.0%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   6. Taylor expanded in j around 0 39.8%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 39.8%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   8. Simplified 39.8%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]

   9. Taylor expanded in b around 0 39.8%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 40.7%

          \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot t} \]

       2. *-commutative 40.7%

          \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]

   11. Simplified 40.7%

       \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]

   if -2.55e-114 < i < 1.06e-246 or 5.4000000000000002e-94 < i < 1.8000000000000001e54

   1. Initial program 75.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 71.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + \left(-1 \cdot \frac{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(c \cdot j\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}{y} + i \cdot j\right)\right)\right)} \]

   5. Simplified 71.9%

      \[\leadsto \color{blue}{\left(\left(j \cdot i - \frac{a \cdot \left(j \cdot c - t \cdot x\right) + b \cdot \left(i \cdot t - c \cdot z\right)}{y}\right) - z \cdot x\right) \cdot \left(-y\right)} \]

   6. Taylor expanded in x around inf 55.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(z + -1 \cdot \frac{a \cdot t}{y}\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r/ 55.3%

         \[\leadsto x \cdot \left(y \cdot \left(z + \color{blue}{\frac{-1 \cdot \left(a \cdot t\right)}{y}}\right)\right) \]

      2. associate-*r* 55.3%

         \[\leadsto x \cdot \left(y \cdot \left(z + \frac{\color{blue}{\left(-1 \cdot a\right) \cdot t}}{y}\right)\right) \]

      3. neg-mul-1 55.3%

         \[\leadsto x \cdot \left(y \cdot \left(z + \frac{\color{blue}{\left(-a\right)} \cdot t}{y}\right)\right) \]

   8. Simplified 55.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(z + \frac{\left(-a\right) \cdot t}{y}\right)\right)} \]

   9. Taylor expanded in y around inf 35.0%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   10. Step-by-step derivation

       1. *-commutative 35.0%

          \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

       2. associate-*l* 37.9%

          \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   11. Simplified 37.9%

       \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if 1.06e-246 < i < 5.4000000000000002e-94

   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 43.4%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 43.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 43.4%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 43.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 43.4%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 43.4%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in t around inf 43.3%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + \frac{a \cdot \left(c \cdot j\right)}{t}\right)} \]
   7. Step-by-step derivation

      1. +-commutative 43.3%

         \[\leadsto t \cdot \color{blue}{\left(\frac{a \cdot \left(c \cdot j\right)}{t} + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 43.3%

         \[\leadsto t \cdot \left(\frac{a \cdot \left(c \cdot j\right)}{t} + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 43.3%

         \[\leadsto t \cdot \color{blue}{\left(\frac{a \cdot \left(c \cdot j\right)}{t} - a \cdot x\right)} \]

      4. associate-/l* 43.3%

         \[\leadsto t \cdot \left(\color{blue}{a \cdot \frac{c \cdot j}{t}} - a \cdot x\right) \]

      5. associate-/l* 49.4%

         \[\leadsto t \cdot \left(a \cdot \color{blue}{\left(c \cdot \frac{j}{t}\right)} - a \cdot x\right) \]

      6. *-commutative 49.4%

         \[\leadsto t \cdot \left(a \cdot \left(c \cdot \frac{j}{t}\right) - \color{blue}{x \cdot a}\right) \]

   8. Simplified 49.4%

      \[\leadsto \color{blue}{t \cdot \left(a \cdot \left(c \cdot \frac{j}{t}\right) - x \cdot a\right)} \]

   9. Taylor expanded in t around 0 25.0%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 40.3%

          \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]

       2. *-commutative 40.3%

          \[\leadsto \color{blue}{\left(c \cdot a\right)} \cdot j \]

   11. Simplified 40.3%

       \[\leadsto \color{blue}{\left(c \cdot a\right) \cdot j} \]

   if 1.8000000000000001e54 < i

   1. Initial program 63.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 63.2%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 63.2%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   5. Simplified 63.2%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   6. Taylor expanded in j around 0 40.2%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 40.2%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   8. Simplified 40.2%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.55 \cdot 10^{-114}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 1.06 \cdot 10^{-246}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 5.4 \cdot 10^{-94}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;i \leq 1.8 \cdot 10^{+54}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 30.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -3.25 \cdot 10^{-114}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 1.45 \cdot 10^{-243}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 6.5 \cdot 10^{-95}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;i \leq 1.85 \cdot 10^{+48}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -3.25e-114)
   (* t (* b i))
   (if (<= i 1.45e-243)
     (* y (* x z))
     (if (<= i 6.5e-95)
       (* j (* a c))
       (if (<= i 1.85e+48) (* x (* y z)) (* b (* t i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -3.25e-114) {
		tmp = t * (b * i);
	} else if (i <= 1.45e-243) {
		tmp = y * (x * z);
	} else if (i <= 6.5e-95) {
		tmp = j * (a * c);
	} else if (i <= 1.85e+48) {
		tmp = x * (y * z);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (i <= (-3.25d-114)) then
        tmp = t * (b * i)
    else if (i <= 1.45d-243) then
        tmp = y * (x * z)
    else if (i <= 6.5d-95) then
        tmp = j * (a * c)
    else if (i <= 1.85d+48) then
        tmp = x * (y * z)
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -3.25e-114) {
		tmp = t * (b * i);
	} else if (i <= 1.45e-243) {
		tmp = y * (x * z);
	} else if (i <= 6.5e-95) {
		tmp = j * (a * c);
	} else if (i <= 1.85e+48) {
		tmp = x * (y * z);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -3.25e-114:
		tmp = t * (b * i)
	elif i <= 1.45e-243:
		tmp = y * (x * z)
	elif i <= 6.5e-95:
		tmp = j * (a * c)
	elif i <= 1.85e+48:
		tmp = x * (y * z)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -3.25e-114)
		tmp = Float64(t * Float64(b * i));
	elseif (i <= 1.45e-243)
		tmp = Float64(y * Float64(x * z));
	elseif (i <= 6.5e-95)
		tmp = Float64(j * Float64(a * c));
	elseif (i <= 1.85e+48)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -3.25e-114)
		tmp = t * (b * i);
	elseif (i <= 1.45e-243)
		tmp = y * (x * z);
	elseif (i <= 6.5e-95)
		tmp = j * (a * c);
	elseif (i <= 1.85e+48)
		tmp = x * (y * z);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -3.25e-114], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.45e-243], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 6.5e-95], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.85e+48], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -3.2499999999999999e-114

   1. Initial program 71.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 61.0%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 61.0%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   5. Simplified 61.0%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   6. Taylor expanded in j around 0 39.8%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 39.8%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   8. Simplified 39.8%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]

   9. Taylor expanded in b around 0 39.8%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 40.7%

          \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot t} \]

       2. *-commutative 40.7%

          \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]

   11. Simplified 40.7%

       \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]

   if -3.2499999999999999e-114 < i < 1.44999999999999988e-243

   1. Initial program 79.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 74.3%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + \left(-1 \cdot \frac{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(c \cdot j\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}{y} + i \cdot j\right)\right)\right)} \]

   5. Simplified 74.3%

      \[\leadsto \color{blue}{\left(\left(j \cdot i - \frac{a \cdot \left(j \cdot c - t \cdot x\right) + b \cdot \left(i \cdot t - c \cdot z\right)}{y}\right) - z \cdot x\right) \cdot \left(-y\right)} \]

   6. Taylor expanded in x around inf 55.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(z + -1 \cdot \frac{a \cdot t}{y}\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r/ 55.9%

         \[\leadsto x \cdot \left(y \cdot \left(z + \color{blue}{\frac{-1 \cdot \left(a \cdot t\right)}{y}}\right)\right) \]

      2. associate-*r* 55.9%

         \[\leadsto x \cdot \left(y \cdot \left(z + \frac{\color{blue}{\left(-1 \cdot a\right) \cdot t}}{y}\right)\right) \]

      3. neg-mul-1 55.9%

         \[\leadsto x \cdot \left(y \cdot \left(z + \frac{\color{blue}{\left(-a\right)} \cdot t}{y}\right)\right) \]

   8. Simplified 55.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(z + \frac{\left(-a\right) \cdot t}{y}\right)\right)} \]

   9. Taylor expanded in y around inf 35.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   10. Step-by-step derivation

       1. *-commutative 35.1%

          \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

       2. associate-*l* 39.6%

          \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   11. Simplified 39.6%

       \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if 1.44999999999999988e-243 < i < 6.49999999999999985e-95

   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 43.4%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 43.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 43.4%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 43.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 43.4%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 43.4%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in t around inf 43.3%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + \frac{a \cdot \left(c \cdot j\right)}{t}\right)} \]
   7. Step-by-step derivation

      1. +-commutative 43.3%

         \[\leadsto t \cdot \color{blue}{\left(\frac{a \cdot \left(c \cdot j\right)}{t} + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 43.3%

         \[\leadsto t \cdot \left(\frac{a \cdot \left(c \cdot j\right)}{t} + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 43.3%

         \[\leadsto t \cdot \color{blue}{\left(\frac{a \cdot \left(c \cdot j\right)}{t} - a \cdot x\right)} \]

      4. associate-/l* 43.3%

         \[\leadsto t \cdot \left(\color{blue}{a \cdot \frac{c \cdot j}{t}} - a \cdot x\right) \]

      5. associate-/l* 49.4%

         \[\leadsto t \cdot \left(a \cdot \color{blue}{\left(c \cdot \frac{j}{t}\right)} - a \cdot x\right) \]

      6. *-commutative 49.4%

         \[\leadsto t \cdot \left(a \cdot \left(c \cdot \frac{j}{t}\right) - \color{blue}{x \cdot a}\right) \]

   8. Simplified 49.4%

      \[\leadsto \color{blue}{t \cdot \left(a \cdot \left(c \cdot \frac{j}{t}\right) - x \cdot a\right)} \]

   9. Taylor expanded in t around 0 25.0%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 40.3%

          \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]

       2. *-commutative 40.3%

          \[\leadsto \color{blue}{\left(c \cdot a\right)} \cdot j \]

   11. Simplified 40.3%

       \[\leadsto \color{blue}{\left(c \cdot a\right) \cdot j} \]

   if 6.49999999999999985e-95 < i < 1.85e48

   1. Initial program 66.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 67.4%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + \left(-1 \cdot \frac{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(c \cdot j\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}{y} + i \cdot j\right)\right)\right)} \]

   5. Simplified 67.4%

      \[\leadsto \color{blue}{\left(\left(j \cdot i - \frac{a \cdot \left(j \cdot c - t \cdot x\right) + b \cdot \left(i \cdot t - c \cdot z\right)}{y}\right) - z \cdot x\right) \cdot \left(-y\right)} \]

   6. Taylor expanded in x around inf 54.0%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(z + -1 \cdot \frac{a \cdot t}{y}\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r/ 54.0%

         \[\leadsto x \cdot \left(y \cdot \left(z + \color{blue}{\frac{-1 \cdot \left(a \cdot t\right)}{y}}\right)\right) \]

      2. associate-*r* 54.0%

         \[\leadsto x \cdot \left(y \cdot \left(z + \frac{\color{blue}{\left(-1 \cdot a\right) \cdot t}}{y}\right)\right) \]

      3. neg-mul-1 54.0%

         \[\leadsto x \cdot \left(y \cdot \left(z + \frac{\color{blue}{\left(-a\right)} \cdot t}{y}\right)\right) \]

   8. Simplified 54.0%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(z + \frac{\left(-a\right) \cdot t}{y}\right)\right)} \]

   9. Taylor expanded in y around inf 34.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   10. Step-by-step derivation

       1. *-commutative 34.9%

          \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

   11. Simplified 34.9%

       \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

   if 1.85e48 < i

   1. Initial program 63.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 63.2%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 63.2%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   5. Simplified 63.2%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   6. Taylor expanded in j around 0 40.2%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 40.2%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   8. Simplified 40.2%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.25 \cdot 10^{-114}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 1.45 \cdot 10^{-243}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 6.5 \cdot 10^{-95}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;i \leq 1.85 \cdot 10^{+48}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 29.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -4.2 \cdot 10^{-159} \lor \neg \left(i \leq 1.6 \cdot 10^{+59}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -4.2e-159) (not (<= i 1.6e+59))) (* b (* t i)) (* a (* c j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -4.2e-159) || !(i <= 1.6e+59)) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((i <= (-4.2d-159)) .or. (.not. (i <= 1.6d+59))) then
        tmp = b * (t * i)
    else
        tmp = a * (c * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -4.2e-159) || !(i <= 1.6e+59)) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (i <= -4.2e-159) or not (i <= 1.6e+59):
		tmp = b * (t * i)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((i <= -4.2e-159) || !(i <= 1.6e+59))
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(a * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((i <= -4.2e-159) || ~((i <= 1.6e+59)))
		tmp = b * (t * i);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[i, -4.2e-159], N[Not[LessEqual[i, 1.6e+59]], $MachinePrecision]], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -4.1999999999999998e-159 or 1.59999999999999991e59 < i

   1. Initial program 69.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 58.3%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 58.3%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   5. Simplified 58.3%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   6. Taylor expanded in j around 0 38.0%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 38.0%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   8. Simplified 38.0%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]

   if -4.1999999999999998e-159 < i < 1.59999999999999991e59

   1. Initial program 76.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 46.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 46.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 46.5%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 46.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 46.5%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 46.5%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around inf 26.2%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 33.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4.2 \cdot 10^{-159} \lor \neg \left(i \leq 1.6 \cdot 10^{+59}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 29.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -4.6 \cdot 10^{-155}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 1.7 \cdot 10^{+59}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -4.6e-155)
   (* t (* b i))
   (if (<= i 1.7e+59) (* a (* c j)) (* b (* t i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -4.6e-155) {
		tmp = t * (b * i);
	} else if (i <= 1.7e+59) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (i <= (-4.6d-155)) then
        tmp = t * (b * i)
    else if (i <= 1.7d+59) then
        tmp = a * (c * j)
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -4.6e-155) {
		tmp = t * (b * i);
	} else if (i <= 1.7e+59) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -4.6e-155:
		tmp = t * (b * i)
	elif i <= 1.7e+59:
		tmp = a * (c * j)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -4.6e-155)
		tmp = Float64(t * Float64(b * i));
	elseif (i <= 1.7e+59)
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -4.6e-155)
		tmp = t * (b * i);
	elseif (i <= 1.7e+59)
		tmp = a * (c * j);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -4.6e-155], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.7e+59], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if i < -4.60000000000000011e-155

   1. Initial program 72.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 55.7%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 55.7%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   5. Simplified 55.7%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   6. Taylor expanded in j around 0 37.0%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 37.0%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   8. Simplified 37.0%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]

   9. Taylor expanded in b around 0 37.0%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 37.9%

          \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot t} \]

       2. *-commutative 37.9%

          \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]

   11. Simplified 37.9%

       \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]

   if -4.60000000000000011e-155 < i < 1.70000000000000003e59

   1. Initial program 76.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 46.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 46.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 46.5%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 46.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 46.5%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 46.5%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around inf 26.2%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

   if 1.70000000000000003e59 < i

   1. Initial program 61.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 64.3%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 64.3%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   5. Simplified 64.3%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   6. Taylor expanded in j around 0 40.2%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 40.2%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   8. Simplified 40.2%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 33.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4.6 \cdot 10^{-155}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 1.7 \cdot 10^{+59}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 21.8% 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 72.4%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
2. Add Preprocessing

3. Taylor expanded in a around inf 36.5%

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
4. Step-by-step derivation

   1. +-commutative 36.5%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

   2. mul-1-neg 36.5%

      \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

   3. unsub-neg 36.5%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. *-commutative 36.5%

      \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

5. Simplified 36.5%

   \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

6. Taylor expanded in j around inf 17.8%

   \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

7. Final simplification 17.8%

   \[\leadsto a \cdot \left(c \cdot j\right) \]
8. Add Preprocessing

Developer target: 59.7% 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 2024055 
(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)))))