Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 72.9% → 83.9%

Time: 34.1s

Alternatives: 33

Speedup: 0.5×

• 58.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

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: 72.9% accurate, 1.0× speedup

Math

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

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: 83.9% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (* j (- (* t c) (* y i)))
          (+ (* x (- (* y z) (* t a))) (* b (- (* a i) (* z c)))))))
   (if (<= t_1 INFINITY)
     t_1
     (* y (- (- (* x z) (/ (* t (- (* x a) (* c j))) y)) (* i 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 = (j * ((t * c) - (y * i))) + ((x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c))));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = y * (((x * z) - ((t * ((x * a) - (c * j))) / y)) - (i * 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 = (j * ((t * c) - (y * i))) + ((x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c))));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = y * (((x * z) - ((t * ((x * a) - (c * j))) / y)) - (i * j));
	}
	return tmp;
}

Python

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 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]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(y * N[(N[(N[(x * z), $MachinePrecision] - N[(N[(t * N[(N[(x * a), $MachinePrecision] - N[(c * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] - N[(i * j), $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 90.8%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in y around -inf 30.9%

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

   5. Simplified 36.7%

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

   6. Taylor expanded in b around 0 61.5%

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

4. Final simplification 84.8%

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

Alternative 2: 29.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(z \cdot \left(-b\right)\right)\\ t_2 := a \cdot \left(t \cdot \left(-x\right)\right)\\ t_3 := c \cdot \left(t \cdot j\right)\\ \mathbf{if}\;j \leq -4.2 \cdot 10^{+136}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq -3.2 \cdot 10^{+112}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq -1.8 \cdot 10^{+31}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -1.5 \cdot 10^{-102}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq -5.7 \cdot 10^{-181}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -1.56 \cdot 10^{-274}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 7.5 \cdot 10^{-250}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;j \leq 6.2 \cdot 10^{-193}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 2150000000000:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* z (- b)))) (t_2 (* a (* t (- x)))) (t_3 (* c (* t j))))
   (if (<= j -4.2e+136)
     t_3
     (if (<= j -3.2e+112)
       (* x (* y z))
       (if (<= j -1.8e+31)
         t_2
         (if (<= j -1.5e-102)
           (* y (* x z))
           (if (<= j -5.7e-181)
             t_2
             (if (<= j -1.56e-274)
               t_1
               (if (<= j 7.5e-250)
                 (* b (* a i))
                 (if (<= j 6.2e-193)
                   t_1
                   (if (<= j 2150000000000.0) 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 = c * (z * -b);
	double t_2 = a * (t * -x);
	double t_3 = c * (t * j);
	double tmp;
	if (j <= -4.2e+136) {
		tmp = t_3;
	} else if (j <= -3.2e+112) {
		tmp = x * (y * z);
	} else if (j <= -1.8e+31) {
		tmp = t_2;
	} else if (j <= -1.5e-102) {
		tmp = y * (x * z);
	} else if (j <= -5.7e-181) {
		tmp = t_2;
	} else if (j <= -1.56e-274) {
		tmp = t_1;
	} else if (j <= 7.5e-250) {
		tmp = b * (a * i);
	} else if (j <= 6.2e-193) {
		tmp = t_1;
	} else if (j <= 2150000000000.0) {
		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 = c * (z * -b)
    t_2 = a * (t * -x)
    t_3 = c * (t * j)
    if (j <= (-4.2d+136)) then
        tmp = t_3
    else if (j <= (-3.2d+112)) then
        tmp = x * (y * z)
    else if (j <= (-1.8d+31)) then
        tmp = t_2
    else if (j <= (-1.5d-102)) then
        tmp = y * (x * z)
    else if (j <= (-5.7d-181)) then
        tmp = t_2
    else if (j <= (-1.56d-274)) then
        tmp = t_1
    else if (j <= 7.5d-250) then
        tmp = b * (a * i)
    else if (j <= 6.2d-193) then
        tmp = t_1
    else if (j <= 2150000000000.0d0) 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 = c * (z * -b);
	double t_2 = a * (t * -x);
	double t_3 = c * (t * j);
	double tmp;
	if (j <= -4.2e+136) {
		tmp = t_3;
	} else if (j <= -3.2e+112) {
		tmp = x * (y * z);
	} else if (j <= -1.8e+31) {
		tmp = t_2;
	} else if (j <= -1.5e-102) {
		tmp = y * (x * z);
	} else if (j <= -5.7e-181) {
		tmp = t_2;
	} else if (j <= -1.56e-274) {
		tmp = t_1;
	} else if (j <= 7.5e-250) {
		tmp = b * (a * i);
	} else if (j <= 6.2e-193) {
		tmp = t_1;
	} else if (j <= 2150000000000.0) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (z * -b)
	t_2 = a * (t * -x)
	t_3 = c * (t * j)
	tmp = 0
	if j <= -4.2e+136:
		tmp = t_3
	elif j <= -3.2e+112:
		tmp = x * (y * z)
	elif j <= -1.8e+31:
		tmp = t_2
	elif j <= -1.5e-102:
		tmp = y * (x * z)
	elif j <= -5.7e-181:
		tmp = t_2
	elif j <= -1.56e-274:
		tmp = t_1
	elif j <= 7.5e-250:
		tmp = b * (a * i)
	elif j <= 6.2e-193:
		tmp = t_1
	elif j <= 2150000000000.0:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(z * Float64(-b)))
	t_2 = Float64(a * Float64(t * Float64(-x)))
	t_3 = Float64(c * Float64(t * j))
	tmp = 0.0
	if (j <= -4.2e+136)
		tmp = t_3;
	elseif (j <= -3.2e+112)
		tmp = Float64(x * Float64(y * z));
	elseif (j <= -1.8e+31)
		tmp = t_2;
	elseif (j <= -1.5e-102)
		tmp = Float64(y * Float64(x * z));
	elseif (j <= -5.7e-181)
		tmp = t_2;
	elseif (j <= -1.56e-274)
		tmp = t_1;
	elseif (j <= 7.5e-250)
		tmp = Float64(b * Float64(a * i));
	elseif (j <= 6.2e-193)
		tmp = t_1;
	elseif (j <= 2150000000000.0)
		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 = c * (z * -b);
	t_2 = a * (t * -x);
	t_3 = c * (t * j);
	tmp = 0.0;
	if (j <= -4.2e+136)
		tmp = t_3;
	elseif (j <= -3.2e+112)
		tmp = x * (y * z);
	elseif (j <= -1.8e+31)
		tmp = t_2;
	elseif (j <= -1.5e-102)
		tmp = y * (x * z);
	elseif (j <= -5.7e-181)
		tmp = t_2;
	elseif (j <= -1.56e-274)
		tmp = t_1;
	elseif (j <= 7.5e-250)
		tmp = b * (a * i);
	elseif (j <= 6.2e-193)
		tmp = t_1;
	elseif (j <= 2150000000000.0)
		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[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -4.2e+136], t$95$3, If[LessEqual[j, -3.2e+112], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.8e+31], t$95$2, If[LessEqual[j, -1.5e-102], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -5.7e-181], t$95$2, If[LessEqual[j, -1.56e-274], t$95$1, If[LessEqual[j, 7.5e-250], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6.2e-193], t$95$1, If[LessEqual[j, 2150000000000.0], t$95$2, t$95$3]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -4.1999999999999998e136 or 2.15e12 < j

   1. Initial program 68.8%

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

   3. Taylor expanded in b around 0 67.0%

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

   4. Taylor expanded in x around inf 64.2%

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

   5. Taylor expanded in c around inf 53.4%

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

      1. *-commutative 53.4%

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

   7. Simplified 53.4%

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

   if -4.1999999999999998e136 < j < -3.19999999999999986e112

   1. Initial program 64.1%

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

   3. Taylor expanded in y around inf 87.6%

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

      1. +-commutative 87.6%

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

      2. mul-1-neg 87.6%

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

      3. unsub-neg 87.6%

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

      4. *-commutative 87.6%

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

   5. Simplified 87.6%

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

   6. Taylor expanded in x around inf 52.3%

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

   if -3.19999999999999986e112 < j < -1.79999999999999998e31 or -1.5e-102 < j < -5.7000000000000002e-181 or 6.2000000000000004e-193 < j < 2.15e12

   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 a around inf 55.8%

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

      1. distribute-lft-out-- 55.8%

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

      2. *-commutative 55.8%

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

      3. *-commutative 55.8%

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

   5. Simplified 55.8%

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

   6. Taylor expanded in x around inf 37.9%

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

      1. associate-*r* 37.9%

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

      2. mul-1-neg 37.9%

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

   8. Simplified 37.9%

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

   if -1.79999999999999998e31 < j < -1.5e-102

   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 y around inf 53.1%

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

      1. +-commutative 53.1%

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

      2. mul-1-neg 53.1%

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

      3. unsub-neg 53.1%

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

      4. *-commutative 53.1%

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

   5. Simplified 53.1%

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

   6. Taylor expanded in x around inf 39.8%

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

   if -5.7000000000000002e-181 < j < -1.55999999999999989e-274 or 7.50000000000000009e-250 < j < 6.2000000000000004e-193

   1. Initial program 75.2%

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

   3. Taylor expanded in b around inf 62.5%

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

      1. *-commutative 62.5%

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

   5. Simplified 62.5%

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

   6. Taylor expanded in a around 0 46.5%

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

      1. associate-*r* 46.5%

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

      2. neg-mul-1 46.5%

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

      3. *-commutative 46.5%

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

   8. Simplified 46.5%

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

   9. Taylor expanded in b around 0 46.5%

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

       1. neg-mul-1 46.5%

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

       2. distribute-lft-neg-in 46.5%

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

       3. *-commutative 46.5%

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

       4. associate-*l* 55.3%

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

   11. Simplified 55.3%

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

   if -1.55999999999999989e-274 < j < 7.50000000000000009e-250

   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 62.5%

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

      1. *-commutative 62.5%

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

   5. Simplified 62.5%

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

   6. Taylor expanded in a around inf 48.7%

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

      1. *-commutative 48.7%

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

   8. Simplified 48.7%

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

4. Final simplification 47.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4.2 \cdot 10^{+136}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;j \leq -3.2 \cdot 10^{+112}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq -1.8 \cdot 10^{+31}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;j \leq -1.5 \cdot 10^{-102}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq -5.7 \cdot 10^{-181}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;j \leq -1.56 \cdot 10^{-274}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;j \leq 7.5 \cdot 10^{-250}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;j \leq 6.2 \cdot 10^{-193}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;j \leq 2150000000000:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 48.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot c - y \cdot i\\ \mathbf{if}\;j \leq -4.2 \cdot 10^{+172}:\\ \;\;\;\;j \cdot t\_1\\ \mathbf{elif}\;j \leq -1.28 \cdot 10^{-104}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq -1.65 \cdot 10^{-202}:\\ \;\;\;\;a \cdot \left(t \cdot \left(b \cdot \frac{i}{t} - x\right)\right)\\ \mathbf{elif}\;j \leq -1.2 \cdot 10^{-210}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 8.2 \cdot 10^{-224}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.65 \cdot 10^{-124}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 5.4 \cdot 10^{+49}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot j\right) \cdot \frac{t\_1}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* t c) (* y i))))
   (if (<= j -4.2e+172)
     (* j t_1)
     (if (<= j -1.28e-104)
       (* x (- (* y z) (* t a)))
       (if (<= j -1.65e-202)
         (* a (* t (- (* b (/ i t)) x)))
         (if (<= j -1.2e-210)
           (* y (* x z))
           (if (<= j 8.2e-224)
             (* b (- (* a i) (* z c)))
             (if (<= j 1.65e-124)
               (* z (- (* x y) (* b c)))
               (if (<= j 5.4e+49)
                 (* t (- (* c j) (* x a)))
                 (* (* x j) (/ t_1 x)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (t * c) - (y * i);
	double tmp;
	if (j <= -4.2e+172) {
		tmp = j * t_1;
	} else if (j <= -1.28e-104) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= -1.65e-202) {
		tmp = a * (t * ((b * (i / t)) - x));
	} else if (j <= -1.2e-210) {
		tmp = y * (x * z);
	} else if (j <= 8.2e-224) {
		tmp = b * ((a * i) - (z * c));
	} else if (j <= 1.65e-124) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 5.4e+49) {
		tmp = t * ((c * j) - (x * a));
	} else {
		tmp = (x * j) * (t_1 / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t * c) - (y * i)
    if (j <= (-4.2d+172)) then
        tmp = j * t_1
    else if (j <= (-1.28d-104)) then
        tmp = x * ((y * z) - (t * a))
    else if (j <= (-1.65d-202)) then
        tmp = a * (t * ((b * (i / t)) - x))
    else if (j <= (-1.2d-210)) then
        tmp = y * (x * z)
    else if (j <= 8.2d-224) then
        tmp = b * ((a * i) - (z * c))
    else if (j <= 1.65d-124) then
        tmp = z * ((x * y) - (b * c))
    else if (j <= 5.4d+49) then
        tmp = t * ((c * j) - (x * a))
    else
        tmp = (x * j) * (t_1 / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (t * c) - (y * i);
	double tmp;
	if (j <= -4.2e+172) {
		tmp = j * t_1;
	} else if (j <= -1.28e-104) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= -1.65e-202) {
		tmp = a * (t * ((b * (i / t)) - x));
	} else if (j <= -1.2e-210) {
		tmp = y * (x * z);
	} else if (j <= 8.2e-224) {
		tmp = b * ((a * i) - (z * c));
	} else if (j <= 1.65e-124) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 5.4e+49) {
		tmp = t * ((c * j) - (x * a));
	} else {
		tmp = (x * j) * (t_1 / x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (t * c) - (y * i)
	tmp = 0
	if j <= -4.2e+172:
		tmp = j * t_1
	elif j <= -1.28e-104:
		tmp = x * ((y * z) - (t * a))
	elif j <= -1.65e-202:
		tmp = a * (t * ((b * (i / t)) - x))
	elif j <= -1.2e-210:
		tmp = y * (x * z)
	elif j <= 8.2e-224:
		tmp = b * ((a * i) - (z * c))
	elif j <= 1.65e-124:
		tmp = z * ((x * y) - (b * c))
	elif j <= 5.4e+49:
		tmp = t * ((c * j) - (x * a))
	else:
		tmp = (x * j) * (t_1 / x)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(t * c) - Float64(y * i))
	tmp = 0.0
	if (j <= -4.2e+172)
		tmp = Float64(j * t_1);
	elseif (j <= -1.28e-104)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (j <= -1.65e-202)
		tmp = Float64(a * Float64(t * Float64(Float64(b * Float64(i / t)) - x)));
	elseif (j <= -1.2e-210)
		tmp = Float64(y * Float64(x * z));
	elseif (j <= 8.2e-224)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (j <= 1.65e-124)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (j <= 5.4e+49)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	else
		tmp = Float64(Float64(x * j) * Float64(t_1 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (t * c) - (y * i);
	tmp = 0.0;
	if (j <= -4.2e+172)
		tmp = j * t_1;
	elseif (j <= -1.28e-104)
		tmp = x * ((y * z) - (t * a));
	elseif (j <= -1.65e-202)
		tmp = a * (t * ((b * (i / t)) - x));
	elseif (j <= -1.2e-210)
		tmp = y * (x * z);
	elseif (j <= 8.2e-224)
		tmp = b * ((a * i) - (z * c));
	elseif (j <= 1.65e-124)
		tmp = z * ((x * y) - (b * c));
	elseif (j <= 5.4e+49)
		tmp = t * ((c * j) - (x * a));
	else
		tmp = (x * j) * (t_1 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -4.2e+172], N[(j * t$95$1), $MachinePrecision], If[LessEqual[j, -1.28e-104], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.65e-202], N[(a * N[(t * N[(N[(b * N[(i / t), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.2e-210], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8.2e-224], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.65e-124], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.4e+49], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * j), $MachinePrecision] * N[(t$95$1 / x), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if j < -4.2000000000000003e172

   1. Initial program 72.7%

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

   3. Taylor expanded in j around inf 75.4%

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

      1. *-commutative 75.4%

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

      2. *-commutative 75.4%

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

   5. Simplified 75.4%

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

   if -4.2000000000000003e172 < j < -1.27999999999999992e-104

   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 y around 0 69.0%

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

   5. Simplified 72.8%

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

   6. Taylor expanded in x around inf 57.6%

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

      1. neg-mul-1 57.6%

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

      2. +-commutative 57.6%

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

      3. sub-neg 57.6%

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

   8. Simplified 57.6%

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

   if -1.27999999999999992e-104 < j < -1.64999999999999995e-202

   1. Initial program 76.3%

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

   3. Taylor expanded in a around inf 61.1%

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

      1. distribute-lft-out-- 61.1%

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

      2. *-commutative 61.1%

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

      3. *-commutative 61.1%

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

   5. Simplified 61.1%

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

   6. Taylor expanded in t around inf 66.7%

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

      1. +-commutative 66.7%

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

      2. neg-mul-1 66.7%

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

      3. unsub-neg 66.7%

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

      4. associate-/l* 72.6%

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

   8. Simplified 72.6%

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

   if -1.64999999999999995e-202 < j < -1.20000000000000002e-210

   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 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%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around inf 100.0%

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

   if -1.20000000000000002e-210 < j < 8.19999999999999972e-224

   1. Initial program 79.5%

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

   3. Taylor expanded in b around inf 70.7%

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

      1. *-commutative 70.7%

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

   5. Simplified 70.7%

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

   if 8.19999999999999972e-224 < j < 1.64999999999999992e-124

   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 z around inf 77.2%

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

      1. *-commutative 77.2%

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

   5. Simplified 77.2%

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

   if 1.64999999999999992e-124 < j < 5.4000000000000002e49

   1. Initial program 73.9%

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

   3. Taylor expanded in t around inf 66.4%

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

      1. +-commutative 66.4%

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

      2. mul-1-neg 66.4%

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

      3. unsub-neg 66.4%

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

      4. *-commutative 66.4%

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

      5. *-commutative 66.4%

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

   5. Simplified 66.4%

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

   if 5.4000000000000002e49 < j

   1. Initial program 65.3%

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

   3. Taylor expanded in b around 0 65.6%

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

   4. Taylor expanded in x around inf 65.8%

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

   5. Taylor expanded in j around inf 62.1%

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

      1. associate-*r* 63.9%

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

      2. *-commutative 63.9%

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

      3. div-sub 69.7%

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

      4. *-commutative 69.7%

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

   7. Simplified 69.7%

      \[\leadsto \color{blue}{\left(j \cdot x\right) \cdot \frac{t \cdot c - y \cdot i}{x}} \]
3. Recombined 8 regimes into one program.

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4.2 \cdot 10^{+172}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -1.28 \cdot 10^{-104}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq -1.65 \cdot 10^{-202}:\\ \;\;\;\;a \cdot \left(t \cdot \left(b \cdot \frac{i}{t} - x\right)\right)\\ \mathbf{elif}\;j \leq -1.2 \cdot 10^{-210}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 8.2 \cdot 10^{-224}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.65 \cdot 10^{-124}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 5.4 \cdot 10^{+49}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot j\right) \cdot \frac{t \cdot c - y \cdot i}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 67.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := y \cdot \left(\left(x \cdot z - \frac{t \cdot \left(x \cdot a - c \cdot j\right)}{y}\right) - i \cdot j\right)\\ \mathbf{if}\;y \leq -65000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{-307}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + t\_1\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-61} \lor \neg \left(y \leq 4 \cdot 10^{+73}\right) \land y \leq 1.8 \cdot 10^{+102}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c))))
        (t_2 (* y (- (- (* x z) (/ (* t (- (* x a) (* c j))) y)) (* i j)))))
   (if (<= y -65000.0)
     t_2
     (if (<= y 1.32e-307)
       (+ (* j (- (* t c) (* y i))) t_1)
       (if (or (<= y 6e-61) (and (not (<= y 4e+73)) (<= y 1.8e+102)))
         (+ (* x (- (* y z) (* t a))) t_1)
         t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = y * (((x * z) - ((t * ((x * a) - (c * j))) / y)) - (i * j));
	double tmp;
	if (y <= -65000.0) {
		tmp = t_2;
	} else if (y <= 1.32e-307) {
		tmp = (j * ((t * c) - (y * i))) + t_1;
	} else if ((y <= 6e-61) || (!(y <= 4e+73) && (y <= 1.8e+102))) {
		tmp = (x * ((y * z) - (t * a))) + t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = y * (((x * z) - ((t * ((x * a) - (c * j))) / y)) - (i * j))
    if (y <= (-65000.0d0)) then
        tmp = t_2
    else if (y <= 1.32d-307) then
        tmp = (j * ((t * c) - (y * i))) + t_1
    else if ((y <= 6d-61) .or. (.not. (y <= 4d+73)) .and. (y <= 1.8d+102)) then
        tmp = (x * ((y * z) - (t * a))) + t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = y * (((x * z) - ((t * ((x * a) - (c * j))) / y)) - (i * j));
	double tmp;
	if (y <= -65000.0) {
		tmp = t_2;
	} else if (y <= 1.32e-307) {
		tmp = (j * ((t * c) - (y * i))) + t_1;
	} else if ((y <= 6e-61) || (!(y <= 4e+73) && (y <= 1.8e+102))) {
		tmp = (x * ((y * z) - (t * a))) + t_1;
	} 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 = y * (((x * z) - ((t * ((x * a) - (c * j))) / y)) - (i * j))
	tmp = 0
	if y <= -65000.0:
		tmp = t_2
	elif y <= 1.32e-307:
		tmp = (j * ((t * c) - (y * i))) + t_1
	elif (y <= 6e-61) or (not (y <= 4e+73) and (y <= 1.8e+102)):
		tmp = (x * ((y * z) - (t * a))) + t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(y * Float64(Float64(Float64(x * z) - Float64(Float64(t * Float64(Float64(x * a) - Float64(c * j))) / y)) - Float64(i * j)))
	tmp = 0.0
	if (y <= -65000.0)
		tmp = t_2;
	elseif (y <= 1.32e-307)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + t_1);
	elseif ((y <= 6e-61) || (!(y <= 4e+73) && (y <= 1.8e+102)))
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = y * (((x * z) - ((t * ((x * a) - (c * j))) / y)) - (i * j));
	tmp = 0.0;
	if (y <= -65000.0)
		tmp = t_2;
	elseif (y <= 1.32e-307)
		tmp = (j * ((t * c) - (y * i))) + t_1;
	elseif ((y <= 6e-61) || (~((y <= 4e+73)) && (y <= 1.8e+102)))
		tmp = (x * ((y * z) - (t * a))) + t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(N[(x * z), $MachinePrecision] - N[(N[(t * N[(N[(x * a), $MachinePrecision] - N[(c * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -65000.0], t$95$2, If[LessEqual[y, 1.32e-307], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[Or[LessEqual[y, 6e-61], And[N[Not[LessEqual[y, 4e+73]], $MachinePrecision], LessEqual[y, 1.8e+102]]], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -65000 or 6.00000000000000024e-61 < y < 3.99999999999999993e73 or 1.8000000000000001e102 < y

   1. Initial program 66.6%

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

   3. Taylor expanded in y around -inf 80.3%

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

   5. Simplified 83.8%

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

   6. Taylor expanded in b around 0 83.9%

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

   if -65000 < y < 1.3199999999999999e-307

   1. Initial program 81.7%

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

   3. Taylor expanded in x around 0 76.6%

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

      1. fma-neg 76.6%

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

      2. *-rgt-identity 76.6%

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

      3. *-commutative 76.6%

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

      4. *-commutative 76.6%

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

      5. fma-neg 76.6%

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

      6. associate-*l* 76.6%

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

      7. *-rgt-identity 76.6%

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

      8. *-commutative 76.6%

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

   5. Simplified 76.6%

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

   if 1.3199999999999999e-307 < y < 6.00000000000000024e-61 or 3.99999999999999993e73 < y < 1.8000000000000001e102

   1. Initial program 75.9%

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

   3. Taylor expanded in j around 0 79.3%

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

      1. *-commutative 79.3%

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

   5. Simplified 79.3%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -65000:\\ \;\;\;\;y \cdot \left(\left(x \cdot z - \frac{t \cdot \left(x \cdot a - c \cdot j\right)}{y}\right) - i \cdot j\right)\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{-307}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-61} \lor \neg \left(y \leq 4 \cdot 10^{+73}\right) \land y \leq 1.8 \cdot 10^{+102}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(x \cdot z - \frac{t \cdot \left(x \cdot a - c \cdot j\right)}{y}\right) - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 59.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := t\_1 + b \cdot \left(a \cdot i\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -3.5 \cdot 10^{+126}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{+86}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-78}:\\ \;\;\;\;t\_3 - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-279}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-116}:\\ \;\;\;\;t\_1 - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+100}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i))))
        (t_2 (+ t_1 (* b (* a i))))
        (t_3 (* x (- (* y z) (* t a)))))
   (if (<= x -3.5e+126)
     t_3
     (if (<= x -9.5e+86)
       t_2
       (if (<= x -3e-78)
         (- t_3 (* i (* y j)))
         (if (<= x 4.2e-279)
           t_2
           (if (<= x 4.5e-116)
             (- t_1 (* b (* z c)))
             (if (<= x 2.4e+100) 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 = j * ((t * c) - (y * i));
	double t_2 = t_1 + (b * (a * i));
	double t_3 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -3.5e+126) {
		tmp = t_3;
	} else if (x <= -9.5e+86) {
		tmp = t_2;
	} else if (x <= -3e-78) {
		tmp = t_3 - (i * (y * j));
	} else if (x <= 4.2e-279) {
		tmp = t_2;
	} else if (x <= 4.5e-116) {
		tmp = t_1 - (b * (z * c));
	} else if (x <= 2.4e+100) {
		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 = j * ((t * c) - (y * i))
    t_2 = t_1 + (b * (a * i))
    t_3 = x * ((y * z) - (t * a))
    if (x <= (-3.5d+126)) then
        tmp = t_3
    else if (x <= (-9.5d+86)) then
        tmp = t_2
    else if (x <= (-3d-78)) then
        tmp = t_3 - (i * (y * j))
    else if (x <= 4.2d-279) then
        tmp = t_2
    else if (x <= 4.5d-116) then
        tmp = t_1 - (b * (z * c))
    else if (x <= 2.4d+100) 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 = j * ((t * c) - (y * i));
	double t_2 = t_1 + (b * (a * i));
	double t_3 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -3.5e+126) {
		tmp = t_3;
	} else if (x <= -9.5e+86) {
		tmp = t_2;
	} else if (x <= -3e-78) {
		tmp = t_3 - (i * (y * j));
	} else if (x <= 4.2e-279) {
		tmp = t_2;
	} else if (x <= 4.5e-116) {
		tmp = t_1 - (b * (z * c));
	} else if (x <= 2.4e+100) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = t_1 + (b * (a * i))
	t_3 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -3.5e+126:
		tmp = t_3
	elif x <= -9.5e+86:
		tmp = t_2
	elif x <= -3e-78:
		tmp = t_3 - (i * (y * j))
	elif x <= 4.2e-279:
		tmp = t_2
	elif x <= 4.5e-116:
		tmp = t_1 - (b * (z * c))
	elif x <= 2.4e+100:
		tmp = t_2
	else:
		tmp = t_3
	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(t_1 + Float64(b * Float64(a * i)))
	t_3 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -3.5e+126)
		tmp = t_3;
	elseif (x <= -9.5e+86)
		tmp = t_2;
	elseif (x <= -3e-78)
		tmp = Float64(t_3 - Float64(i * Float64(y * j)));
	elseif (x <= 4.2e-279)
		tmp = t_2;
	elseif (x <= 4.5e-116)
		tmp = Float64(t_1 - Float64(b * Float64(z * c)));
	elseif (x <= 2.4e+100)
		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 = j * ((t * c) - (y * i));
	t_2 = t_1 + (b * (a * i));
	t_3 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -3.5e+126)
		tmp = t_3;
	elseif (x <= -9.5e+86)
		tmp = t_2;
	elseif (x <= -3e-78)
		tmp = t_3 - (i * (y * j));
	elseif (x <= 4.2e-279)
		tmp = t_2;
	elseif (x <= 4.5e-116)
		tmp = t_1 - (b * (z * c));
	elseif (x <= 2.4e+100)
		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[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.5e+126], t$95$3, If[LessEqual[x, -9.5e+86], t$95$2, If[LessEqual[x, -3e-78], N[(t$95$3 - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.2e-279], t$95$2, If[LessEqual[x, 4.5e-116], N[(t$95$1 - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.4e+100], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.5000000000000003e126 or 2.40000000000000012e100 < x

   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 0 58.1%

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

   5. Simplified 64.6%

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

   6. Taylor expanded in x around inf 77.6%

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

      1. neg-mul-1 77.6%

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

      2. +-commutative 77.6%

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

      3. sub-neg 77.6%

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

   8. Simplified 77.6%

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

   if -3.5000000000000003e126 < x < -9.50000000000000028e86 or -2.99999999999999988e-78 < x < 4.20000000000000011e-279 or 4.50000000000000012e-116 < x < 2.40000000000000012e100

   1. Initial program 75.7%

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

   3. Taylor expanded in i around inf 74.8%

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

      1. associate-/l* 72.0%

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

   5. Simplified 72.0%

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

   6. Taylor expanded in x around 0 76.7%

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

      1. cancel-sign-sub-inv 76.7%

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

      2. +-commutative 76.7%

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

      3. +-commutative 76.7%

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

      4. cancel-sign-sub-inv 76.7%

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

      5. *-commutative 76.7%

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

      6. *-commutative 76.7%

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

      7. associate-/l* 74.8%

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

   8. Simplified 74.8%

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

   9. Taylor expanded in i around inf 70.1%

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

       1. associate-*r* 70.1%

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

       2. neg-mul-1 70.1%

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

   11. Simplified 70.1%

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

   if -9.50000000000000028e86 < x < -2.99999999999999988e-78

   1. Initial program 75.0%

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

   3. Taylor expanded in b around 0 65.7%

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

   4. Taylor expanded in c around 0 66.4%

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

      1. +-commutative 66.4%

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

      2. cancel-sign-sub-inv 66.4%

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

      3. fma-define 66.4%

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

      4. mul-1-neg 66.4%

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

      5. unsub-neg 66.4%

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

      6. fma-define 66.4%

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

      7. cancel-sign-sub-inv 66.4%

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

      8. *-commutative 66.4%

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

   6. Simplified 66.4%

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

   if 4.20000000000000011e-279 < x < 4.50000000000000012e-116

   1. Initial program 70.8%

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

   3. Taylor expanded in i around inf 68.2%

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

      1. associate-/l* 62.1%

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

   5. Simplified 62.1%

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

   6. Taylor expanded in x around 0 74.1%

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

      1. cancel-sign-sub-inv 74.1%

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

      2. +-commutative 74.1%

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

      3. +-commutative 74.1%

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

      4. cancel-sign-sub-inv 74.1%

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

      5. *-commutative 74.1%

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

      6. *-commutative 74.1%

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

      7. associate-/l* 68.3%

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

   8. Simplified 68.3%

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

   9. Taylor expanded in i around 0 76.7%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+126}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{+86}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-78}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-279}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-116}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+100}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 49.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.5 \cdot 10^{+172}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -4.5 \cdot 10^{-103}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq -1.65 \cdot 10^{-202}:\\ \;\;\;\;a \cdot \left(t \cdot \left(b \cdot \frac{i}{t} - x\right)\right)\\ \mathbf{elif}\;j \leq -1.9 \cdot 10^{-210}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 8 \cdot 10^{-222}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 7.2 \cdot 10^{-125}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 3.8 \cdot 10^{+26}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))))
   (if (<= j -1.5e+172)
     t_1
     (if (<= j -4.5e-103)
       (* x (- (* y z) (* t a)))
       (if (<= j -1.65e-202)
         (* a (* t (- (* b (/ i t)) x)))
         (if (<= j -1.9e-210)
           (* y (* x z))
           (if (<= j 8e-222)
             (* b (- (* a i) (* z c)))
             (if (<= j 7.2e-125)
               (* z (- (* x y) (* b c)))
               (if (<= j 3.8e+26) (* t (- (* c j) (* x a))) t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -1.5e+172) {
		tmp = t_1;
	} else if (j <= -4.5e-103) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= -1.65e-202) {
		tmp = a * (t * ((b * (i / t)) - x));
	} else if (j <= -1.9e-210) {
		tmp = y * (x * z);
	} else if (j <= 8e-222) {
		tmp = b * ((a * i) - (z * c));
	} else if (j <= 7.2e-125) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 3.8e+26) {
		tmp = t * ((c * j) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    if (j <= (-1.5d+172)) then
        tmp = t_1
    else if (j <= (-4.5d-103)) then
        tmp = x * ((y * z) - (t * a))
    else if (j <= (-1.65d-202)) then
        tmp = a * (t * ((b * (i / t)) - x))
    else if (j <= (-1.9d-210)) then
        tmp = y * (x * z)
    else if (j <= 8d-222) then
        tmp = b * ((a * i) - (z * c))
    else if (j <= 7.2d-125) then
        tmp = z * ((x * y) - (b * c))
    else if (j <= 3.8d+26) then
        tmp = t * ((c * j) - (x * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -1.5e+172) {
		tmp = t_1;
	} else if (j <= -4.5e-103) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= -1.65e-202) {
		tmp = a * (t * ((b * (i / t)) - x));
	} else if (j <= -1.9e-210) {
		tmp = y * (x * z);
	} else if (j <= 8e-222) {
		tmp = b * ((a * i) - (z * c));
	} else if (j <= 7.2e-125) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 3.8e+26) {
		tmp = t * ((c * j) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -1.5e+172:
		tmp = t_1
	elif j <= -4.5e-103:
		tmp = x * ((y * z) - (t * a))
	elif j <= -1.65e-202:
		tmp = a * (t * ((b * (i / t)) - x))
	elif j <= -1.9e-210:
		tmp = y * (x * z)
	elif j <= 8e-222:
		tmp = b * ((a * i) - (z * c))
	elif j <= 7.2e-125:
		tmp = z * ((x * y) - (b * c))
	elif j <= 3.8e+26:
		tmp = t * ((c * j) - (x * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -1.5e+172)
		tmp = t_1;
	elseif (j <= -4.5e-103)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (j <= -1.65e-202)
		tmp = Float64(a * Float64(t * Float64(Float64(b * Float64(i / t)) - x)));
	elseif (j <= -1.9e-210)
		tmp = Float64(y * Float64(x * z));
	elseif (j <= 8e-222)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (j <= 7.2e-125)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (j <= 3.8e+26)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -1.5e+172)
		tmp = t_1;
	elseif (j <= -4.5e-103)
		tmp = x * ((y * z) - (t * a));
	elseif (j <= -1.65e-202)
		tmp = a * (t * ((b * (i / t)) - x));
	elseif (j <= -1.9e-210)
		tmp = y * (x * z);
	elseif (j <= 8e-222)
		tmp = b * ((a * i) - (z * c));
	elseif (j <= 7.2e-125)
		tmp = z * ((x * y) - (b * c));
	elseif (j <= 3.8e+26)
		tmp = t * ((c * j) - (x * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.5e+172], t$95$1, If[LessEqual[j, -4.5e-103], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.65e-202], N[(a * N[(t * N[(N[(b * N[(i / t), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.9e-210], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8e-222], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7.2e-125], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.8e+26], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if j < -1.5e172 or 3.8000000000000002e26 < j

   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 71.7%

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

      1. *-commutative 71.7%

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

      2. *-commutative 71.7%

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

   5. Simplified 71.7%

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

   if -1.5e172 < j < -4.5e-103

   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 y around 0 69.0%

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

   5. Simplified 72.8%

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

   6. Taylor expanded in x around inf 57.6%

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

      1. neg-mul-1 57.6%

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

      2. +-commutative 57.6%

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

      3. sub-neg 57.6%

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

   8. Simplified 57.6%

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

   if -4.5e-103 < j < -1.64999999999999995e-202

   1. Initial program 76.3%

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

   3. Taylor expanded in a around inf 61.1%

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

      1. distribute-lft-out-- 61.1%

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

      2. *-commutative 61.1%

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

      3. *-commutative 61.1%

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

   5. Simplified 61.1%

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

   6. Taylor expanded in t around inf 66.7%

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

      1. +-commutative 66.7%

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

      2. neg-mul-1 66.7%

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

      3. unsub-neg 66.7%

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

      4. associate-/l* 72.6%

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

   8. Simplified 72.6%

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

   if -1.64999999999999995e-202 < j < -1.90000000000000002e-210

   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 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%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around inf 100.0%

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

   if -1.90000000000000002e-210 < j < 8.00000000000000038e-222

   1. Initial program 79.5%

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

   3. Taylor expanded in b around inf 70.7%

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

      1. *-commutative 70.7%

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

   5. Simplified 70.7%

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

   if 8.00000000000000038e-222 < j < 7.2000000000000004e-125

   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 z around inf 77.2%

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

      1. *-commutative 77.2%

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

   5. Simplified 77.2%

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

   if 7.2000000000000004e-125 < j < 3.8000000000000002e26

   1. Initial program 72.4%

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

   3. Taylor expanded in t around inf 64.5%

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

      1. +-commutative 64.5%

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

      2. mul-1-neg 64.5%

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

      3. unsub-neg 64.5%

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

      4. *-commutative 64.5%

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

      5. *-commutative 64.5%

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

   5. Simplified 64.5%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.5 \cdot 10^{+172}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -4.5 \cdot 10^{-103}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq -1.65 \cdot 10^{-202}:\\ \;\;\;\;a \cdot \left(t \cdot \left(b \cdot \frac{i}{t} - x\right)\right)\\ \mathbf{elif}\;j \leq -1.9 \cdot 10^{-210}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 8 \cdot 10^{-222}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 7.2 \cdot 10^{-125}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 3.8 \cdot 10^{+26}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 49.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.5 \cdot 10^{+172}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -5.5 \cdot 10^{-103}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq -1.65 \cdot 10^{-202}:\\ \;\;\;\;a \cdot \left(i \cdot \left(b - t \cdot \frac{x}{i}\right)\right)\\ \mathbf{elif}\;j \leq -2.1 \cdot 10^{-210}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 1.75 \cdot 10^{-224}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 2.1 \cdot 10^{-125}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 7 \cdot 10^{+24}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))))
   (if (<= j -1.5e+172)
     t_1
     (if (<= j -5.5e-103)
       (* x (- (* y z) (* t a)))
       (if (<= j -1.65e-202)
         (* a (* i (- b (* t (/ x i)))))
         (if (<= j -2.1e-210)
           (* y (* x z))
           (if (<= j 1.75e-224)
             (* b (- (* a i) (* z c)))
             (if (<= j 2.1e-125)
               (* z (- (* x y) (* b c)))
               (if (<= j 7e+24) (* t (- (* c j) (* x a))) t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -1.5e+172) {
		tmp = t_1;
	} else if (j <= -5.5e-103) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= -1.65e-202) {
		tmp = a * (i * (b - (t * (x / i))));
	} else if (j <= -2.1e-210) {
		tmp = y * (x * z);
	} else if (j <= 1.75e-224) {
		tmp = b * ((a * i) - (z * c));
	} else if (j <= 2.1e-125) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 7e+24) {
		tmp = t * ((c * j) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    if (j <= (-1.5d+172)) then
        tmp = t_1
    else if (j <= (-5.5d-103)) then
        tmp = x * ((y * z) - (t * a))
    else if (j <= (-1.65d-202)) then
        tmp = a * (i * (b - (t * (x / i))))
    else if (j <= (-2.1d-210)) then
        tmp = y * (x * z)
    else if (j <= 1.75d-224) then
        tmp = b * ((a * i) - (z * c))
    else if (j <= 2.1d-125) then
        tmp = z * ((x * y) - (b * c))
    else if (j <= 7d+24) then
        tmp = t * ((c * j) - (x * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -1.5e+172) {
		tmp = t_1;
	} else if (j <= -5.5e-103) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= -1.65e-202) {
		tmp = a * (i * (b - (t * (x / i))));
	} else if (j <= -2.1e-210) {
		tmp = y * (x * z);
	} else if (j <= 1.75e-224) {
		tmp = b * ((a * i) - (z * c));
	} else if (j <= 2.1e-125) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 7e+24) {
		tmp = t * ((c * j) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -1.5e+172:
		tmp = t_1
	elif j <= -5.5e-103:
		tmp = x * ((y * z) - (t * a))
	elif j <= -1.65e-202:
		tmp = a * (i * (b - (t * (x / i))))
	elif j <= -2.1e-210:
		tmp = y * (x * z)
	elif j <= 1.75e-224:
		tmp = b * ((a * i) - (z * c))
	elif j <= 2.1e-125:
		tmp = z * ((x * y) - (b * c))
	elif j <= 7e+24:
		tmp = t * ((c * j) - (x * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -1.5e+172)
		tmp = t_1;
	elseif (j <= -5.5e-103)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (j <= -1.65e-202)
		tmp = Float64(a * Float64(i * Float64(b - Float64(t * Float64(x / i)))));
	elseif (j <= -2.1e-210)
		tmp = Float64(y * Float64(x * z));
	elseif (j <= 1.75e-224)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (j <= 2.1e-125)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (j <= 7e+24)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -1.5e+172)
		tmp = t_1;
	elseif (j <= -5.5e-103)
		tmp = x * ((y * z) - (t * a));
	elseif (j <= -1.65e-202)
		tmp = a * (i * (b - (t * (x / i))));
	elseif (j <= -2.1e-210)
		tmp = y * (x * z);
	elseif (j <= 1.75e-224)
		tmp = b * ((a * i) - (z * c));
	elseif (j <= 2.1e-125)
		tmp = z * ((x * y) - (b * c));
	elseif (j <= 7e+24)
		tmp = t * ((c * j) - (x * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.5e+172], t$95$1, If[LessEqual[j, -5.5e-103], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.65e-202], N[(a * N[(i * N[(b - N[(t * N[(x / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.1e-210], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.75e-224], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.1e-125], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7e+24], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if j < -1.5e172 or 7.0000000000000004e24 < j

   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 71.7%

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

      1. *-commutative 71.7%

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

      2. *-commutative 71.7%

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

   5. Simplified 71.7%

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

   if -1.5e172 < j < -5.50000000000000032e-103

   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 y around 0 69.0%

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

   5. Simplified 72.8%

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

   6. Taylor expanded in x around inf 57.6%

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

      1. neg-mul-1 57.6%

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

      2. +-commutative 57.6%

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

      3. sub-neg 57.6%

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

   8. Simplified 57.6%

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

   if -5.50000000000000032e-103 < j < -1.64999999999999995e-202

   1. Initial program 76.3%

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

   3. Taylor expanded in a around inf 61.1%

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

      1. distribute-lft-out-- 61.1%

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

      2. *-commutative 61.1%

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

      3. *-commutative 61.1%

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

   5. Simplified 61.1%

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

   6. Taylor expanded in i around inf 72.1%

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

      1. mul-1-neg 72.1%

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

      2. unsub-neg 72.1%

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

      3. associate-/l* 72.1%

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

   8. Simplified 72.1%

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

   if -1.64999999999999995e-202 < j < -2.10000000000000016e-210

   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 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%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around inf 100.0%

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

   if -2.10000000000000016e-210 < j < 1.75000000000000009e-224

   1. Initial program 79.5%

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

   3. Taylor expanded in b around inf 70.7%

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

      1. *-commutative 70.7%

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

   5. Simplified 70.7%

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

   if 1.75000000000000009e-224 < j < 2.1e-125

   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 z around inf 77.2%

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

      1. *-commutative 77.2%

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

   5. Simplified 77.2%

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

   if 2.1e-125 < j < 7.0000000000000004e24

   1. Initial program 72.4%

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

   3. Taylor expanded in t around inf 64.5%

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

      1. +-commutative 64.5%

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

      2. mul-1-neg 64.5%

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

      3. unsub-neg 64.5%

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

      4. *-commutative 64.5%

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

      5. *-commutative 64.5%

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

   5. Simplified 64.5%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.5 \cdot 10^{+172}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -5.5 \cdot 10^{-103}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq -1.65 \cdot 10^{-202}:\\ \;\;\;\;a \cdot \left(i \cdot \left(b - t \cdot \frac{x}{i}\right)\right)\\ \mathbf{elif}\;j \leq -2.1 \cdot 10^{-210}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 1.75 \cdot 10^{-224}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 2.1 \cdot 10^{-125}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 7 \cdot 10^{+24}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 28.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.42 \cdot 10^{+137}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq -26500:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq -1.4 \cdot 10^{-109}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;c \leq -1.5 \cdot 10^{-237}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{-296}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq 4.8 \cdot 10^{-85}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{+125}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -1.42e+137)
   (* b (* z (- c)))
   (if (<= c -26500.0)
     (* x (* t (- a)))
     (if (<= c -1.4e-109)
       (* i (* a b))
       (if (<= c -1.5e-237)
         (* a (* t (- x)))
         (if (<= c 2.9e-296)
           (* b (* a i))
           (if (<= c 4.8e-85)
             (* y (* x z))
             (if (<= c 2.2e+125) (* i (* y (- 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 tmp;
	if (c <= -1.42e+137) {
		tmp = b * (z * -c);
	} else if (c <= -26500.0) {
		tmp = x * (t * -a);
	} else if (c <= -1.4e-109) {
		tmp = i * (a * b);
	} else if (c <= -1.5e-237) {
		tmp = a * (t * -x);
	} else if (c <= 2.9e-296) {
		tmp = b * (a * i);
	} else if (c <= 4.8e-85) {
		tmp = y * (x * z);
	} else if (c <= 2.2e+125) {
		tmp = i * (y * -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) :: tmp
    if (c <= (-1.42d+137)) then
        tmp = b * (z * -c)
    else if (c <= (-26500.0d0)) then
        tmp = x * (t * -a)
    else if (c <= (-1.4d-109)) then
        tmp = i * (a * b)
    else if (c <= (-1.5d-237)) then
        tmp = a * (t * -x)
    else if (c <= 2.9d-296) then
        tmp = b * (a * i)
    else if (c <= 4.8d-85) then
        tmp = y * (x * z)
    else if (c <= 2.2d+125) then
        tmp = i * (y * -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 tmp;
	if (c <= -1.42e+137) {
		tmp = b * (z * -c);
	} else if (c <= -26500.0) {
		tmp = x * (t * -a);
	} else if (c <= -1.4e-109) {
		tmp = i * (a * b);
	} else if (c <= -1.5e-237) {
		tmp = a * (t * -x);
	} else if (c <= 2.9e-296) {
		tmp = b * (a * i);
	} else if (c <= 4.8e-85) {
		tmp = y * (x * z);
	} else if (c <= 2.2e+125) {
		tmp = i * (y * -j);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -1.42e+137:
		tmp = b * (z * -c)
	elif c <= -26500.0:
		tmp = x * (t * -a)
	elif c <= -1.4e-109:
		tmp = i * (a * b)
	elif c <= -1.5e-237:
		tmp = a * (t * -x)
	elif c <= 2.9e-296:
		tmp = b * (a * i)
	elif c <= 4.8e-85:
		tmp = y * (x * z)
	elif c <= 2.2e+125:
		tmp = i * (y * -j)
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -1.42e+137)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (c <= -26500.0)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (c <= -1.4e-109)
		tmp = Float64(i * Float64(a * b));
	elseif (c <= -1.5e-237)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (c <= 2.9e-296)
		tmp = Float64(b * Float64(a * i));
	elseif (c <= 4.8e-85)
		tmp = Float64(y * Float64(x * z));
	elseif (c <= 2.2e+125)
		tmp = Float64(i * Float64(y * 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)
	tmp = 0.0;
	if (c <= -1.42e+137)
		tmp = b * (z * -c);
	elseif (c <= -26500.0)
		tmp = x * (t * -a);
	elseif (c <= -1.4e-109)
		tmp = i * (a * b);
	elseif (c <= -1.5e-237)
		tmp = a * (t * -x);
	elseif (c <= 2.9e-296)
		tmp = b * (a * i);
	elseif (c <= 4.8e-85)
		tmp = y * (x * z);
	elseif (c <= 2.2e+125)
		tmp = i * (y * -j);
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -1.42e+137], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -26500.0], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.4e-109], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.5e-237], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.9e-296], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.8e-85], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.2e+125], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if c < -1.42e137

   1. Initial program 56.4%

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

   3. Taylor expanded in b around inf 55.0%

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

      1. *-commutative 55.0%

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

   5. Simplified 55.0%

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

   6. Taylor expanded in a around 0 52.7%

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

      1. associate-*r* 52.7%

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

      2. neg-mul-1 52.7%

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

      3. *-commutative 52.7%

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

   8. Simplified 52.7%

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

   if -1.42e137 < c < -26500

   1. Initial program 65.2%

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

   3. Taylor expanded in b around 0 69.0%

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

   4. Taylor expanded in x around inf 61.8%

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

   5. Taylor expanded in a around inf 41.3%

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

      1. neg-mul-1 41.3%

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

      2. distribute-lft-neg-in 41.3%

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

      3. *-commutative 41.3%

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

   7. Simplified 41.3%

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

   if -26500 < c < -1.39999999999999989e-109

   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 b around inf 68.6%

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

      1. *-commutative 68.6%

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

   5. Simplified 68.6%

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

   6. Taylor expanded in a around inf 57.1%

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

      1. associate-*r* 61.0%

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

      2. *-commutative 61.0%

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

   8. Simplified 61.0%

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

   if -1.39999999999999989e-109 < c < -1.50000000000000012e-237

   1. Initial program 86.5%

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

   3. Taylor expanded in a around inf 50.2%

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

      1. distribute-lft-out-- 50.2%

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

      2. *-commutative 50.2%

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

      3. *-commutative 50.2%

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

   5. Simplified 50.2%

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

   6. Taylor expanded in x around inf 38.9%

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

      1. associate-*r* 38.9%

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

      2. mul-1-neg 38.9%

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

   8. Simplified 38.9%

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

   if -1.50000000000000012e-237 < c < 2.89999999999999983e-296

   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 b around inf 47.9%

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

      1. *-commutative 47.9%

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

   5. Simplified 47.9%

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

   6. Taylor expanded in a around inf 47.9%

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

      1. *-commutative 47.9%

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

   8. Simplified 47.9%

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

   if 2.89999999999999983e-296 < c < 4.8000000000000001e-85

   1. Initial program 77.8%

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

   3. Taylor expanded in y around inf 60.3%

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

      1. +-commutative 60.3%

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

      2. mul-1-neg 60.3%

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

      3. unsub-neg 60.3%

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

      4. *-commutative 60.3%

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

   5. Simplified 60.3%

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

   6. Taylor expanded in x around inf 45.3%

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

   if 4.8000000000000001e-85 < c < 2.19999999999999991e125

   1. Initial program 73.0%

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

   3. Taylor expanded in y around inf 48.9%

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

      1. +-commutative 48.9%

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

      2. mul-1-neg 48.9%

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

      3. unsub-neg 48.9%

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

      4. *-commutative 48.9%

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

   5. Simplified 48.9%

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

   6. Taylor expanded in x around 0 37.8%

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

      1. associate-*r* 37.8%

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

      2. neg-mul-1 37.8%

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

      3. *-commutative 37.8%

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

   8. Simplified 37.8%

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

   if 2.19999999999999991e125 < c

   1. Initial program 66.0%

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

   3. Taylor expanded in b around 0 63.0%

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

   4. Taylor expanded in x around inf 59.7%

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

   5. Taylor expanded in c around inf 49.6%

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

      1. *-commutative 49.6%

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

   7. Simplified 49.6%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.42 \cdot 10^{+137}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq -26500:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq -1.4 \cdot 10^{-109}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;c \leq -1.5 \cdot 10^{-237}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{-296}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq 4.8 \cdot 10^{-85}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{+125}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 28.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2 \cdot 10^{+138}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq -14000:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq -3.4 \cdot 10^{-109}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;c \leq -1.4 \cdot 10^{-236}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;c \leq 4 \cdot 10^{-296}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq 4.6 \cdot 10^{-85}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 4.8 \cdot 10^{+126}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -2e+138)
   (* b (* z (- c)))
   (if (<= c -14000.0)
     (* x (* t (- a)))
     (if (<= c -3.4e-109)
       (* i (* a b))
       (if (<= c -1.4e-236)
         (* a (* t (- x)))
         (if (<= c 4e-296)
           (* b (* a i))
           (if (<= c 4.6e-85)
             (* y (* x z))
             (if (<= c 4.8e+126) (* 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 tmp;
	if (c <= -2e+138) {
		tmp = b * (z * -c);
	} else if (c <= -14000.0) {
		tmp = x * (t * -a);
	} else if (c <= -3.4e-109) {
		tmp = i * (a * b);
	} else if (c <= -1.4e-236) {
		tmp = a * (t * -x);
	} else if (c <= 4e-296) {
		tmp = b * (a * i);
	} else if (c <= 4.6e-85) {
		tmp = y * (x * z);
	} else if (c <= 4.8e+126) {
		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) :: tmp
    if (c <= (-2d+138)) then
        tmp = b * (z * -c)
    else if (c <= (-14000.0d0)) then
        tmp = x * (t * -a)
    else if (c <= (-3.4d-109)) then
        tmp = i * (a * b)
    else if (c <= (-1.4d-236)) then
        tmp = a * (t * -x)
    else if (c <= 4d-296) then
        tmp = b * (a * i)
    else if (c <= 4.6d-85) then
        tmp = y * (x * z)
    else if (c <= 4.8d+126) 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 tmp;
	if (c <= -2e+138) {
		tmp = b * (z * -c);
	} else if (c <= -14000.0) {
		tmp = x * (t * -a);
	} else if (c <= -3.4e-109) {
		tmp = i * (a * b);
	} else if (c <= -1.4e-236) {
		tmp = a * (t * -x);
	} else if (c <= 4e-296) {
		tmp = b * (a * i);
	} else if (c <= 4.6e-85) {
		tmp = y * (x * z);
	} else if (c <= 4.8e+126) {
		tmp = y * (i * -j);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -2e+138:
		tmp = b * (z * -c)
	elif c <= -14000.0:
		tmp = x * (t * -a)
	elif c <= -3.4e-109:
		tmp = i * (a * b)
	elif c <= -1.4e-236:
		tmp = a * (t * -x)
	elif c <= 4e-296:
		tmp = b * (a * i)
	elif c <= 4.6e-85:
		tmp = y * (x * z)
	elif c <= 4.8e+126:
		tmp = y * (i * -j)
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -2e+138)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (c <= -14000.0)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (c <= -3.4e-109)
		tmp = Float64(i * Float64(a * b));
	elseif (c <= -1.4e-236)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (c <= 4e-296)
		tmp = Float64(b * Float64(a * i));
	elseif (c <= 4.6e-85)
		tmp = Float64(y * Float64(x * z));
	elseif (c <= 4.8e+126)
		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)
	tmp = 0.0;
	if (c <= -2e+138)
		tmp = b * (z * -c);
	elseif (c <= -14000.0)
		tmp = x * (t * -a);
	elseif (c <= -3.4e-109)
		tmp = i * (a * b);
	elseif (c <= -1.4e-236)
		tmp = a * (t * -x);
	elseif (c <= 4e-296)
		tmp = b * (a * i);
	elseif (c <= 4.6e-85)
		tmp = y * (x * z);
	elseif (c <= 4.8e+126)
		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_] := If[LessEqual[c, -2e+138], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -14000.0], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -3.4e-109], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.4e-236], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4e-296], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.6e-85], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.8e+126], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if c < -2.0000000000000001e138

   1. Initial program 56.4%

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

   3. Taylor expanded in b around inf 55.0%

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

      1. *-commutative 55.0%

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

   5. Simplified 55.0%

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

   6. Taylor expanded in a around 0 52.7%

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

      1. associate-*r* 52.7%

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

      2. neg-mul-1 52.7%

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

      3. *-commutative 52.7%

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

   8. Simplified 52.7%

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

   if -2.0000000000000001e138 < c < -14000

   1. Initial program 65.2%

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

   3. Taylor expanded in b around 0 69.0%

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

   4. Taylor expanded in x around inf 61.8%

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

   5. Taylor expanded in a around inf 41.3%

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

      1. neg-mul-1 41.3%

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

      2. distribute-lft-neg-in 41.3%

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

      3. *-commutative 41.3%

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

   7. Simplified 41.3%

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

   if -14000 < c < -3.40000000000000012e-109

   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 b around inf 68.6%

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

      1. *-commutative 68.6%

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

   5. Simplified 68.6%

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

   6. Taylor expanded in a around inf 57.1%

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

      1. associate-*r* 61.0%

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

      2. *-commutative 61.0%

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

   8. Simplified 61.0%

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

   if -3.40000000000000012e-109 < c < -1.39999999999999993e-236

   1. Initial program 86.5%

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

   3. Taylor expanded in a around inf 50.2%

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

      1. distribute-lft-out-- 50.2%

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

      2. *-commutative 50.2%

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

      3. *-commutative 50.2%

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

   5. Simplified 50.2%

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

   6. Taylor expanded in x around inf 38.9%

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

      1. associate-*r* 38.9%

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

      2. mul-1-neg 38.9%

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

   8. Simplified 38.9%

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

   if -1.39999999999999993e-236 < c < 4e-296

   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 b around inf 47.9%

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

      1. *-commutative 47.9%

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

   5. Simplified 47.9%

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

   6. Taylor expanded in a around inf 47.9%

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

      1. *-commutative 47.9%

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

   8. Simplified 47.9%

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

   if 4e-296 < c < 4.6000000000000001e-85

   1. Initial program 77.8%

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

   3. Taylor expanded in y around inf 60.3%

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

      1. +-commutative 60.3%

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

      2. mul-1-neg 60.3%

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

      3. unsub-neg 60.3%

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

      4. *-commutative 60.3%

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

   5. Simplified 60.3%

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

   6. Taylor expanded in x around inf 45.3%

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

   if 4.6000000000000001e-85 < c < 4.80000000000000024e126

   1. Initial program 73.0%

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

   3. Taylor expanded in y around inf 48.9%

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

      1. +-commutative 48.9%

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

      2. mul-1-neg 48.9%

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

      3. unsub-neg 48.9%

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

      4. *-commutative 48.9%

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

   5. Simplified 48.9%

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

   6. Taylor expanded in x around 0 35.6%

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

      1. mul-1-neg 35.6%

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

      2. distribute-rgt-neg-in 35.6%

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

   8. Simplified 35.6%

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

   if 4.80000000000000024e126 < c

   1. Initial program 66.0%

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

   3. Taylor expanded in b around 0 63.0%

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

   4. Taylor expanded in x around inf 59.7%

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

   5. Taylor expanded in c around inf 49.6%

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

      1. *-commutative 49.6%

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

   7. Simplified 49.6%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 46.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2 \cdot 10^{+138}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq -14000:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq -3.4 \cdot 10^{-109}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;c \leq -1.4 \cdot 10^{-236}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;c \leq 4 \cdot 10^{-296}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq 4.6 \cdot 10^{-85}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 4.8 \cdot 10^{+126}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := t\_1 + b \cdot \left(a \cdot i\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -2.3 \cdot 10^{+186}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-89}:\\ \;\;\;\;y \cdot \left(x \cdot z + \left(\frac{a \cdot \left(b \cdot i\right)}{y} - i \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 3.25 \cdot 10^{-273}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-116}:\\ \;\;\;\;t\_1 - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+84}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i))))
        (t_2 (+ t_1 (* b (* a i))))
        (t_3 (* x (- (* y z) (* t a)))))
   (if (<= x -2.3e+186)
     t_3
     (if (<= x -2e-89)
       (* y (+ (* x z) (- (/ (* a (* b i)) y) (* i j))))
       (if (<= x 3.25e-273)
         t_2
         (if (<= x 1.1e-116)
           (- t_1 (* b (* z c)))
           (if (<= x 3.9e+84) 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 = j * ((t * c) - (y * i));
	double t_2 = t_1 + (b * (a * i));
	double t_3 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -2.3e+186) {
		tmp = t_3;
	} else if (x <= -2e-89) {
		tmp = y * ((x * z) + (((a * (b * i)) / y) - (i * j)));
	} else if (x <= 3.25e-273) {
		tmp = t_2;
	} else if (x <= 1.1e-116) {
		tmp = t_1 - (b * (z * c));
	} else if (x <= 3.9e+84) {
		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 = j * ((t * c) - (y * i))
    t_2 = t_1 + (b * (a * i))
    t_3 = x * ((y * z) - (t * a))
    if (x <= (-2.3d+186)) then
        tmp = t_3
    else if (x <= (-2d-89)) then
        tmp = y * ((x * z) + (((a * (b * i)) / y) - (i * j)))
    else if (x <= 3.25d-273) then
        tmp = t_2
    else if (x <= 1.1d-116) then
        tmp = t_1 - (b * (z * c))
    else if (x <= 3.9d+84) 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 = j * ((t * c) - (y * i));
	double t_2 = t_1 + (b * (a * i));
	double t_3 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -2.3e+186) {
		tmp = t_3;
	} else if (x <= -2e-89) {
		tmp = y * ((x * z) + (((a * (b * i)) / y) - (i * j)));
	} else if (x <= 3.25e-273) {
		tmp = t_2;
	} else if (x <= 1.1e-116) {
		tmp = t_1 - (b * (z * c));
	} else if (x <= 3.9e+84) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = t_1 + (b * (a * i))
	t_3 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -2.3e+186:
		tmp = t_3
	elif x <= -2e-89:
		tmp = y * ((x * z) + (((a * (b * i)) / y) - (i * j)))
	elif x <= 3.25e-273:
		tmp = t_2
	elif x <= 1.1e-116:
		tmp = t_1 - (b * (z * c))
	elif x <= 3.9e+84:
		tmp = t_2
	else:
		tmp = t_3
	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(t_1 + Float64(b * Float64(a * i)))
	t_3 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -2.3e+186)
		tmp = t_3;
	elseif (x <= -2e-89)
		tmp = Float64(y * Float64(Float64(x * z) + Float64(Float64(Float64(a * Float64(b * i)) / y) - Float64(i * j))));
	elseif (x <= 3.25e-273)
		tmp = t_2;
	elseif (x <= 1.1e-116)
		tmp = Float64(t_1 - Float64(b * Float64(z * c)));
	elseif (x <= 3.9e+84)
		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 = j * ((t * c) - (y * i));
	t_2 = t_1 + (b * (a * i));
	t_3 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -2.3e+186)
		tmp = t_3;
	elseif (x <= -2e-89)
		tmp = y * ((x * z) + (((a * (b * i)) / y) - (i * j)));
	elseif (x <= 3.25e-273)
		tmp = t_2;
	elseif (x <= 1.1e-116)
		tmp = t_1 - (b * (z * c));
	elseif (x <= 3.9e+84)
		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[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.3e+186], t$95$3, If[LessEqual[x, -2e-89], N[(y * N[(N[(x * z), $MachinePrecision] + N[(N[(N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.25e-273], t$95$2, If[LessEqual[x, 1.1e-116], N[(t$95$1 - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.9e+84], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.30000000000000013e186 or 3.90000000000000016e84 < x

   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 y around 0 52.1%

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

   5. Simplified 60.0%

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

   6. Taylor expanded in x around inf 79.7%

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

      1. neg-mul-1 79.7%

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

      2. +-commutative 79.7%

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

      3. sub-neg 79.7%

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

   8. Simplified 79.7%

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

   if -2.30000000000000013e186 < x < -2.00000000000000008e-89

   1. Initial program 76.5%

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

   3. Taylor expanded in y around -inf 74.8%

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

   5. Simplified 80.1%

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

   6. Taylor expanded in i around inf 70.3%

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

   if -2.00000000000000008e-89 < x < 3.2499999999999999e-273 or 1.10000000000000005e-116 < x < 3.90000000000000016e84

   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 i around inf 73.7%

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

      1. associate-/l* 70.6%

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

   5. Simplified 70.6%

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

   6. Taylor expanded in x around 0 76.0%

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

      1. cancel-sign-sub-inv 76.0%

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

      2. +-commutative 76.0%

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

      3. +-commutative 76.0%

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

      4. cancel-sign-sub-inv 76.0%

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

      5. *-commutative 76.0%

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

      6. *-commutative 76.0%

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

      7. associate-/l* 75.0%

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

   8. Simplified 75.0%

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

   9. Taylor expanded in i around inf 69.0%

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

       1. associate-*r* 69.0%

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

       2. neg-mul-1 69.0%

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

   11. Simplified 69.0%

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

   if 3.2499999999999999e-273 < x < 1.10000000000000005e-116

   1. Initial program 70.8%

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

   3. Taylor expanded in i around inf 68.2%

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

      1. associate-/l* 62.1%

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

   5. Simplified 62.1%

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

   6. Taylor expanded in x around 0 74.1%

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

      1. cancel-sign-sub-inv 74.1%

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

      2. +-commutative 74.1%

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

      3. +-commutative 74.1%

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

      4. cancel-sign-sub-inv 74.1%

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

      5. *-commutative 74.1%

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

      6. *-commutative 74.1%

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

      7. associate-/l* 68.3%

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

   8. Simplified 68.3%

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

   9. Taylor expanded in i around 0 76.7%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+186}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-89}:\\ \;\;\;\;y \cdot \left(x \cdot z + \left(\frac{a \cdot \left(b \cdot i\right)}{y} - i \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 3.25 \cdot 10^{-273}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-116}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+84}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 68.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;y \leq -12:\\ \;\;\;\;y \cdot \left(\left(x \cdot z - \frac{t \cdot \left(x \cdot a - c \cdot j\right)}{y}\right) - i \cdot j\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-304}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + t\_1\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-61}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(c \cdot j - x \cdot a\right) - y \cdot \left(i \cdot j - x \cdot z\right)\right) - b \cdot \left(z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= y -12.0)
     (* y (- (- (* x z) (/ (* t (- (* x a) (* c j))) y)) (* i j)))
     (if (<= y 1.2e-304)
       (+ (* j (- (* t c) (* y i))) t_1)
       (if (<= y 9.5e-61)
         (+ (* x (- (* y z) (* t a))) t_1)
         (-
          (- (* t (- (* c j) (* x a))) (* y (- (* i j) (* x z))))
          (* b (* 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 = b * ((a * i) - (z * c));
	double tmp;
	if (y <= -12.0) {
		tmp = y * (((x * z) - ((t * ((x * a) - (c * j))) / y)) - (i * j));
	} else if (y <= 1.2e-304) {
		tmp = (j * ((t * c) - (y * i))) + t_1;
	} else if (y <= 9.5e-61) {
		tmp = (x * ((y * z) - (t * a))) + t_1;
	} else {
		tmp = ((t * ((c * j) - (x * a))) - (y * ((i * j) - (x * z)))) - (b * (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 = b * ((a * i) - (z * c))
    if (y <= (-12.0d0)) then
        tmp = y * (((x * z) - ((t * ((x * a) - (c * j))) / y)) - (i * j))
    else if (y <= 1.2d-304) then
        tmp = (j * ((t * c) - (y * i))) + t_1
    else if (y <= 9.5d-61) then
        tmp = (x * ((y * z) - (t * a))) + t_1
    else
        tmp = ((t * ((c * j) - (x * a))) - (y * ((i * j) - (x * z)))) - (b * (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 = b * ((a * i) - (z * c));
	double tmp;
	if (y <= -12.0) {
		tmp = y * (((x * z) - ((t * ((x * a) - (c * j))) / y)) - (i * j));
	} else if (y <= 1.2e-304) {
		tmp = (j * ((t * c) - (y * i))) + t_1;
	} else if (y <= 9.5e-61) {
		tmp = (x * ((y * z) - (t * a))) + t_1;
	} else {
		tmp = ((t * ((c * j) - (x * a))) - (y * ((i * j) - (x * z)))) - (b * (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	tmp = 0
	if y <= -12.0:
		tmp = y * (((x * z) - ((t * ((x * a) - (c * j))) / y)) - (i * j))
	elif y <= 1.2e-304:
		tmp = (j * ((t * c) - (y * i))) + t_1
	elif y <= 9.5e-61:
		tmp = (x * ((y * z) - (t * a))) + t_1
	else:
		tmp = ((t * ((c * j) - (x * a))) - (y * ((i * j) - (x * z)))) - (b * (z * c))
	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 (y <= -12.0)
		tmp = Float64(y * Float64(Float64(Float64(x * z) - Float64(Float64(t * Float64(Float64(x * a) - Float64(c * j))) / y)) - Float64(i * j)));
	elseif (y <= 1.2e-304)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + t_1);
	elseif (y <= 9.5e-61)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_1);
	else
		tmp = Float64(Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) - Float64(y * Float64(Float64(i * j) - Float64(x * z)))) - Float64(b * Float64(z * c)));
	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 (y <= -12.0)
		tmp = y * (((x * z) - ((t * ((x * a) - (c * j))) / y)) - (i * j));
	elseif (y <= 1.2e-304)
		tmp = (j * ((t * c) - (y * i))) + t_1;
	elseif (y <= 9.5e-61)
		tmp = (x * ((y * z) - (t * a))) + t_1;
	else
		tmp = ((t * ((c * j) - (x * a))) - (y * ((i * j) - (x * z)))) - (b * (z * c));
	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[y, -12.0], N[(y * N[(N[(N[(x * z), $MachinePrecision] - N[(N[(t * N[(N[(x * a), $MachinePrecision] - N[(c * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e-304], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[y, 9.5e-61], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(i * j), $MachinePrecision] - N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -12

   1. Initial program 64.7%

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

   3. Taylor expanded in y around -inf 82.2%

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

   5. Simplified 85.1%

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

   6. Taylor expanded in b around 0 83.4%

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

   if -12 < y < 1.2e-304

   1. Initial program 81.7%

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

   3. Taylor expanded in x around 0 76.6%

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

      1. fma-neg 76.6%

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

      2. *-rgt-identity 76.6%

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

      3. *-commutative 76.6%

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

      4. *-commutative 76.6%

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

      5. fma-neg 76.6%

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

      6. associate-*l* 76.6%

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

      7. *-rgt-identity 76.6%

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

      8. *-commutative 76.6%

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

   5. Simplified 76.6%

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

   if 1.2e-304 < y < 9.49999999999999986e-61

   1. Initial program 73.4%

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

   3. Taylor expanded in j around 0 77.1%

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

      1. *-commutative 77.1%

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

   5. Simplified 77.1%

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

   if 9.49999999999999986e-61 < y

   1. Initial program 71.0%

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

   3. Taylor expanded in y around 0 77.5%

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

   5. Simplified 81.3%

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

   6. Taylor expanded in z around inf 78.9%

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

      1. *-commutative 78.9%

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

   8. Simplified 78.9%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -12:\\ \;\;\;\;y \cdot \left(\left(x \cdot z - \frac{t \cdot \left(x \cdot a - c \cdot j\right)}{y}\right) - i \cdot j\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-304}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-61}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(c \cdot j - x \cdot a\right) - y \cdot \left(i \cdot j - x \cdot z\right)\right) - b \cdot \left(z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 66.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right) + t\_1\\ \mathbf{if}\;x \leq -1.9 \cdot 10^{+42}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-110}:\\ \;\;\;\;y \cdot \left(x \cdot z + \left(\frac{a \cdot \left(b \cdot i\right)}{y} - i \cdot j\right)\right)\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-143}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;x \leq 1.06 \cdot 10^{+70}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c))))
        (t_2 (+ (* x (- (* y z) (* t a))) t_1)))
   (if (<= x -1.9e+42)
     t_2
     (if (<= x -3e-110)
       (* y (+ (* x z) (- (/ (* a (* b i)) y) (* i j))))
       (if (<= x -1.35e-143)
         (* t (- (* c j) (* x a)))
         (if (<= x 1.06e+70) (+ (* j (- (* t c) (* y i))) t_1) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = (x * ((y * z) - (t * a))) + t_1;
	double tmp;
	if (x <= -1.9e+42) {
		tmp = t_2;
	} else if (x <= -3e-110) {
		tmp = y * ((x * z) + (((a * (b * i)) / y) - (i * j)));
	} else if (x <= -1.35e-143) {
		tmp = t * ((c * j) - (x * a));
	} else if (x <= 1.06e+70) {
		tmp = (j * ((t * c) - (y * i))) + t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = (x * ((y * z) - (t * a))) + t_1
    if (x <= (-1.9d+42)) then
        tmp = t_2
    else if (x <= (-3d-110)) then
        tmp = y * ((x * z) + (((a * (b * i)) / y) - (i * j)))
    else if (x <= (-1.35d-143)) then
        tmp = t * ((c * j) - (x * a))
    else if (x <= 1.06d+70) then
        tmp = (j * ((t * c) - (y * i))) + t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = (x * ((y * z) - (t * a))) + t_1;
	double tmp;
	if (x <= -1.9e+42) {
		tmp = t_2;
	} else if (x <= -3e-110) {
		tmp = y * ((x * z) + (((a * (b * i)) / y) - (i * j)));
	} else if (x <= -1.35e-143) {
		tmp = t * ((c * j) - (x * a));
	} else if (x <= 1.06e+70) {
		tmp = (j * ((t * c) - (y * i))) + t_1;
	} 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 = (x * ((y * z) - (t * a))) + t_1
	tmp = 0
	if x <= -1.9e+42:
		tmp = t_2
	elif x <= -3e-110:
		tmp = y * ((x * z) + (((a * (b * i)) / y) - (i * j)))
	elif x <= -1.35e-143:
		tmp = t * ((c * j) - (x * a))
	elif x <= 1.06e+70:
		tmp = (j * ((t * c) - (y * i))) + t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_1)
	tmp = 0.0
	if (x <= -1.9e+42)
		tmp = t_2;
	elseif (x <= -3e-110)
		tmp = Float64(y * Float64(Float64(x * z) + Float64(Float64(Float64(a * Float64(b * i)) / y) - Float64(i * j))));
	elseif (x <= -1.35e-143)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (x <= 1.06e+70)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = (x * ((y * z) - (t * a))) + t_1;
	tmp = 0.0;
	if (x <= -1.9e+42)
		tmp = t_2;
	elseif (x <= -3e-110)
		tmp = y * ((x * z) + (((a * (b * i)) / y) - (i * j)));
	elseif (x <= -1.35e-143)
		tmp = t * ((c * j) - (x * a));
	elseif (x <= 1.06e+70)
		tmp = (j * ((t * c) - (y * i))) + t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[x, -1.9e+42], t$95$2, If[LessEqual[x, -3e-110], N[(y * N[(N[(x * z), $MachinePrecision] + N[(N[(N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.35e-143], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.06e+70], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.8999999999999999e42 or 1.06e70 < x

   1. Initial program 69.9%

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

   3. Taylor expanded in j around 0 76.8%

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

      1. *-commutative 76.8%

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

   5. Simplified 76.8%

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

   if -1.8999999999999999e42 < x < -2.99999999999999986e-110

   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 y around -inf 78.5%

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

   5. Simplified 78.2%

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

   6. Taylor expanded in i around inf 78.9%

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

   if -2.99999999999999986e-110 < x < -1.35000000000000005e-143

   1. Initial program 71.2%

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

   3. Taylor expanded in t around inf 86.6%

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

      1. +-commutative 86.6%

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

      2. mul-1-neg 86.6%

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

      3. unsub-neg 86.6%

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

      4. *-commutative 86.6%

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

      5. *-commutative 86.6%

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

   5. Simplified 86.6%

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

   if -1.35000000000000005e-143 < x < 1.06e70

   1. Initial program 73.8%

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

   3. Taylor expanded in x around 0 78.7%

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

      1. fma-neg 81.2%

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

      2. *-rgt-identity 81.2%

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

      3. *-commutative 81.2%

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

      4. *-commutative 81.2%

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

      5. fma-neg 78.7%

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

      6. associate-*l* 78.7%

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

      7. *-rgt-identity 78.7%

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

      8. *-commutative 78.7%

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

   5. Simplified 78.7%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-110}:\\ \;\;\;\;y \cdot \left(x \cdot z + \left(\frac{a \cdot \left(b \cdot i\right)}{y} - i \cdot j\right)\right)\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-143}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;x \leq 1.06 \cdot 10^{+70}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 59.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -2.2 \cdot 10^{+186}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-91}:\\ \;\;\;\;y \cdot \left(x \cdot z + \left(\frac{a \cdot \left(b \cdot i\right)}{y} - i \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-177}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+86}:\\ \;\;\;\;b \cdot \left(i \cdot \left(a - z \cdot \frac{c}{i}\right)\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= x -2.2e+186)
     t_1
     (if (<= x -1.3e-91)
       (* y (+ (* x z) (- (/ (* a (* b i)) y) (* i j))))
       (if (<= x 1.85e-177)
         (+ (* j (- (* t c) (* y i))) (* b (* a i)))
         (if (<= x 4.8e+86)
           (- (* b (* i (- a (* z (/ c i))))) (* i (* y j)))
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -2.2e+186) {
		tmp = t_1;
	} else if (x <= -1.3e-91) {
		tmp = y * ((x * z) + (((a * (b * i)) / y) - (i * j)));
	} else if (x <= 1.85e-177) {
		tmp = (j * ((t * c) - (y * i))) + (b * (a * i));
	} else if (x <= 4.8e+86) {
		tmp = (b * (i * (a - (z * (c / i))))) - (i * (y * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (x <= (-2.2d+186)) then
        tmp = t_1
    else if (x <= (-1.3d-91)) then
        tmp = y * ((x * z) + (((a * (b * i)) / y) - (i * j)))
    else if (x <= 1.85d-177) then
        tmp = (j * ((t * c) - (y * i))) + (b * (a * i))
    else if (x <= 4.8d+86) then
        tmp = (b * (i * (a - (z * (c / i))))) - (i * (y * j))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -2.2e+186) {
		tmp = t_1;
	} else if (x <= -1.3e-91) {
		tmp = y * ((x * z) + (((a * (b * i)) / y) - (i * j)));
	} else if (x <= 1.85e-177) {
		tmp = (j * ((t * c) - (y * i))) + (b * (a * i));
	} else if (x <= 4.8e+86) {
		tmp = (b * (i * (a - (z * (c / i))))) - (i * (y * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -2.2e+186:
		tmp = t_1
	elif x <= -1.3e-91:
		tmp = y * ((x * z) + (((a * (b * i)) / y) - (i * j)))
	elif x <= 1.85e-177:
		tmp = (j * ((t * c) - (y * i))) + (b * (a * i))
	elif x <= 4.8e+86:
		tmp = (b * (i * (a - (z * (c / i))))) - (i * (y * j))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -2.2e+186)
		tmp = t_1;
	elseif (x <= -1.3e-91)
		tmp = Float64(y * Float64(Float64(x * z) + Float64(Float64(Float64(a * Float64(b * i)) / y) - Float64(i * j))));
	elseif (x <= 1.85e-177)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(b * Float64(a * i)));
	elseif (x <= 4.8e+86)
		tmp = Float64(Float64(b * Float64(i * Float64(a - Float64(z * Float64(c / i))))) - Float64(i * Float64(y * j)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -2.2e+186)
		tmp = t_1;
	elseif (x <= -1.3e-91)
		tmp = y * ((x * z) + (((a * (b * i)) / y) - (i * j)));
	elseif (x <= 1.85e-177)
		tmp = (j * ((t * c) - (y * i))) + (b * (a * i));
	elseif (x <= 4.8e+86)
		tmp = (b * (i * (a - (z * (c / i))))) - (i * (y * j));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.2e+186], t$95$1, If[LessEqual[x, -1.3e-91], N[(y * N[(N[(x * z), $MachinePrecision] + N[(N[(N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.85e-177], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.8e+86], N[(N[(b * N[(i * N[(a - N[(z * N[(c / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.1999999999999998e186 or 4.8000000000000001e86 < x

   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 y around 0 52.1%

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

   5. Simplified 60.0%

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

   6. Taylor expanded in x around inf 79.7%

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

      1. neg-mul-1 79.7%

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

      2. +-commutative 79.7%

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

      3. sub-neg 79.7%

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

   8. Simplified 79.7%

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

   if -2.1999999999999998e186 < x < -1.30000000000000007e-91

   1. Initial program 76.5%

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

   3. Taylor expanded in y around -inf 74.8%

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

   5. Simplified 80.1%

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

   6. Taylor expanded in i around inf 70.3%

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

   if -1.30000000000000007e-91 < x < 1.84999999999999997e-177

   1. Initial program 69.9%

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

   3. Taylor expanded in i around inf 67.3%

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

      1. associate-/l* 63.1%

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

   5. Simplified 63.1%

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

   6. Taylor expanded in x around 0 76.8%

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

      1. cancel-sign-sub-inv 76.8%

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

      2. +-commutative 76.8%

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

      3. +-commutative 76.8%

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

      4. cancel-sign-sub-inv 76.8%

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

      5. *-commutative 76.8%

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

      6. *-commutative 76.8%

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

      7. associate-/l* 72.8%

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

   8. Simplified 72.8%

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

   9. Taylor expanded in i around inf 67.5%

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

       1. associate-*r* 67.5%

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

       2. neg-mul-1 67.5%

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

   11. Simplified 67.5%

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

   if 1.84999999999999997e-177 < x < 4.8000000000000001e86

   1. Initial program 78.4%

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

   3. Taylor expanded in i around inf 78.5%

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

      1. associate-/l* 75.2%

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

   5. Simplified 75.2%

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

   6. Taylor expanded in x around 0 73.9%

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

      1. cancel-sign-sub-inv 73.9%

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

      2. +-commutative 73.9%

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

      3. +-commutative 73.9%

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

      4. cancel-sign-sub-inv 73.9%

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

      5. *-commutative 73.9%

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

      6. *-commutative 73.9%

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

      7. associate-/l* 73.9%

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

   8. Simplified 73.9%

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

   9. Taylor expanded in c around 0 69.0%

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

       1. associate-*r* 69.0%

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

       2. neg-mul-1 69.0%

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

       3. *-commutative 69.0%

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

   11. Simplified 69.0%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+186}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-91}:\\ \;\;\;\;y \cdot \left(x \cdot z + \left(\frac{a \cdot \left(b \cdot i\right)}{y} - i \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-177}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+86}:\\ \;\;\;\;b \cdot \left(i \cdot \left(a - z \cdot \frac{c}{i}\right)\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 28.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ \mathbf{if}\;c \leq -13000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -2 \cdot 10^{-110}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;c \leq -9.6 \cdot 10^{-238}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;c \leq 4.1 \cdot 10^{-296}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{-85}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 2 \cdot 10^{+125}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j))))
   (if (<= c -13000.0)
     t_1
     (if (<= c -2e-110)
       (* i (* a b))
       (if (<= c -9.6e-238)
         (* a (* t (- x)))
         (if (<= c 4.1e-296)
           (* b (* a i))
           (if (<= c 1.1e-85)
             (* y (* x z))
             (if (<= c 2e+125) (* y (* i (- j))) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double tmp;
	if (c <= -13000.0) {
		tmp = t_1;
	} else if (c <= -2e-110) {
		tmp = i * (a * b);
	} else if (c <= -9.6e-238) {
		tmp = a * (t * -x);
	} else if (c <= 4.1e-296) {
		tmp = b * (a * i);
	} else if (c <= 1.1e-85) {
		tmp = y * (x * z);
	} else if (c <= 2e+125) {
		tmp = y * (i * -j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (t * j)
    if (c <= (-13000.0d0)) then
        tmp = t_1
    else if (c <= (-2d-110)) then
        tmp = i * (a * b)
    else if (c <= (-9.6d-238)) then
        tmp = a * (t * -x)
    else if (c <= 4.1d-296) then
        tmp = b * (a * i)
    else if (c <= 1.1d-85) then
        tmp = y * (x * z)
    else if (c <= 2d+125) then
        tmp = y * (i * -j)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double tmp;
	if (c <= -13000.0) {
		tmp = t_1;
	} else if (c <= -2e-110) {
		tmp = i * (a * b);
	} else if (c <= -9.6e-238) {
		tmp = a * (t * -x);
	} else if (c <= 4.1e-296) {
		tmp = b * (a * i);
	} else if (c <= 1.1e-85) {
		tmp = y * (x * z);
	} else if (c <= 2e+125) {
		tmp = y * (i * -j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (t * j)
	tmp = 0
	if c <= -13000.0:
		tmp = t_1
	elif c <= -2e-110:
		tmp = i * (a * b)
	elif c <= -9.6e-238:
		tmp = a * (t * -x)
	elif c <= 4.1e-296:
		tmp = b * (a * i)
	elif c <= 1.1e-85:
		tmp = y * (x * z)
	elif c <= 2e+125:
		tmp = y * (i * -j)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(t * j))
	tmp = 0.0
	if (c <= -13000.0)
		tmp = t_1;
	elseif (c <= -2e-110)
		tmp = Float64(i * Float64(a * b));
	elseif (c <= -9.6e-238)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (c <= 4.1e-296)
		tmp = Float64(b * Float64(a * i));
	elseif (c <= 1.1e-85)
		tmp = Float64(y * Float64(x * z));
	elseif (c <= 2e+125)
		tmp = Float64(y * Float64(i * Float64(-j)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (t * j);
	tmp = 0.0;
	if (c <= -13000.0)
		tmp = t_1;
	elseif (c <= -2e-110)
		tmp = i * (a * b);
	elseif (c <= -9.6e-238)
		tmp = a * (t * -x);
	elseif (c <= 4.1e-296)
		tmp = b * (a * i);
	elseif (c <= 1.1e-85)
		tmp = y * (x * z);
	elseif (c <= 2e+125)
		tmp = y * (i * -j);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -13000.0], t$95$1, If[LessEqual[c, -2e-110], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -9.6e-238], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.1e-296], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.1e-85], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2e+125], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -13000 or 1.9999999999999998e125 < c

   1. Initial program 61.6%

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

   3. Taylor expanded in b around 0 55.9%

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

   4. Taylor expanded in x around inf 53.1%

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

   5. Taylor expanded in c around inf 43.1%

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

      1. *-commutative 43.1%

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

   7. Simplified 43.1%

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

   if -13000 < c < -2.0000000000000001e-110

   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 b around inf 68.6%

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

      1. *-commutative 68.6%

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

   5. Simplified 68.6%

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

   6. Taylor expanded in a around inf 57.1%

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

      1. associate-*r* 61.0%

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

      2. *-commutative 61.0%

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

   8. Simplified 61.0%

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

   if -2.0000000000000001e-110 < c < -9.5999999999999994e-238

   1. Initial program 86.5%

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

   3. Taylor expanded in a around inf 50.2%

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

      1. distribute-lft-out-- 50.2%

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

      2. *-commutative 50.2%

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

      3. *-commutative 50.2%

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

   5. Simplified 50.2%

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

   6. Taylor expanded in x around inf 38.9%

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

      1. associate-*r* 38.9%

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

      2. mul-1-neg 38.9%

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

   8. Simplified 38.9%

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

   if -9.5999999999999994e-238 < c < 4.09999999999999994e-296

   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 b around inf 47.9%

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

      1. *-commutative 47.9%

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

   5. Simplified 47.9%

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

   6. Taylor expanded in a around inf 47.9%

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

      1. *-commutative 47.9%

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

   8. Simplified 47.9%

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

   if 4.09999999999999994e-296 < c < 1.1e-85

   1. Initial program 77.8%

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

   3. Taylor expanded in y around inf 60.3%

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

      1. +-commutative 60.3%

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

      2. mul-1-neg 60.3%

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

      3. unsub-neg 60.3%

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

      4. *-commutative 60.3%

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

   5. Simplified 60.3%

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

   6. Taylor expanded in x around inf 45.3%

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

   if 1.1e-85 < c < 1.9999999999999998e125

   1. Initial program 73.0%

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

   3. Taylor expanded in y around inf 48.9%

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

      1. +-commutative 48.9%

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

      2. mul-1-neg 48.9%

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

      3. unsub-neg 48.9%

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

      4. *-commutative 48.9%

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

   5. Simplified 48.9%

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

   6. Taylor expanded in x around 0 35.6%

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

      1. mul-1-neg 35.6%

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

      2. distribute-rgt-neg-in 35.6%

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

   8. Simplified 35.6%

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

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -13000:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;c \leq -2 \cdot 10^{-110}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;c \leq -9.6 \cdot 10^{-238}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;c \leq 4.1 \cdot 10^{-296}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{-85}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 2 \cdot 10^{+125}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 30.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t \cdot \left(-x\right)\right)\\ t_2 := c \cdot \left(t \cdot j\right)\\ \mathbf{if}\;t \leq -6.5 \cdot 10^{+242}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{+99}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-29}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-193}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-72}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+179}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* t (- x)))) (t_2 (* c (* t j))))
   (if (<= t -6.5e+242)
     t_2
     (if (<= t -1.65e+99)
       t_1
       (if (<= t -3.3e-29)
         t_2
         (if (<= t 1.8e-193)
           (* b (* a i))
           (if (<= t 7.2e-72)
             (* y (* x z))
             (if (<= t 1.15e+179) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (t * -x);
	double t_2 = c * (t * j);
	double tmp;
	if (t <= -6.5e+242) {
		tmp = t_2;
	} else if (t <= -1.65e+99) {
		tmp = t_1;
	} else if (t <= -3.3e-29) {
		tmp = t_2;
	} else if (t <= 1.8e-193) {
		tmp = b * (a * i);
	} else if (t <= 7.2e-72) {
		tmp = y * (x * z);
	} else if (t <= 1.15e+179) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (t * -x)
    t_2 = c * (t * j)
    if (t <= (-6.5d+242)) then
        tmp = t_2
    else if (t <= (-1.65d+99)) then
        tmp = t_1
    else if (t <= (-3.3d-29)) then
        tmp = t_2
    else if (t <= 1.8d-193) then
        tmp = b * (a * i)
    else if (t <= 7.2d-72) then
        tmp = y * (x * z)
    else if (t <= 1.15d+179) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (t * -x);
	double t_2 = c * (t * j);
	double tmp;
	if (t <= -6.5e+242) {
		tmp = t_2;
	} else if (t <= -1.65e+99) {
		tmp = t_1;
	} else if (t <= -3.3e-29) {
		tmp = t_2;
	} else if (t <= 1.8e-193) {
		tmp = b * (a * i);
	} else if (t <= 7.2e-72) {
		tmp = y * (x * z);
	} else if (t <= 1.15e+179) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (t * -x)
	t_2 = c * (t * j)
	tmp = 0
	if t <= -6.5e+242:
		tmp = t_2
	elif t <= -1.65e+99:
		tmp = t_1
	elif t <= -3.3e-29:
		tmp = t_2
	elif t <= 1.8e-193:
		tmp = b * (a * i)
	elif t <= 7.2e-72:
		tmp = y * (x * z)
	elif t <= 1.15e+179:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(t * Float64(-x)))
	t_2 = Float64(c * Float64(t * j))
	tmp = 0.0
	if (t <= -6.5e+242)
		tmp = t_2;
	elseif (t <= -1.65e+99)
		tmp = t_1;
	elseif (t <= -3.3e-29)
		tmp = t_2;
	elseif (t <= 1.8e-193)
		tmp = Float64(b * Float64(a * i));
	elseif (t <= 7.2e-72)
		tmp = Float64(y * Float64(x * z));
	elseif (t <= 1.15e+179)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (t * -x);
	t_2 = c * (t * j);
	tmp = 0.0;
	if (t <= -6.5e+242)
		tmp = t_2;
	elseif (t <= -1.65e+99)
		tmp = t_1;
	elseif (t <= -3.3e-29)
		tmp = t_2;
	elseif (t <= 1.8e-193)
		tmp = b * (a * i);
	elseif (t <= 7.2e-72)
		tmp = y * (x * z);
	elseif (t <= 1.15e+179)
		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[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.5e+242], t$95$2, If[LessEqual[t, -1.65e+99], t$95$1, If[LessEqual[t, -3.3e-29], t$95$2, If[LessEqual[t, 1.8e-193], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.2e-72], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e+179], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.49999999999999992e242 or -1.65e99 < t < -3.30000000000000028e-29 or 1.14999999999999997e179 < 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 b around 0 59.7%

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

   4. Taylor expanded in x around inf 56.2%

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

   5. Taylor expanded in c around inf 50.3%

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

      1. *-commutative 50.3%

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

   7. Simplified 50.3%

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

   if -6.49999999999999992e242 < t < -1.65e99 or 7.2e-72 < t < 1.14999999999999997e179

   1. Initial program 71.2%

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

   3. Taylor expanded in a around inf 48.0%

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

      1. distribute-lft-out-- 48.0%

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

      2. *-commutative 48.0%

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

      3. *-commutative 48.0%

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

   5. Simplified 48.0%

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

   6. Taylor expanded in x around inf 38.2%

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

      1. associate-*r* 38.2%

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

      2. mul-1-neg 38.2%

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

   8. Simplified 38.2%

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

   if -3.30000000000000028e-29 < t < 1.7999999999999999e-193

   1. Initial program 88.5%

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

   3. Taylor expanded in b around inf 56.2%

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

      1. *-commutative 56.2%

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

   5. Simplified 56.2%

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

   6. Taylor expanded in a around inf 38.6%

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

      1. *-commutative 38.6%

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

   8. Simplified 38.6%

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

   if 1.7999999999999999e-193 < t < 7.2e-72

   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 y around inf 56.8%

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

      1. +-commutative 56.8%

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

      2. mul-1-neg 56.8%

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

      3. unsub-neg 56.8%

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

      4. *-commutative 56.8%

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

   5. Simplified 56.8%

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

   6. Taylor expanded in x around inf 44.0%

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

4. Final simplification 42.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+242}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{+99}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-29}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-193}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-72}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+179}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 68.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := a \cdot \left(b \cdot i\right) + \left(t\_1 - i \cdot \left(y \cdot j\right)\right)\\ \mathbf{if}\;x \leq -4.05 \cdot 10^{-84}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+66}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + t\_2\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+194}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1 + t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (* b (- (* a i) (* z c))))
        (t_3 (+ (* a (* b i)) (- t_1 (* i (* y j))))))
   (if (<= x -4.05e-84)
     t_3
     (if (<= x 4.5e+66)
       (+ (* j (- (* t c) (* y i))) t_2)
       (if (<= x 8e+194) t_3 (+ 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));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = (a * (b * i)) + (t_1 - (i * (y * j)));
	double tmp;
	if (x <= -4.05e-84) {
		tmp = t_3;
	} else if (x <= 4.5e+66) {
		tmp = (j * ((t * c) - (y * i))) + t_2;
	} else if (x <= 8e+194) {
		tmp = t_3;
	} else {
		tmp = t_1 + t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = b * ((a * i) - (z * c))
    t_3 = (a * (b * i)) + (t_1 - (i * (y * j)))
    if (x <= (-4.05d-84)) then
        tmp = t_3
    else if (x <= 4.5d+66) then
        tmp = (j * ((t * c) - (y * i))) + t_2
    else if (x <= 8d+194) then
        tmp = t_3
    else
        tmp = t_1 + t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = (a * (b * i)) + (t_1 - (i * (y * j)));
	double tmp;
	if (x <= -4.05e-84) {
		tmp = t_3;
	} else if (x <= 4.5e+66) {
		tmp = (j * ((t * c) - (y * i))) + t_2;
	} else if (x <= 8e+194) {
		tmp = t_3;
	} else {
		tmp = t_1 + t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = b * ((a * i) - (z * c))
	t_3 = (a * (b * i)) + (t_1 - (i * (y * j)))
	tmp = 0
	if x <= -4.05e-84:
		tmp = t_3
	elif x <= 4.5e+66:
		tmp = (j * ((t * c) - (y * i))) + t_2
	elif x <= 8e+194:
		tmp = t_3
	else:
		tmp = t_1 + t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_3 = Float64(Float64(a * Float64(b * i)) + Float64(t_1 - Float64(i * Float64(y * j))))
	tmp = 0.0
	if (x <= -4.05e-84)
		tmp = t_3;
	elseif (x <= 4.5e+66)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + t_2);
	elseif (x <= 8e+194)
		tmp = t_3;
	else
		tmp = Float64(t_1 + t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = b * ((a * i) - (z * c));
	t_3 = (a * (b * i)) + (t_1 - (i * (y * j)));
	tmp = 0.0;
	if (x <= -4.05e-84)
		tmp = t_3;
	elseif (x <= 4.5e+66)
		tmp = (j * ((t * c) - (y * i))) + t_2;
	elseif (x <= 8e+194)
		tmp = t_3;
	else
		tmp = t_1 + t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.05e-84], t$95$3, If[LessEqual[x, 4.5e+66], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[x, 8e+194], t$95$3, N[(t$95$1 + t$95$2), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.0499999999999999e-84 or 4.4999999999999998e66 < x < 7.99999999999999956e194

   1. Initial program 70.4%

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

   3. Taylor expanded in c around 0 78.7%

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

   if -4.0499999999999999e-84 < x < 4.4999999999999998e66

   1. Initial program 74.1%

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

   3. Taylor expanded in x around 0 77.9%

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

      1. fma-neg 80.3%

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

      2. *-rgt-identity 80.3%

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

      3. *-commutative 80.3%

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

      4. *-commutative 80.3%

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

      5. fma-neg 77.9%

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

      6. associate-*l* 77.9%

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

      7. *-rgt-identity 77.9%

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

      8. *-commutative 77.9%

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

   5. Simplified 77.9%

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

   if 7.99999999999999956e194 < x

   1. Initial program 71.3%

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

   3. Taylor expanded in j around 0 89.1%

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

      1. *-commutative 89.1%

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

   5. Simplified 89.1%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.05 \cdot 10^{-84}:\\ \;\;\;\;a \cdot \left(b \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+66}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+194}:\\ \;\;\;\;a \cdot \left(b \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 58.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{if}\;j \leq -1.2 \cdot 10^{+173}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -9 \cdot 10^{-71}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 4.7 \cdot 10^{-101}:\\ \;\;\;\;b \cdot \left(\left(a \cdot i + \frac{x \cdot \left(y \cdot z\right)}{b}\right) - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1100000000:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* j (- (* t c) (* y i))) (* b (* a i))))
        (t_2 (- (* x (- (* y z) (* t a))) (* i (* y j)))))
   (if (<= j -1.2e+173)
     t_1
     (if (<= j -9e-71)
       t_2
       (if (<= j 4.7e-101)
         (* b (- (+ (* a i) (/ (* x (* y z)) b)) (* z c)))
         (if (<= j 1100000000.0) 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 = (j * ((t * c) - (y * i))) + (b * (a * i));
	double t_2 = (x * ((y * z) - (t * a))) - (i * (y * j));
	double tmp;
	if (j <= -1.2e+173) {
		tmp = t_1;
	} else if (j <= -9e-71) {
		tmp = t_2;
	} else if (j <= 4.7e-101) {
		tmp = b * (((a * i) + ((x * (y * z)) / b)) - (z * c));
	} else if (j <= 1100000000.0) {
		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 = (j * ((t * c) - (y * i))) + (b * (a * i))
    t_2 = (x * ((y * z) - (t * a))) - (i * (y * j))
    if (j <= (-1.2d+173)) then
        tmp = t_1
    else if (j <= (-9d-71)) then
        tmp = t_2
    else if (j <= 4.7d-101) then
        tmp = b * (((a * i) + ((x * (y * z)) / b)) - (z * c))
    else if (j <= 1100000000.0d0) 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 = (j * ((t * c) - (y * i))) + (b * (a * i));
	double t_2 = (x * ((y * z) - (t * a))) - (i * (y * j));
	double tmp;
	if (j <= -1.2e+173) {
		tmp = t_1;
	} else if (j <= -9e-71) {
		tmp = t_2;
	} else if (j <= 4.7e-101) {
		tmp = b * (((a * i) + ((x * (y * z)) / b)) - (z * c));
	} else if (j <= 1100000000.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((t * c) - (y * i))) + (b * (a * i))
	t_2 = (x * ((y * z) - (t * a))) - (i * (y * j))
	tmp = 0
	if j <= -1.2e+173:
		tmp = t_1
	elif j <= -9e-71:
		tmp = t_2
	elif j <= 4.7e-101:
		tmp = b * (((a * i) + ((x * (y * z)) / b)) - (z * c))
	elif j <= 1100000000.0:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(b * Float64(a * i)))
	t_2 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(i * Float64(y * j)))
	tmp = 0.0
	if (j <= -1.2e+173)
		tmp = t_1;
	elseif (j <= -9e-71)
		tmp = t_2;
	elseif (j <= 4.7e-101)
		tmp = Float64(b * Float64(Float64(Float64(a * i) + Float64(Float64(x * Float64(y * z)) / b)) - Float64(z * c)));
	elseif (j <= 1100000000.0)
		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 = (j * ((t * c) - (y * i))) + (b * (a * i));
	t_2 = (x * ((y * z) - (t * a))) - (i * (y * j));
	tmp = 0.0;
	if (j <= -1.2e+173)
		tmp = t_1;
	elseif (j <= -9e-71)
		tmp = t_2;
	elseif (j <= 4.7e-101)
		tmp = b * (((a * i) + ((x * (y * z)) / b)) - (z * c));
	elseif (j <= 1100000000.0)
		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[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.2e+173], t$95$1, If[LessEqual[j, -9e-71], t$95$2, If[LessEqual[j, 4.7e-101], N[(b * N[(N[(N[(a * i), $MachinePrecision] + N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1100000000.0], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.2e173 or 1.1e9 < j

   1. Initial program 69.3%

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

   3. Taylor expanded in i around inf 66.1%

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

      1. associate-/l* 64.0%

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

   5. Simplified 64.0%

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

   6. Taylor expanded in x around 0 70.6%

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

      1. cancel-sign-sub-inv 70.6%

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

      2. +-commutative 70.6%

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

      3. +-commutative 70.6%

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

      4. cancel-sign-sub-inv 70.6%

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

      5. *-commutative 70.6%

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

      6. *-commutative 70.6%

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

      7. associate-/l* 68.5%

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

   8. Simplified 68.5%

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

   9. Taylor expanded in i around inf 74.9%

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

       1. associate-*r* 74.9%

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

       2. neg-mul-1 74.9%

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

   11. Simplified 74.9%

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

   if -1.2e173 < j < -9.0000000000000004e-71 or 4.6999999999999999e-101 < j < 1.1e9

   1. Initial program 73.3%

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

   3. Taylor expanded in b around 0 68.5%

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

   4. Taylor expanded in c around 0 67.2%

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

      1. +-commutative 67.2%

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

      2. cancel-sign-sub-inv 67.2%

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

      3. fma-define 67.2%

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

      4. mul-1-neg 67.2%

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

      5. unsub-neg 67.2%

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

      6. fma-define 67.2%

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

      7. cancel-sign-sub-inv 67.2%

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

      8. *-commutative 67.2%

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

   6. Simplified 67.2%

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

   if -9.0000000000000004e-71 < j < 4.6999999999999999e-101

   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 y around 0 79.4%

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

   5. Simplified 82.3%

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

   6. Taylor expanded in b around inf 73.9%

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

   7. Taylor expanded in z around inf 69.5%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.2 \cdot 10^{+173}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;j \leq -9 \cdot 10^{-71}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;j \leq 4.7 \cdot 10^{-101}:\\ \;\;\;\;b \cdot \left(\left(a \cdot i + \frac{x \cdot \left(y \cdot z\right)}{b}\right) - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1100000000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 57.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -3.3 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-109}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq -1.22 \cdot 10^{-151}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;x \leq 4.05 \cdot 10^{+89}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= x -3.3e+42)
     t_1
     (if (<= x -1.9e-109)
       (* y (- (* x z) (* i j)))
       (if (<= x -1.22e-151)
         (* t (- (* c j) (* x a)))
         (if (<= x 4.05e+89)
           (- (* j (- (* t c) (* y i))) (* b (* z c)))
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -3.3e+42) {
		tmp = t_1;
	} else if (x <= -1.9e-109) {
		tmp = y * ((x * z) - (i * j));
	} else if (x <= -1.22e-151) {
		tmp = t * ((c * j) - (x * a));
	} else if (x <= 4.05e+89) {
		tmp = (j * ((t * c) - (y * i))) - (b * (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (x <= (-3.3d+42)) then
        tmp = t_1
    else if (x <= (-1.9d-109)) then
        tmp = y * ((x * z) - (i * j))
    else if (x <= (-1.22d-151)) then
        tmp = t * ((c * j) - (x * a))
    else if (x <= 4.05d+89) then
        tmp = (j * ((t * c) - (y * i))) - (b * (z * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -3.3e+42) {
		tmp = t_1;
	} else if (x <= -1.9e-109) {
		tmp = y * ((x * z) - (i * j));
	} else if (x <= -1.22e-151) {
		tmp = t * ((c * j) - (x * a));
	} else if (x <= 4.05e+89) {
		tmp = (j * ((t * c) - (y * i))) - (b * (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -3.3e+42:
		tmp = t_1
	elif x <= -1.9e-109:
		tmp = y * ((x * z) - (i * j))
	elif x <= -1.22e-151:
		tmp = t * ((c * j) - (x * a))
	elif x <= 4.05e+89:
		tmp = (j * ((t * c) - (y * i))) - (b * (z * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -3.3e+42)
		tmp = t_1;
	elseif (x <= -1.9e-109)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (x <= -1.22e-151)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (x <= 4.05e+89)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) - Float64(b * Float64(z * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -3.3e+42)
		tmp = t_1;
	elseif (x <= -1.9e-109)
		tmp = y * ((x * z) - (i * j));
	elseif (x <= -1.22e-151)
		tmp = t * ((c * j) - (x * a));
	elseif (x <= 4.05e+89)
		tmp = (j * ((t * c) - (y * i))) - (b * (z * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.3e+42], t$95$1, If[LessEqual[x, -1.9e-109], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.22e-151], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.05e+89], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.2999999999999999e42 or 4.05e89 < x

   1. Initial program 70.3%

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

   3. Taylor expanded in y around 0 61.0%

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

   5. Simplified 68.4%

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

   6. Taylor expanded in x around inf 73.0%

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

      1. neg-mul-1 73.0%

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

      2. +-commutative 73.0%

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

      3. sub-neg 73.0%

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

   8. Simplified 73.0%

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

   if -3.2999999999999999e42 < x < -1.90000000000000001e-109

   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 y around inf 60.8%

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

      1. +-commutative 60.8%

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

      2. mul-1-neg 60.8%

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

      3. unsub-neg 60.8%

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

      4. *-commutative 60.8%

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

   5. Simplified 60.8%

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

   if -1.90000000000000001e-109 < x < -1.21999999999999997e-151

   1. Initial program 56.2%

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

   3. Taylor expanded in t around inf 64.3%

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

      1. +-commutative 64.3%

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

      2. mul-1-neg 64.3%

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

      3. unsub-neg 64.3%

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

      4. *-commutative 64.3%

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

      5. *-commutative 64.3%

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

   5. Simplified 64.3%

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

   if -1.21999999999999997e-151 < x < 4.05e89

   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 i around inf 73.3%

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

      1. associate-/l* 70.0%

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

   5. Simplified 70.0%

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

   6. Taylor expanded in x around 0 77.8%

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

      1. cancel-sign-sub-inv 77.8%

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

      2. +-commutative 77.8%

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

      3. +-commutative 77.8%

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

      4. cancel-sign-sub-inv 77.8%

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

      5. *-commutative 77.8%

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

      6. *-commutative 77.8%

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

      7. associate-/l* 75.3%

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

   8. Simplified 75.3%

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

   9. Taylor expanded in i around 0 64.4%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-109}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq -1.22 \cdot 10^{-151}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;x \leq 4.05 \cdot 10^{+89}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 43.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;j \leq -3.8 \cdot 10^{+138}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -5.8 \cdot 10^{+97}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;j \leq 7.2 \cdot 10^{-49}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.35 \cdot 10^{+54} \lor \neg \left(j \leq 2.2 \cdot 10^{+73}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))))
   (if (<= j -3.8e+138)
     t_1
     (if (<= j -5.8e+97)
       (* i (* y (- j)))
       (if (<= j 7.2e-49)
         (* b (- (* a i) (* z c)))
         (if (or (<= j 1.35e+54) (not (<= j 2.2e+73)))
           t_1
           (* y (* i (- 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 = c * ((t * j) - (z * b));
	double tmp;
	if (j <= -3.8e+138) {
		tmp = t_1;
	} else if (j <= -5.8e+97) {
		tmp = i * (y * -j);
	} else if (j <= 7.2e-49) {
		tmp = b * ((a * i) - (z * c));
	} else if ((j <= 1.35e+54) || !(j <= 2.2e+73)) {
		tmp = t_1;
	} else {
		tmp = y * (i * -j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((t * j) - (z * b))
    if (j <= (-3.8d+138)) then
        tmp = t_1
    else if (j <= (-5.8d+97)) then
        tmp = i * (y * -j)
    else if (j <= 7.2d-49) then
        tmp = b * ((a * i) - (z * c))
    else if ((j <= 1.35d+54) .or. (.not. (j <= 2.2d+73))) then
        tmp = t_1
    else
        tmp = y * (i * -j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double tmp;
	if (j <= -3.8e+138) {
		tmp = t_1;
	} else if (j <= -5.8e+97) {
		tmp = i * (y * -j);
	} else if (j <= 7.2e-49) {
		tmp = b * ((a * i) - (z * c));
	} else if ((j <= 1.35e+54) || !(j <= 2.2e+73)) {
		tmp = t_1;
	} else {
		tmp = y * (i * -j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	tmp = 0
	if j <= -3.8e+138:
		tmp = t_1
	elif j <= -5.8e+97:
		tmp = i * (y * -j)
	elif j <= 7.2e-49:
		tmp = b * ((a * i) - (z * c))
	elif (j <= 1.35e+54) or not (j <= 2.2e+73):
		tmp = t_1
	else:
		tmp = y * (i * -j)
	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 (j <= -3.8e+138)
		tmp = t_1;
	elseif (j <= -5.8e+97)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (j <= 7.2e-49)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif ((j <= 1.35e+54) || !(j <= 2.2e+73))
		tmp = t_1;
	else
		tmp = Float64(y * Float64(i * Float64(-j)));
	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 (j <= -3.8e+138)
		tmp = t_1;
	elseif (j <= -5.8e+97)
		tmp = i * (y * -j);
	elseif (j <= 7.2e-49)
		tmp = b * ((a * i) - (z * c));
	elseif ((j <= 1.35e+54) || ~((j <= 2.2e+73)))
		tmp = t_1;
	else
		tmp = y * (i * -j);
	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[j, -3.8e+138], t$95$1, If[LessEqual[j, -5.8e+97], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7.2e-49], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[j, 1.35e+54], N[Not[LessEqual[j, 2.2e+73]], $MachinePrecision]], t$95$1, N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -3.80000000000000012e138 or 7.19999999999999939e-49 < j < 1.35000000000000005e54 or 2.2e73 < j

   1. Initial program 69.3%

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

   3. Taylor expanded in c around inf 59.0%

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

      1. *-commutative 59.0%

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

      2. *-commutative 59.0%

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

   5. Simplified 59.0%

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

   if -3.80000000000000012e138 < j < -5.79999999999999974e97

   1. Initial program 55.7%

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

   3. Taylor expanded in y around inf 91.0%

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

      1. +-commutative 91.0%

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

      2. mul-1-neg 91.0%

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

      3. unsub-neg 91.0%

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

      4. *-commutative 91.0%

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

   5. Simplified 91.0%

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

   6. Taylor expanded in x around 0 74.8%

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

      1. associate-*r* 74.8%

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

      2. neg-mul-1 74.8%

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

      3. *-commutative 74.8%

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

   8. Simplified 74.8%

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

   if -5.79999999999999974e97 < j < 7.19999999999999939e-49

   1. Initial program 76.1%

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

   3. Taylor expanded in b around inf 48.6%

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

      1. *-commutative 48.6%

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

   5. Simplified 48.6%

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

   if 1.35000000000000005e54 < j < 2.2e73

   1. Initial program 71.2%

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

   3. Taylor expanded in y around inf 71.6%

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

      1. +-commutative 71.6%

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

      2. mul-1-neg 71.6%

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

      3. unsub-neg 71.6%

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

      4. *-commutative 71.6%

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

   5. Simplified 71.6%

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

   6. Taylor expanded in x around 0 71.6%

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

      1. mul-1-neg 71.6%

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

      2. distribute-rgt-neg-in 71.6%

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

   8. Simplified 71.6%

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

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.8 \cdot 10^{+138}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq -5.8 \cdot 10^{+97}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;j \leq 7.2 \cdot 10^{-49}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.35 \cdot 10^{+54} \lor \neg \left(j \leq 2.2 \cdot 10^{+73}\right):\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 49.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.5 \cdot 10^{+172}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -8.5 \cdot 10^{-217}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 9.5 \cdot 10^{-226}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 9.2 \cdot 10^{-124}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 9.5 \cdot 10^{+26}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))))
   (if (<= j -1.5e+172)
     t_1
     (if (<= j -8.5e-217)
       (* x (- (* y z) (* t a)))
       (if (<= j 9.5e-226)
         (* b (- (* a i) (* z c)))
         (if (<= j 9.2e-124)
           (* z (- (* x y) (* b c)))
           (if (<= j 9.5e+26) (* t (- (* c j) (* x a))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -1.5e+172) {
		tmp = t_1;
	} else if (j <= -8.5e-217) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= 9.5e-226) {
		tmp = b * ((a * i) - (z * c));
	} else if (j <= 9.2e-124) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 9.5e+26) {
		tmp = t * ((c * j) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    if (j <= (-1.5d+172)) then
        tmp = t_1
    else if (j <= (-8.5d-217)) then
        tmp = x * ((y * z) - (t * a))
    else if (j <= 9.5d-226) then
        tmp = b * ((a * i) - (z * c))
    else if (j <= 9.2d-124) then
        tmp = z * ((x * y) - (b * c))
    else if (j <= 9.5d+26) then
        tmp = t * ((c * j) - (x * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -1.5e+172) {
		tmp = t_1;
	} else if (j <= -8.5e-217) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= 9.5e-226) {
		tmp = b * ((a * i) - (z * c));
	} else if (j <= 9.2e-124) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 9.5e+26) {
		tmp = t * ((c * j) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -1.5e+172:
		tmp = t_1
	elif j <= -8.5e-217:
		tmp = x * ((y * z) - (t * a))
	elif j <= 9.5e-226:
		tmp = b * ((a * i) - (z * c))
	elif j <= 9.2e-124:
		tmp = z * ((x * y) - (b * c))
	elif j <= 9.5e+26:
		tmp = t * ((c * j) - (x * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -1.5e+172)
		tmp = t_1;
	elseif (j <= -8.5e-217)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (j <= 9.5e-226)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (j <= 9.2e-124)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (j <= 9.5e+26)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -1.5e+172)
		tmp = t_1;
	elseif (j <= -8.5e-217)
		tmp = x * ((y * z) - (t * a));
	elseif (j <= 9.5e-226)
		tmp = b * ((a * i) - (z * c));
	elseif (j <= 9.2e-124)
		tmp = z * ((x * y) - (b * c));
	elseif (j <= 9.5e+26)
		tmp = t * ((c * j) - (x * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.5e+172], t$95$1, If[LessEqual[j, -8.5e-217], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 9.5e-226], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 9.2e-124], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 9.5e+26], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -1.5e172 or 9.50000000000000054e26 < j

   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 71.7%

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

      1. *-commutative 71.7%

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

      2. *-commutative 71.7%

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

   5. Simplified 71.7%

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

   if -1.5e172 < j < -8.4999999999999994e-217

   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 y around 0 70.8%

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

   5. Simplified 72.0%

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

   6. Taylor expanded in x around inf 55.9%

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

      1. neg-mul-1 55.9%

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

      2. +-commutative 55.9%

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

      3. sub-neg 55.9%

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

   8. Simplified 55.9%

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

   if -8.4999999999999994e-217 < j < 9.5000000000000007e-226

   1. Initial program 79.5%

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

   3. Taylor expanded in b around inf 70.7%

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

      1. *-commutative 70.7%

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

   5. Simplified 70.7%

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

   if 9.5000000000000007e-226 < j < 9.20000000000000048e-124

   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 z around inf 77.2%

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

      1. *-commutative 77.2%

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

   5. Simplified 77.2%

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

   if 9.20000000000000048e-124 < j < 9.50000000000000054e26

   1. Initial program 72.4%

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

   3. Taylor expanded in t around inf 64.5%

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

      1. +-commutative 64.5%

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

      2. mul-1-neg 64.5%

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

      3. unsub-neg 64.5%

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

      4. *-commutative 64.5%

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

      5. *-commutative 64.5%

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

   5. Simplified 64.5%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.5 \cdot 10^{+172}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -8.5 \cdot 10^{-217}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 9.5 \cdot 10^{-226}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 9.2 \cdot 10^{-124}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 9.5 \cdot 10^{+26}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 48.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.5 \cdot 10^{+172}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -8.5 \cdot 10^{-213}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 9.5 \cdot 10^{-175}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 6 \cdot 10^{-125}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;j \leq 2.2 \cdot 10^{+26}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))))
   (if (<= j -1.5e+172)
     t_1
     (if (<= j -8.5e-213)
       (* x (- (* y z) (* t a)))
       (if (<= j 9.5e-175)
         (* b (- (* a i) (* z c)))
         (if (<= j 6e-125)
           (* y (- (* x z) (* i j)))
           (if (<= j 2.2e+26) (* t (- (* c j) (* x a))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -1.5e+172) {
		tmp = t_1;
	} else if (j <= -8.5e-213) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= 9.5e-175) {
		tmp = b * ((a * i) - (z * c));
	} else if (j <= 6e-125) {
		tmp = y * ((x * z) - (i * j));
	} else if (j <= 2.2e+26) {
		tmp = t * ((c * j) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    if (j <= (-1.5d+172)) then
        tmp = t_1
    else if (j <= (-8.5d-213)) then
        tmp = x * ((y * z) - (t * a))
    else if (j <= 9.5d-175) then
        tmp = b * ((a * i) - (z * c))
    else if (j <= 6d-125) then
        tmp = y * ((x * z) - (i * j))
    else if (j <= 2.2d+26) then
        tmp = t * ((c * j) - (x * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -1.5e+172) {
		tmp = t_1;
	} else if (j <= -8.5e-213) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= 9.5e-175) {
		tmp = b * ((a * i) - (z * c));
	} else if (j <= 6e-125) {
		tmp = y * ((x * z) - (i * j));
	} else if (j <= 2.2e+26) {
		tmp = t * ((c * j) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -1.5e+172:
		tmp = t_1
	elif j <= -8.5e-213:
		tmp = x * ((y * z) - (t * a))
	elif j <= 9.5e-175:
		tmp = b * ((a * i) - (z * c))
	elif j <= 6e-125:
		tmp = y * ((x * z) - (i * j))
	elif j <= 2.2e+26:
		tmp = t * ((c * j) - (x * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -1.5e+172)
		tmp = t_1;
	elseif (j <= -8.5e-213)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (j <= 9.5e-175)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (j <= 6e-125)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (j <= 2.2e+26)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -1.5e+172)
		tmp = t_1;
	elseif (j <= -8.5e-213)
		tmp = x * ((y * z) - (t * a));
	elseif (j <= 9.5e-175)
		tmp = b * ((a * i) - (z * c));
	elseif (j <= 6e-125)
		tmp = y * ((x * z) - (i * j));
	elseif (j <= 2.2e+26)
		tmp = t * ((c * j) - (x * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.5e+172], t$95$1, If[LessEqual[j, -8.5e-213], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 9.5e-175], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6e-125], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.2e+26], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -1.5e172 or 2.20000000000000007e26 < j

   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 71.7%

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

      1. *-commutative 71.7%

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

      2. *-commutative 71.7%

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

   5. Simplified 71.7%

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

   if -1.5e172 < j < -8.49999999999999994e-213

   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 y around 0 70.8%

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

   5. Simplified 72.0%

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

   6. Taylor expanded in x around inf 55.9%

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

      1. neg-mul-1 55.9%

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

      2. +-commutative 55.9%

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

      3. sub-neg 55.9%

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

   8. Simplified 55.9%

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

   if -8.49999999999999994e-213 < j < 9.50000000000000052e-175

   1. Initial program 78.2%

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

   3. Taylor expanded in b around inf 66.1%

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

      1. *-commutative 66.1%

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

   5. Simplified 66.1%

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

   if 9.50000000000000052e-175 < j < 5.99999999999999981e-125

   1. Initial program 56.3%

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

   3. Taylor expanded in y around inf 73.8%

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

      1. +-commutative 73.8%

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

      2. mul-1-neg 73.8%

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

      3. unsub-neg 73.8%

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

      4. *-commutative 73.8%

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

   5. Simplified 73.8%

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

   if 5.99999999999999981e-125 < j < 2.20000000000000007e26

   1. Initial program 72.4%

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

   3. Taylor expanded in t around inf 64.5%

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

      1. +-commutative 64.5%

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

      2. mul-1-neg 64.5%

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

      3. unsub-neg 64.5%

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

      4. *-commutative 64.5%

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

      5. *-commutative 64.5%

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

   5. Simplified 64.5%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.5 \cdot 10^{+172}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -8.5 \cdot 10^{-213}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 9.5 \cdot 10^{-175}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 6 \cdot 10^{-125}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;j \leq 2.2 \cdot 10^{+26}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 65.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -2.7 \cdot 10^{+186}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -5.1 \cdot 10^{-84}:\\ \;\;\;\;y \cdot \left(x \cdot z + \left(\frac{a \cdot \left(b \cdot i\right)}{y} - i \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{+98}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= x -2.7e+186)
     t_1
     (if (<= x -5.1e-84)
       (* y (+ (* x z) (- (/ (* a (* b i)) y) (* i j))))
       (if (<= x 1.95e+98)
         (+ (* j (- (* t c) (* y i))) (* b (- (* a i) (* z c))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -2.7e+186) {
		tmp = t_1;
	} else if (x <= -5.1e-84) {
		tmp = y * ((x * z) + (((a * (b * i)) / y) - (i * j)));
	} else if (x <= 1.95e+98) {
		tmp = (j * ((t * c) - (y * i))) + (b * ((a * i) - (z * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (x <= (-2.7d+186)) then
        tmp = t_1
    else if (x <= (-5.1d-84)) then
        tmp = y * ((x * z) + (((a * (b * i)) / y) - (i * j)))
    else if (x <= 1.95d+98) then
        tmp = (j * ((t * c) - (y * i))) + (b * ((a * i) - (z * c)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -2.7e+186) {
		tmp = t_1;
	} else if (x <= -5.1e-84) {
		tmp = y * ((x * z) + (((a * (b * i)) / y) - (i * j)));
	} else if (x <= 1.95e+98) {
		tmp = (j * ((t * c) - (y * i))) + (b * ((a * i) - (z * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -2.7e+186:
		tmp = t_1
	elif x <= -5.1e-84:
		tmp = y * ((x * z) + (((a * (b * i)) / y) - (i * j)))
	elif x <= 1.95e+98:
		tmp = (j * ((t * c) - (y * i))) + (b * ((a * i) - (z * c)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -2.7e+186)
		tmp = t_1;
	elseif (x <= -5.1e-84)
		tmp = Float64(y * Float64(Float64(x * z) + Float64(Float64(Float64(a * Float64(b * i)) / y) - Float64(i * j))));
	elseif (x <= 1.95e+98)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -2.7e+186)
		tmp = t_1;
	elseif (x <= -5.1e-84)
		tmp = y * ((x * z) + (((a * (b * i)) / y) - (i * j)));
	elseif (x <= 1.95e+98)
		tmp = (j * ((t * c) - (y * i))) + (b * ((a * i) - (z * c)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.7e+186], t$95$1, If[LessEqual[x, -5.1e-84], N[(y * N[(N[(x * z), $MachinePrecision] + N[(N[(N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.95e+98], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.6999999999999999e186 or 1.95e98 < x

   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 y around 0 52.1%

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

   5. Simplified 60.0%

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

   6. Taylor expanded in x around inf 79.7%

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

      1. neg-mul-1 79.7%

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

      2. +-commutative 79.7%

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

      3. sub-neg 79.7%

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

   8. Simplified 79.7%

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

   if -2.6999999999999999e186 < x < -5.0999999999999996e-84

   1. Initial program 76.5%

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

   3. Taylor expanded in y around -inf 74.8%

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

   5. Simplified 80.1%

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

   6. Taylor expanded in i around inf 70.3%

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

   if -5.0999999999999996e-84 < x < 1.95e98

   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 x around 0 77.5%

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

      1. fma-neg 79.8%

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

      2. *-rgt-identity 79.8%

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

      3. *-commutative 79.8%

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

      4. *-commutative 79.8%

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

      5. fma-neg 77.5%

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

      6. associate-*l* 77.5%

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

      7. *-rgt-identity 77.5%

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

      8. *-commutative 77.5%

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

   5. Simplified 77.5%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c - a \cdot i\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+186}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -5.1 \cdot 10^{-84}:\\ \;\;\;\;y \cdot \left(x \cdot z + \left(\frac{a \cdot \left(b \cdot i\right)}{y} - i \cdot j\right)\right)\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{+98}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 39.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ \mathbf{if}\;j \leq -1.7 \cdot 10^{+141}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -1.55 \cdot 10^{+99}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;j \leq 1.32 \cdot 10^{-36}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.15 \cdot 10^{+54} \lor \neg \left(j \leq 1.38 \cdot 10^{+191}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j))))
   (if (<= j -1.7e+141)
     t_1
     (if (<= j -1.55e+99)
       (* i (* y (- j)))
       (if (<= j 1.32e-36)
         (* b (- (* a i) (* z c)))
         (if (or (<= j 1.15e+54) (not (<= j 1.38e+191)))
           t_1
           (* y (* i (- 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 = c * (t * j);
	double tmp;
	if (j <= -1.7e+141) {
		tmp = t_1;
	} else if (j <= -1.55e+99) {
		tmp = i * (y * -j);
	} else if (j <= 1.32e-36) {
		tmp = b * ((a * i) - (z * c));
	} else if ((j <= 1.15e+54) || !(j <= 1.38e+191)) {
		tmp = t_1;
	} else {
		tmp = y * (i * -j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (t * j)
    if (j <= (-1.7d+141)) then
        tmp = t_1
    else if (j <= (-1.55d+99)) then
        tmp = i * (y * -j)
    else if (j <= 1.32d-36) then
        tmp = b * ((a * i) - (z * c))
    else if ((j <= 1.15d+54) .or. (.not. (j <= 1.38d+191))) then
        tmp = t_1
    else
        tmp = y * (i * -j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double tmp;
	if (j <= -1.7e+141) {
		tmp = t_1;
	} else if (j <= -1.55e+99) {
		tmp = i * (y * -j);
	} else if (j <= 1.32e-36) {
		tmp = b * ((a * i) - (z * c));
	} else if ((j <= 1.15e+54) || !(j <= 1.38e+191)) {
		tmp = t_1;
	} else {
		tmp = y * (i * -j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (t * j)
	tmp = 0
	if j <= -1.7e+141:
		tmp = t_1
	elif j <= -1.55e+99:
		tmp = i * (y * -j)
	elif j <= 1.32e-36:
		tmp = b * ((a * i) - (z * c))
	elif (j <= 1.15e+54) or not (j <= 1.38e+191):
		tmp = t_1
	else:
		tmp = y * (i * -j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(t * j))
	tmp = 0.0
	if (j <= -1.7e+141)
		tmp = t_1;
	elseif (j <= -1.55e+99)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (j <= 1.32e-36)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif ((j <= 1.15e+54) || !(j <= 1.38e+191))
		tmp = t_1;
	else
		tmp = Float64(y * Float64(i * Float64(-j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (t * j);
	tmp = 0.0;
	if (j <= -1.7e+141)
		tmp = t_1;
	elseif (j <= -1.55e+99)
		tmp = i * (y * -j);
	elseif (j <= 1.32e-36)
		tmp = b * ((a * i) - (z * c));
	elseif ((j <= 1.15e+54) || ~((j <= 1.38e+191)))
		tmp = t_1;
	else
		tmp = y * (i * -j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.7e+141], t$95$1, If[LessEqual[j, -1.55e+99], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.32e-36], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[j, 1.15e+54], N[Not[LessEqual[j, 1.38e+191]], $MachinePrecision]], t$95$1, N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.6999999999999999e141 or 1.31999999999999993e-36 < j < 1.14999999999999997e54 or 1.38e191 < j

   1. Initial program 69.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 68.8%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   4. Taylor expanded in x around inf 64.0%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot z + \frac{j \cdot \left(c \cdot t - i \cdot y\right)}{x}\right) - a \cdot t\right)} \]

   5. Taylor expanded in c around inf 60.4%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   6. Step-by-step derivation

      1. *-commutative 60.4%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

   7. Simplified 60.4%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if -1.6999999999999999e141 < j < -1.55e99

   1. Initial program 55.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 91.0%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 91.0%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 91.0%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 91.0%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 91.0%

         \[\leadsto y \cdot \left(x \cdot z - \color{blue}{j \cdot i}\right) \]

   5. Simplified 91.0%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z - j \cdot i\right)} \]

   6. Taylor expanded in x around 0 74.8%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 74.8%

         \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(j \cdot y\right)} \]

      2. neg-mul-1 74.8%

         \[\leadsto \color{blue}{\left(-i\right)} \cdot \left(j \cdot y\right) \]

      3. *-commutative 74.8%

         \[\leadsto \left(-i\right) \cdot \color{blue}{\left(y \cdot j\right)} \]

   8. Simplified 74.8%

      \[\leadsto \color{blue}{\left(-i\right) \cdot \left(y \cdot j\right)} \]

   if -1.55e99 < j < 1.31999999999999993e-36

   1. Initial program 75.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 48.3%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 48.3%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   5. Simplified 48.3%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   if 1.14999999999999997e54 < j < 1.38e191

   1. Initial program 69.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 63.7%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 63.7%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 63.7%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 63.7%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 63.7%

         \[\leadsto y \cdot \left(x \cdot z - \color{blue}{j \cdot i}\right) \]

   5. Simplified 63.7%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z - j \cdot i\right)} \]

   6. Taylor expanded in x around 0 50.6%

      \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 50.6%

         \[\leadsto y \cdot \color{blue}{\left(-i \cdot j\right)} \]

      2. distribute-rgt-neg-in 50.6%

         \[\leadsto y \cdot \color{blue}{\left(i \cdot \left(-j\right)\right)} \]

   8. Simplified 50.6%

      \[\leadsto y \cdot \color{blue}{\left(i \cdot \left(-j\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.7 \cdot 10^{+141}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;j \leq -1.55 \cdot 10^{+99}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;j \leq 1.32 \cdot 10^{-36}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.15 \cdot 10^{+54} \lor \neg \left(j \leq 1.38 \cdot 10^{+191}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 49.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.5 \cdot 10^{+172}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -7.6 \cdot 10^{-211}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{-103}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 9.8 \cdot 10^{+26}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))))
   (if (<= j -1.5e+172)
     t_1
     (if (<= j -7.6e-211)
       (* x (- (* y z) (* t a)))
       (if (<= j 1.7e-103)
         (* b (- (* a i) (* z c)))
         (if (<= j 9.8e+26) (* t (- (* c j) (* x a))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -1.5e+172) {
		tmp = t_1;
	} else if (j <= -7.6e-211) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= 1.7e-103) {
		tmp = b * ((a * i) - (z * c));
	} else if (j <= 9.8e+26) {
		tmp = t * ((c * j) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    if (j <= (-1.5d+172)) then
        tmp = t_1
    else if (j <= (-7.6d-211)) then
        tmp = x * ((y * z) - (t * a))
    else if (j <= 1.7d-103) then
        tmp = b * ((a * i) - (z * c))
    else if (j <= 9.8d+26) then
        tmp = t * ((c * j) - (x * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -1.5e+172) {
		tmp = t_1;
	} else if (j <= -7.6e-211) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= 1.7e-103) {
		tmp = b * ((a * i) - (z * c));
	} else if (j <= 9.8e+26) {
		tmp = t * ((c * j) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -1.5e+172:
		tmp = t_1
	elif j <= -7.6e-211:
		tmp = x * ((y * z) - (t * a))
	elif j <= 1.7e-103:
		tmp = b * ((a * i) - (z * c))
	elif j <= 9.8e+26:
		tmp = t * ((c * j) - (x * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -1.5e+172)
		tmp = t_1;
	elseif (j <= -7.6e-211)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (j <= 1.7e-103)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (j <= 9.8e+26)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -1.5e+172)
		tmp = t_1;
	elseif (j <= -7.6e-211)
		tmp = x * ((y * z) - (t * a));
	elseif (j <= 1.7e-103)
		tmp = b * ((a * i) - (z * c));
	elseif (j <= 9.8e+26)
		tmp = t * ((c * j) - (x * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.5e+172], t$95$1, If[LessEqual[j, -7.6e-211], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.7e-103], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 9.8e+26], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.5e172 or 9.79999999999999947e26 < j

   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 71.7%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-commutative 71.7%

         \[\leadsto j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      2. *-commutative 71.7%

         \[\leadsto j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   5. Simplified 71.7%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot c - y \cdot i\right)} \]

   if -1.5e172 < j < -7.60000000000000023e-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 y around 0 70.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(c \cdot \left(j \cdot t\right) + y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]

   5. Simplified 72.0%

      \[\leadsto \color{blue}{\left(t \cdot \left(j \cdot c - x \cdot a\right) + y \cdot \left(x \cdot z - j \cdot i\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)} \]

   6. Taylor expanded in x around inf 55.9%

      \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)} \]
   7. Step-by-step derivation

      1. neg-mul-1 55.9%

         \[\leadsto x \cdot \left(\color{blue}{\left(-a \cdot t\right)} + y \cdot z\right) \]

      2. +-commutative 55.9%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z + \left(-a \cdot t\right)\right)} \]

      3. sub-neg 55.9%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z - a \cdot t\right)} \]

   8. Simplified 55.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]

   if -7.60000000000000023e-211 < j < 1.70000000000000001e-103

   1. Initial program 72.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 59.0%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 59.0%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   5. Simplified 59.0%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   if 1.70000000000000001e-103 < j < 9.79999999999999947e26

   1. Initial program 75.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 66.3%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 66.3%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 66.3%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 66.3%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

      4. *-commutative 66.3%

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) \]

      5. *-commutative 66.3%

         \[\leadsto t \cdot \left(j \cdot c - \color{blue}{x \cdot a}\right) \]

   5. Simplified 66.3%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - x \cdot a\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.5 \cdot 10^{+172}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -7.6 \cdot 10^{-211}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{-103}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 9.8 \cdot 10^{+26}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 59.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -1.02 \cdot 10^{-143}:\\ \;\;\;\;t\_1 - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+98}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= x -1.02e-143)
     (- t_1 (* i (* y j)))
     (if (<= x 5.2e+98) (- (* j (- (* t c) (* y i))) (* b (* z c))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.02e-143) {
		tmp = t_1 - (i * (y * j));
	} else if (x <= 5.2e+98) {
		tmp = (j * ((t * c) - (y * i))) - (b * (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (x <= (-1.02d-143)) then
        tmp = t_1 - (i * (y * j))
    else if (x <= 5.2d+98) then
        tmp = (j * ((t * c) - (y * i))) - (b * (z * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.02e-143) {
		tmp = t_1 - (i * (y * j));
	} else if (x <= 5.2e+98) {
		tmp = (j * ((t * c) - (y * i))) - (b * (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -1.02e-143:
		tmp = t_1 - (i * (y * j))
	elif x <= 5.2e+98:
		tmp = (j * ((t * c) - (y * i))) - (b * (z * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -1.02e-143)
		tmp = Float64(t_1 - Float64(i * Float64(y * j)));
	elseif (x <= 5.2e+98)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) - Float64(b * Float64(z * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -1.02e-143)
		tmp = t_1 - (i * (y * j));
	elseif (x <= 5.2e+98)
		tmp = (j * ((t * c) - (y * i))) - (b * (z * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.02e-143], N[(t$95$1 - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.2e+98], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.02e-143

   1. Initial program 73.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 70.2%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   4. Taylor expanded in c around 0 67.3%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]
   5. Step-by-step derivation

      1. +-commutative 67.3%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) + -1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]

      2. cancel-sign-sub-inv 67.3%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z + \left(-a\right) \cdot t\right)} + -1 \cdot \left(i \cdot \left(j \cdot y\right)\right) \]

      3. fma-define 67.3%

         \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left(y, z, \left(-a\right) \cdot t\right)} + -1 \cdot \left(i \cdot \left(j \cdot y\right)\right) \]

      4. mul-1-neg 67.3%

         \[\leadsto x \cdot \mathsf{fma}\left(y, z, \left(-a\right) \cdot t\right) + \color{blue}{\left(-i \cdot \left(j \cdot y\right)\right)} \]

      5. unsub-neg 67.3%

         \[\leadsto \color{blue}{x \cdot \mathsf{fma}\left(y, z, \left(-a\right) \cdot t\right) - i \cdot \left(j \cdot y\right)} \]

      6. fma-define 67.3%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z + \left(-a\right) \cdot t\right)} - i \cdot \left(j \cdot y\right) \]

      7. cancel-sign-sub-inv 67.3%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z - a \cdot t\right)} - i \cdot \left(j \cdot y\right) \]

      8. *-commutative 67.3%

         \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) - i \cdot \color{blue}{\left(y \cdot j\right)} \]

   6. Simplified 67.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - i \cdot \left(y \cdot j\right)} \]

   if -1.02e-143 < x < 5.1999999999999999e98

   1. Initial program 73.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 71.9%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(i \cdot \left(\frac{c \cdot z}{i} - a\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   4. Step-by-step derivation

      1. associate-/l* 68.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(i \cdot \left(\color{blue}{c \cdot \frac{z}{i}} - a\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   5. Simplified 68.6%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(i \cdot \left(c \cdot \frac{z}{i} - a\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   6. Taylor expanded in x around 0 76.2%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) - b \cdot \left(i \cdot \left(\frac{c \cdot z}{i} - a\right)\right)} \]
   7. Step-by-step derivation

      1. cancel-sign-sub-inv 76.2%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t + \left(-i\right) \cdot y\right)} - b \cdot \left(i \cdot \left(\frac{c \cdot z}{i} - a\right)\right) \]

      2. +-commutative 76.2%

         \[\leadsto j \cdot \color{blue}{\left(\left(-i\right) \cdot y + c \cdot t\right)} - b \cdot \left(i \cdot \left(\frac{c \cdot z}{i} - a\right)\right) \]

      3. +-commutative 76.2%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t + \left(-i\right) \cdot y\right)} - b \cdot \left(i \cdot \left(\frac{c \cdot z}{i} - a\right)\right) \]

      4. cancel-sign-sub-inv 76.2%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t - i \cdot y\right)} - b \cdot \left(i \cdot \left(\frac{c \cdot z}{i} - a\right)\right) \]

      5. *-commutative 76.2%

         \[\leadsto j \cdot \left(c \cdot t - \color{blue}{y \cdot i}\right) - b \cdot \left(i \cdot \left(\frac{c \cdot z}{i} - a\right)\right) \]

      6. *-commutative 76.2%

         \[\leadsto j \cdot \left(c \cdot t - y \cdot i\right) - b \cdot \left(i \cdot \left(\frac{\color{blue}{z \cdot c}}{i} - a\right)\right) \]

      7. associate-/l* 73.7%

         \[\leadsto j \cdot \left(c \cdot t - y \cdot i\right) - b \cdot \left(i \cdot \left(\color{blue}{z \cdot \frac{c}{i}} - a\right)\right) \]

   8. Simplified 73.7%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - y \cdot i\right) - b \cdot \left(i \cdot \left(z \cdot \frac{c}{i} - a\right)\right)} \]

   9. Taylor expanded in i around 0 63.1%

      \[\leadsto j \cdot \left(c \cdot t - y \cdot i\right) - b \cdot \color{blue}{\left(c \cdot z\right)} \]

   if 5.1999999999999999e98 < 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 0 56.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(c \cdot \left(j \cdot t\right) + y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]

   5. Simplified 57.9%

      \[\leadsto \color{blue}{\left(t \cdot \left(j \cdot c - x \cdot a\right) + y \cdot \left(x \cdot z - j \cdot i\right)\right) - b \cdot \left(z \cdot c - a \cdot i\right)} \]

   6. Taylor expanded in x around inf 75.2%

      \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)} \]
   7. Step-by-step derivation

      1. neg-mul-1 75.2%

         \[\leadsto x \cdot \left(\color{blue}{\left(-a \cdot t\right)} + y \cdot z\right) \]

      2. +-commutative 75.2%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z + \left(-a \cdot t\right)\right)} \]

      3. sub-neg 75.2%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z - a \cdot t\right)} \]

   8. Simplified 75.2%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{-143}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+98}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 51.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -5.8 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 7 \cdot 10^{-105}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 3.6 \cdot 10^{+26}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))))
   (if (<= j -5.8e+33)
     t_1
     (if (<= j 7e-105)
       (* b (- (* a i) (* z c)))
       (if (<= j 3.6e+26) (* t (- (* c j) (* x a))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -5.8e+33) {
		tmp = t_1;
	} else if (j <= 7e-105) {
		tmp = b * ((a * i) - (z * c));
	} else if (j <= 3.6e+26) {
		tmp = t * ((c * j) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    if (j <= (-5.8d+33)) then
        tmp = t_1
    else if (j <= 7d-105) then
        tmp = b * ((a * i) - (z * c))
    else if (j <= 3.6d+26) then
        tmp = t * ((c * j) - (x * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -5.8e+33) {
		tmp = t_1;
	} else if (j <= 7e-105) {
		tmp = b * ((a * i) - (z * c));
	} else if (j <= 3.6e+26) {
		tmp = t * ((c * j) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -5.8e+33:
		tmp = t_1
	elif j <= 7e-105:
		tmp = b * ((a * i) - (z * c))
	elif j <= 3.6e+26:
		tmp = t * ((c * j) - (x * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -5.8e+33)
		tmp = t_1;
	elseif (j <= 7e-105)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (j <= 3.6e+26)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -5.8e+33)
		tmp = t_1;
	elseif (j <= 7e-105)
		tmp = b * ((a * i) - (z * c));
	elseif (j <= 3.6e+26)
		tmp = t * ((c * j) - (x * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -5.8e+33], t$95$1, If[LessEqual[j, 7e-105], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.6e+26], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if j < -5.80000000000000049e33 or 3.60000000000000024e26 < j

   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 j around inf 67.2%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-commutative 67.2%

         \[\leadsto j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      2. *-commutative 67.2%

         \[\leadsto j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   5. Simplified 67.2%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot c - y \cdot i\right)} \]

   if -5.80000000000000049e33 < j < 7e-105

   1. Initial program 76.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 51.6%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 51.6%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   5. Simplified 51.6%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   if 7e-105 < j < 3.60000000000000024e26

   1. Initial program 75.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 66.3%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 66.3%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 66.3%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 66.3%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

      4. *-commutative 66.3%

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) \]

      5. *-commutative 66.3%

         \[\leadsto t \cdot \left(j \cdot c - \color{blue}{x \cdot a}\right) \]

   5. Simplified 66.3%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - x \cdot a\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -5.8 \cdot 10^{+33}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 7 \cdot 10^{-105}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 3.6 \cdot 10^{+26}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 30.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.66 \cdot 10^{+89}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-182}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+142}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -1.66e+89)
   (* c (* z (- b)))
   (if (<= z -4.4e-182)
     (* i (* a b))
     (if (<= z 3.4e+142) (* x (* t (- a))) (* y (* x z))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -1.66e+89) {
		tmp = c * (z * -b);
	} else if (z <= -4.4e-182) {
		tmp = i * (a * b);
	} else if (z <= 3.4e+142) {
		tmp = x * (t * -a);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-1.66d+89)) then
        tmp = c * (z * -b)
    else if (z <= (-4.4d-182)) then
        tmp = i * (a * b)
    else if (z <= 3.4d+142) then
        tmp = x * (t * -a)
    else
        tmp = y * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -1.66e+89) {
		tmp = c * (z * -b);
	} else if (z <= -4.4e-182) {
		tmp = i * (a * b);
	} else if (z <= 3.4e+142) {
		tmp = x * (t * -a);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -1.66e+89:
		tmp = c * (z * -b)
	elif z <= -4.4e-182:
		tmp = i * (a * b)
	elif z <= 3.4e+142:
		tmp = x * (t * -a)
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -1.66e+89)
		tmp = Float64(c * Float64(z * Float64(-b)));
	elseif (z <= -4.4e-182)
		tmp = Float64(i * Float64(a * b));
	elseif (z <= 3.4e+142)
		tmp = Float64(x * Float64(t * Float64(-a)));
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -1.66e+89)
		tmp = c * (z * -b);
	elseif (z <= -4.4e-182)
		tmp = i * (a * b);
	elseif (z <= 3.4e+142)
		tmp = x * (t * -a);
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -1.66e+89], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.4e-182], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.4e+142], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.6599999999999999e89

   1. Initial program 71.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 63.5%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 63.5%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   5. Simplified 63.5%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   6. Taylor expanded in a around 0 43.7%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 43.7%

         \[\leadsto \color{blue}{\left(-1 \cdot b\right) \cdot \left(c \cdot z\right)} \]

      2. neg-mul-1 43.7%

         \[\leadsto \color{blue}{\left(-b\right)} \cdot \left(c \cdot z\right) \]

      3. *-commutative 43.7%

         \[\leadsto \left(-b\right) \cdot \color{blue}{\left(z \cdot c\right)} \]

   8. Simplified 43.7%

      \[\leadsto \color{blue}{\left(-b\right) \cdot \left(z \cdot c\right)} \]

   9. Taylor expanded in b around 0 43.7%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. neg-mul-1 43.7%

          \[\leadsto \color{blue}{-b \cdot \left(c \cdot z\right)} \]

       2. distribute-lft-neg-in 43.7%

          \[\leadsto \color{blue}{\left(-b\right) \cdot \left(c \cdot z\right)} \]

       3. *-commutative 43.7%

          \[\leadsto \color{blue}{\left(c \cdot z\right) \cdot \left(-b\right)} \]

       4. associate-*l* 41.7%

          \[\leadsto \color{blue}{c \cdot \left(z \cdot \left(-b\right)\right)} \]

   11. Simplified 41.7%

       \[\leadsto \color{blue}{c \cdot \left(z \cdot \left(-b\right)\right)} \]

   if -1.6599999999999999e89 < z < -4.3999999999999999e-182

   1. Initial program 77.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 54.6%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 54.6%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   5. Simplified 54.6%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   6. Taylor expanded in a around inf 37.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 42.3%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot i} \]

      2. *-commutative 42.3%

         \[\leadsto \color{blue}{\left(b \cdot a\right)} \cdot i \]

   8. Simplified 42.3%

      \[\leadsto \color{blue}{\left(b \cdot a\right) \cdot i} \]

   if -4.3999999999999999e-182 < z < 3.3999999999999998e142

   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 b around 0 67.6%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   4. Taylor expanded in x around inf 61.0%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot z + \frac{j \cdot \left(c \cdot t - i \cdot y\right)}{x}\right) - a \cdot t\right)} \]

   5. Taylor expanded in a around inf 35.2%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(a \cdot t\right)\right)} \]
   6. Step-by-step derivation

      1. neg-mul-1 35.2%

         \[\leadsto x \cdot \color{blue}{\left(-a \cdot t\right)} \]

      2. distribute-lft-neg-in 35.2%

         \[\leadsto x \cdot \color{blue}{\left(\left(-a\right) \cdot t\right)} \]

      3. *-commutative 35.2%

         \[\leadsto x \cdot \color{blue}{\left(t \cdot \left(-a\right)\right)} \]

   7. Simplified 35.2%

      \[\leadsto x \cdot \color{blue}{\left(t \cdot \left(-a\right)\right)} \]

   if 3.3999999999999998e142 < z

   1. Initial program 58.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 49.7%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 49.7%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 49.7%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 49.7%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 49.7%

         \[\leadsto y \cdot \left(x \cdot z - \color{blue}{j \cdot i}\right) \]

   5. Simplified 49.7%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z - j \cdot i\right)} \]

   6. Taylor expanded in x around inf 44.4%

      \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 38.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.66 \cdot 10^{+89}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-182}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+142}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 30.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ \mathbf{if}\;t \leq -2.05 \cdot 10^{-25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-196}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+41}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j))))
   (if (<= t -2.05e-25)
     t_1
     (if (<= t 7.8e-196)
       (* b (* a i))
       (if (<= t 2.7e+41) (* y (* x z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double tmp;
	if (t <= -2.05e-25) {
		tmp = t_1;
	} else if (t <= 7.8e-196) {
		tmp = b * (a * i);
	} else if (t <= 2.7e+41) {
		tmp = y * (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (t * j)
    if (t <= (-2.05d-25)) then
        tmp = t_1
    else if (t <= 7.8d-196) then
        tmp = b * (a * i)
    else if (t <= 2.7d+41) then
        tmp = y * (x * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double tmp;
	if (t <= -2.05e-25) {
		tmp = t_1;
	} else if (t <= 7.8e-196) {
		tmp = b * (a * i);
	} else if (t <= 2.7e+41) {
		tmp = y * (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (t * j)
	tmp = 0
	if t <= -2.05e-25:
		tmp = t_1
	elif t <= 7.8e-196:
		tmp = b * (a * i)
	elif t <= 2.7e+41:
		tmp = y * (x * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(t * j))
	tmp = 0.0
	if (t <= -2.05e-25)
		tmp = t_1;
	elseif (t <= 7.8e-196)
		tmp = Float64(b * Float64(a * i));
	elseif (t <= 2.7e+41)
		tmp = Float64(y * Float64(x * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (t * j);
	tmp = 0.0;
	if (t <= -2.05e-25)
		tmp = t_1;
	elseif (t <= 7.8e-196)
		tmp = b * (a * i);
	elseif (t <= 2.7e+41)
		tmp = y * (x * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.05e-25], t$95$1, If[LessEqual[t, 7.8e-196], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.7e+41], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.04999999999999994e-25 or 2.7e41 < t

   1. Initial program 62.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 60.4%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   4. Taylor expanded in x around inf 57.7%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot z + \frac{j \cdot \left(c \cdot t - i \cdot y\right)}{x}\right) - a \cdot t\right)} \]

   5. Taylor expanded in c around inf 40.1%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   6. Step-by-step derivation

      1. *-commutative 40.1%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

   7. Simplified 40.1%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if -2.04999999999999994e-25 < t < 7.80000000000000031e-196

   1. Initial program 88.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 56.2%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 56.2%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   5. Simplified 56.2%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   6. Taylor expanded in a around inf 38.6%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]
   7. Step-by-step derivation

      1. *-commutative 38.6%

         \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]

   8. Simplified 38.6%

      \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]

   if 7.80000000000000031e-196 < t < 2.7e41

   1. Initial program 78.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 50.1%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 50.1%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 50.1%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 50.1%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 50.1%

         \[\leadsto y \cdot \left(x \cdot z - \color{blue}{j \cdot i}\right) \]

   5. Simplified 50.1%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z - j \cdot i\right)} \]

   6. Taylor expanded in x around inf 32.2%

      \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 38.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{-25}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-196}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+41}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 30.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ \mathbf{if}\;t \leq -9.8 \cdot 10^{-26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-197}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j))))
   (if (<= t -9.8e-26)
     t_1
     (if (<= t 1.8e-197)
       (* b (* a i))
       (if (<= t 8.2e+42) (* x (* y z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double tmp;
	if (t <= -9.8e-26) {
		tmp = t_1;
	} else if (t <= 1.8e-197) {
		tmp = b * (a * i);
	} else if (t <= 8.2e+42) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (t * j)
    if (t <= (-9.8d-26)) then
        tmp = t_1
    else if (t <= 1.8d-197) then
        tmp = b * (a * i)
    else if (t <= 8.2d+42) then
        tmp = x * (y * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double tmp;
	if (t <= -9.8e-26) {
		tmp = t_1;
	} else if (t <= 1.8e-197) {
		tmp = b * (a * i);
	} else if (t <= 8.2e+42) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (t * j)
	tmp = 0
	if t <= -9.8e-26:
		tmp = t_1
	elif t <= 1.8e-197:
		tmp = b * (a * i)
	elif t <= 8.2e+42:
		tmp = x * (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(t * j))
	tmp = 0.0
	if (t <= -9.8e-26)
		tmp = t_1;
	elseif (t <= 1.8e-197)
		tmp = Float64(b * Float64(a * i));
	elseif (t <= 8.2e+42)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (t * j);
	tmp = 0.0;
	if (t <= -9.8e-26)
		tmp = t_1;
	elseif (t <= 1.8e-197)
		tmp = b * (a * i);
	elseif (t <= 8.2e+42)
		tmp = x * (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.8e-26], t$95$1, If[LessEqual[t, 1.8e-197], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.2e+42], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.7999999999999998e-26 or 8.2000000000000001e42 < t

   1. Initial program 62.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 60.4%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   4. Taylor expanded in x around inf 57.7%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot z + \frac{j \cdot \left(c \cdot t - i \cdot y\right)}{x}\right) - a \cdot t\right)} \]

   5. Taylor expanded in c around inf 40.1%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   6. Step-by-step derivation

      1. *-commutative 40.1%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

   7. Simplified 40.1%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if -9.7999999999999998e-26 < t < 1.7999999999999999e-197

   1. Initial program 88.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 56.2%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 56.2%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   5. Simplified 56.2%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   6. Taylor expanded in a around inf 38.6%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]
   7. Step-by-step derivation

      1. *-commutative 38.6%

         \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]

   8. Simplified 38.6%

      \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]

   if 1.7999999999999999e-197 < t < 8.2000000000000001e42

   1. Initial program 78.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 50.1%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 50.1%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 50.1%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 50.1%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 50.1%

         \[\leadsto y \cdot \left(x \cdot z - \color{blue}{j \cdot i}\right) \]

   5. Simplified 50.1%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z - j \cdot i\right)} \]

   6. Taylor expanded in x around inf 30.5%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 37.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.8 \cdot 10^{-26}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-197}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 51.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.45 \cdot 10^{+34} \lor \neg \left(j \leq 5.2 \cdot 10^{-37}\right):\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -1.45e+34) (not (<= j 5.2e-37)))
   (* j (- (* t c) (* y i)))
   (* 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 tmp;
	if ((j <= -1.45e+34) || !(j <= 5.2e-37)) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = 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) :: tmp
    if ((j <= (-1.45d+34)) .or. (.not. (j <= 5.2d-37))) then
        tmp = j * ((t * c) - (y * i))
    else
        tmp = 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 tmp;
	if ((j <= -1.45e+34) || !(j <= 5.2e-37)) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = b * ((a * i) - (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -1.45e+34) or not (j <= 5.2e-37):
		tmp = j * ((t * c) - (y * i))
	else:
		tmp = b * ((a * i) - (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -1.45e+34) || !(j <= 5.2e-37))
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	else
		tmp = 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)
	tmp = 0.0;
	if ((j <= -1.45e+34) || ~((j <= 5.2e-37)))
		tmp = j * ((t * c) - (y * i));
	else
		tmp = b * ((a * i) - (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -1.45e+34], N[Not[LessEqual[j, 5.2e-37]], $MachinePrecision]], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -1.4500000000000001e34 or 5.19999999999999959e-37 < j

   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 65.2%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-commutative 65.2%

         \[\leadsto j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      2. *-commutative 65.2%

         \[\leadsto j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   5. Simplified 65.2%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot c - y \cdot i\right)} \]

   if -1.4500000000000001e34 < j < 5.19999999999999959e-37

   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 b around inf 49.2%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 49.2%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   5. Simplified 49.2%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.45 \cdot 10^{+34} \lor \neg \left(j \leq 5.2 \cdot 10^{-37}\right):\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 31: 29.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -28500 \lor \neg \left(c \leq 6 \cdot 10^{+73}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -28500.0) (not (<= c 6e+73))) (* c (* t j)) (* 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 ((c <= -28500.0) || !(c <= 6e+73)) {
		tmp = c * (t * j);
	} 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 ((c <= (-28500.0d0)) .or. (.not. (c <= 6d+73))) then
        tmp = c * (t * j)
    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 ((c <= -28500.0) || !(c <= 6e+73)) {
		tmp = c * (t * j);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -28500.0) or not (c <= 6e+73):
		tmp = c * (t * j)
	else:
		tmp = b * (a * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -28500.0) || !(c <= 6e+73))
		tmp = Float64(c * Float64(t * j));
	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 ((c <= -28500.0) || ~((c <= 6e+73)))
		tmp = c * (t * j);
	else
		tmp = b * (a * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -28500.0], N[Not[LessEqual[c, 6e+73]], $MachinePrecision]], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -28500 or 6.00000000000000021e73 < c

   1. Initial program 61.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 55.4%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   4. Taylor expanded in x around inf 52.9%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot z + \frac{j \cdot \left(c \cdot t - i \cdot y\right)}{x}\right) - a \cdot t\right)} \]

   5. Taylor expanded in c around inf 42.1%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   6. Step-by-step derivation

      1. *-commutative 42.1%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

   7. Simplified 42.1%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if -28500 < c < 6.00000000000000021e73

   1. Initial program 80.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 41.9%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 41.9%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   5. Simplified 41.9%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   6. Taylor expanded in a around inf 33.7%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]
   7. Step-by-step derivation

      1. *-commutative 33.7%

         \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]

   8. Simplified 33.7%

      \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -28500 \lor \neg \left(c \leq 6 \cdot 10^{+73}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 32: 22.3% 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 72.3%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
2. Add Preprocessing

3. Taylor expanded in b around inf 40.1%

   \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
4. Step-by-step derivation

   1. *-commutative 40.1%

      \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

5. Simplified 40.1%

   \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

6. Taylor expanded in a around inf 22.1%

   \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]
7. Step-by-step derivation

   1. *-commutative 22.1%

      \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]

8. Simplified 22.1%

   \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]

9. Final simplification 22.1%

   \[\leadsto b \cdot \left(a \cdot i\right) \]
10. Add Preprocessing

Alternative 33: 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 72.3%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
2. Add Preprocessing

3. Taylor expanded in b around inf 40.1%

   \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
4. Step-by-step derivation

   1. *-commutative 40.1%

      \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

5. Simplified 40.1%

   \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

6. Taylor expanded in a around inf 21.4%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
7. Step-by-step derivation

   1. *-commutative 21.4%

      \[\leadsto a \cdot \color{blue}{\left(i \cdot b\right)} \]

8. Simplified 21.4%

   \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]

9. Final simplification 21.4%

   \[\leadsto a \cdot \left(b \cdot i\right) \]
10. Add Preprocessing

Developer target: 67.8% 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 2024110 
(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)))))