Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.5% → 83.6%

Time: 26.2s

Alternatives: 27

Speedup: 0.5×

• 57.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 83.6% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 90.6%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in c around 0 26.1%

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

   4. Taylor expanded in i around -inf 42.2%

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

   5. Taylor expanded in a around inf 56.4%

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

      1. associate-*r/ 56.4%

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

      2. mul-1-neg 56.4%

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

      3. distribute-rgt-neg-in 56.4%

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

      4. distribute-rgt-neg-in 56.4%

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

   7. Simplified 56.4%

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

4. Final simplification 83.9%

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

Alternative 2: 29.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i\right)\\ t_2 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;t \leq -1.8 \cdot 10^{+106}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq -4600000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.22 \cdot 10^{-233}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.26 \cdot 10^{-272}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-275}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-247}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-191}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-70}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{+79}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* a i))) (t_2 (* y (* x z))))
   (if (<= t -1.8e+106)
     (* t (* c j))
     (if (<= t -4600000.0)
       t_1
       (if (<= t -1.22e-233)
         t_2
         (if (<= t -1.26e-272)
           t_1
           (if (<= t 1.02e-275)
             t_2
             (if (<= t 9.2e-247)
               t_1
               (if (<= t 2.5e-191)
                 (* c (* z (- b)))
                 (if (<= t 1.9e-70)
                   (* i (* a b))
                   (if (<= t 4.7e+79)
                     (* y (* i (- j)))
                     (* c (* t j)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (a * i);
	double t_2 = y * (x * z);
	double tmp;
	if (t <= -1.8e+106) {
		tmp = t * (c * j);
	} else if (t <= -4600000.0) {
		tmp = t_1;
	} else if (t <= -1.22e-233) {
		tmp = t_2;
	} else if (t <= -1.26e-272) {
		tmp = t_1;
	} else if (t <= 1.02e-275) {
		tmp = t_2;
	} else if (t <= 9.2e-247) {
		tmp = t_1;
	} else if (t <= 2.5e-191) {
		tmp = c * (z * -b);
	} else if (t <= 1.9e-70) {
		tmp = i * (a * b);
	} else if (t <= 4.7e+79) {
		tmp = y * (i * -j);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (a * i)
    t_2 = y * (x * z)
    if (t <= (-1.8d+106)) then
        tmp = t * (c * j)
    else if (t <= (-4600000.0d0)) then
        tmp = t_1
    else if (t <= (-1.22d-233)) then
        tmp = t_2
    else if (t <= (-1.26d-272)) then
        tmp = t_1
    else if (t <= 1.02d-275) then
        tmp = t_2
    else if (t <= 9.2d-247) then
        tmp = t_1
    else if (t <= 2.5d-191) then
        tmp = c * (z * -b)
    else if (t <= 1.9d-70) then
        tmp = i * (a * b)
    else if (t <= 4.7d+79) then
        tmp = y * (i * -j)
    else
        tmp = c * (t * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (a * i);
	double t_2 = y * (x * z);
	double tmp;
	if (t <= -1.8e+106) {
		tmp = t * (c * j);
	} else if (t <= -4600000.0) {
		tmp = t_1;
	} else if (t <= -1.22e-233) {
		tmp = t_2;
	} else if (t <= -1.26e-272) {
		tmp = t_1;
	} else if (t <= 1.02e-275) {
		tmp = t_2;
	} else if (t <= 9.2e-247) {
		tmp = t_1;
	} else if (t <= 2.5e-191) {
		tmp = c * (z * -b);
	} else if (t <= 1.9e-70) {
		tmp = i * (a * b);
	} else if (t <= 4.7e+79) {
		tmp = y * (i * -j);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (a * i)
	t_2 = y * (x * z)
	tmp = 0
	if t <= -1.8e+106:
		tmp = t * (c * j)
	elif t <= -4600000.0:
		tmp = t_1
	elif t <= -1.22e-233:
		tmp = t_2
	elif t <= -1.26e-272:
		tmp = t_1
	elif t <= 1.02e-275:
		tmp = t_2
	elif t <= 9.2e-247:
		tmp = t_1
	elif t <= 2.5e-191:
		tmp = c * (z * -b)
	elif t <= 1.9e-70:
		tmp = i * (a * b)
	elif t <= 4.7e+79:
		tmp = y * (i * -j)
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(a * i))
	t_2 = Float64(y * Float64(x * z))
	tmp = 0.0
	if (t <= -1.8e+106)
		tmp = Float64(t * Float64(c * j));
	elseif (t <= -4600000.0)
		tmp = t_1;
	elseif (t <= -1.22e-233)
		tmp = t_2;
	elseif (t <= -1.26e-272)
		tmp = t_1;
	elseif (t <= 1.02e-275)
		tmp = t_2;
	elseif (t <= 9.2e-247)
		tmp = t_1;
	elseif (t <= 2.5e-191)
		tmp = Float64(c * Float64(z * Float64(-b)));
	elseif (t <= 1.9e-70)
		tmp = Float64(i * Float64(a * b));
	elseif (t <= 4.7e+79)
		tmp = Float64(y * Float64(i * Float64(-j)));
	else
		tmp = Float64(c * Float64(t * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (a * i);
	t_2 = y * (x * z);
	tmp = 0.0;
	if (t <= -1.8e+106)
		tmp = t * (c * j);
	elseif (t <= -4600000.0)
		tmp = t_1;
	elseif (t <= -1.22e-233)
		tmp = t_2;
	elseif (t <= -1.26e-272)
		tmp = t_1;
	elseif (t <= 1.02e-275)
		tmp = t_2;
	elseif (t <= 9.2e-247)
		tmp = t_1;
	elseif (t <= 2.5e-191)
		tmp = c * (z * -b);
	elseif (t <= 1.9e-70)
		tmp = i * (a * b);
	elseif (t <= 4.7e+79)
		tmp = y * (i * -j);
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.8e+106], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4600000.0], t$95$1, If[LessEqual[t, -1.22e-233], t$95$2, If[LessEqual[t, -1.26e-272], t$95$1, If[LessEqual[t, 1.02e-275], t$95$2, If[LessEqual[t, 9.2e-247], t$95$1, If[LessEqual[t, 2.5e-191], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.9e-70], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.7e+79], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -1.8e106

   1. Initial program 52.0%

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

   3. Taylor expanded in j around inf 49.3%

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

   4. Taylor expanded in t around inf 74.6%

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

      1. associate-*r* 69.9%

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

      2. associate-*r/ 69.9%

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

      3. mul-1-neg 69.9%

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

      4. *-commutative 69.9%

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

   6. Simplified 69.9%

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

   7. Taylor expanded in j around inf 46.3%

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

      1. associate-*r* 48.6%

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

   9. Simplified 48.6%

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

   if -1.8e106 < t < -4.6e6 or -1.21999999999999989e-233 < t < -1.25999999999999995e-272 or 1.01999999999999994e-275 < t < 9.2000000000000001e-247

   1. Initial program 86.2%

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

   3. Taylor expanded in b around inf 67.4%

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

      1. *-commutative 67.4%

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

   5. Simplified 67.4%

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

   6. Taylor expanded in i around inf 59.3%

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

   if -4.6e6 < t < -1.21999999999999989e-233 or -1.25999999999999995e-272 < t < 1.01999999999999994e-275

   1. Initial program 90.3%

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

   3. Taylor expanded in y around inf 59.1%

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

      1. +-commutative 59.1%

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

      2. mul-1-neg 59.1%

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

      3. unsub-neg 59.1%

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

      4. *-commutative 59.1%

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

      5. *-commutative 59.1%

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

   5. Simplified 59.1%

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

   6. Taylor expanded in z around inf 41.7%

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

      1. *-commutative 41.7%

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

   8. Simplified 41.7%

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

   if 9.2000000000000001e-247 < t < 2.5e-191

   1. Initial program 58.3%

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

   3. Taylor expanded in c around inf 82.1%

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

   4. Taylor expanded in j around 0 82.1%

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

      1. neg-mul-1 82.1%

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

      2. distribute-rgt-neg-in 82.1%

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

   6. Simplified 82.1%

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

   if 2.5e-191 < t < 1.8999999999999999e-70

   1. Initial program 69.5%

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

   3. Taylor expanded in c around 0 78.2%

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

   4. Taylor expanded in i around -inf 59.7%

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

      1. associate-*r* 59.7%

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

      2. neg-mul-1 59.7%

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

      3. *-commutative 59.7%

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

   6. Simplified 59.7%

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

   7. Taylor expanded in j around 0 44.8%

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

      1. mul-1-neg 44.8%

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

      2. *-commutative 44.8%

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

      3. distribute-rgt-neg-in 44.8%

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

   9. Simplified 44.8%

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

   if 1.8999999999999999e-70 < t < 4.70000000000000023e79

   1. Initial program 74.7%

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

   3. Taylor expanded in y around inf 52.3%

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

      1. +-commutative 52.3%

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

      2. mul-1-neg 52.3%

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

      3. unsub-neg 52.3%

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

      4. *-commutative 52.3%

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

      5. *-commutative 52.3%

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

   5. Simplified 52.3%

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

   6. Taylor expanded in z around 0 44.0%

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

      1. neg-mul-1 44.0%

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

      2. distribute-lft-neg-in 44.0%

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

   8. Simplified 44.0%

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

   if 4.70000000000000023e79 < t

   1. Initial program 61.8%

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

   3. Taylor expanded in j around inf 59.9%

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

   4. Taylor expanded in t around inf 53.1%

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

      1. associate-*r* 64.5%

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

      2. associate-*r/ 64.5%

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

      3. mul-1-neg 64.5%

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

      4. *-commutative 64.5%

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

   6. Simplified 64.5%

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

   7. Taylor expanded in c around inf 44.2%

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

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+106}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq -4600000:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;t \leq -1.22 \cdot 10^{-233}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq -1.26 \cdot 10^{-272}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-275}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-247}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-191}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-70}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{+79}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 29.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i\right)\\ t_2 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;t \leq -1 \cdot 10^{+105}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq -8200000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3.15 \cdot 10^{-235}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -8.4 \cdot 10^{-274}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-273}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-246}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-191}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-73}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{+78}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* a i))) (t_2 (* y (* x z))))
   (if (<= t -1e+105)
     (* t (* c j))
     (if (<= t -8200000.0)
       t_1
       (if (<= t -3.15e-235)
         t_2
         (if (<= t -8.4e-274)
           t_1
           (if (<= t 1.25e-273)
             t_2
             (if (<= t 1.7e-246)
               t_1
               (if (<= t 2.5e-191)
                 (* c (* z (- b)))
                 (if (<= t 7e-73)
                   t_1
                   (if (<= t 4.1e+78)
                     (* y (* i (- j)))
                     (* c (* t j)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (a * i);
	double t_2 = y * (x * z);
	double tmp;
	if (t <= -1e+105) {
		tmp = t * (c * j);
	} else if (t <= -8200000.0) {
		tmp = t_1;
	} else if (t <= -3.15e-235) {
		tmp = t_2;
	} else if (t <= -8.4e-274) {
		tmp = t_1;
	} else if (t <= 1.25e-273) {
		tmp = t_2;
	} else if (t <= 1.7e-246) {
		tmp = t_1;
	} else if (t <= 2.5e-191) {
		tmp = c * (z * -b);
	} else if (t <= 7e-73) {
		tmp = t_1;
	} else if (t <= 4.1e+78) {
		tmp = y * (i * -j);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (a * i)
    t_2 = y * (x * z)
    if (t <= (-1d+105)) then
        tmp = t * (c * j)
    else if (t <= (-8200000.0d0)) then
        tmp = t_1
    else if (t <= (-3.15d-235)) then
        tmp = t_2
    else if (t <= (-8.4d-274)) then
        tmp = t_1
    else if (t <= 1.25d-273) then
        tmp = t_2
    else if (t <= 1.7d-246) then
        tmp = t_1
    else if (t <= 2.5d-191) then
        tmp = c * (z * -b)
    else if (t <= 7d-73) then
        tmp = t_1
    else if (t <= 4.1d+78) then
        tmp = y * (i * -j)
    else
        tmp = c * (t * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (a * i);
	double t_2 = y * (x * z);
	double tmp;
	if (t <= -1e+105) {
		tmp = t * (c * j);
	} else if (t <= -8200000.0) {
		tmp = t_1;
	} else if (t <= -3.15e-235) {
		tmp = t_2;
	} else if (t <= -8.4e-274) {
		tmp = t_1;
	} else if (t <= 1.25e-273) {
		tmp = t_2;
	} else if (t <= 1.7e-246) {
		tmp = t_1;
	} else if (t <= 2.5e-191) {
		tmp = c * (z * -b);
	} else if (t <= 7e-73) {
		tmp = t_1;
	} else if (t <= 4.1e+78) {
		tmp = y * (i * -j);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (a * i)
	t_2 = y * (x * z)
	tmp = 0
	if t <= -1e+105:
		tmp = t * (c * j)
	elif t <= -8200000.0:
		tmp = t_1
	elif t <= -3.15e-235:
		tmp = t_2
	elif t <= -8.4e-274:
		tmp = t_1
	elif t <= 1.25e-273:
		tmp = t_2
	elif t <= 1.7e-246:
		tmp = t_1
	elif t <= 2.5e-191:
		tmp = c * (z * -b)
	elif t <= 7e-73:
		tmp = t_1
	elif t <= 4.1e+78:
		tmp = y * (i * -j)
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(a * i))
	t_2 = Float64(y * Float64(x * z))
	tmp = 0.0
	if (t <= -1e+105)
		tmp = Float64(t * Float64(c * j));
	elseif (t <= -8200000.0)
		tmp = t_1;
	elseif (t <= -3.15e-235)
		tmp = t_2;
	elseif (t <= -8.4e-274)
		tmp = t_1;
	elseif (t <= 1.25e-273)
		tmp = t_2;
	elseif (t <= 1.7e-246)
		tmp = t_1;
	elseif (t <= 2.5e-191)
		tmp = Float64(c * Float64(z * Float64(-b)));
	elseif (t <= 7e-73)
		tmp = t_1;
	elseif (t <= 4.1e+78)
		tmp = Float64(y * Float64(i * Float64(-j)));
	else
		tmp = Float64(c * Float64(t * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (a * i);
	t_2 = y * (x * z);
	tmp = 0.0;
	if (t <= -1e+105)
		tmp = t * (c * j);
	elseif (t <= -8200000.0)
		tmp = t_1;
	elseif (t <= -3.15e-235)
		tmp = t_2;
	elseif (t <= -8.4e-274)
		tmp = t_1;
	elseif (t <= 1.25e-273)
		tmp = t_2;
	elseif (t <= 1.7e-246)
		tmp = t_1;
	elseif (t <= 2.5e-191)
		tmp = c * (z * -b);
	elseif (t <= 7e-73)
		tmp = t_1;
	elseif (t <= 4.1e+78)
		tmp = y * (i * -j);
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1e+105], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -8200000.0], t$95$1, If[LessEqual[t, -3.15e-235], t$95$2, If[LessEqual[t, -8.4e-274], t$95$1, If[LessEqual[t, 1.25e-273], t$95$2, If[LessEqual[t, 1.7e-246], t$95$1, If[LessEqual[t, 2.5e-191], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e-73], t$95$1, If[LessEqual[t, 4.1e+78], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -9.9999999999999994e104

   1. Initial program 52.0%

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

   3. Taylor expanded in j around inf 49.3%

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

   4. Taylor expanded in t around inf 74.6%

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

      1. associate-*r* 69.9%

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

      2. associate-*r/ 69.9%

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

      3. mul-1-neg 69.9%

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

      4. *-commutative 69.9%

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

   6. Simplified 69.9%

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

   7. Taylor expanded in j around inf 46.3%

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

      1. associate-*r* 48.6%

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

   9. Simplified 48.6%

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

   if -9.9999999999999994e104 < t < -8.2e6 or -3.1499999999999997e-235 < t < -8.39999999999999977e-274 or 1.24999999999999991e-273 < t < 1.7000000000000001e-246 or 2.5e-191 < t < 6.9999999999999995e-73

   1. Initial program 79.7%

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

   3. Taylor expanded in b around inf 61.8%

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

      1. *-commutative 61.8%

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

   5. Simplified 61.8%

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

   6. Taylor expanded in i around inf 53.6%

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

   if -8.2e6 < t < -3.1499999999999997e-235 or -8.39999999999999977e-274 < t < 1.24999999999999991e-273

   1. Initial program 90.3%

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

   3. Taylor expanded in y around inf 59.1%

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

      1. +-commutative 59.1%

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

      2. mul-1-neg 59.1%

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

      3. unsub-neg 59.1%

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

      4. *-commutative 59.1%

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

      5. *-commutative 59.1%

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

   5. Simplified 59.1%

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

   6. Taylor expanded in z around inf 41.7%

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

      1. *-commutative 41.7%

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

   8. Simplified 41.7%

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

   if 1.7000000000000001e-246 < t < 2.5e-191

   1. Initial program 58.3%

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

   3. Taylor expanded in c around inf 82.1%

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

   4. Taylor expanded in j around 0 82.1%

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

      1. neg-mul-1 82.1%

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

      2. distribute-rgt-neg-in 82.1%

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

   6. Simplified 82.1%

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

   if 6.9999999999999995e-73 < t < 4.0999999999999997e78

   1. Initial program 74.7%

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

   3. Taylor expanded in y around inf 52.3%

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

      1. +-commutative 52.3%

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

      2. mul-1-neg 52.3%

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

      3. unsub-neg 52.3%

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

      4. *-commutative 52.3%

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

      5. *-commutative 52.3%

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

   5. Simplified 52.3%

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

   6. Taylor expanded in z around 0 44.0%

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

      1. neg-mul-1 44.0%

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

      2. distribute-lft-neg-in 44.0%

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

   8. Simplified 44.0%

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

   if 4.0999999999999997e78 < t

   1. Initial program 61.8%

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

   3. Taylor expanded in j around inf 59.9%

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

   4. Taylor expanded in t around inf 53.1%

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

      1. associate-*r* 64.5%

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

      2. associate-*r/ 64.5%

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

      3. mul-1-neg 64.5%

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

      4. *-commutative 64.5%

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

   6. Simplified 64.5%

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

   7. Taylor expanded in c around inf 44.2%

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

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+105}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq -8200000:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;t \leq -3.15 \cdot 10^{-235}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq -8.4 \cdot 10^{-274}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-273}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-246}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-191}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-73}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{+78}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 49.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := \left(i \cdot j\right) \cdot \left(a \cdot \frac{b}{j} - y\right)\\ t_3 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{+75}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{+15}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-306}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-226}:\\ \;\;\;\;i \cdot \left(b \cdot \left(a - \frac{y \cdot j}{b}\right)\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-32}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{+95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+206}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a))))
        (t_2 (* (* i j) (- (* a (/ b j)) y)))
        (t_3 (* z (- (* x y) (* b c)))))
   (if (<= z -2.1e+75)
     t_3
     (if (<= z -4.8e+15)
       t_2
       (if (<= z 5.6e-306)
         t_1
         (if (<= z 5.1e-226)
           (* i (* b (- a (/ (* y j) b))))
           (if (<= z 4.5e-137)
             t_1
             (if (<= z 1.4e-32)
               (* i (- (* a b) (* y j)))
               (if (<= z 1.32e+95) t_1 (if (<= z 1.5e+206) 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 = t * ((c * j) - (x * a));
	double t_2 = (i * j) * ((a * (b / j)) - y);
	double t_3 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -2.1e+75) {
		tmp = t_3;
	} else if (z <= -4.8e+15) {
		tmp = t_2;
	} else if (z <= 5.6e-306) {
		tmp = t_1;
	} else if (z <= 5.1e-226) {
		tmp = i * (b * (a - ((y * j) / b)));
	} else if (z <= 4.5e-137) {
		tmp = t_1;
	} else if (z <= 1.4e-32) {
		tmp = i * ((a * b) - (y * j));
	} else if (z <= 1.32e+95) {
		tmp = t_1;
	} else if (z <= 1.5e+206) {
		tmp = 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) :: tmp
    t_1 = t * ((c * j) - (x * a))
    t_2 = (i * j) * ((a * (b / j)) - y)
    t_3 = z * ((x * y) - (b * c))
    if (z <= (-2.1d+75)) then
        tmp = t_3
    else if (z <= (-4.8d+15)) then
        tmp = t_2
    else if (z <= 5.6d-306) then
        tmp = t_1
    else if (z <= 5.1d-226) then
        tmp = i * (b * (a - ((y * j) / b)))
    else if (z <= 4.5d-137) then
        tmp = t_1
    else if (z <= 1.4d-32) then
        tmp = i * ((a * b) - (y * j))
    else if (z <= 1.32d+95) then
        tmp = t_1
    else if (z <= 1.5d+206) then
        tmp = 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 = t * ((c * j) - (x * a));
	double t_2 = (i * j) * ((a * (b / j)) - y);
	double t_3 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -2.1e+75) {
		tmp = t_3;
	} else if (z <= -4.8e+15) {
		tmp = t_2;
	} else if (z <= 5.6e-306) {
		tmp = t_1;
	} else if (z <= 5.1e-226) {
		tmp = i * (b * (a - ((y * j) / b)));
	} else if (z <= 4.5e-137) {
		tmp = t_1;
	} else if (z <= 1.4e-32) {
		tmp = i * ((a * b) - (y * j));
	} else if (z <= 1.32e+95) {
		tmp = t_1;
	} else if (z <= 1.5e+206) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	t_2 = (i * j) * ((a * (b / j)) - y)
	t_3 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -2.1e+75:
		tmp = t_3
	elif z <= -4.8e+15:
		tmp = t_2
	elif z <= 5.6e-306:
		tmp = t_1
	elif z <= 5.1e-226:
		tmp = i * (b * (a - ((y * j) / b)))
	elif z <= 4.5e-137:
		tmp = t_1
	elif z <= 1.4e-32:
		tmp = i * ((a * b) - (y * j))
	elif z <= 1.32e+95:
		tmp = t_1
	elif z <= 1.5e+206:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_2 = Float64(Float64(i * j) * Float64(Float64(a * Float64(b / j)) - y))
	t_3 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (z <= -2.1e+75)
		tmp = t_3;
	elseif (z <= -4.8e+15)
		tmp = t_2;
	elseif (z <= 5.6e-306)
		tmp = t_1;
	elseif (z <= 5.1e-226)
		tmp = Float64(i * Float64(b * Float64(a - Float64(Float64(y * j) / b))));
	elseif (z <= 4.5e-137)
		tmp = t_1;
	elseif (z <= 1.4e-32)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (z <= 1.32e+95)
		tmp = t_1;
	elseif (z <= 1.5e+206)
		tmp = 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 = t * ((c * j) - (x * a));
	t_2 = (i * j) * ((a * (b / j)) - y);
	t_3 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -2.1e+75)
		tmp = t_3;
	elseif (z <= -4.8e+15)
		tmp = t_2;
	elseif (z <= 5.6e-306)
		tmp = t_1;
	elseif (z <= 5.1e-226)
		tmp = i * (b * (a - ((y * j) / b)));
	elseif (z <= 4.5e-137)
		tmp = t_1;
	elseif (z <= 1.4e-32)
		tmp = i * ((a * b) - (y * j));
	elseif (z <= 1.32e+95)
		tmp = t_1;
	elseif (z <= 1.5e+206)
		tmp = 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[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(i * j), $MachinePrecision] * N[(N[(a * N[(b / j), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.1e+75], t$95$3, If[LessEqual[z, -4.8e+15], t$95$2, If[LessEqual[z, 5.6e-306], t$95$1, If[LessEqual[z, 5.1e-226], N[(i * N[(b * N[(a - N[(N[(y * j), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e-137], t$95$1, If[LessEqual[z, 1.4e-32], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.32e+95], t$95$1, If[LessEqual[z, 1.5e+206], t$95$2, t$95$3]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.09999999999999999e75 or 1.5000000000000001e206 < z

   1. Initial program 66.2%

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

   3. Taylor expanded in z around inf 80.3%

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

      1. *-commutative 80.3%

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

      2. *-commutative 80.3%

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

   5. Simplified 80.3%

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

   if -2.09999999999999999e75 < z < -4.8e15 or 1.32e95 < z < 1.5000000000000001e206

   1. Initial program 82.6%

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

   3. Taylor expanded in j around inf 65.8%

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

   4. Taylor expanded in i around -inf 66.2%

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

      1. associate-*r* 69.4%

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

      2. *-commutative 69.4%

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

      3. neg-mul-1 69.4%

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

      4. +-commutative 69.4%

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

      5. unsub-neg 69.4%

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

      6. associate-/l* 76.1%

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

   6. Simplified 76.1%

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

   if -4.8e15 < z < 5.6000000000000003e-306 or 5.09999999999999973e-226 < z < 4.4999999999999997e-137 or 1.3999999999999999e-32 < z < 1.32e95

   1. Initial program 73.7%

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

   3. Taylor expanded in t around inf 59.9%

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

      1. +-commutative 59.9%

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

      2. mul-1-neg 59.9%

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

      3. unsub-neg 59.9%

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

      4. *-commutative 59.9%

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

   5. Simplified 59.9%

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

   if 5.6000000000000003e-306 < z < 5.09999999999999973e-226

   1. Initial program 81.1%

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

   3. Taylor expanded in c around 0 78.0%

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

   4. Taylor expanded in i around -inf 67.6%

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

      1. associate-*r* 67.6%

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

      2. neg-mul-1 67.6%

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

      3. *-commutative 67.6%

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

   6. Simplified 67.6%

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

   7. Taylor expanded in b around inf 67.6%

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

   if 4.4999999999999997e-137 < z < 1.3999999999999999e-32

   1. Initial program 69.0%

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

   3. Taylor expanded in c around 0 74.2%

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

   4. Taylor expanded in i around -inf 58.9%

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

      1. associate-*r* 58.9%

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

      2. neg-mul-1 58.9%

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

      3. *-commutative 58.9%

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

   6. Simplified 58.9%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+75}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{+15}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(a \cdot \frac{b}{j} - y\right)\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-306}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-226}:\\ \;\;\;\;i \cdot \left(b \cdot \left(a - \frac{y \cdot j}{b}\right)\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-137}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-32}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{+95}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+206}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(a \cdot \frac{b}{j} - y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := \left(i \cdot j\right) \cdot \left(a \cdot \frac{b}{j} - y\right)\\ t_3 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_4 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{+75}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+17}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 10^{-305}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-229}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-140}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-32}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+94}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+201}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a))))
        (t_2 (* (* i j) (- (* a (/ b j)) y)))
        (t_3 (* i (- (* a b) (* y j))))
        (t_4 (* z (- (* x y) (* b c)))))
   (if (<= z -1.3e+75)
     t_4
     (if (<= z -3.8e+17)
       t_2
       (if (<= z 1e-305)
         t_1
         (if (<= z 9.5e-229)
           t_3
           (if (<= z 2.05e-140)
             t_1
             (if (<= z 9.2e-32)
               t_3
               (if (<= z 5.2e+94) t_1 (if (<= z 4.4e+201) t_2 t_4))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double t_2 = (i * j) * ((a * (b / j)) - y);
	double t_3 = i * ((a * b) - (y * j));
	double t_4 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -1.3e+75) {
		tmp = t_4;
	} else if (z <= -3.8e+17) {
		tmp = t_2;
	} else if (z <= 1e-305) {
		tmp = t_1;
	} else if (z <= 9.5e-229) {
		tmp = t_3;
	} else if (z <= 2.05e-140) {
		tmp = t_1;
	} else if (z <= 9.2e-32) {
		tmp = t_3;
	} else if (z <= 5.2e+94) {
		tmp = t_1;
	} else if (z <= 4.4e+201) {
		tmp = t_2;
	} else {
		tmp = t_4;
	}
	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) :: tmp
    t_1 = t * ((c * j) - (x * a))
    t_2 = (i * j) * ((a * (b / j)) - y)
    t_3 = i * ((a * b) - (y * j))
    t_4 = z * ((x * y) - (b * c))
    if (z <= (-1.3d+75)) then
        tmp = t_4
    else if (z <= (-3.8d+17)) then
        tmp = t_2
    else if (z <= 1d-305) then
        tmp = t_1
    else if (z <= 9.5d-229) then
        tmp = t_3
    else if (z <= 2.05d-140) then
        tmp = t_1
    else if (z <= 9.2d-32) then
        tmp = t_3
    else if (z <= 5.2d+94) then
        tmp = t_1
    else if (z <= 4.4d+201) then
        tmp = t_2
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double t_2 = (i * j) * ((a * (b / j)) - y);
	double t_3 = i * ((a * b) - (y * j));
	double t_4 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -1.3e+75) {
		tmp = t_4;
	} else if (z <= -3.8e+17) {
		tmp = t_2;
	} else if (z <= 1e-305) {
		tmp = t_1;
	} else if (z <= 9.5e-229) {
		tmp = t_3;
	} else if (z <= 2.05e-140) {
		tmp = t_1;
	} else if (z <= 9.2e-32) {
		tmp = t_3;
	} else if (z <= 5.2e+94) {
		tmp = t_1;
	} else if (z <= 4.4e+201) {
		tmp = t_2;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	t_2 = (i * j) * ((a * (b / j)) - y)
	t_3 = i * ((a * b) - (y * j))
	t_4 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -1.3e+75:
		tmp = t_4
	elif z <= -3.8e+17:
		tmp = t_2
	elif z <= 1e-305:
		tmp = t_1
	elif z <= 9.5e-229:
		tmp = t_3
	elif z <= 2.05e-140:
		tmp = t_1
	elif z <= 9.2e-32:
		tmp = t_3
	elif z <= 5.2e+94:
		tmp = t_1
	elif z <= 4.4e+201:
		tmp = t_2
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_2 = Float64(Float64(i * j) * Float64(Float64(a * Float64(b / j)) - y))
	t_3 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	t_4 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (z <= -1.3e+75)
		tmp = t_4;
	elseif (z <= -3.8e+17)
		tmp = t_2;
	elseif (z <= 1e-305)
		tmp = t_1;
	elseif (z <= 9.5e-229)
		tmp = t_3;
	elseif (z <= 2.05e-140)
		tmp = t_1;
	elseif (z <= 9.2e-32)
		tmp = t_3;
	elseif (z <= 5.2e+94)
		tmp = t_1;
	elseif (z <= 4.4e+201)
		tmp = t_2;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((c * j) - (x * a));
	t_2 = (i * j) * ((a * (b / j)) - y);
	t_3 = i * ((a * b) - (y * j));
	t_4 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -1.3e+75)
		tmp = t_4;
	elseif (z <= -3.8e+17)
		tmp = t_2;
	elseif (z <= 1e-305)
		tmp = t_1;
	elseif (z <= 9.5e-229)
		tmp = t_3;
	elseif (z <= 2.05e-140)
		tmp = t_1;
	elseif (z <= 9.2e-32)
		tmp = t_3;
	elseif (z <= 5.2e+94)
		tmp = t_1;
	elseif (z <= 4.4e+201)
		tmp = t_2;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(i * j), $MachinePrecision] * N[(N[(a * N[(b / j), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.3e+75], t$95$4, If[LessEqual[z, -3.8e+17], t$95$2, If[LessEqual[z, 1e-305], t$95$1, If[LessEqual[z, 9.5e-229], t$95$3, If[LessEqual[z, 2.05e-140], t$95$1, If[LessEqual[z, 9.2e-32], t$95$3, If[LessEqual[z, 5.2e+94], t$95$1, If[LessEqual[z, 4.4e+201], t$95$2, t$95$4]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.29999999999999992e75 or 4.4e201 < z

   1. Initial program 66.2%

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

   3. Taylor expanded in z around inf 80.3%

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

      1. *-commutative 80.3%

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

      2. *-commutative 80.3%

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

   5. Simplified 80.3%

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

   if -1.29999999999999992e75 < z < -3.8e17 or 5.1999999999999998e94 < z < 4.4e201

   1. Initial program 82.6%

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

   3. Taylor expanded in j around inf 65.8%

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

   4. Taylor expanded in i around -inf 66.2%

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

      1. associate-*r* 69.4%

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

      2. *-commutative 69.4%

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

      3. neg-mul-1 69.4%

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

      4. +-commutative 69.4%

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

      5. unsub-neg 69.4%

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

      6. associate-/l* 76.1%

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

   6. Simplified 76.1%

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

   if -3.8e17 < z < 9.99999999999999996e-306 or 9.4999999999999997e-229 < z < 2.0500000000000001e-140 or 9.2000000000000002e-32 < z < 5.1999999999999998e94

   1. Initial program 74.0%

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

   3. Taylor expanded in t around inf 59.4%

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

      1. +-commutative 59.4%

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

      2. mul-1-neg 59.4%

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

      3. unsub-neg 59.4%

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

      4. *-commutative 59.4%

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

   5. Simplified 59.4%

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

   if 9.99999999999999996e-306 < z < 9.4999999999999997e-229 or 2.0500000000000001e-140 < z < 9.2000000000000002e-32

   1. Initial program 75.6%

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

   3. Taylor expanded in c around 0 75.9%

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

   4. Taylor expanded in i around -inf 65.3%

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

      1. associate-*r* 65.3%

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

      2. neg-mul-1 65.3%

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

      3. *-commutative 65.3%

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

   6. Simplified 65.3%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+75}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+17}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(a \cdot \frac{b}{j} - y\right)\\ \mathbf{elif}\;z \leq 10^{-305}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-229}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-140}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-32}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+94}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+201}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(a \cdot \frac{b}{j} - y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -4.4 \cdot 10^{+88}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1060000000:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-64}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-94}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-139}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-234}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-26}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+115}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j)))) (t_2 (* t (- (* c j) (* x a)))))
   (if (<= t -4.4e+88)
     t_2
     (if (<= t -1060000000.0)
       (* i (- (* a b) (* y j)))
       (if (<= t -1.9e-64)
         (* x (- (* y z) (* t a)))
         (if (<= t -1.1e-94)
           t_1
           (if (<= t -3.1e-139)
             t_2
             (if (<= t -3.2e-234)
               t_1
               (if (<= t 2e-26)
                 (* b (- (* a i) (* z c)))
                 (if (<= t 1.25e+115) (* j (- (* t c) (* y i))) t_2))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -4.4e+88) {
		tmp = t_2;
	} else if (t <= -1060000000.0) {
		tmp = i * ((a * b) - (y * j));
	} else if (t <= -1.9e-64) {
		tmp = x * ((y * z) - (t * a));
	} else if (t <= -1.1e-94) {
		tmp = t_1;
	} else if (t <= -3.1e-139) {
		tmp = t_2;
	} else if (t <= -3.2e-234) {
		tmp = t_1;
	} else if (t <= 2e-26) {
		tmp = b * ((a * i) - (z * c));
	} else if (t <= 1.25e+115) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((x * z) - (i * j))
    t_2 = t * ((c * j) - (x * a))
    if (t <= (-4.4d+88)) then
        tmp = t_2
    else if (t <= (-1060000000.0d0)) then
        tmp = i * ((a * b) - (y * j))
    else if (t <= (-1.9d-64)) then
        tmp = x * ((y * z) - (t * a))
    else if (t <= (-1.1d-94)) then
        tmp = t_1
    else if (t <= (-3.1d-139)) then
        tmp = t_2
    else if (t <= (-3.2d-234)) then
        tmp = t_1
    else if (t <= 2d-26) then
        tmp = b * ((a * i) - (z * c))
    else if (t <= 1.25d+115) then
        tmp = j * ((t * c) - (y * i))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -4.4e+88) {
		tmp = t_2;
	} else if (t <= -1060000000.0) {
		tmp = i * ((a * b) - (y * j));
	} else if (t <= -1.9e-64) {
		tmp = x * ((y * z) - (t * a));
	} else if (t <= -1.1e-94) {
		tmp = t_1;
	} else if (t <= -3.1e-139) {
		tmp = t_2;
	} else if (t <= -3.2e-234) {
		tmp = t_1;
	} else if (t <= 2e-26) {
		tmp = b * ((a * i) - (z * c));
	} else if (t <= 1.25e+115) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	t_2 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -4.4e+88:
		tmp = t_2
	elif t <= -1060000000.0:
		tmp = i * ((a * b) - (y * j))
	elif t <= -1.9e-64:
		tmp = x * ((y * z) - (t * a))
	elif t <= -1.1e-94:
		tmp = t_1
	elif t <= -3.1e-139:
		tmp = t_2
	elif t <= -3.2e-234:
		tmp = t_1
	elif t <= 2e-26:
		tmp = b * ((a * i) - (z * c))
	elif t <= 1.25e+115:
		tmp = j * ((t * c) - (y * i))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_2 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -4.4e+88)
		tmp = t_2;
	elseif (t <= -1060000000.0)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (t <= -1.9e-64)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (t <= -1.1e-94)
		tmp = t_1;
	elseif (t <= -3.1e-139)
		tmp = t_2;
	elseif (t <= -3.2e-234)
		tmp = t_1;
	elseif (t <= 2e-26)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (t <= 1.25e+115)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((x * z) - (i * j));
	t_2 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -4.4e+88)
		tmp = t_2;
	elseif (t <= -1060000000.0)
		tmp = i * ((a * b) - (y * j));
	elseif (t <= -1.9e-64)
		tmp = x * ((y * z) - (t * a));
	elseif (t <= -1.1e-94)
		tmp = t_1;
	elseif (t <= -3.1e-139)
		tmp = t_2;
	elseif (t <= -3.2e-234)
		tmp = t_1;
	elseif (t <= 2e-26)
		tmp = b * ((a * i) - (z * c));
	elseif (t <= 1.25e+115)
		tmp = j * ((t * c) - (y * i));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.4e+88], t$95$2, If[LessEqual[t, -1060000000.0], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.9e-64], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.1e-94], t$95$1, If[LessEqual[t, -3.1e-139], t$95$2, If[LessEqual[t, -3.2e-234], t$95$1, If[LessEqual[t, 2e-26], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.25e+115], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -4.40000000000000017e88 or -1.10000000000000001e-94 < t < -3.0999999999999999e-139 or 1.25000000000000002e115 < t

   1. Initial program 59.6%

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

   3. Taylor expanded in t around inf 72.4%

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

      1. +-commutative 72.4%

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

      2. mul-1-neg 72.4%

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

      3. unsub-neg 72.4%

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

      4. *-commutative 72.4%

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

   5. Simplified 72.4%

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

   if -4.40000000000000017e88 < t < -1.06e9

   1. Initial program 91.9%

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

   3. Taylor expanded in c around 0 61.5%

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

   4. Taylor expanded in i around -inf 69.7%

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

      1. associate-*r* 69.7%

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

      2. neg-mul-1 69.7%

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

      3. *-commutative 69.7%

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

   6. Simplified 69.7%

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

   if -1.06e9 < t < -1.9000000000000001e-64

   1. Initial program 89.7%

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

   3. Taylor expanded in x around inf 66.7%

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

      1. *-commutative 66.7%

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

   5. Simplified 66.7%

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

   if -1.9000000000000001e-64 < t < -1.10000000000000001e-94 or -3.0999999999999999e-139 < t < -3.1999999999999999e-234

   1. Initial program 96.4%

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

   3. Taylor expanded in y around inf 73.1%

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

      1. +-commutative 73.1%

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

      2. mul-1-neg 73.1%

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

      3. unsub-neg 73.1%

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

      4. *-commutative 73.1%

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

      5. *-commutative 73.1%

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

   5. Simplified 73.1%

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

   if -3.1999999999999999e-234 < t < 2.0000000000000001e-26

   1. Initial program 71.4%

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

   3. Taylor expanded in b around inf 60.2%

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

      1. *-commutative 60.2%

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

   5. Simplified 60.2%

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

   if 2.0000000000000001e-26 < t < 1.25000000000000002e115

   1. Initial program 80.1%

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

   3. Taylor expanded in j around inf 59.9%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+88}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -1060000000:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-64}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-94}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-139}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-234}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-26}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+115}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_3 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -2.4 \cdot 10^{+99}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -6800000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-66}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-88}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-139}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -1.36 \cdot 10^{-235}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{+112}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c))))
        (t_2 (* y (- (* x z) (* i j))))
        (t_3 (* t (- (* c j) (* x a)))))
   (if (<= t -2.4e+99)
     t_3
     (if (<= t -6800000.0)
       t_1
       (if (<= t -2.7e-66)
         (* x (- (* y z) (* t a)))
         (if (<= t -1.2e-88)
           t_2
           (if (<= t -2.4e-139)
             t_3
             (if (<= t -1.36e-235)
               t_2
               (if (<= t 7.6e-28)
                 t_1
                 (if (<= t 3.7e+112) (* j (- (* t c) (* y i))) 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 * ((a * i) - (z * c));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -2.4e+99) {
		tmp = t_3;
	} else if (t <= -6800000.0) {
		tmp = t_1;
	} else if (t <= -2.7e-66) {
		tmp = x * ((y * z) - (t * a));
	} else if (t <= -1.2e-88) {
		tmp = t_2;
	} else if (t <= -2.4e-139) {
		tmp = t_3;
	} else if (t <= -1.36e-235) {
		tmp = t_2;
	} else if (t <= 7.6e-28) {
		tmp = t_1;
	} else if (t <= 3.7e+112) {
		tmp = j * ((t * c) - (y * i));
	} 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 * ((a * i) - (z * c))
    t_2 = y * ((x * z) - (i * j))
    t_3 = t * ((c * j) - (x * a))
    if (t <= (-2.4d+99)) then
        tmp = t_3
    else if (t <= (-6800000.0d0)) then
        tmp = t_1
    else if (t <= (-2.7d-66)) then
        tmp = x * ((y * z) - (t * a))
    else if (t <= (-1.2d-88)) then
        tmp = t_2
    else if (t <= (-2.4d-139)) then
        tmp = t_3
    else if (t <= (-1.36d-235)) then
        tmp = t_2
    else if (t <= 7.6d-28) then
        tmp = t_1
    else if (t <= 3.7d+112) then
        tmp = j * ((t * c) - (y * i))
    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 * ((a * i) - (z * c));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -2.4e+99) {
		tmp = t_3;
	} else if (t <= -6800000.0) {
		tmp = t_1;
	} else if (t <= -2.7e-66) {
		tmp = x * ((y * z) - (t * a));
	} else if (t <= -1.2e-88) {
		tmp = t_2;
	} else if (t <= -2.4e-139) {
		tmp = t_3;
	} else if (t <= -1.36e-235) {
		tmp = t_2;
	} else if (t <= 7.6e-28) {
		tmp = t_1;
	} else if (t <= 3.7e+112) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = y * ((x * z) - (i * j))
	t_3 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -2.4e+99:
		tmp = t_3
	elif t <= -6800000.0:
		tmp = t_1
	elif t <= -2.7e-66:
		tmp = x * ((y * z) - (t * a))
	elif t <= -1.2e-88:
		tmp = t_2
	elif t <= -2.4e-139:
		tmp = t_3
	elif t <= -1.36e-235:
		tmp = t_2
	elif t <= 7.6e-28:
		tmp = t_1
	elif t <= 3.7e+112:
		tmp = j * ((t * c) - (y * i))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_3 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -2.4e+99)
		tmp = t_3;
	elseif (t <= -6800000.0)
		tmp = t_1;
	elseif (t <= -2.7e-66)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (t <= -1.2e-88)
		tmp = t_2;
	elseif (t <= -2.4e-139)
		tmp = t_3;
	elseif (t <= -1.36e-235)
		tmp = t_2;
	elseif (t <= 7.6e-28)
		tmp = t_1;
	elseif (t <= 3.7e+112)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	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 * ((a * i) - (z * c));
	t_2 = y * ((x * z) - (i * j));
	t_3 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -2.4e+99)
		tmp = t_3;
	elseif (t <= -6800000.0)
		tmp = t_1;
	elseif (t <= -2.7e-66)
		tmp = x * ((y * z) - (t * a));
	elseif (t <= -1.2e-88)
		tmp = t_2;
	elseif (t <= -2.4e-139)
		tmp = t_3;
	elseif (t <= -1.36e-235)
		tmp = t_2;
	elseif (t <= 7.6e-28)
		tmp = t_1;
	elseif (t <= 3.7e+112)
		tmp = j * ((t * c) - (y * i));
	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[(a * 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]}, Block[{t$95$3 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.4e+99], t$95$3, If[LessEqual[t, -6800000.0], t$95$1, If[LessEqual[t, -2.7e-66], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.2e-88], t$95$2, If[LessEqual[t, -2.4e-139], t$95$3, If[LessEqual[t, -1.36e-235], t$95$2, If[LessEqual[t, 7.6e-28], t$95$1, If[LessEqual[t, 3.7e+112], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.4000000000000001e99 or -1.2e-88 < t < -2.40000000000000015e-139 or 3.70000000000000004e112 < t

   1. Initial program 59.2%

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

   3. Taylor expanded in t around inf 73.0%

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

      1. +-commutative 73.0%

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

      2. mul-1-neg 73.0%

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

      3. unsub-neg 73.0%

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

      4. *-commutative 73.0%

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

   5. Simplified 73.0%

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

   if -2.4000000000000001e99 < t < -6.8e6 or -1.35999999999999992e-235 < t < 7.60000000000000018e-28

   1. Initial program 74.7%

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

   3. Taylor expanded in b around inf 60.9%

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

      1. *-commutative 60.9%

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

   5. Simplified 60.9%

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

   if -6.8e6 < t < -2.69999999999999996e-66

   1. Initial program 89.7%

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

   3. Taylor expanded in x around inf 66.7%

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

      1. *-commutative 66.7%

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

   5. Simplified 66.7%

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

   if -2.69999999999999996e-66 < t < -1.2e-88 or -2.40000000000000015e-139 < t < -1.35999999999999992e-235

   1. Initial program 96.4%

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

   3. Taylor expanded in y around inf 73.1%

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

      1. +-commutative 73.1%

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

      2. mul-1-neg 73.1%

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

      3. unsub-neg 73.1%

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

      4. *-commutative 73.1%

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

      5. *-commutative 73.1%

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

   5. Simplified 73.1%

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

   if 7.60000000000000018e-28 < t < 3.70000000000000004e112

   1. Initial program 80.1%

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

   3. Taylor expanded in j around inf 59.9%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+99}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -6800000:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-66}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-88}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-139}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -1.36 \cdot 10^{-235}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{-28}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{+112}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 49.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -7 \cdot 10^{+96}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -4800000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-73}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-90}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-136}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-235}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-25}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 10^{+108}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (* b (- (* a i) (* z c))))
        (t_3 (* t (- (* c j) (* x a)))))
   (if (<= t -7e+96)
     t_3
     (if (<= t -4800000.0)
       t_2
       (if (<= t -1.4e-73)
         t_1
         (if (<= t -1.65e-90)
           (* i (* y (- j)))
           (if (<= t -2.2e-136)
             t_3
             (if (<= t -9e-235)
               t_1
               (if (<= t 2.3e-25)
                 t_2
                 (if (<= t 1e+108) (* j (- (* t c) (* y i))) t_3))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -7e+96) {
		tmp = t_3;
	} else if (t <= -4800000.0) {
		tmp = t_2;
	} else if (t <= -1.4e-73) {
		tmp = t_1;
	} else if (t <= -1.65e-90) {
		tmp = i * (y * -j);
	} else if (t <= -2.2e-136) {
		tmp = t_3;
	} else if (t <= -9e-235) {
		tmp = t_1;
	} else if (t <= 2.3e-25) {
		tmp = t_2;
	} else if (t <= 1e+108) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = b * ((a * i) - (z * c))
    t_3 = t * ((c * j) - (x * a))
    if (t <= (-7d+96)) then
        tmp = t_3
    else if (t <= (-4800000.0d0)) then
        tmp = t_2
    else if (t <= (-1.4d-73)) then
        tmp = t_1
    else if (t <= (-1.65d-90)) then
        tmp = i * (y * -j)
    else if (t <= (-2.2d-136)) then
        tmp = t_3
    else if (t <= (-9d-235)) then
        tmp = t_1
    else if (t <= 2.3d-25) then
        tmp = t_2
    else if (t <= 1d+108) then
        tmp = j * ((t * c) - (y * i))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -7e+96) {
		tmp = t_3;
	} else if (t <= -4800000.0) {
		tmp = t_2;
	} else if (t <= -1.4e-73) {
		tmp = t_1;
	} else if (t <= -1.65e-90) {
		tmp = i * (y * -j);
	} else if (t <= -2.2e-136) {
		tmp = t_3;
	} else if (t <= -9e-235) {
		tmp = t_1;
	} else if (t <= 2.3e-25) {
		tmp = t_2;
	} else if (t <= 1e+108) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = b * ((a * i) - (z * c))
	t_3 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -7e+96:
		tmp = t_3
	elif t <= -4800000.0:
		tmp = t_2
	elif t <= -1.4e-73:
		tmp = t_1
	elif t <= -1.65e-90:
		tmp = i * (y * -j)
	elif t <= -2.2e-136:
		tmp = t_3
	elif t <= -9e-235:
		tmp = t_1
	elif t <= 2.3e-25:
		tmp = t_2
	elif t <= 1e+108:
		tmp = j * ((t * c) - (y * i))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_3 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -7e+96)
		tmp = t_3;
	elseif (t <= -4800000.0)
		tmp = t_2;
	elseif (t <= -1.4e-73)
		tmp = t_1;
	elseif (t <= -1.65e-90)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (t <= -2.2e-136)
		tmp = t_3;
	elseif (t <= -9e-235)
		tmp = t_1;
	elseif (t <= 2.3e-25)
		tmp = t_2;
	elseif (t <= 1e+108)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = b * ((a * i) - (z * c));
	t_3 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -7e+96)
		tmp = t_3;
	elseif (t <= -4800000.0)
		tmp = t_2;
	elseif (t <= -1.4e-73)
		tmp = t_1;
	elseif (t <= -1.65e-90)
		tmp = i * (y * -j);
	elseif (t <= -2.2e-136)
		tmp = t_3;
	elseif (t <= -9e-235)
		tmp = t_1;
	elseif (t <= 2.3e-25)
		tmp = t_2;
	elseif (t <= 1e+108)
		tmp = j * ((t * c) - (y * i));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7e+96], t$95$3, If[LessEqual[t, -4800000.0], t$95$2, If[LessEqual[t, -1.4e-73], t$95$1, If[LessEqual[t, -1.65e-90], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.2e-136], t$95$3, If[LessEqual[t, -9e-235], t$95$1, If[LessEqual[t, 2.3e-25], t$95$2, If[LessEqual[t, 1e+108], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -6.9999999999999998e96 or -1.65e-90 < t < -2.2000000000000001e-136 or 1e108 < t

   1. Initial program 58.8%

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

   3. Taylor expanded in t around inf 72.8%

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

      1. +-commutative 72.8%

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

      2. mul-1-neg 72.8%

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

      3. unsub-neg 72.8%

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

      4. *-commutative 72.8%

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

   5. Simplified 72.8%

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

   if -6.9999999999999998e96 < t < -4.8e6 or -8.9999999999999996e-235 < t < 2.2999999999999999e-25

   1. Initial program 74.7%

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

   3. Taylor expanded in b around inf 60.9%

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

      1. *-commutative 60.9%

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

   5. Simplified 60.9%

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

   if -4.8e6 < t < -1.40000000000000006e-73 or -2.2000000000000001e-136 < t < -8.9999999999999996e-235

   1. Initial program 96.8%

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

   3. Taylor expanded in x around inf 56.0%

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

      1. *-commutative 56.0%

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

   5. Simplified 56.0%

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

   if -1.40000000000000006e-73 < t < -1.65e-90

   1. Initial program 83.3%

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

   3. Taylor expanded in y around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. *-commutative 100.0%

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

      5. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around 0 67.7%

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

      1. associate-*r* 67.7%

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

      2. neg-mul-1 67.7%

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

   8. Simplified 67.7%

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

   if 2.2999999999999999e-25 < t < 1e108

   1. Initial program 80.1%

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

   3. Taylor expanded in j around inf 59.9%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+96}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -4800000:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-73}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-90}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-136}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-235}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-25}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 10^{+108}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 47.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -3.5 \cdot 10^{+96}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3950000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-78}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-88}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-140}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{-234}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{+107}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))) (t_2 (* t (- (* c j) (* x a)))))
   (if (<= t -3.5e+96)
     t_2
     (if (<= t -3950000.0)
       t_1
       (if (<= t -1.1e-78)
         (* y (* x z))
         (if (<= t -8e-88)
           (* y (* i (- j)))
           (if (<= t -2.7e-140)
             t_2
             (if (<= t -4.1e-234)
               (* x (* y z))
               (if (<= t 5e-24)
                 t_1
                 (if (<= t 6.4e+107) (* j (- (* t c) (* y i))) 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 * ((a * i) - (z * c));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -3.5e+96) {
		tmp = t_2;
	} else if (t <= -3950000.0) {
		tmp = t_1;
	} else if (t <= -1.1e-78) {
		tmp = y * (x * z);
	} else if (t <= -8e-88) {
		tmp = y * (i * -j);
	} else if (t <= -2.7e-140) {
		tmp = t_2;
	} else if (t <= -4.1e-234) {
		tmp = x * (y * z);
	} else if (t <= 5e-24) {
		tmp = t_1;
	} else if (t <= 6.4e+107) {
		tmp = j * ((t * c) - (y * i));
	} 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 * ((a * i) - (z * c))
    t_2 = t * ((c * j) - (x * a))
    if (t <= (-3.5d+96)) then
        tmp = t_2
    else if (t <= (-3950000.0d0)) then
        tmp = t_1
    else if (t <= (-1.1d-78)) then
        tmp = y * (x * z)
    else if (t <= (-8d-88)) then
        tmp = y * (i * -j)
    else if (t <= (-2.7d-140)) then
        tmp = t_2
    else if (t <= (-4.1d-234)) then
        tmp = x * (y * z)
    else if (t <= 5d-24) then
        tmp = t_1
    else if (t <= 6.4d+107) then
        tmp = j * ((t * c) - (y * i))
    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 * ((a * i) - (z * c));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -3.5e+96) {
		tmp = t_2;
	} else if (t <= -3950000.0) {
		tmp = t_1;
	} else if (t <= -1.1e-78) {
		tmp = y * (x * z);
	} else if (t <= -8e-88) {
		tmp = y * (i * -j);
	} else if (t <= -2.7e-140) {
		tmp = t_2;
	} else if (t <= -4.1e-234) {
		tmp = x * (y * z);
	} else if (t <= 5e-24) {
		tmp = t_1;
	} else if (t <= 6.4e+107) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -3.5e+96:
		tmp = t_2
	elif t <= -3950000.0:
		tmp = t_1
	elif t <= -1.1e-78:
		tmp = y * (x * z)
	elif t <= -8e-88:
		tmp = y * (i * -j)
	elif t <= -2.7e-140:
		tmp = t_2
	elif t <= -4.1e-234:
		tmp = x * (y * z)
	elif t <= 5e-24:
		tmp = t_1
	elif t <= 6.4e+107:
		tmp = j * ((t * c) - (y * i))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -3.5e+96)
		tmp = t_2;
	elseif (t <= -3950000.0)
		tmp = t_1;
	elseif (t <= -1.1e-78)
		tmp = Float64(y * Float64(x * z));
	elseif (t <= -8e-88)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (t <= -2.7e-140)
		tmp = t_2;
	elseif (t <= -4.1e-234)
		tmp = Float64(x * Float64(y * z));
	elseif (t <= 5e-24)
		tmp = t_1;
	elseif (t <= 6.4e+107)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	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 * ((a * i) - (z * c));
	t_2 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -3.5e+96)
		tmp = t_2;
	elseif (t <= -3950000.0)
		tmp = t_1;
	elseif (t <= -1.1e-78)
		tmp = y * (x * z);
	elseif (t <= -8e-88)
		tmp = y * (i * -j);
	elseif (t <= -2.7e-140)
		tmp = t_2;
	elseif (t <= -4.1e-234)
		tmp = x * (y * z);
	elseif (t <= 5e-24)
		tmp = t_1;
	elseif (t <= 6.4e+107)
		tmp = j * ((t * c) - (y * i));
	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[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.5e+96], t$95$2, If[LessEqual[t, -3950000.0], t$95$1, If[LessEqual[t, -1.1e-78], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -8e-88], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.7e-140], t$95$2, If[LessEqual[t, -4.1e-234], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5e-24], t$95$1, If[LessEqual[t, 6.4e+107], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -3.4999999999999999e96 or -7.99999999999999947e-88 < t < -2.7e-140 or 6.40000000000000058e107 < t

   1. Initial program 59.2%

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

   3. Taylor expanded in t around inf 73.0%

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

      1. +-commutative 73.0%

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

      2. mul-1-neg 73.0%

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

      3. unsub-neg 73.0%

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

      4. *-commutative 73.0%

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

   5. Simplified 73.0%

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

   if -3.4999999999999999e96 < t < -3.95e6 or -4.10000000000000011e-234 < t < 4.9999999999999998e-24

   1. Initial program 74.7%

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

   3. Taylor expanded in b around inf 60.9%

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

      1. *-commutative 60.9%

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

   5. Simplified 60.9%

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

   if -3.95e6 < t < -1.0999999999999999e-78

   1. Initial program 90.6%

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

   3. Taylor expanded in y around inf 47.2%

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

      1. +-commutative 47.2%

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

      2. mul-1-neg 47.2%

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

      3. unsub-neg 47.2%

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

      4. *-commutative 47.2%

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

      5. *-commutative 47.2%

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

   5. Simplified 47.2%

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

   6. Taylor expanded in z around inf 47.4%

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

      1. *-commutative 47.4%

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

   8. Simplified 47.4%

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

   if -1.0999999999999999e-78 < t < -7.99999999999999947e-88

   1. Initial program 80.0%

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

   3. Taylor expanded in y around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. *-commutative 100.0%

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

      5. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around 0 80.2%

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

      1. neg-mul-1 80.2%

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

      2. distribute-lft-neg-in 80.2%

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

   8. Simplified 80.2%

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

   if -2.7e-140 < t < -4.10000000000000011e-234

   1. Initial program 99.9%

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

   3. Taylor expanded in c around 0 87.5%

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

   4. Taylor expanded in x around inf 49.5%

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

      1. *-commutative 49.5%

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

      2. *-commutative 49.5%

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

   6. Simplified 49.5%

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

   7. Taylor expanded in z around inf 45.3%

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

   if 4.9999999999999998e-24 < t < 6.40000000000000058e107

   1. Initial program 80.1%

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

   3. Taylor expanded in j around inf 59.9%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+96}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -3950000:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-78}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-88}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-140}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{-234}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-24}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{+107}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 30.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i\right)\\ t_2 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;t \leq -2.3 \cdot 10^{+105}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq -170000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4.3 \cdot 10^{-235}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3.15 \cdot 10^{-273}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{-278}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-246}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-191}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-57}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* a i))) (t_2 (* y (* x z))))
   (if (<= t -2.3e+105)
     (* t (* c j))
     (if (<= t -170000000.0)
       t_1
       (if (<= t -4.3e-235)
         t_2
         (if (<= t -3.15e-273)
           t_1
           (if (<= t 5.3e-278)
             t_2
             (if (<= t 1.7e-246)
               t_1
               (if (<= t 1.3e-191)
                 (* c (* z (- b)))
                 (if (<= t 5.8e-57) t_1 (* c (* t j))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (a * i);
	double t_2 = y * (x * z);
	double tmp;
	if (t <= -2.3e+105) {
		tmp = t * (c * j);
	} else if (t <= -170000000.0) {
		tmp = t_1;
	} else if (t <= -4.3e-235) {
		tmp = t_2;
	} else if (t <= -3.15e-273) {
		tmp = t_1;
	} else if (t <= 5.3e-278) {
		tmp = t_2;
	} else if (t <= 1.7e-246) {
		tmp = t_1;
	} else if (t <= 1.3e-191) {
		tmp = c * (z * -b);
	} else if (t <= 5.8e-57) {
		tmp = t_1;
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (a * i)
    t_2 = y * (x * z)
    if (t <= (-2.3d+105)) then
        tmp = t * (c * j)
    else if (t <= (-170000000.0d0)) then
        tmp = t_1
    else if (t <= (-4.3d-235)) then
        tmp = t_2
    else if (t <= (-3.15d-273)) then
        tmp = t_1
    else if (t <= 5.3d-278) then
        tmp = t_2
    else if (t <= 1.7d-246) then
        tmp = t_1
    else if (t <= 1.3d-191) then
        tmp = c * (z * -b)
    else if (t <= 5.8d-57) then
        tmp = t_1
    else
        tmp = c * (t * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (a * i);
	double t_2 = y * (x * z);
	double tmp;
	if (t <= -2.3e+105) {
		tmp = t * (c * j);
	} else if (t <= -170000000.0) {
		tmp = t_1;
	} else if (t <= -4.3e-235) {
		tmp = t_2;
	} else if (t <= -3.15e-273) {
		tmp = t_1;
	} else if (t <= 5.3e-278) {
		tmp = t_2;
	} else if (t <= 1.7e-246) {
		tmp = t_1;
	} else if (t <= 1.3e-191) {
		tmp = c * (z * -b);
	} else if (t <= 5.8e-57) {
		tmp = t_1;
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (a * i)
	t_2 = y * (x * z)
	tmp = 0
	if t <= -2.3e+105:
		tmp = t * (c * j)
	elif t <= -170000000.0:
		tmp = t_1
	elif t <= -4.3e-235:
		tmp = t_2
	elif t <= -3.15e-273:
		tmp = t_1
	elif t <= 5.3e-278:
		tmp = t_2
	elif t <= 1.7e-246:
		tmp = t_1
	elif t <= 1.3e-191:
		tmp = c * (z * -b)
	elif t <= 5.8e-57:
		tmp = t_1
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(a * i))
	t_2 = Float64(y * Float64(x * z))
	tmp = 0.0
	if (t <= -2.3e+105)
		tmp = Float64(t * Float64(c * j));
	elseif (t <= -170000000.0)
		tmp = t_1;
	elseif (t <= -4.3e-235)
		tmp = t_2;
	elseif (t <= -3.15e-273)
		tmp = t_1;
	elseif (t <= 5.3e-278)
		tmp = t_2;
	elseif (t <= 1.7e-246)
		tmp = t_1;
	elseif (t <= 1.3e-191)
		tmp = Float64(c * Float64(z * Float64(-b)));
	elseif (t <= 5.8e-57)
		tmp = t_1;
	else
		tmp = Float64(c * Float64(t * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (a * i);
	t_2 = y * (x * z);
	tmp = 0.0;
	if (t <= -2.3e+105)
		tmp = t * (c * j);
	elseif (t <= -170000000.0)
		tmp = t_1;
	elseif (t <= -4.3e-235)
		tmp = t_2;
	elseif (t <= -3.15e-273)
		tmp = t_1;
	elseif (t <= 5.3e-278)
		tmp = t_2;
	elseif (t <= 1.7e-246)
		tmp = t_1;
	elseif (t <= 1.3e-191)
		tmp = c * (z * -b);
	elseif (t <= 5.8e-57)
		tmp = t_1;
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.3e+105], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -170000000.0], t$95$1, If[LessEqual[t, -4.3e-235], t$95$2, If[LessEqual[t, -3.15e-273], t$95$1, If[LessEqual[t, 5.3e-278], t$95$2, If[LessEqual[t, 1.7e-246], t$95$1, If[LessEqual[t, 1.3e-191], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.8e-57], t$95$1, N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.2999999999999998e105

   1. Initial program 52.0%

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

   3. Taylor expanded in j around inf 49.3%

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

   4. Taylor expanded in t around inf 74.6%

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

      1. associate-*r* 69.9%

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

      2. associate-*r/ 69.9%

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

      3. mul-1-neg 69.9%

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

      4. *-commutative 69.9%

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

   6. Simplified 69.9%

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

   7. Taylor expanded in j around inf 46.3%

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

      1. associate-*r* 48.6%

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

   9. Simplified 48.6%

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

   if -2.2999999999999998e105 < t < -1.7e8 or -4.30000000000000024e-235 < t < -3.14999999999999989e-273 or 5.3e-278 < t < 1.7000000000000001e-246 or 1.29999999999999993e-191 < t < 5.8000000000000005e-57

   1. Initial program 78.9%

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

   3. Taylor expanded in b around inf 61.5%

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

      1. *-commutative 61.5%

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

   5. Simplified 61.5%

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

   6. Taylor expanded in i around inf 51.9%

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

   if -1.7e8 < t < -4.30000000000000024e-235 or -3.14999999999999989e-273 < t < 5.3e-278

   1. Initial program 90.3%

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

   3. Taylor expanded in y around inf 59.1%

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

      1. +-commutative 59.1%

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

      2. mul-1-neg 59.1%

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

      3. unsub-neg 59.1%

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

      4. *-commutative 59.1%

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

      5. *-commutative 59.1%

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

   5. Simplified 59.1%

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

   6. Taylor expanded in z around inf 41.7%

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

      1. *-commutative 41.7%

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

   8. Simplified 41.7%

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

   if 1.7000000000000001e-246 < t < 1.29999999999999993e-191

   1. Initial program 58.3%

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

   3. Taylor expanded in c around inf 82.1%

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

   4. Taylor expanded in j around 0 82.1%

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

      1. neg-mul-1 82.1%

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

      2. distribute-rgt-neg-in 82.1%

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

   6. Simplified 82.1%

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

   if 5.8000000000000005e-57 < t

   1. Initial program 67.5%

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

   3. Taylor expanded in j around inf 63.9%

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

   4. Taylor expanded in t around inf 44.6%

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

      1. associate-*r* 51.4%

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

      2. associate-*r/ 51.4%

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

      3. mul-1-neg 51.4%

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

      4. *-commutative 51.4%

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

   6. Simplified 51.4%

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

   7. Taylor expanded in c around inf 35.9%

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

4. Final simplification 45.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+105}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq -170000000:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;t \leq -4.3 \cdot 10^{-235}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq -3.15 \cdot 10^{-273}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{-278}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-246}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-191}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-57}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 30.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i\right)\\ t_2 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;t \leq -1.16 \cdot 10^{+109}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq -190000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-235}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-273}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.1 \cdot 10^{-274}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{-247}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-191}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* a i))) (t_2 (* y (* x z))))
   (if (<= t -1.16e+109)
     (* t (* c j))
     (if (<= t -190000000.0)
       t_1
       (if (<= t -3.5e-235)
         t_2
         (if (<= t -1e-273)
           t_1
           (if (<= t 7.1e-274)
             t_2
             (if (<= t 9.8e-247)
               t_1
               (if (<= t 1.7e-191)
                 (* (* z c) (- b))
                 (if (<= t 3e-59) t_1 (* c (* t j))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (a * i);
	double t_2 = y * (x * z);
	double tmp;
	if (t <= -1.16e+109) {
		tmp = t * (c * j);
	} else if (t <= -190000000.0) {
		tmp = t_1;
	} else if (t <= -3.5e-235) {
		tmp = t_2;
	} else if (t <= -1e-273) {
		tmp = t_1;
	} else if (t <= 7.1e-274) {
		tmp = t_2;
	} else if (t <= 9.8e-247) {
		tmp = t_1;
	} else if (t <= 1.7e-191) {
		tmp = (z * c) * -b;
	} else if (t <= 3e-59) {
		tmp = t_1;
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (a * i)
    t_2 = y * (x * z)
    if (t <= (-1.16d+109)) then
        tmp = t * (c * j)
    else if (t <= (-190000000.0d0)) then
        tmp = t_1
    else if (t <= (-3.5d-235)) then
        tmp = t_2
    else if (t <= (-1d-273)) then
        tmp = t_1
    else if (t <= 7.1d-274) then
        tmp = t_2
    else if (t <= 9.8d-247) then
        tmp = t_1
    else if (t <= 1.7d-191) then
        tmp = (z * c) * -b
    else if (t <= 3d-59) then
        tmp = t_1
    else
        tmp = c * (t * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (a * i);
	double t_2 = y * (x * z);
	double tmp;
	if (t <= -1.16e+109) {
		tmp = t * (c * j);
	} else if (t <= -190000000.0) {
		tmp = t_1;
	} else if (t <= -3.5e-235) {
		tmp = t_2;
	} else if (t <= -1e-273) {
		tmp = t_1;
	} else if (t <= 7.1e-274) {
		tmp = t_2;
	} else if (t <= 9.8e-247) {
		tmp = t_1;
	} else if (t <= 1.7e-191) {
		tmp = (z * c) * -b;
	} else if (t <= 3e-59) {
		tmp = t_1;
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (a * i)
	t_2 = y * (x * z)
	tmp = 0
	if t <= -1.16e+109:
		tmp = t * (c * j)
	elif t <= -190000000.0:
		tmp = t_1
	elif t <= -3.5e-235:
		tmp = t_2
	elif t <= -1e-273:
		tmp = t_1
	elif t <= 7.1e-274:
		tmp = t_2
	elif t <= 9.8e-247:
		tmp = t_1
	elif t <= 1.7e-191:
		tmp = (z * c) * -b
	elif t <= 3e-59:
		tmp = t_1
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(a * i))
	t_2 = Float64(y * Float64(x * z))
	tmp = 0.0
	if (t <= -1.16e+109)
		tmp = Float64(t * Float64(c * j));
	elseif (t <= -190000000.0)
		tmp = t_1;
	elseif (t <= -3.5e-235)
		tmp = t_2;
	elseif (t <= -1e-273)
		tmp = t_1;
	elseif (t <= 7.1e-274)
		tmp = t_2;
	elseif (t <= 9.8e-247)
		tmp = t_1;
	elseif (t <= 1.7e-191)
		tmp = Float64(Float64(z * c) * Float64(-b));
	elseif (t <= 3e-59)
		tmp = t_1;
	else
		tmp = Float64(c * Float64(t * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (a * i);
	t_2 = y * (x * z);
	tmp = 0.0;
	if (t <= -1.16e+109)
		tmp = t * (c * j);
	elseif (t <= -190000000.0)
		tmp = t_1;
	elseif (t <= -3.5e-235)
		tmp = t_2;
	elseif (t <= -1e-273)
		tmp = t_1;
	elseif (t <= 7.1e-274)
		tmp = t_2;
	elseif (t <= 9.8e-247)
		tmp = t_1;
	elseif (t <= 1.7e-191)
		tmp = (z * c) * -b;
	elseif (t <= 3e-59)
		tmp = t_1;
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.16e+109], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -190000000.0], t$95$1, If[LessEqual[t, -3.5e-235], t$95$2, If[LessEqual[t, -1e-273], t$95$1, If[LessEqual[t, 7.1e-274], t$95$2, If[LessEqual[t, 9.8e-247], t$95$1, If[LessEqual[t, 1.7e-191], N[(N[(z * c), $MachinePrecision] * (-b)), $MachinePrecision], If[LessEqual[t, 3e-59], t$95$1, N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.16000000000000003e109

   1. Initial program 52.0%

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

   3. Taylor expanded in j around inf 49.3%

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

   4. Taylor expanded in t around inf 74.6%

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

      1. associate-*r* 69.9%

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

      2. associate-*r/ 69.9%

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

      3. mul-1-neg 69.9%

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

      4. *-commutative 69.9%

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

   6. Simplified 69.9%

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

   7. Taylor expanded in j around inf 46.3%

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

      1. associate-*r* 48.6%

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

   9. Simplified 48.6%

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

   if -1.16000000000000003e109 < t < -1.9e8 or -3.4999999999999999e-235 < t < -1e-273 or 7.09999999999999964e-274 < t < 9.8e-247 or 1.69999999999999997e-191 < t < 3.0000000000000001e-59

   1. Initial program 78.9%

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

   3. Taylor expanded in b around inf 61.5%

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

      1. *-commutative 61.5%

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

   5. Simplified 61.5%

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

   6. Taylor expanded in i around inf 51.9%

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

   if -1.9e8 < t < -3.4999999999999999e-235 or -1e-273 < t < 7.09999999999999964e-274

   1. Initial program 90.3%

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

   3. Taylor expanded in y around inf 59.1%

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

      1. +-commutative 59.1%

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

      2. mul-1-neg 59.1%

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

      3. unsub-neg 59.1%

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

      4. *-commutative 59.1%

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

      5. *-commutative 59.1%

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

   5. Simplified 59.1%

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

   6. Taylor expanded in z around inf 41.7%

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

      1. *-commutative 41.7%

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

   8. Simplified 41.7%

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

   if 9.8e-247 < t < 1.69999999999999997e-191

   1. Initial program 58.3%

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

   3. Taylor expanded in b around inf 75.3%

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

      1. *-commutative 75.3%

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

   5. Simplified 75.3%

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

   6. Taylor expanded in i around 0 74.5%

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

      1. neg-mul-1 74.5%

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

   8. Simplified 74.5%

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

   if 3.0000000000000001e-59 < t

   1. Initial program 67.5%

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

   3. Taylor expanded in j around inf 63.9%

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

   4. Taylor expanded in t around inf 44.6%

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

      1. associate-*r* 51.4%

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

      2. associate-*r/ 51.4%

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

      3. mul-1-neg 51.4%

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

      4. *-commutative 51.4%

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

   6. Simplified 51.4%

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

   7. Taylor expanded in c around inf 35.9%

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

4. Final simplification 44.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.16 \cdot 10^{+109}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq -190000000:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-235}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-273}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;t \leq 7.1 \cdot 10^{-274}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{-247}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-191}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-59}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 57.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -8 \cdot 10^{+129}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;y \leq 7.3 \cdot 10^{-16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+68}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(x \cdot \frac{z}{j} - i\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+126}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* j (* t c)) (* b (- (* a i) (* z c)))))
        (t_2 (* y (- (* x z) (* i j)))))
   (if (<= y -8e+129)
     t_2
     (if (<= y -6.5e+58)
       t_1
       (if (<= y -2.2e-7)
         (* x (- (* y z) (* t a)))
         (if (<= y 7.3e-16)
           t_1
           (if (<= y 1.9e+68)
             (* (* y j) (- (* x (/ z j)) i))
             (if (<= y 3.8e+126) (- (* c (* t j)) (* 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 = (j * (t * c)) + (b * ((a * i) - (z * c)));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -8e+129) {
		tmp = t_2;
	} else if (y <= -6.5e+58) {
		tmp = t_1;
	} else if (y <= -2.2e-7) {
		tmp = x * ((y * z) - (t * a));
	} else if (y <= 7.3e-16) {
		tmp = t_1;
	} else if (y <= 1.9e+68) {
		tmp = (y * j) * ((x * (z / j)) - i);
	} else if (y <= 3.8e+126) {
		tmp = (c * (t * j)) - (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) :: tmp
    t_1 = (j * (t * c)) + (b * ((a * i) - (z * c)))
    t_2 = y * ((x * z) - (i * j))
    if (y <= (-8d+129)) then
        tmp = t_2
    else if (y <= (-6.5d+58)) then
        tmp = t_1
    else if (y <= (-2.2d-7)) then
        tmp = x * ((y * z) - (t * a))
    else if (y <= 7.3d-16) then
        tmp = t_1
    else if (y <= 1.9d+68) then
        tmp = (y * j) * ((x * (z / j)) - i)
    else if (y <= 3.8d+126) then
        tmp = (c * (t * j)) - (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 = (j * (t * c)) + (b * ((a * i) - (z * c)));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -8e+129) {
		tmp = t_2;
	} else if (y <= -6.5e+58) {
		tmp = t_1;
	} else if (y <= -2.2e-7) {
		tmp = x * ((y * z) - (t * a));
	} else if (y <= 7.3e-16) {
		tmp = t_1;
	} else if (y <= 1.9e+68) {
		tmp = (y * j) * ((x * (z / j)) - i);
	} else if (y <= 3.8e+126) {
		tmp = (c * (t * j)) - (b * (z * c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * (t * c)) + (b * ((a * i) - (z * c)))
	t_2 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -8e+129:
		tmp = t_2
	elif y <= -6.5e+58:
		tmp = t_1
	elif y <= -2.2e-7:
		tmp = x * ((y * z) - (t * a))
	elif y <= 7.3e-16:
		tmp = t_1
	elif y <= 1.9e+68:
		tmp = (y * j) * ((x * (z / j)) - i)
	elif y <= 3.8e+126:
		tmp = (c * (t * j)) - (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(j * Float64(t * c)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -8e+129)
		tmp = t_2;
	elseif (y <= -6.5e+58)
		tmp = t_1;
	elseif (y <= -2.2e-7)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (y <= 7.3e-16)
		tmp = t_1;
	elseif (y <= 1.9e+68)
		tmp = Float64(Float64(y * j) * Float64(Float64(x * Float64(z / j)) - i));
	elseif (y <= 3.8e+126)
		tmp = Float64(Float64(c * Float64(t * j)) - 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 = (j * (t * c)) + (b * ((a * i) - (z * c)));
	t_2 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -8e+129)
		tmp = t_2;
	elseif (y <= -6.5e+58)
		tmp = t_1;
	elseif (y <= -2.2e-7)
		tmp = x * ((y * z) - (t * a));
	elseif (y <= 7.3e-16)
		tmp = t_1;
	elseif (y <= 1.9e+68)
		tmp = (y * j) * ((x * (z / j)) - i);
	elseif (y <= 3.8e+126)
		tmp = (c * (t * j)) - (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[(j * N[(t * c), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * 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, -8e+129], t$95$2, If[LessEqual[y, -6.5e+58], t$95$1, If[LessEqual[y, -2.2e-7], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.3e-16], t$95$1, If[LessEqual[y, 1.9e+68], N[(N[(y * j), $MachinePrecision] * N[(N[(x * N[(z / j), $MachinePrecision]), $MachinePrecision] - i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.8e+126], N[(N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -8e129 or 3.80000000000000017e126 < y

   1. Initial program 57.9%

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

   3. Taylor expanded in y around inf 70.9%

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

      1. +-commutative 70.9%

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

      2. mul-1-neg 70.9%

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

      3. unsub-neg 70.9%

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

      4. *-commutative 70.9%

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

      5. *-commutative 70.9%

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

   5. Simplified 70.9%

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

   if -8e129 < y < -6.49999999999999998e58 or -2.2000000000000001e-7 < y < 7.3000000000000003e-16

   1. Initial program 80.1%

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

   3. Taylor expanded in x around 0 70.5%

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

      1. *-commutative 70.5%

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

   5. Simplified 70.5%

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

   6. Taylor expanded in c around inf 65.7%

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

   if -6.49999999999999998e58 < y < -2.2000000000000001e-7

   1. Initial program 81.9%

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

   3. Taylor expanded in x around inf 74.1%

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

      1. *-commutative 74.1%

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

   5. Simplified 74.1%

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

   if 7.3000000000000003e-16 < y < 1.9e68

   1. Initial program 63.0%

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

   3. Taylor expanded in j around inf 52.7%

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

   4. Taylor expanded in y around inf 53.7%

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

      1. associate-*r* 51.0%

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

      2. associate-/l* 56.2%

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

   6. Simplified 56.2%

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

   if 1.9e68 < y < 3.80000000000000017e126

   1. Initial program 63.5%

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

   3. Taylor expanded in c around inf 73.3%

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

   4. Taylor expanded in j around 0 81.9%

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

      1. +-commutative 81.9%

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

      2. mul-1-neg 81.9%

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

      3. sub-neg 81.9%

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

   6. Simplified 81.9%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+129}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{+58}:\\ \;\;\;\;j \cdot \left(t \cdot c\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;y \leq 7.3 \cdot 10^{-16}:\\ \;\;\;\;j \cdot \left(t \cdot c\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+68}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(x \cdot \frac{z}{j} - i\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+126}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 66.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -0.0017:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(a \cdot \frac{b}{j} - y\right)\\ \mathbf{elif}\;i \leq 1.12 \cdot 10^{+47} \lor \neg \left(i \leq 5.7 \cdot 10^{+122}\right) \land i \leq 1.3 \cdot 10^{+162}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - c \cdot \left(z \cdot b - t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -0.0017)
   (* (* i j) (- (* a (/ b j)) y))
   (if (or (<= i 1.12e+47) (and (not (<= i 5.7e+122)) (<= i 1.3e+162)))
     (- (* x (- (* y z) (* t a))) (* c (- (* z b) (* t j))))
     (* i (- (* a b) (* y j))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -0.0017) {
		tmp = (i * j) * ((a * (b / j)) - y);
	} else if ((i <= 1.12e+47) || (!(i <= 5.7e+122) && (i <= 1.3e+162))) {
		tmp = (x * ((y * z) - (t * a))) - (c * ((z * b) - (t * j)));
	} else {
		tmp = i * ((a * b) - (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 (i <= (-0.0017d0)) then
        tmp = (i * j) * ((a * (b / j)) - y)
    else if ((i <= 1.12d+47) .or. (.not. (i <= 5.7d+122)) .and. (i <= 1.3d+162)) then
        tmp = (x * ((y * z) - (t * a))) - (c * ((z * b) - (t * j)))
    else
        tmp = i * ((a * b) - (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 (i <= -0.0017) {
		tmp = (i * j) * ((a * (b / j)) - y);
	} else if ((i <= 1.12e+47) || (!(i <= 5.7e+122) && (i <= 1.3e+162))) {
		tmp = (x * ((y * z) - (t * a))) - (c * ((z * b) - (t * j)));
	} else {
		tmp = i * ((a * b) - (y * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -0.0017:
		tmp = (i * j) * ((a * (b / j)) - y)
	elif (i <= 1.12e+47) or (not (i <= 5.7e+122) and (i <= 1.3e+162)):
		tmp = (x * ((y * z) - (t * a))) - (c * ((z * b) - (t * j)))
	else:
		tmp = i * ((a * b) - (y * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -0.0017)
		tmp = Float64(Float64(i * j) * Float64(Float64(a * Float64(b / j)) - y));
	elseif ((i <= 1.12e+47) || (!(i <= 5.7e+122) && (i <= 1.3e+162)))
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(c * Float64(Float64(z * b) - Float64(t * j))));
	else
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -0.0017)
		tmp = (i * j) * ((a * (b / j)) - y);
	elseif ((i <= 1.12e+47) || (~((i <= 5.7e+122)) && (i <= 1.3e+162)))
		tmp = (x * ((y * z) - (t * a))) - (c * ((z * b) - (t * j)));
	else
		tmp = i * ((a * b) - (y * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -0.0017], N[(N[(i * j), $MachinePrecision] * N[(N[(a * N[(b / j), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[i, 1.12e+47], And[N[Not[LessEqual[i, 5.7e+122]], $MachinePrecision], LessEqual[i, 1.3e+162]]], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(N[(z * b), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if i < -0.00169999999999999991

   1. Initial program 69.0%

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

   3. Taylor expanded in j around inf 58.6%

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

   4. Taylor expanded in i around -inf 65.7%

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

      1. associate-*r* 65.8%

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

      2. *-commutative 65.8%

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

      3. neg-mul-1 65.8%

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

      4. +-commutative 65.8%

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

      5. unsub-neg 65.8%

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

      6. associate-/l* 67.3%

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

   6. Simplified 67.3%

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

   if -0.00169999999999999991 < i < 1.12000000000000007e47 or 5.70000000000000006e122 < i < 1.3e162

   1. Initial program 78.5%

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

   3. Taylor expanded in c around 0 79.5%

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

   4. Taylor expanded in i around 0 78.9%

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

   if 1.12000000000000007e47 < i < 5.70000000000000006e122 or 1.3e162 < i

   1. Initial program 62.1%

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

   3. Taylor expanded in c around 0 62.0%

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

   4. Taylor expanded in i around -inf 70.6%

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

      1. associate-*r* 70.6%

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

      2. neg-mul-1 70.6%

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

      3. *-commutative 70.6%

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

   6. Simplified 70.6%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -0.0017:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(a \cdot \frac{b}{j} - y\right)\\ \mathbf{elif}\;i \leq 1.12 \cdot 10^{+47} \lor \neg \left(i \leq 5.7 \cdot 10^{+122}\right) \land i \leq 1.3 \cdot 10^{+162}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - c \cdot \left(z \cdot b - t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 69.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;i \leq -5.5 \cdot 10^{+181}:\\ \;\;\;\;i \cdot \left(b \cdot \left(a - \frac{y \cdot j}{b}\right)\right)\\ \mathbf{elif}\;i \leq -0.007:\\ \;\;\;\;t\_2 + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq 9.5 \cdot 10^{-104}:\\ \;\;\;\;t\_1 - c \cdot \left(z \cdot b - t \cdot j\right)\\ \mathbf{elif}\;i \leq 3.2 \cdot 10^{+40}:\\ \;\;\;\;t\_1 + t\_2\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (* j (- (* t c) (* y i)))))
   (if (<= i -5.5e+181)
     (* i (* b (- a (/ (* y j) b))))
     (if (<= i -0.007)
       (+ t_2 (* b (- (* a i) (* z c))))
       (if (<= i 9.5e-104)
         (- t_1 (* c (- (* z b) (* t j))))
         (if (<= i 3.2e+40) (+ t_1 t_2) (* i (- (* a b) (* y j)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (i <= -5.5e+181) {
		tmp = i * (b * (a - ((y * j) / b)));
	} else if (i <= -0.007) {
		tmp = t_2 + (b * ((a * i) - (z * c)));
	} else if (i <= 9.5e-104) {
		tmp = t_1 - (c * ((z * b) - (t * j)));
	} else if (i <= 3.2e+40) {
		tmp = t_1 + t_2;
	} else {
		tmp = i * ((a * b) - (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) :: t_2
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = j * ((t * c) - (y * i))
    if (i <= (-5.5d+181)) then
        tmp = i * (b * (a - ((y * j) / b)))
    else if (i <= (-0.007d0)) then
        tmp = t_2 + (b * ((a * i) - (z * c)))
    else if (i <= 9.5d-104) then
        tmp = t_1 - (c * ((z * b) - (t * j)))
    else if (i <= 3.2d+40) then
        tmp = t_1 + t_2
    else
        tmp = i * ((a * b) - (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 = x * ((y * z) - (t * a));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (i <= -5.5e+181) {
		tmp = i * (b * (a - ((y * j) / b)));
	} else if (i <= -0.007) {
		tmp = t_2 + (b * ((a * i) - (z * c)));
	} else if (i <= 9.5e-104) {
		tmp = t_1 - (c * ((z * b) - (t * j)));
	} else if (i <= 3.2e+40) {
		tmp = t_1 + t_2;
	} else {
		tmp = i * ((a * b) - (y * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = j * ((t * c) - (y * i))
	tmp = 0
	if i <= -5.5e+181:
		tmp = i * (b * (a - ((y * j) / b)))
	elif i <= -0.007:
		tmp = t_2 + (b * ((a * i) - (z * c)))
	elif i <= 9.5e-104:
		tmp = t_1 - (c * ((z * b) - (t * j)))
	elif i <= 3.2e+40:
		tmp = t_1 + t_2
	else:
		tmp = i * ((a * b) - (y * j))
	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(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (i <= -5.5e+181)
		tmp = Float64(i * Float64(b * Float64(a - Float64(Float64(y * j) / b))));
	elseif (i <= -0.007)
		tmp = Float64(t_2 + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (i <= 9.5e-104)
		tmp = Float64(t_1 - Float64(c * Float64(Float64(z * b) - Float64(t * j))));
	elseif (i <= 3.2e+40)
		tmp = Float64(t_1 + t_2);
	else
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (i <= -5.5e+181)
		tmp = i * (b * (a - ((y * j) / b)));
	elseif (i <= -0.007)
		tmp = t_2 + (b * ((a * i) - (z * c)));
	elseif (i <= 9.5e-104)
		tmp = t_1 - (c * ((z * b) - (t * j)));
	elseif (i <= 3.2e+40)
		tmp = t_1 + t_2;
	else
		tmp = i * ((a * b) - (y * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -5.5e+181], N[(i * N[(b * N[(a - N[(N[(y * j), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -0.007], N[(t$95$2 + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 9.5e-104], N[(t$95$1 - N[(c * N[(N[(z * b), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.2e+40], N[(t$95$1 + t$95$2), $MachinePrecision], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -5.49999999999999991e181

   1. Initial program 59.9%

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

   3. Taylor expanded in c around 0 52.1%

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

   4. Taylor expanded in i around -inf 78.5%

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

      1. associate-*r* 78.5%

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

      2. neg-mul-1 78.5%

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

      3. *-commutative 78.5%

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

   6. Simplified 78.5%

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

   7. Taylor expanded in b around inf 82.2%

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

   if -5.49999999999999991e181 < i < -0.00700000000000000015

   1. Initial program 74.8%

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

   3. Taylor expanded in x around 0 80.2%

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

      1. *-commutative 80.2%

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

   5. Simplified 80.2%

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

   if -0.00700000000000000015 < i < 9.5000000000000002e-104

   1. Initial program 77.7%

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

   3. Taylor expanded in c around 0 81.1%

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

   4. Taylor expanded in i around 0 82.1%

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

   if 9.5000000000000002e-104 < i < 3.19999999999999981e40

   1. Initial program 86.7%

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

   3. Taylor expanded in b around 0 83.1%

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

   if 3.19999999999999981e40 < i

   1. Initial program 60.9%

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

   3. Taylor expanded in c around 0 64.3%

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

   4. Taylor expanded in i around -inf 63.3%

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

      1. associate-*r* 63.3%

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

      2. neg-mul-1 63.3%

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

      3. *-commutative 63.3%

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

   6. Simplified 63.3%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -5.5 \cdot 10^{+181}:\\ \;\;\;\;i \cdot \left(b \cdot \left(a - \frac{y \cdot j}{b}\right)\right)\\ \mathbf{elif}\;i \leq -0.007:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq 9.5 \cdot 10^{-104}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - c \cdot \left(z \cdot b - t \cdot j\right)\\ \mathbf{elif}\;i \leq 3.2 \cdot 10^{+40}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 60.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z + \left(\frac{c \cdot \left(t \cdot j\right)}{y} - i \cdot j\right)\right)\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{+115}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{+39}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-21} \lor \neg \left(y \leq 4.4 \cdot 10^{-16}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (+ (* x z) (- (/ (* c (* t j)) y) (* i j))))))
   (if (<= y -3.6e+115)
     t_1
     (if (<= y -1.9e+39)
       (* t (- (* c j) (* x a)))
       (if (or (<= y -6.5e-21) (not (<= y 4.4e-16)))
         t_1
         (+ (* j (* t c)) (* b (- (* a i) (* z c)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) + (((c * (t * j)) / y) - (i * j)));
	double tmp;
	if (y <= -3.6e+115) {
		tmp = t_1;
	} else if (y <= -1.9e+39) {
		tmp = t * ((c * j) - (x * a));
	} else if ((y <= -6.5e-21) || !(y <= 4.4e-16)) {
		tmp = t_1;
	} else {
		tmp = (j * (t * c)) + (b * ((a * i) - (z * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((x * z) + (((c * (t * j)) / y) - (i * j)))
    if (y <= (-3.6d+115)) then
        tmp = t_1
    else if (y <= (-1.9d+39)) then
        tmp = t * ((c * j) - (x * a))
    else if ((y <= (-6.5d-21)) .or. (.not. (y <= 4.4d-16))) then
        tmp = t_1
    else
        tmp = (j * (t * c)) + (b * ((a * i) - (z * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) + (((c * (t * j)) / y) - (i * j)));
	double tmp;
	if (y <= -3.6e+115) {
		tmp = t_1;
	} else if (y <= -1.9e+39) {
		tmp = t * ((c * j) - (x * a));
	} else if ((y <= -6.5e-21) || !(y <= 4.4e-16)) {
		tmp = t_1;
	} else {
		tmp = (j * (t * c)) + (b * ((a * i) - (z * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) + (((c * (t * j)) / y) - (i * j)))
	tmp = 0
	if y <= -3.6e+115:
		tmp = t_1
	elif y <= -1.9e+39:
		tmp = t * ((c * j) - (x * a))
	elif (y <= -6.5e-21) or not (y <= 4.4e-16):
		tmp = t_1
	else:
		tmp = (j * (t * c)) + (b * ((a * i) - (z * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) + Float64(Float64(Float64(c * Float64(t * j)) / y) - Float64(i * j))))
	tmp = 0.0
	if (y <= -3.6e+115)
		tmp = t_1;
	elseif (y <= -1.9e+39)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif ((y <= -6.5e-21) || !(y <= 4.4e-16))
		tmp = t_1;
	else
		tmp = Float64(Float64(j * Float64(t * c)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((x * z) + (((c * (t * j)) / y) - (i * j)));
	tmp = 0.0;
	if (y <= -3.6e+115)
		tmp = t_1;
	elseif (y <= -1.9e+39)
		tmp = t * ((c * j) - (x * a));
	elseif ((y <= -6.5e-21) || ~((y <= 4.4e-16)))
		tmp = t_1;
	else
		tmp = (j * (t * c)) + (b * ((a * i) - (z * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(N[(x * z), $MachinePrecision] + N[(N[(N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.6e+115], t$95$1, If[LessEqual[y, -1.9e+39], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -6.5e-21], N[Not[LessEqual[y, 4.4e-16]], $MachinePrecision]], t$95$1, N[(N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.6000000000000001e115 or -1.8999999999999999e39 < y < -6.49999999999999987e-21 or 4.40000000000000001e-16 < y

   1. Initial program 63.7%

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

   3. Taylor expanded in y around -inf 73.2%

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

   5. Simplified 75.0%

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

   6. Taylor expanded in j around inf 68.9%

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

   if -3.6000000000000001e115 < y < -1.8999999999999999e39

   1. Initial program 67.3%

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

   3. Taylor expanded in t around inf 75.0%

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

      1. +-commutative 75.0%

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

      2. mul-1-neg 75.0%

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

      3. unsub-neg 75.0%

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

      4. *-commutative 75.0%

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

   5. Simplified 75.0%

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

   if -6.49999999999999987e-21 < y < 4.40000000000000001e-16

   1. Initial program 81.3%

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

   3. Taylor expanded in x around 0 70.4%

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

      1. *-commutative 70.4%

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

   5. Simplified 70.4%

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

   6. Taylor expanded in c around inf 65.8%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+115}:\\ \;\;\;\;y \cdot \left(x \cdot z + \left(\frac{c \cdot \left(t \cdot j\right)}{y} - i \cdot j\right)\right)\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{+39}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-21} \lor \neg \left(y \leq 4.4 \cdot 10^{-16}\right):\\ \;\;\;\;y \cdot \left(x \cdot z + \left(\frac{c \cdot \left(t \cdot j\right)}{y} - i \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 57.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - \left(i \cdot j + \frac{a \cdot \left(x \cdot t\right)}{y}\right)\right)\\ t_2 := j \cdot \left(t \cdot c\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;x \leq -2.2 \cdot 10^{-24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -8.2 \cdot 10^{-167}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-251}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-67}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (+ (* i j) (/ (* a (* x t)) y)))))
        (t_2 (+ (* j (* t c)) (* b (- (* a i) (* z c))))))
   (if (<= x -2.2e-24)
     t_1
     (if (<= x -8.2e-167)
       t_2
       (if (<= x -1.3e-251)
         (* j (- (* t c) (* y i)))
         (if (<= x 2.2e-67) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - ((i * j) + ((a * (x * t)) / y)));
	double t_2 = (j * (t * c)) + (b * ((a * i) - (z * c)));
	double tmp;
	if (x <= -2.2e-24) {
		tmp = t_1;
	} else if (x <= -8.2e-167) {
		tmp = t_2;
	} else if (x <= -1.3e-251) {
		tmp = j * ((t * c) - (y * i));
	} else if (x <= 2.2e-67) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((x * z) - ((i * j) + ((a * (x * t)) / y)))
    t_2 = (j * (t * c)) + (b * ((a * i) - (z * c)))
    if (x <= (-2.2d-24)) then
        tmp = t_1
    else if (x <= (-8.2d-167)) then
        tmp = t_2
    else if (x <= (-1.3d-251)) then
        tmp = j * ((t * c) - (y * i))
    else if (x <= 2.2d-67) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - ((i * j) + ((a * (x * t)) / y)));
	double t_2 = (j * (t * c)) + (b * ((a * i) - (z * c)));
	double tmp;
	if (x <= -2.2e-24) {
		tmp = t_1;
	} else if (x <= -8.2e-167) {
		tmp = t_2;
	} else if (x <= -1.3e-251) {
		tmp = j * ((t * c) - (y * i));
	} else if (x <= 2.2e-67) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - ((i * j) + ((a * (x * t)) / y)))
	t_2 = (j * (t * c)) + (b * ((a * i) - (z * c)))
	tmp = 0
	if x <= -2.2e-24:
		tmp = t_1
	elif x <= -8.2e-167:
		tmp = t_2
	elif x <= -1.3e-251:
		tmp = j * ((t * c) - (y * i))
	elif x <= 2.2e-67:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(Float64(i * j) + Float64(Float64(a * Float64(x * t)) / y))))
	t_2 = Float64(Float64(j * Float64(t * c)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))))
	tmp = 0.0
	if (x <= -2.2e-24)
		tmp = t_1;
	elseif (x <= -8.2e-167)
		tmp = t_2;
	elseif (x <= -1.3e-251)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (x <= 2.2e-67)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((x * z) - ((i * j) + ((a * (x * t)) / y)));
	t_2 = (j * (t * c)) + (b * ((a * i) - (z * c)));
	tmp = 0.0;
	if (x <= -2.2e-24)
		tmp = t_1;
	elseif (x <= -8.2e-167)
		tmp = t_2;
	elseif (x <= -1.3e-251)
		tmp = j * ((t * c) - (y * i));
	elseif (x <= 2.2e-67)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(N[(i * j), $MachinePrecision] + N[(N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.2e-24], t$95$1, If[LessEqual[x, -8.2e-167], t$95$2, If[LessEqual[x, -1.3e-251], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.2e-67], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.20000000000000002e-24 or 2.2000000000000001e-67 < x

   1. Initial program 68.1%

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

   3. Taylor expanded in y around -inf 59.6%

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

   5. Simplified 60.8%

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

   6. Taylor expanded in x around inf 60.7%

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

      1. associate-*r/ 60.7%

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

      2. associate-*r* 60.7%

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

      3. neg-mul-1 60.7%

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

   8. Simplified 60.7%

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

   if -2.20000000000000002e-24 < x < -8.20000000000000036e-167 or -1.3e-251 < x < 2.2000000000000001e-67

   1. Initial program 80.0%

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

   3. Taylor expanded in x around 0 74.6%

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

      1. *-commutative 74.6%

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

   5. Simplified 74.6%

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

   6. Taylor expanded in c around inf 74.7%

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

   if -8.20000000000000036e-167 < x < -1.3e-251

   1. Initial program 82.7%

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

   3. Taylor expanded in j around inf 93.3%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-24}:\\ \;\;\;\;y \cdot \left(x \cdot z - \left(i \cdot j + \frac{a \cdot \left(x \cdot t\right)}{y}\right)\right)\\ \mathbf{elif}\;x \leq -8.2 \cdot 10^{-167}:\\ \;\;\;\;j \cdot \left(t \cdot c\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-251}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-67}:\\ \;\;\;\;j \cdot \left(t \cdot c\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - \left(i \cdot j + \frac{a \cdot \left(x \cdot t\right)}{y}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 30.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i\right)\\ t_2 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;t \leq -7.5 \cdot 10^{+104}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq -18000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-236}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-272}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-274}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-52}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* a i))) (t_2 (* y (* x z))))
   (if (<= t -7.5e+104)
     (* t (* c j))
     (if (<= t -18000000.0)
       t_1
       (if (<= t -6.5e-236)
         t_2
         (if (<= t -1.6e-272)
           t_1
           (if (<= t 2e-274) t_2 (if (<= t 2.5e-52) t_1 (* c (* t j))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (a * i);
	double t_2 = y * (x * z);
	double tmp;
	if (t <= -7.5e+104) {
		tmp = t * (c * j);
	} else if (t <= -18000000.0) {
		tmp = t_1;
	} else if (t <= -6.5e-236) {
		tmp = t_2;
	} else if (t <= -1.6e-272) {
		tmp = t_1;
	} else if (t <= 2e-274) {
		tmp = t_2;
	} else if (t <= 2.5e-52) {
		tmp = t_1;
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (a * i)
    t_2 = y * (x * z)
    if (t <= (-7.5d+104)) then
        tmp = t * (c * j)
    else if (t <= (-18000000.0d0)) then
        tmp = t_1
    else if (t <= (-6.5d-236)) then
        tmp = t_2
    else if (t <= (-1.6d-272)) then
        tmp = t_1
    else if (t <= 2d-274) then
        tmp = t_2
    else if (t <= 2.5d-52) then
        tmp = t_1
    else
        tmp = c * (t * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (a * i);
	double t_2 = y * (x * z);
	double tmp;
	if (t <= -7.5e+104) {
		tmp = t * (c * j);
	} else if (t <= -18000000.0) {
		tmp = t_1;
	} else if (t <= -6.5e-236) {
		tmp = t_2;
	} else if (t <= -1.6e-272) {
		tmp = t_1;
	} else if (t <= 2e-274) {
		tmp = t_2;
	} else if (t <= 2.5e-52) {
		tmp = t_1;
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (a * i)
	t_2 = y * (x * z)
	tmp = 0
	if t <= -7.5e+104:
		tmp = t * (c * j)
	elif t <= -18000000.0:
		tmp = t_1
	elif t <= -6.5e-236:
		tmp = t_2
	elif t <= -1.6e-272:
		tmp = t_1
	elif t <= 2e-274:
		tmp = t_2
	elif t <= 2.5e-52:
		tmp = t_1
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(a * i))
	t_2 = Float64(y * Float64(x * z))
	tmp = 0.0
	if (t <= -7.5e+104)
		tmp = Float64(t * Float64(c * j));
	elseif (t <= -18000000.0)
		tmp = t_1;
	elseif (t <= -6.5e-236)
		tmp = t_2;
	elseif (t <= -1.6e-272)
		tmp = t_1;
	elseif (t <= 2e-274)
		tmp = t_2;
	elseif (t <= 2.5e-52)
		tmp = t_1;
	else
		tmp = Float64(c * Float64(t * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (a * i);
	t_2 = y * (x * z);
	tmp = 0.0;
	if (t <= -7.5e+104)
		tmp = t * (c * j);
	elseif (t <= -18000000.0)
		tmp = t_1;
	elseif (t <= -6.5e-236)
		tmp = t_2;
	elseif (t <= -1.6e-272)
		tmp = t_1;
	elseif (t <= 2e-274)
		tmp = t_2;
	elseif (t <= 2.5e-52)
		tmp = t_1;
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.5e+104], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -18000000.0], t$95$1, If[LessEqual[t, -6.5e-236], t$95$2, If[LessEqual[t, -1.6e-272], t$95$1, If[LessEqual[t, 2e-274], t$95$2, If[LessEqual[t, 2.5e-52], t$95$1, N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.5000000000000002e104

   1. Initial program 52.0%

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

   3. Taylor expanded in j around inf 49.3%

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

   4. Taylor expanded in t around inf 74.6%

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

      1. associate-*r* 69.9%

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

      2. associate-*r/ 69.9%

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

      3. mul-1-neg 69.9%

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

      4. *-commutative 69.9%

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

   6. Simplified 69.9%

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

   7. Taylor expanded in j around inf 46.3%

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

      1. associate-*r* 48.6%

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

   9. Simplified 48.6%

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

   if -7.5000000000000002e104 < t < -1.8e7 or -6.5000000000000001e-236 < t < -1.6e-272 or 1.99999999999999993e-274 < t < 2.5e-52

   1. Initial program 75.5%

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

   3. Taylor expanded in b around inf 63.8%

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

      1. *-commutative 63.8%

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

   5. Simplified 63.8%

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

   6. Taylor expanded in i around inf 47.8%

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

   if -1.8e7 < t < -6.5000000000000001e-236 or -1.6e-272 < t < 1.99999999999999993e-274

   1. Initial program 90.3%

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

   3. Taylor expanded in y around inf 59.1%

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

      1. +-commutative 59.1%

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

      2. mul-1-neg 59.1%

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

      3. unsub-neg 59.1%

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

      4. *-commutative 59.1%

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

      5. *-commutative 59.1%

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

   5. Simplified 59.1%

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

   6. Taylor expanded in z around inf 41.7%

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

      1. *-commutative 41.7%

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

   8. Simplified 41.7%

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

   if 2.5e-52 < t

   1. Initial program 67.5%

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

   3. Taylor expanded in j around inf 63.9%

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

   4. Taylor expanded in t around inf 44.6%

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

      1. associate-*r* 51.4%

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

      2. associate-*r/ 51.4%

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

      3. mul-1-neg 51.4%

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

      4. *-commutative 51.4%

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

   6. Simplified 51.4%

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

   7. Taylor expanded in c around inf 35.9%

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

4. Final simplification 42.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+104}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq -18000000:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-236}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-272}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-274}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-52}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 29.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i\right)\\ t_2 := y \cdot \left(x \cdot z\right)\\ t_3 := t \cdot \left(c \cdot j\right)\\ \mathbf{if}\;t \leq -5.8 \cdot 10^{+106}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -12000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.25 \cdot 10^{-234}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.95 \cdot 10^{-272}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.28 \cdot 10^{-273}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-53}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* a i))) (t_2 (* y (* x z))) (t_3 (* t (* c j))))
   (if (<= t -5.8e+106)
     t_3
     (if (<= t -12000000.0)
       t_1
       (if (<= t -2.25e-234)
         t_2
         (if (<= t -2.95e-272)
           t_1
           (if (<= t 1.28e-273) t_2 (if (<= t 1.65e-53) 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 * (a * i);
	double t_2 = y * (x * z);
	double t_3 = t * (c * j);
	double tmp;
	if (t <= -5.8e+106) {
		tmp = t_3;
	} else if (t <= -12000000.0) {
		tmp = t_1;
	} else if (t <= -2.25e-234) {
		tmp = t_2;
	} else if (t <= -2.95e-272) {
		tmp = t_1;
	} else if (t <= 1.28e-273) {
		tmp = t_2;
	} else if (t <= 1.65e-53) {
		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 = b * (a * i)
    t_2 = y * (x * z)
    t_3 = t * (c * j)
    if (t <= (-5.8d+106)) then
        tmp = t_3
    else if (t <= (-12000000.0d0)) then
        tmp = t_1
    else if (t <= (-2.25d-234)) then
        tmp = t_2
    else if (t <= (-2.95d-272)) then
        tmp = t_1
    else if (t <= 1.28d-273) then
        tmp = t_2
    else if (t <= 1.65d-53) 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 = b * (a * i);
	double t_2 = y * (x * z);
	double t_3 = t * (c * j);
	double tmp;
	if (t <= -5.8e+106) {
		tmp = t_3;
	} else if (t <= -12000000.0) {
		tmp = t_1;
	} else if (t <= -2.25e-234) {
		tmp = t_2;
	} else if (t <= -2.95e-272) {
		tmp = t_1;
	} else if (t <= 1.28e-273) {
		tmp = t_2;
	} else if (t <= 1.65e-53) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (a * i)
	t_2 = y * (x * z)
	t_3 = t * (c * j)
	tmp = 0
	if t <= -5.8e+106:
		tmp = t_3
	elif t <= -12000000.0:
		tmp = t_1
	elif t <= -2.25e-234:
		tmp = t_2
	elif t <= -2.95e-272:
		tmp = t_1
	elif t <= 1.28e-273:
		tmp = t_2
	elif t <= 1.65e-53:
		tmp = 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(a * i))
	t_2 = Float64(y * Float64(x * z))
	t_3 = Float64(t * Float64(c * j))
	tmp = 0.0
	if (t <= -5.8e+106)
		tmp = t_3;
	elseif (t <= -12000000.0)
		tmp = t_1;
	elseif (t <= -2.25e-234)
		tmp = t_2;
	elseif (t <= -2.95e-272)
		tmp = t_1;
	elseif (t <= 1.28e-273)
		tmp = t_2;
	elseif (t <= 1.65e-53)
		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 = b * (a * i);
	t_2 = y * (x * z);
	t_3 = t * (c * j);
	tmp = 0.0;
	if (t <= -5.8e+106)
		tmp = t_3;
	elseif (t <= -12000000.0)
		tmp = t_1;
	elseif (t <= -2.25e-234)
		tmp = t_2;
	elseif (t <= -2.95e-272)
		tmp = t_1;
	elseif (t <= 1.28e-273)
		tmp = t_2;
	elseif (t <= 1.65e-53)
		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[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.8e+106], t$95$3, If[LessEqual[t, -12000000.0], t$95$1, If[LessEqual[t, -2.25e-234], t$95$2, If[LessEqual[t, -2.95e-272], t$95$1, If[LessEqual[t, 1.28e-273], t$95$2, If[LessEqual[t, 1.65e-53], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.8000000000000004e106 or 1.65000000000000002e-53 < t

   1. Initial program 62.5%

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

   3. Taylor expanded in j around inf 59.2%

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

   4. Taylor expanded in t around inf 54.3%

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

      1. associate-*r* 57.4%

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

      2. associate-*r/ 57.4%

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

      3. mul-1-neg 57.4%

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

      4. *-commutative 57.4%

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

   6. Simplified 57.4%

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

   7. Taylor expanded in j around inf 39.2%

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

      1. associate-*r* 39.2%

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

   9. Simplified 39.2%

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

   if -5.8000000000000004e106 < t < -1.2e7 or -2.25000000000000005e-234 < t < -2.95e-272 or 1.27999999999999992e-273 < t < 1.65000000000000002e-53

   1. Initial program 75.5%

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

   3. Taylor expanded in b around inf 63.8%

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

      1. *-commutative 63.8%

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

   5. Simplified 63.8%

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

   6. Taylor expanded in i around inf 47.8%

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

   if -1.2e7 < t < -2.25000000000000005e-234 or -2.95e-272 < t < 1.27999999999999992e-273

   1. Initial program 90.3%

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

   3. Taylor expanded in y around inf 59.1%

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

      1. +-commutative 59.1%

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

      2. mul-1-neg 59.1%

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

      3. unsub-neg 59.1%

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

      4. *-commutative 59.1%

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

      5. *-commutative 59.1%

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

   5. Simplified 59.1%

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

   6. Taylor expanded in z around inf 41.7%

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

      1. *-commutative 41.7%

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

   8. Simplified 41.7%

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

4. Final simplification 42.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+106}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq -12000000:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;t \leq -2.25 \cdot 10^{-234}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq -2.95 \cdot 10^{-272}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;t \leq 1.28 \cdot 10^{-273}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-53}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 43.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -6.4 \cdot 10^{+196}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -4.4 \cdot 10^{-271}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq -4 \cdot 10^{-306}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 6.4 \cdot 10^{-174}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 1.5 \cdot 10^{-87}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))))
   (if (<= c -6.4e+196)
     t_1
     (if (<= c -4.4e-271)
       (* b (- (* a i) (* z c)))
       (if (<= c -4e-306)
         (* y (* x z))
         (if (<= c 6.4e-174)
           (* i (* y (- j)))
           (if (<= c 1.5e-87) (* b (* a i)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -6.4e+196) {
		tmp = t_1;
	} else if (c <= -4.4e-271) {
		tmp = b * ((a * i) - (z * c));
	} else if (c <= -4e-306) {
		tmp = y * (x * z);
	} else if (c <= 6.4e-174) {
		tmp = i * (y * -j);
	} else if (c <= 1.5e-87) {
		tmp = b * (a * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((t * j) - (z * b))
    if (c <= (-6.4d+196)) then
        tmp = t_1
    else if (c <= (-4.4d-271)) then
        tmp = b * ((a * i) - (z * c))
    else if (c <= (-4d-306)) then
        tmp = y * (x * z)
    else if (c <= 6.4d-174) then
        tmp = i * (y * -j)
    else if (c <= 1.5d-87) then
        tmp = b * (a * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -6.4e+196) {
		tmp = t_1;
	} else if (c <= -4.4e-271) {
		tmp = b * ((a * i) - (z * c));
	} else if (c <= -4e-306) {
		tmp = y * (x * z);
	} else if (c <= 6.4e-174) {
		tmp = i * (y * -j);
	} else if (c <= 1.5e-87) {
		tmp = b * (a * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -6.4e+196:
		tmp = t_1
	elif c <= -4.4e-271:
		tmp = b * ((a * i) - (z * c))
	elif c <= -4e-306:
		tmp = y * (x * z)
	elif c <= 6.4e-174:
		tmp = i * (y * -j)
	elif c <= 1.5e-87:
		tmp = b * (a * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -6.4e+196)
		tmp = t_1;
	elseif (c <= -4.4e-271)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (c <= -4e-306)
		tmp = Float64(y * Float64(x * z));
	elseif (c <= 6.4e-174)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (c <= 1.5e-87)
		tmp = Float64(b * Float64(a * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -6.4e+196)
		tmp = t_1;
	elseif (c <= -4.4e-271)
		tmp = b * ((a * i) - (z * c));
	elseif (c <= -4e-306)
		tmp = y * (x * z);
	elseif (c <= 6.4e-174)
		tmp = i * (y * -j);
	elseif (c <= 1.5e-87)
		tmp = b * (a * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -6.4e+196], t$95$1, If[LessEqual[c, -4.4e-271], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -4e-306], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.4e-174], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.5e-87], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -6.39999999999999985e196 or 1.50000000000000008e-87 < c

   1. Initial program 64.2%

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

   3. Taylor expanded in c around inf 69.8%

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

   if -6.39999999999999985e196 < c < -4.3999999999999999e-271

   1. Initial program 78.5%

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

   3. Taylor expanded in b around inf 46.8%

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

      1. *-commutative 46.8%

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

   5. Simplified 46.8%

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

   if -4.3999999999999999e-271 < c < -4.00000000000000011e-306

   1. Initial program 83.4%

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

   3. Taylor expanded in y around inf 67.2%

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

      1. +-commutative 67.2%

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

      2. mul-1-neg 67.2%

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

      3. unsub-neg 67.2%

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

      4. *-commutative 67.2%

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

      5. *-commutative 67.2%

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

   5. Simplified 67.2%

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

   6. Taylor expanded in z around inf 67.6%

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

      1. *-commutative 67.6%

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

   8. Simplified 67.6%

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

   if -4.00000000000000011e-306 < c < 6.4e-174

   1. Initial program 79.2%

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

   3. Taylor expanded in y around inf 43.9%

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

      1. +-commutative 43.9%

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

      2. mul-1-neg 43.9%

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

      3. unsub-neg 43.9%

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

      4. *-commutative 43.9%

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

      5. *-commutative 43.9%

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

   5. Simplified 43.9%

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

   6. Taylor expanded in z around 0 43.6%

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

      1. associate-*r* 43.6%

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

      2. neg-mul-1 43.6%

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

   8. Simplified 43.6%

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

   if 6.4e-174 < c < 1.50000000000000008e-87

   1. Initial program 79.9%

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

   3. Taylor expanded in b around inf 58.6%

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

      1. *-commutative 58.6%

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

   5. Simplified 58.6%

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

   6. Taylor expanded in i around inf 58.7%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.4 \cdot 10^{+196}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -4.4 \cdot 10^{-271}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq -4 \cdot 10^{-306}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 6.4 \cdot 10^{-174}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 1.5 \cdot 10^{-87}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 64.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;j \leq -3.9 \cdot 10^{+108}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(c \cdot \frac{t}{i} - y\right)\\ \mathbf{elif}\;j \leq -3.25 \cdot 10^{-270}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + t\_1\\ \mathbf{elif}\;j \leq 3.4 \cdot 10^{+30}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - c \cdot \left(z \cdot b - t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= j -3.9e+108)
     (* (* i j) (- (* c (/ t i)) y))
     (if (<= j -3.25e-270)
       (+ (* t (- (* c j) (* x a))) t_1)
       (if (<= j 3.4e+30)
         (- (* x (- (* y z) (* t a))) (* c (- (* z b) (* t j))))
         (+ (* j (- (* t c) (* y i))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (j <= -3.9e+108) {
		tmp = (i * j) * ((c * (t / i)) - y);
	} else if (j <= -3.25e-270) {
		tmp = (t * ((c * j) - (x * a))) + t_1;
	} else if (j <= 3.4e+30) {
		tmp = (x * ((y * z) - (t * a))) - (c * ((z * b) - (t * j)));
	} else {
		tmp = (j * ((t * c) - (y * i))) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    if (j <= (-3.9d+108)) then
        tmp = (i * j) * ((c * (t / i)) - y)
    else if (j <= (-3.25d-270)) then
        tmp = (t * ((c * j) - (x * a))) + t_1
    else if (j <= 3.4d+30) then
        tmp = (x * ((y * z) - (t * a))) - (c * ((z * b) - (t * j)))
    else
        tmp = (j * ((t * c) - (y * i))) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (j <= -3.9e+108) {
		tmp = (i * j) * ((c * (t / i)) - y);
	} else if (j <= -3.25e-270) {
		tmp = (t * ((c * j) - (x * a))) + t_1;
	} else if (j <= 3.4e+30) {
		tmp = (x * ((y * z) - (t * a))) - (c * ((z * b) - (t * j)));
	} else {
		tmp = (j * ((t * c) - (y * i))) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	tmp = 0
	if j <= -3.9e+108:
		tmp = (i * j) * ((c * (t / i)) - y)
	elif j <= -3.25e-270:
		tmp = (t * ((c * j) - (x * a))) + t_1
	elif j <= 3.4e+30:
		tmp = (x * ((y * z) - (t * a))) - (c * ((z * b) - (t * j)))
	else:
		tmp = (j * ((t * c) - (y * i))) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (j <= -3.9e+108)
		tmp = Float64(Float64(i * j) * Float64(Float64(c * Float64(t / i)) - y));
	elseif (j <= -3.25e-270)
		tmp = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) + t_1);
	elseif (j <= 3.4e+30)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(c * Float64(Float64(z * b) - Float64(t * j))));
	else
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (j <= -3.9e+108)
		tmp = (i * j) * ((c * (t / i)) - y);
	elseif (j <= -3.25e-270)
		tmp = (t * ((c * j) - (x * a))) + t_1;
	elseif (j <= 3.4e+30)
		tmp = (x * ((y * z) - (t * a))) - (c * ((z * b) - (t * j)));
	else
		tmp = (j * ((t * c) - (y * i))) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.9e+108], N[(N[(i * j), $MachinePrecision] * N[(N[(c * N[(t / i), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3.25e-270], N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[j, 3.4e+30], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(N[(z * b), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -3.89999999999999985e108

   1. Initial program 66.7%

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

   3. Taylor expanded in c around 0 56.6%

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

   4. Taylor expanded in i around -inf 57.0%

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

   5. Taylor expanded in j around inf 77.0%

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

      1. associate-*r* 73.7%

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

      2. *-commutative 73.7%

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

      3. mul-1-neg 73.7%

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

      4. unsub-neg 73.7%

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

      5. associate-/l* 73.7%

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

   7. Simplified 73.7%

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

   if -3.89999999999999985e108 < j < -3.25e-270

   1. Initial program 77.6%

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

   3. Taylor expanded in y around 0 79.4%

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

      1. mul-1-neg 79.4%

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

      2. associate-*r* 78.3%

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

      3. *-commutative 78.3%

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

      4. associate-*l* 78.2%

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

      5. distribute-rgt-neg-in 78.2%

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

      6. mul-1-neg 78.2%

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

      7. *-commutative 78.2%

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

      8. *-commutative 78.2%

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

      9. associate-*r* 79.0%

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

      10. *-commutative 79.0%

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

      11. distribute-lft-in 80.2%

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

      12. +-commutative 80.2%

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

      13. mul-1-neg 80.2%

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

      14. unsub-neg 80.2%

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

      15. *-commutative 80.2%

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

      16. *-commutative 80.2%

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

   5. Simplified 80.2%

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

   if -3.25e-270 < j < 3.4000000000000002e30

   1. Initial program 67.2%

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

   3. Taylor expanded in c around 0 85.2%

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

   4. Taylor expanded in i around 0 78.1%

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

   if 3.4000000000000002e30 < j

   1. Initial program 77.0%

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

   3. Taylor expanded in x around 0 71.3%

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

      1. *-commutative 71.3%

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

   5. Simplified 71.3%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.9 \cdot 10^{+108}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(c \cdot \frac{t}{i} - y\right)\\ \mathbf{elif}\;j \leq -3.25 \cdot 10^{-270}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 3.4 \cdot 10^{+30}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - c \cdot \left(z \cdot b - t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 62.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;j \leq -2.4 \cdot 10^{+111}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(c \cdot \frac{t}{i} - y\right)\\ \mathbf{elif}\;j \leq -4.2 \cdot 10^{-211}:\\ \;\;\;\;j \cdot \left(t \cdot c\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 30000:\\ \;\;\;\;t\_1 - c \cdot \left(z \cdot b - t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= j -2.4e+111)
     (* (* i j) (- (* c (/ t i)) y))
     (if (<= j -4.2e-211)
       (+ (* j (* t c)) (* b (- (* a i) (* z c))))
       (if (<= j 30000.0)
         (- t_1 (* c (- (* z b) (* t j))))
         (+ t_1 (* j (- (* t c) (* y 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 = x * ((y * z) - (t * a));
	double tmp;
	if (j <= -2.4e+111) {
		tmp = (i * j) * ((c * (t / i)) - y);
	} else if (j <= -4.2e-211) {
		tmp = (j * (t * c)) + (b * ((a * i) - (z * c)));
	} else if (j <= 30000.0) {
		tmp = t_1 - (c * ((z * b) - (t * j)));
	} else {
		tmp = t_1 + (j * ((t * c) - (y * 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 = x * ((y * z) - (t * a))
    if (j <= (-2.4d+111)) then
        tmp = (i * j) * ((c * (t / i)) - y)
    else if (j <= (-4.2d-211)) then
        tmp = (j * (t * c)) + (b * ((a * i) - (z * c)))
    else if (j <= 30000.0d0) then
        tmp = t_1 - (c * ((z * b) - (t * j)))
    else
        tmp = t_1 + (j * ((t * c) - (y * 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 = x * ((y * z) - (t * a));
	double tmp;
	if (j <= -2.4e+111) {
		tmp = (i * j) * ((c * (t / i)) - y);
	} else if (j <= -4.2e-211) {
		tmp = (j * (t * c)) + (b * ((a * i) - (z * c)));
	} else if (j <= 30000.0) {
		tmp = t_1 - (c * ((z * b) - (t * j)));
	} else {
		tmp = t_1 + (j * ((t * c) - (y * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if j <= -2.4e+111:
		tmp = (i * j) * ((c * (t / i)) - y)
	elif j <= -4.2e-211:
		tmp = (j * (t * c)) + (b * ((a * i) - (z * c)))
	elif j <= 30000.0:
		tmp = t_1 - (c * ((z * b) - (t * j)))
	else:
		tmp = t_1 + (j * ((t * c) - (y * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (j <= -2.4e+111)
		tmp = Float64(Float64(i * j) * Float64(Float64(c * Float64(t / i)) - y));
	elseif (j <= -4.2e-211)
		tmp = Float64(Float64(j * Float64(t * c)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (j <= 30000.0)
		tmp = Float64(t_1 - Float64(c * Float64(Float64(z * b) - Float64(t * j))));
	else
		tmp = Float64(t_1 + Float64(j * Float64(Float64(t * c) - Float64(y * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (j <= -2.4e+111)
		tmp = (i * j) * ((c * (t / i)) - y);
	elseif (j <= -4.2e-211)
		tmp = (j * (t * c)) + (b * ((a * i) - (z * c)));
	elseif (j <= 30000.0)
		tmp = t_1 - (c * ((z * b) - (t * j)));
	else
		tmp = t_1 + (j * ((t * c) - (y * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.4e+111], N[(N[(i * j), $MachinePrecision] * N[(N[(c * N[(t / i), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -4.2e-211], N[(N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 30000.0], N[(t$95$1 - N[(c * N[(N[(z * b), $MachinePrecision] - N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -2.40000000000000006e111

   1. Initial program 66.7%

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

   3. Taylor expanded in c around 0 56.6%

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

   4. Taylor expanded in i around -inf 57.0%

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

   5. Taylor expanded in j around inf 77.0%

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

      1. associate-*r* 73.7%

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

      2. *-commutative 73.7%

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

      3. mul-1-neg 73.7%

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

      4. unsub-neg 73.7%

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

      5. associate-/l* 73.7%

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

   7. Simplified 73.7%

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

   if -2.40000000000000006e111 < j < -4.20000000000000015e-211

   1. Initial program 74.9%

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

   3. Taylor expanded in x around 0 67.1%

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

      1. *-commutative 67.1%

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

   5. Simplified 67.1%

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

   6. Taylor expanded in c around inf 68.0%

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

   if -4.20000000000000015e-211 < j < 3e4

   1. Initial program 70.2%

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

   3. Taylor expanded in c around 0 83.2%

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

   4. Taylor expanded in i around 0 77.8%

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

   if 3e4 < j

   1. Initial program 77.2%

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

   3. Taylor expanded in b around 0 71.8%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.4 \cdot 10^{+111}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(c \cdot \frac{t}{i} - y\right)\\ \mathbf{elif}\;j \leq -4.2 \cdot 10^{-211}:\\ \;\;\;\;j \cdot \left(t \cdot c\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 30000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - c \cdot \left(z \cdot b - t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 51.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1700000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-249}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{-223}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-52}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))) (t_2 (* b (- (* a i) (* z c)))))
   (if (<= b -1700000000000.0)
     t_2
     (if (<= b 2.1e-249)
       t_1
       (if (<= b 1.25e-223) (* x (* y z)) (if (<= b 2.4e-52) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1700000000000.0) {
		tmp = t_2;
	} else if (b <= 2.1e-249) {
		tmp = t_1;
	} else if (b <= 1.25e-223) {
		tmp = x * (y * z);
	} else if (b <= 2.4e-52) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = b * ((a * i) - (z * c))
    if (b <= (-1700000000000.0d0)) then
        tmp = t_2
    else if (b <= 2.1d-249) then
        tmp = t_1
    else if (b <= 1.25d-223) then
        tmp = x * (y * z)
    else if (b <= 2.4d-52) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1700000000000.0) {
		tmp = t_2;
	} else if (b <= 2.1e-249) {
		tmp = t_1;
	} else if (b <= 1.25e-223) {
		tmp = x * (y * z);
	} else if (b <= 2.4e-52) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -1700000000000.0:
		tmp = t_2
	elif b <= 2.1e-249:
		tmp = t_1
	elif b <= 1.25e-223:
		tmp = x * (y * z)
	elif b <= 2.4e-52:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -1700000000000.0)
		tmp = t_2;
	elseif (b <= 2.1e-249)
		tmp = t_1;
	elseif (b <= 1.25e-223)
		tmp = Float64(x * Float64(y * z));
	elseif (b <= 2.4e-52)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -1700000000000.0)
		tmp = t_2;
	elseif (b <= 2.1e-249)
		tmp = t_1;
	elseif (b <= 1.25e-223)
		tmp = x * (y * z);
	elseif (b <= 2.4e-52)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1700000000000.0], t$95$2, If[LessEqual[b, 2.1e-249], t$95$1, If[LessEqual[b, 1.25e-223], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.4e-52], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.7e12 or 2.4000000000000002e-52 < b

   1. Initial program 70.2%

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

   3. Taylor expanded in b around inf 61.2%

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

      1. *-commutative 61.2%

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

   5. Simplified 61.2%

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

   if -1.7e12 < b < 2.09999999999999993e-249 or 1.25000000000000006e-223 < b < 2.4000000000000002e-52

   1. Initial program 75.8%

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

   3. Taylor expanded in j around inf 50.5%

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

   if 2.09999999999999993e-249 < b < 1.25000000000000006e-223

   1. Initial program 79.7%

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

   3. Taylor expanded in c around 0 70.3%

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

   4. Taylor expanded in x around inf 80.8%

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

      1. *-commutative 80.8%

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

      2. *-commutative 80.8%

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

   6. Simplified 80.8%

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

   7. Taylor expanded in z around inf 61.0%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1700000000000:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-249}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{-223}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-52}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 41.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+109}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq 150000000000:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+77}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+80}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -3e+109)
   (* t (* c j))
   (if (<= t 150000000000.0)
     (* b (- (* a i) (* z c)))
     (if (<= t 1.05e+77)
       (* i (* y (- j)))
       (if (<= t 1.3e+80) (* (* z c) (- b)) (* c (* t j)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -3e+109) {
		tmp = t * (c * j);
	} else if (t <= 150000000000.0) {
		tmp = b * ((a * i) - (z * c));
	} else if (t <= 1.05e+77) {
		tmp = i * (y * -j);
	} else if (t <= 1.3e+80) {
		tmp = (z * c) * -b;
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (t <= (-3d+109)) then
        tmp = t * (c * j)
    else if (t <= 150000000000.0d0) then
        tmp = b * ((a * i) - (z * c))
    else if (t <= 1.05d+77) then
        tmp = i * (y * -j)
    else if (t <= 1.3d+80) then
        tmp = (z * c) * -b
    else
        tmp = c * (t * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -3e+109) {
		tmp = t * (c * j);
	} else if (t <= 150000000000.0) {
		tmp = b * ((a * i) - (z * c));
	} else if (t <= 1.05e+77) {
		tmp = i * (y * -j);
	} else if (t <= 1.3e+80) {
		tmp = (z * c) * -b;
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -3e+109:
		tmp = t * (c * j)
	elif t <= 150000000000.0:
		tmp = b * ((a * i) - (z * c))
	elif t <= 1.05e+77:
		tmp = i * (y * -j)
	elif t <= 1.3e+80:
		tmp = (z * c) * -b
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -3e+109)
		tmp = Float64(t * Float64(c * j));
	elseif (t <= 150000000000.0)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (t <= 1.05e+77)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (t <= 1.3e+80)
		tmp = Float64(Float64(z * c) * Float64(-b));
	else
		tmp = Float64(c * Float64(t * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -3e+109)
		tmp = t * (c * j);
	elseif (t <= 150000000000.0)
		tmp = b * ((a * i) - (z * c));
	elseif (t <= 1.05e+77)
		tmp = i * (y * -j);
	elseif (t <= 1.3e+80)
		tmp = (z * c) * -b;
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -3e+109], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 150000000000.0], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.05e+77], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.3e+80], N[(N[(z * c), $MachinePrecision] * (-b)), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3.00000000000000015e109

   1. Initial program 52.0%

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

   3. Taylor expanded in j around inf 49.3%

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

   4. Taylor expanded in t around inf 74.6%

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

      1. associate-*r* 69.9%

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

      2. associate-*r/ 69.9%

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

      3. mul-1-neg 69.9%

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

      4. *-commutative 69.9%

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

   6. Simplified 69.9%

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

   7. Taylor expanded in j around inf 46.3%

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

      1. associate-*r* 48.6%

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

   9. Simplified 48.6%

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

   if -3.00000000000000015e109 < t < 1.5e11

   1. Initial program 81.0%

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

   3. Taylor expanded in b around inf 50.8%

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

      1. *-commutative 50.8%

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

   5. Simplified 50.8%

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

   if 1.5e11 < t < 1.0499999999999999e77

   1. Initial program 86.4%

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

   3. Taylor expanded in y around inf 67.2%

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

      1. +-commutative 67.2%

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

      2. mul-1-neg 67.2%

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

      3. unsub-neg 67.2%

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

      4. *-commutative 67.2%

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

      5. *-commutative 67.2%

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

   5. Simplified 67.2%

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

   6. Taylor expanded in z around 0 54.5%

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

      1. associate-*r* 54.5%

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

      2. neg-mul-1 54.5%

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

   8. Simplified 54.5%

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

   if 1.0499999999999999e77 < t < 1.29999999999999991e80

   1. Initial program 0.0%

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

   3. Taylor expanded in b around inf 100.0%

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

      1. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in i around 0 100.0%

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

      1. neg-mul-1 100.0%

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

   8. Simplified 100.0%

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

   if 1.29999999999999991e80 < t

   1. Initial program 61.8%

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

   3. Taylor expanded in j around inf 59.9%

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

   4. Taylor expanded in t around inf 53.1%

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

      1. associate-*r* 64.5%

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

      2. associate-*r/ 64.5%

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

      3. mul-1-neg 64.5%

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

      4. *-commutative 64.5%

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

   6. Simplified 64.5%

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

   7. Taylor expanded in c around inf 44.2%

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

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+109}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq 150000000000:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+77}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+80}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 28.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+74} \lor \neg \left(z \leq 8 \cdot 10^{+168}\right):\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= z -6.6e+74) (not (<= z 8e+168))) (* y (* x z)) (* b (* a i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((z <= -6.6e+74) || !(z <= 8e+168)) {
		tmp = y * (x * z);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((z <= (-6.6d+74)) .or. (.not. (z <= 8d+168))) then
        tmp = y * (x * z)
    else
        tmp = b * (a * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((z <= -6.6e+74) || !(z <= 8e+168)) {
		tmp = y * (x * z);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (z <= -6.6e+74) or not (z <= 8e+168):
		tmp = y * (x * z)
	else:
		tmp = b * (a * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((z <= -6.6e+74) || !(z <= 8e+168))
		tmp = Float64(y * Float64(x * z));
	else
		tmp = Float64(b * Float64(a * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((z <= -6.6e+74) || ~((z <= 8e+168)))
		tmp = y * (x * z);
	else
		tmp = b * (a * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[z, -6.6e+74], N[Not[LessEqual[z, 8e+168]], $MachinePrecision]], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.6000000000000004e74 or 7.9999999999999995e168 < z

   1. Initial program 67.8%

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

   3. Taylor expanded in y around inf 47.7%

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

      1. +-commutative 47.7%

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

      2. mul-1-neg 47.7%

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

      3. unsub-neg 47.7%

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

      4. *-commutative 47.7%

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

      5. *-commutative 47.7%

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

   5. Simplified 47.7%

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

   6. Taylor expanded in z around inf 47.5%

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

      1. *-commutative 47.5%

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

   8. Simplified 47.5%

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

   if -6.6000000000000004e74 < z < 7.9999999999999995e168

   1. Initial program 75.4%

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

   3. Taylor expanded in b around inf 37.1%

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

      1. *-commutative 37.1%

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

   5. Simplified 37.1%

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

   6. Taylor expanded in i around inf 27.7%

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

4. Final simplification 34.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+74} \lor \neg \left(z \leq 8 \cdot 10^{+168}\right):\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 30.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -0.0026 \lor \neg \left(i \leq 1.65 \cdot 10^{-31}\right):\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -0.0026) (not (<= i 1.65e-31))) (* b (* a i)) (* 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 ((i <= -0.0026) || !(i <= 1.65e-31)) {
		tmp = b * (a * i);
	} 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 ((i <= (-0.0026d0)) .or. (.not. (i <= 1.65d-31))) then
        tmp = b * (a * i)
    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 ((i <= -0.0026) || !(i <= 1.65e-31)) {
		tmp = b * (a * i);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (i <= -0.0026) or not (i <= 1.65e-31):
		tmp = b * (a * i)
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((i <= -0.0026) || !(i <= 1.65e-31))
		tmp = Float64(b * Float64(a * i));
	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 ((i <= -0.0026) || ~((i <= 1.65e-31)))
		tmp = b * (a * i);
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[i, -0.0026], N[Not[LessEqual[i, 1.65e-31]], $MachinePrecision]], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -0.0025999999999999999 or 1.65e-31 < i

   1. Initial program 66.1%

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

   3. Taylor expanded in b around inf 50.5%

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

      1. *-commutative 50.5%

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

   5. Simplified 50.5%

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

   6. Taylor expanded in i around inf 40.8%

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

   if -0.0025999999999999999 < i < 1.65e-31

   1. Initial program 80.5%

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

   3. Taylor expanded in c around 0 80.1%

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

   4. Taylor expanded in x around inf 48.0%

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

      1. *-commutative 48.0%

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

      2. *-commutative 48.0%

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

   6. Simplified 48.0%

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

   7. Taylor expanded in z around inf 28.0%

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

4. Final simplification 34.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -0.0026 \lor \neg \left(i \leq 1.65 \cdot 10^{-31}\right):\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 22.5% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ b \cdot \left(a \cdot i\right) \end{array} \]

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 72.9%

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

3. Taylor expanded in b around inf 40.5%

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

   1. *-commutative 40.5%

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

5. Simplified 40.5%

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

6. Taylor expanded in i around inf 23.5%

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

Alternative 27: 22.2% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(b \cdot i\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 72.9%

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

3. Taylor expanded in b around inf 40.5%

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

   1. *-commutative 40.5%

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

5. Simplified 40.5%

   \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

6. Taylor expanded in i around inf 20.7%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
7. Add Preprocessing

Developer target: 68.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ t_2 := x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{if}\;t < -8.120978919195912 \cdot 10^{-33}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < -4.712553818218485 \cdot 10^{-169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t < -7.633533346031584 \cdot 10^{-308}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 1.0535888557455487 \cdot 10^{-139}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
          (/
           (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0)))
           (+ (* c t) (* i y)))))
        (t_2
         (-
          (* x (- (* z y) (* a t)))
          (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))
   (if (< t -8.120978919195912e-33)
     t_2
     (if (< t -4.712553818218485e-169)
       t_1
       (if (< t -7.633533346031584e-308)
         t_2
         (if (< t 1.0535888557455487e-139) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (pow((c * t), 2.0) - pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ** 2.0d0) - ((i * y) ** 2.0d0))) / ((c * t) + (i * y)))
    t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
    if (t < (-8.120978919195912d-33)) then
        tmp = t_2
    else if (t < (-4.712553818218485d-169)) then
        tmp = t_1
    else if (t < (-7.633533346031584d-308)) then
        tmp = t_2
    else if (t < 1.0535888557455487d-139) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (Math.pow((c * t), 2.0) - Math.pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (math.pow((c * t), 2.0) - math.pow((i * y), 2.0))) / ((c * t) + (i * y)))
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
	tmp = 0
	if t < -8.120978919195912e-33:
		tmp = t_2
	elif t < -4.712553818218485e-169:
		tmp = t_1
	elif t < -7.633533346031584e-308:
		tmp = t_2
	elif t < 1.0535888557455487e-139:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(Float64(j * Float64((Float64(c * t) ^ 2.0) - (Float64(i * y) ^ 2.0))) / Float64(Float64(c * t) + Float64(i * y))))
	t_2 = Float64(Float64(x * Float64(Float64(z * y) - Float64(a * t))) - Float64(Float64(b * Float64(Float64(z * c) - Float64(a * i))) - Float64(Float64(Float64(c * t) - Float64(y * i)) * j)))
	tmp = 0.0
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ^ 2.0) - ((i * y) ^ 2.0))) / ((c * t) + (i * y)));
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	tmp = 0.0;
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[Power[N[(c * t), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(i * y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * t), $MachinePrecision] + N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(c * t), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -8.120978919195912e-33], t$95$2, If[Less[t, -4.712553818218485e-169], t$95$1, If[Less[t, -7.633533346031584e-308], t$95$2, If[Less[t, 1.0535888557455487e-139], t$95$1, t$95$2]]]]]]

Reproduce

herbie shell --seed 2024085 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :alt
  (if (< t -8.120978919195912e-33) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -4.712553818218485e-169) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (if (< t -7.633533346031584e-308) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 1.0535888557455487e-139) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))