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

Percentage Accurate: 73.4% → 81.5%

Time: 17.6s

Alternatives: 19

Speedup: 0.5×

• 58.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 81.5% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 94.6%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in t around inf 20.5%

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

      1. sub-neg 20.5%

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

      2. +-commutative 20.5%

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

      3. associate-+r+ 20.5%

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

      4. +-commutative 20.5%

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

      5. mul-1-neg 20.5%

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

      6. unsub-neg 20.5%

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

      7. *-commutative 20.5%

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

      8. associate-*l* 25.0%

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

      9. associate-/l* 27.3%

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

   5. Simplified 40.9%

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

   6. Taylor expanded in x around inf 51.3%

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

      1. associate-*r* 53.4%

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

      2. associate-/l* 53.4%

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

   8. Simplified 53.4%

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

4. Final simplification 87.5%

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

Alternative 2: 51.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;j \leq -8.2 \cdot 10^{+55}:\\ \;\;\;\;j \cdot \left(y \cdot \left(a \cdot \frac{c}{y} - i\right)\right)\\ \mathbf{elif}\;j \leq -1.1 \cdot 10^{-158}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 5.5 \cdot 10^{-131}:\\ \;\;\;\;b \cdot \left(t \cdot \left(i - \frac{z \cdot c}{t}\right)\right)\\ \mathbf{elif}\;j \leq 4 \cdot 10^{+106}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= j -8.2e+55)
     (* j (* y (- (* a (/ c y)) i)))
     (if (<= j -1.1e-158)
       t_1
       (if (<= j 5.5e-131)
         (* b (* t (- i (/ (* z c) t))))
         (if (<= j 4e+106) t_1 (* j (- (* a c) (* y i)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (j <= -8.2e+55) {
		tmp = j * (y * ((a * (c / y)) - i));
	} else if (j <= -1.1e-158) {
		tmp = t_1;
	} else if (j <= 5.5e-131) {
		tmp = b * (t * (i - ((z * c) / t)));
	} else if (j <= 4e+106) {
		tmp = t_1;
	} else {
		tmp = j * ((a * c) - (y * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (j <= (-8.2d+55)) then
        tmp = j * (y * ((a * (c / y)) - i))
    else if (j <= (-1.1d-158)) then
        tmp = t_1
    else if (j <= 5.5d-131) then
        tmp = b * (t * (i - ((z * c) / t)))
    else if (j <= 4d+106) then
        tmp = t_1
    else
        tmp = j * ((a * c) - (y * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (j <= -8.2e+55) {
		tmp = j * (y * ((a * (c / y)) - i));
	} else if (j <= -1.1e-158) {
		tmp = t_1;
	} else if (j <= 5.5e-131) {
		tmp = b * (t * (i - ((z * c) / t)));
	} else if (j <= 4e+106) {
		tmp = t_1;
	} else {
		tmp = j * ((a * c) - (y * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if j <= -8.2e+55:
		tmp = j * (y * ((a * (c / y)) - i))
	elif j <= -1.1e-158:
		tmp = t_1
	elif j <= 5.5e-131:
		tmp = b * (t * (i - ((z * c) / t)))
	elif j <= 4e+106:
		tmp = t_1
	else:
		tmp = j * ((a * c) - (y * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (j <= -8.2e+55)
		tmp = Float64(j * Float64(y * Float64(Float64(a * Float64(c / y)) - i)));
	elseif (j <= -1.1e-158)
		tmp = t_1;
	elseif (j <= 5.5e-131)
		tmp = Float64(b * Float64(t * Float64(i - Float64(Float64(z * c) / t))));
	elseif (j <= 4e+106)
		tmp = t_1;
	else
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (j <= -8.2e+55)
		tmp = j * (y * ((a * (c / y)) - i));
	elseif (j <= -1.1e-158)
		tmp = t_1;
	elseif (j <= 5.5e-131)
		tmp = b * (t * (i - ((z * c) / t)));
	elseif (j <= 4e+106)
		tmp = t_1;
	else
		tmp = j * ((a * c) - (y * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -8.2e+55], N[(j * N[(y * N[(N[(a * N[(c / y), $MachinePrecision]), $MachinePrecision] - i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.1e-158], t$95$1, If[LessEqual[j, 5.5e-131], N[(b * N[(t * N[(i - N[(N[(z * c), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4e+106], t$95$1, N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -8.19999999999999962e55

   1. Initial program 79.7%

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

   3. Taylor expanded in x around 0 75.2%

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

   4. Taylor expanded in j around inf 67.1%

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

      1. *-commutative 67.1%

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

   6. Simplified 67.1%

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

   7. Taylor expanded in y around inf 67.1%

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

      1. associate-/l* 67.1%

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

   9. Simplified 67.1%

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

   if -8.19999999999999962e55 < j < -1.1000000000000001e-158 or 5.4999999999999997e-131 < j < 4.00000000000000036e106

   1. Initial program 75.6%

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

   3. Taylor expanded in t around inf 63.4%

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

      1. sub-neg 63.4%

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

      2. +-commutative 63.4%

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

      3. associate-+r+ 63.4%

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

      4. +-commutative 63.4%

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

      5. mul-1-neg 63.4%

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

      6. unsub-neg 63.4%

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

      7. *-commutative 63.4%

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

      8. associate-*l* 62.4%

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

      9. associate-/l* 62.3%

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

   5. Simplified 64.4%

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

   6. Taylor expanded in t around 0 73.5%

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

   7. Taylor expanded in x around inf 52.5%

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

      1. +-commutative 52.5%

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

      2. mul-1-neg 52.5%

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

      3. unsub-neg 52.5%

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

   9. Simplified 52.5%

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

   if -1.1000000000000001e-158 < j < 5.4999999999999997e-131

   1. Initial program 77.6%

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

   3. Taylor expanded in t around inf 73.6%

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

      1. sub-neg 73.6%

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

      2. +-commutative 73.6%

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

      3. associate-+r+ 73.6%

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

      4. +-commutative 73.6%

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

      5. mul-1-neg 73.6%

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

      6. unsub-neg 73.6%

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

      7. *-commutative 73.6%

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

      8. associate-*l* 72.7%

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

      9. associate-/l* 68.8%

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

   5. Simplified 64.9%

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

   6. Taylor expanded in b around inf 60.1%

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

   if 4.00000000000000036e106 < j

   1. Initial program 82.6%

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

   3. Taylor expanded in j around inf 87.0%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -8.2 \cdot 10^{+55}:\\ \;\;\;\;j \cdot \left(y \cdot \left(a \cdot \frac{c}{y} - i\right)\right)\\ \mathbf{elif}\;j \leq -1.1 \cdot 10^{-158}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 5.5 \cdot 10^{-131}:\\ \;\;\;\;b \cdot \left(t \cdot \left(i - \frac{z \cdot c}{t}\right)\right)\\ \mathbf{elif}\;j \leq 4 \cdot 10^{+106}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.65 \cdot 10^{+56}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -1.76 \cdot 10^{-158}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 6.2 \cdot 10^{-140}:\\ \;\;\;\;b \cdot \left(t \cdot \left(i - \frac{z \cdot c}{t}\right)\right)\\ \mathbf{elif}\;j \leq 1.16 \cdot 10^{+107}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (* j (- (* a c) (* y i)))))
   (if (<= j -1.65e+56)
     t_2
     (if (<= j -1.76e-158)
       t_1
       (if (<= j 6.2e-140)
         (* b (* t (- i (/ (* z c) t))))
         (if (<= j 1.16e+107) 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 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -1.65e+56) {
		tmp = t_2;
	} else if (j <= -1.76e-158) {
		tmp = t_1;
	} else if (j <= 6.2e-140) {
		tmp = b * (t * (i - ((z * c) / t)));
	} else if (j <= 1.16e+107) {
		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))
    t_2 = j * ((a * c) - (y * i))
    if (j <= (-1.65d+56)) then
        tmp = t_2
    else if (j <= (-1.76d-158)) then
        tmp = t_1
    else if (j <= 6.2d-140) then
        tmp = b * (t * (i - ((z * c) / t)))
    else if (j <= 1.16d+107) 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));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -1.65e+56) {
		tmp = t_2;
	} else if (j <= -1.76e-158) {
		tmp = t_1;
	} else if (j <= 6.2e-140) {
		tmp = b * (t * (i - ((z * c) / t)));
	} else if (j <= 1.16e+107) {
		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))
	t_2 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -1.65e+56:
		tmp = t_2
	elif j <= -1.76e-158:
		tmp = t_1
	elif j <= 6.2e-140:
		tmp = b * (t * (i - ((z * c) / t)))
	elif j <= 1.16e+107:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -1.65e+56)
		tmp = t_2;
	elseif (j <= -1.76e-158)
		tmp = t_1;
	elseif (j <= 6.2e-140)
		tmp = Float64(b * Float64(t * Float64(i - Float64(Float64(z * c) / t))));
	elseif (j <= 1.16e+107)
		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));
	t_2 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -1.65e+56)
		tmp = t_2;
	elseif (j <= -1.76e-158)
		tmp = t_1;
	elseif (j <= 6.2e-140)
		tmp = b * (t * (i - ((z * c) / t)));
	elseif (j <= 1.16e+107)
		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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.65e+56], t$95$2, If[LessEqual[j, -1.76e-158], t$95$1, If[LessEqual[j, 6.2e-140], N[(b * N[(t * N[(i - N[(N[(z * c), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.16e+107], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.65000000000000001e56 or 1.1600000000000001e107 < j

   1. Initial program 81.0%

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

   3. Taylor expanded in j around inf 76.4%

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

   if -1.65000000000000001e56 < j < -1.76e-158 or 6.1999999999999998e-140 < j < 1.1600000000000001e107

   1. Initial program 75.6%

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

   3. Taylor expanded in t around inf 63.4%

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

      1. sub-neg 63.4%

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

      2. +-commutative 63.4%

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

      3. associate-+r+ 63.4%

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

      4. +-commutative 63.4%

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

      5. mul-1-neg 63.4%

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

      6. unsub-neg 63.4%

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

      7. *-commutative 63.4%

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

      8. associate-*l* 62.4%

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

      9. associate-/l* 62.3%

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

   5. Simplified 64.4%

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

   6. Taylor expanded in t around 0 73.5%

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

   7. Taylor expanded in x around inf 52.5%

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

      1. +-commutative 52.5%

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

      2. mul-1-neg 52.5%

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

      3. unsub-neg 52.5%

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

   9. Simplified 52.5%

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

   if -1.76e-158 < j < 6.1999999999999998e-140

   1. Initial program 77.6%

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

   3. Taylor expanded in t around inf 73.6%

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

      1. sub-neg 73.6%

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

      2. +-commutative 73.6%

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

      3. associate-+r+ 73.6%

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

      4. +-commutative 73.6%

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

      5. mul-1-neg 73.6%

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

      6. unsub-neg 73.6%

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

      7. *-commutative 73.6%

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

      8. associate-*l* 72.7%

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

      9. associate-/l* 68.8%

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

   5. Simplified 64.9%

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

   6. Taylor expanded in b around inf 60.1%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.65 \cdot 10^{+56}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -1.76 \cdot 10^{-158}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 6.2 \cdot 10^{-140}:\\ \;\;\;\;b \cdot \left(t \cdot \left(i - \frac{z \cdot c}{t}\right)\right)\\ \mathbf{elif}\;j \leq 1.16 \cdot 10^{+107}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 52.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.2 \cdot 10^{+56}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -9.2 \cdot 10^{-159}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{-143}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 4.2 \cdot 10^{+106}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (* j (- (* a c) (* y i)))))
   (if (<= j -1.2e+56)
     t_2
     (if (<= j -9.2e-159)
       t_1
       (if (<= j 2.6e-143)
         (* b (- (* t i) (* z c)))
         (if (<= j 4.2e+106) 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 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -1.2e+56) {
		tmp = t_2;
	} else if (j <= -9.2e-159) {
		tmp = t_1;
	} else if (j <= 2.6e-143) {
		tmp = b * ((t * i) - (z * c));
	} else if (j <= 4.2e+106) {
		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))
    t_2 = j * ((a * c) - (y * i))
    if (j <= (-1.2d+56)) then
        tmp = t_2
    else if (j <= (-9.2d-159)) then
        tmp = t_1
    else if (j <= 2.6d-143) then
        tmp = b * ((t * i) - (z * c))
    else if (j <= 4.2d+106) 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));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -1.2e+56) {
		tmp = t_2;
	} else if (j <= -9.2e-159) {
		tmp = t_1;
	} else if (j <= 2.6e-143) {
		tmp = b * ((t * i) - (z * c));
	} else if (j <= 4.2e+106) {
		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))
	t_2 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -1.2e+56:
		tmp = t_2
	elif j <= -9.2e-159:
		tmp = t_1
	elif j <= 2.6e-143:
		tmp = b * ((t * i) - (z * c))
	elif j <= 4.2e+106:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -1.2e+56)
		tmp = t_2;
	elseif (j <= -9.2e-159)
		tmp = t_1;
	elseif (j <= 2.6e-143)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (j <= 4.2e+106)
		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));
	t_2 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -1.2e+56)
		tmp = t_2;
	elseif (j <= -9.2e-159)
		tmp = t_1;
	elseif (j <= 2.6e-143)
		tmp = b * ((t * i) - (z * c));
	elseif (j <= 4.2e+106)
		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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.2e+56], t$95$2, If[LessEqual[j, -9.2e-159], t$95$1, If[LessEqual[j, 2.6e-143], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.2e+106], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.20000000000000007e56 or 4.2000000000000001e106 < j

   1. Initial program 81.0%

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

   3. Taylor expanded in j around inf 76.4%

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

   if -1.20000000000000007e56 < j < -9.19999999999999914e-159 or 2.59999999999999987e-143 < j < 4.2000000000000001e106

   1. Initial program 75.6%

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

   3. Taylor expanded in t around inf 63.4%

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

      1. sub-neg 63.4%

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

      2. +-commutative 63.4%

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

      3. associate-+r+ 63.4%

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

      4. +-commutative 63.4%

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

      5. mul-1-neg 63.4%

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

      6. unsub-neg 63.4%

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

      7. *-commutative 63.4%

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

      8. associate-*l* 62.4%

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

      9. associate-/l* 62.3%

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

   5. Simplified 64.4%

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

   6. Taylor expanded in t around 0 73.5%

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

   7. Taylor expanded in x around inf 52.5%

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

      1. +-commutative 52.5%

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

      2. mul-1-neg 52.5%

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

      3. unsub-neg 52.5%

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

   9. Simplified 52.5%

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

   if -9.19999999999999914e-159 < j < 2.59999999999999987e-143

   1. Initial program 77.6%

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

   3. Taylor expanded in b around inf 60.1%

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

      1. *-commutative 60.1%

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

   5. Simplified 60.1%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.2 \cdot 10^{+56}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -9.2 \cdot 10^{-159}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{-143}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 4.2 \cdot 10^{+106}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 64.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.55 \cdot 10^{+147} \lor \neg \left(j \leq 9.6 \cdot 10^{+117}\right):\\ \;\;\;\;j \cdot \left(y \cdot \left(a \cdot \frac{c}{y} - i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -1.55e+147) (not (<= j 9.6e+117)))
   (* j (* y (- (* a (/ c y)) i)))
   (+ (* z (- (* x y) (* b c))) (* a (- (* c j) (* x t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -1.55e+147) || !(j <= 9.6e+117)) {
		tmp = j * (y * ((a * (c / y)) - i));
	} else {
		tmp = (z * ((x * y) - (b * c))) + (a * ((c * j) - (x * t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((j <= (-1.55d+147)) .or. (.not. (j <= 9.6d+117))) then
        tmp = j * (y * ((a * (c / y)) - i))
    else
        tmp = (z * ((x * y) - (b * c))) + (a * ((c * j) - (x * t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -1.55e+147) || !(j <= 9.6e+117)) {
		tmp = j * (y * ((a * (c / y)) - i));
	} else {
		tmp = (z * ((x * y) - (b * c))) + (a * ((c * j) - (x * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -1.55e+147) or not (j <= 9.6e+117):
		tmp = j * (y * ((a * (c / y)) - i))
	else:
		tmp = (z * ((x * y) - (b * c))) + (a * ((c * j) - (x * t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -1.55e+147) || !(j <= 9.6e+117))
		tmp = Float64(j * Float64(y * Float64(Float64(a * Float64(c / y)) - i)));
	else
		tmp = Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) + Float64(a * Float64(Float64(c * j) - Float64(x * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -1.55e+147) || ~((j <= 9.6e+117)))
		tmp = j * (y * ((a * (c / y)) - i));
	else
		tmp = (z * ((x * y) - (b * c))) + (a * ((c * j) - (x * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -1.55e+147], N[Not[LessEqual[j, 9.6e+117]], $MachinePrecision]], N[(j * N[(y * N[(N[(a * N[(c / y), $MachinePrecision]), $MachinePrecision] - i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -1.55e147 or 9.5999999999999996e117 < j

   1. Initial program 81.3%

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

   3. Taylor expanded in x around 0 81.4%

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

   4. Taylor expanded in j around inf 84.1%

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

      1. *-commutative 84.1%

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

   6. Simplified 84.1%

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

   7. Taylor expanded in y around inf 84.1%

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

      1. associate-/l* 84.1%

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

   9. Simplified 84.1%

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

   if -1.55e147 < j < 9.5999999999999996e117

   1. Initial program 76.9%

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

   3. Taylor expanded in t around inf 64.3%

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

      1. sub-neg 64.3%

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

      2. +-commutative 64.3%

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

      3. associate-+r+ 64.3%

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

      4. +-commutative 64.3%

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

      5. mul-1-neg 64.3%

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

      6. unsub-neg 64.3%

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

      7. *-commutative 64.3%

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

      8. associate-*l* 64.1%

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

      9. associate-/l* 62.9%

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

   5. Simplified 62.8%

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

   6. Taylor expanded in t around 0 72.9%

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

   7. Taylor expanded in i around 0 57.4%

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

      1. sub-neg 57.4%

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

      2. associate-+r+ 57.4%

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

      3. neg-mul-1 57.4%

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

      4. distribute-rgt-neg-in 57.4%

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

      5. mul-1-neg 57.4%

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

      6. distribute-lft-in 57.9%

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

      7. associate-+l+ 58.0%

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

      8. +-commutative 58.0%

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

      9. mul-1-neg 58.0%

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

      10. unsub-neg 58.0%

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

      11. *-commutative 58.0%

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

      12. sub-neg 58.0%

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

      13. associate-*r* 58.3%

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

      14. associate-*r* 60.0%

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

   9. Simplified 62.4%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.55 \cdot 10^{+147} \lor \neg \left(j \leq 9.6 \cdot 10^{+117}\right):\\ \;\;\;\;j \cdot \left(y \cdot \left(a \cdot \frac{c}{y} - i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) + a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(z \cdot c - t \cdot i\right)\\ \mathbf{if}\;x \leq -1 \cdot 10^{+73}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - t\_1\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+59}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \left(\frac{y \cdot z}{t} - a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* z c) (* t i)))))
   (if (<= x -1e+73)
     (- (* x (- (* y z) (* t a))) t_1)
     (if (<= x 1.65e+59)
       (- (* j (- (* a c) (* y i))) t_1)
       (* t (* x (- (/ (* y z) t) a)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((z * c) - (t * i));
	double tmp;
	if (x <= -1e+73) {
		tmp = (x * ((y * z) - (t * a))) - t_1;
	} else if (x <= 1.65e+59) {
		tmp = (j * ((a * c) - (y * i))) - t_1;
	} else {
		tmp = t * (x * (((y * z) / t) - a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((z * c) - (t * i))
    if (x <= (-1d+73)) then
        tmp = (x * ((y * z) - (t * a))) - t_1
    else if (x <= 1.65d+59) then
        tmp = (j * ((a * c) - (y * i))) - t_1
    else
        tmp = t * (x * (((y * z) / t) - a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((z * c) - (t * i));
	double tmp;
	if (x <= -1e+73) {
		tmp = (x * ((y * z) - (t * a))) - t_1;
	} else if (x <= 1.65e+59) {
		tmp = (j * ((a * c) - (y * i))) - t_1;
	} else {
		tmp = t * (x * (((y * z) / t) - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((z * c) - (t * i))
	tmp = 0
	if x <= -1e+73:
		tmp = (x * ((y * z) - (t * a))) - t_1
	elif x <= 1.65e+59:
		tmp = (j * ((a * c) - (y * i))) - t_1
	else:
		tmp = t * (x * (((y * z) / t) - a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(z * c) - Float64(t * i)))
	tmp = 0.0
	if (x <= -1e+73)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - t_1);
	elseif (x <= 1.65e+59)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) - t_1);
	else
		tmp = Float64(t * Float64(x * Float64(Float64(Float64(y * z) / t) - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((z * c) - (t * i));
	tmp = 0.0;
	if (x <= -1e+73)
		tmp = (x * ((y * z) - (t * a))) - t_1;
	elseif (x <= 1.65e+59)
		tmp = (j * ((a * c) - (y * i))) - t_1;
	else
		tmp = t * (x * (((y * z) / t) - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(z * c), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1e+73], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[x, 1.65e+59], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(t * N[(x * N[(N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.99999999999999983e72

   1. Initial program 85.6%

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

   3. Taylor expanded in j around 0 79.5%

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

   if -9.99999999999999983e72 < x < 1.65e59

   1. Initial program 77.2%

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

   3. Taylor expanded in x around 0 75.3%

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

   if 1.65e59 < x

   1. Initial program 75.4%

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

   3. Taylor expanded in t around inf 63.5%

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

      1. sub-neg 63.5%

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

      2. +-commutative 63.5%

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

      3. associate-+r+ 63.5%

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

      4. +-commutative 63.5%

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

      5. mul-1-neg 63.5%

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

      6. unsub-neg 63.5%

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

      7. *-commutative 63.5%

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

      8. associate-*l* 61.5%

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

      9. associate-/l* 61.4%

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

   5. Simplified 59.3%

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

   6. Taylor expanded in x around inf 78.2%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+73}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+59}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c - t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \left(\frac{y \cdot z}{t} - a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+71}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+59}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c - t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \left(\frac{y \cdot z}{t} - a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x -3e+71)
   (* x (- (* y z) (* t a)))
   (if (<= x 1.65e+59)
     (- (* j (- (* a c) (* y i))) (* b (- (* z c) (* t i))))
     (* t (* x (- (/ (* y z) t) a))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -3e+71) {
		tmp = x * ((y * z) - (t * a));
	} else if (x <= 1.65e+59) {
		tmp = (j * ((a * c) - (y * i))) - (b * ((z * c) - (t * i)));
	} else {
		tmp = t * (x * (((y * z) / t) - a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (x <= (-3d+71)) then
        tmp = x * ((y * z) - (t * a))
    else if (x <= 1.65d+59) then
        tmp = (j * ((a * c) - (y * i))) - (b * ((z * c) - (t * i)))
    else
        tmp = t * (x * (((y * z) / t) - a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -3e+71) {
		tmp = x * ((y * z) - (t * a));
	} else if (x <= 1.65e+59) {
		tmp = (j * ((a * c) - (y * i))) - (b * ((z * c) - (t * i)));
	} else {
		tmp = t * (x * (((y * z) / t) - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if x <= -3e+71:
		tmp = x * ((y * z) - (t * a))
	elif x <= 1.65e+59:
		tmp = (j * ((a * c) - (y * i))) - (b * ((z * c) - (t * i)))
	else:
		tmp = t * (x * (((y * z) / t) - a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= -3e+71)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (x <= 1.65e+59)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) - Float64(b * Float64(Float64(z * c) - Float64(t * i))));
	else
		tmp = Float64(t * Float64(x * Float64(Float64(Float64(y * z) / t) - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (x <= -3e+71)
		tmp = x * ((y * z) - (t * a));
	elseif (x <= 1.65e+59)
		tmp = (j * ((a * c) - (y * i))) - (b * ((z * c) - (t * i)));
	else
		tmp = t * (x * (((y * z) / t) - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, -3e+71], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.65e+59], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(z * c), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(x * N[(N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.00000000000000013e71

   1. Initial program 83.8%

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

   3. Taylor expanded in t around inf 56.9%

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

      1. sub-neg 56.9%

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

      2. +-commutative 56.9%

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

      3. associate-+r+ 56.9%

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

      4. +-commutative 56.9%

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

      5. mul-1-neg 56.9%

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

      6. unsub-neg 56.9%

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

      7. *-commutative 56.9%

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

      8. associate-*l* 55.9%

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

      9. associate-/l* 55.9%

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

   5. Simplified 55.9%

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

   6. Taylor expanded in t around 0 71.3%

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

   7. Taylor expanded in x around inf 69.8%

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

      1. +-commutative 69.8%

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

      2. mul-1-neg 69.8%

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

      3. unsub-neg 69.8%

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

   9. Simplified 69.8%

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

   if -3.00000000000000013e71 < x < 1.65e59

   1. Initial program 77.6%

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

   3. Taylor expanded in x around 0 75.8%

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

   if 1.65e59 < x

   1. Initial program 75.4%

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

   3. Taylor expanded in t around inf 63.5%

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

      1. sub-neg 63.5%

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

      2. +-commutative 63.5%

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

      3. associate-+r+ 63.5%

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

      4. +-commutative 63.5%

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

      5. mul-1-neg 63.5%

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

      6. unsub-neg 63.5%

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

      7. *-commutative 63.5%

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

      8. associate-*l* 61.5%

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

      9. associate-/l* 61.4%

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

   5. Simplified 59.3%

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

   6. Taylor expanded in x around inf 78.2%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+71}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+59}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c - t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \left(\frac{y \cdot z}{t} - a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -8.8 \cdot 10^{+147}:\\ \;\;\;\;j \cdot \left(y \cdot \left(a \cdot \frac{c}{y} - i\right)\right)\\ \mathbf{elif}\;j \leq 9.2 \cdot 10^{+106}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -8.8e+147)
   (* j (* y (- (* a (/ c y)) i)))
   (if (<= j 9.2e+106)
     (- (* z (- (* x y) (* b c))) (* a (* x t)))
     (* j (- (* a c) (* y i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -8.8e+147) {
		tmp = j * (y * ((a * (c / y)) - i));
	} else if (j <= 9.2e+106) {
		tmp = (z * ((x * y) - (b * c))) - (a * (x * t));
	} else {
		tmp = j * ((a * c) - (y * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (j <= (-8.8d+147)) then
        tmp = j * (y * ((a * (c / y)) - i))
    else if (j <= 9.2d+106) then
        tmp = (z * ((x * y) - (b * c))) - (a * (x * t))
    else
        tmp = j * ((a * c) - (y * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -8.8e+147) {
		tmp = j * (y * ((a * (c / y)) - i));
	} else if (j <= 9.2e+106) {
		tmp = (z * ((x * y) - (b * c))) - (a * (x * t));
	} else {
		tmp = j * ((a * c) - (y * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -8.8e+147:
		tmp = j * (y * ((a * (c / y)) - i))
	elif j <= 9.2e+106:
		tmp = (z * ((x * y) - (b * c))) - (a * (x * t))
	else:
		tmp = j * ((a * c) - (y * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -8.8e+147)
		tmp = Float64(j * Float64(y * Float64(Float64(a * Float64(c / y)) - i)));
	elseif (j <= 9.2e+106)
		tmp = Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) - Float64(a * Float64(x * t)));
	else
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -8.8e+147)
		tmp = j * (y * ((a * (c / y)) - i));
	elseif (j <= 9.2e+106)
		tmp = (z * ((x * y) - (b * c))) - (a * (x * t));
	else
		tmp = j * ((a * c) - (y * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -8.8e+147], N[(j * N[(y * N[(N[(a * N[(c / y), $MachinePrecision]), $MachinePrecision] - i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 9.2e+106], N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -8.8000000000000007e147

   1. Initial program 81.0%

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

   3. Taylor expanded in x around 0 86.4%

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

   4. Taylor expanded in j around inf 78.5%

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

      1. *-commutative 78.5%

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

   6. Simplified 78.5%

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

   7. Taylor expanded in y around inf 78.5%

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

      1. associate-/l* 78.6%

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

   9. Simplified 78.6%

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

   if -8.8000000000000007e147 < j < 9.2000000000000008e106

   1. Initial program 76.4%

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

   3. Taylor expanded in t around inf 64.9%

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

      1. sub-neg 64.9%

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

      2. +-commutative 64.9%

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

      3. associate-+r+ 64.9%

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

      4. +-commutative 64.9%

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

      5. mul-1-neg 64.9%

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

      6. unsub-neg 64.9%

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

      7. *-commutative 64.9%

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

      8. associate-*l* 64.6%

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

      9. associate-/l* 63.4%

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

   5. Simplified 63.3%

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

   6. Taylor expanded in t around 0 72.4%

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

   7. Taylor expanded in i around 0 56.6%

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

      1. sub-neg 56.6%

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

      2. associate-+r+ 56.6%

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

      3. neg-mul-1 56.6%

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

      4. distribute-rgt-neg-in 56.6%

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

      5. mul-1-neg 56.6%

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

      6. distribute-lft-in 57.2%

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

      7. associate-+l+ 57.2%

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

      8. +-commutative 57.2%

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

      9. mul-1-neg 57.2%

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

      10. unsub-neg 57.2%

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

      11. *-commutative 57.2%

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

      12. sub-neg 57.2%

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

      13. associate-*r* 57.6%

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

      14. associate-*r* 59.3%

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

   9. Simplified 61.7%

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

   10. Taylor expanded in j around 0 55.3%

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

       1. associate-*r* 55.3%

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

       2. mul-1-neg 55.3%

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

   12. Simplified 55.3%

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

   if 9.2000000000000008e106 < j

   1. Initial program 82.6%

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

   3. Taylor expanded in j around inf 87.0%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -8.8 \cdot 10^{+147}:\\ \;\;\;\;j \cdot \left(y \cdot \left(a \cdot \frac{c}{y} - i\right)\right)\\ \mathbf{elif}\;j \leq 9.2 \cdot 10^{+106}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 41.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.25 \cdot 10^{+110}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-227}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-103}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -1.25e+110)
     t_1
     (if (<= a 6.5e-227)
       (* y (* x z))
       (if (<= a 1.35e-103) (* b (* t i)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.25e+110) {
		tmp = t_1;
	} else if (a <= 6.5e-227) {
		tmp = y * (x * z);
	} else if (a <= 1.35e-103) {
		tmp = b * (t * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (a <= (-1.25d+110)) then
        tmp = t_1
    else if (a <= 6.5d-227) then
        tmp = y * (x * z)
    else if (a <= 1.35d-103) then
        tmp = b * (t * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.25e+110) {
		tmp = t_1;
	} else if (a <= 6.5e-227) {
		tmp = y * (x * z);
	} else if (a <= 1.35e-103) {
		tmp = b * (t * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -1.25e+110:
		tmp = t_1
	elif a <= 6.5e-227:
		tmp = y * (x * z)
	elif a <= 1.35e-103:
		tmp = b * (t * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -1.25e+110)
		tmp = t_1;
	elseif (a <= 6.5e-227)
		tmp = Float64(y * Float64(x * z));
	elseif (a <= 1.35e-103)
		tmp = Float64(b * Float64(t * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -1.25e+110)
		tmp = t_1;
	elseif (a <= 6.5e-227)
		tmp = y * (x * z);
	elseif (a <= 1.35e-103)
		tmp = b * (t * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.25e+110], t$95$1, If[LessEqual[a, 6.5e-227], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.35e-103], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.24999999999999995e110 or 1.35000000000000005e-103 < a

   1. Initial program 73.6%

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

   3. Taylor expanded in a around inf 61.6%

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

      1. +-commutative 61.6%

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

      2. mul-1-neg 61.6%

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

      3. unsub-neg 61.6%

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

   5. Simplified 61.6%

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

   if -1.24999999999999995e110 < a < 6.4999999999999996e-227

   1. Initial program 85.6%

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

   3. Taylor expanded in 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%

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

   5. Simplified 53.1%

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

   6. Taylor expanded in z around inf 39.4%

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

      1. *-commutative 39.4%

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

   8. Simplified 39.4%

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

   if 6.4999999999999996e-227 < a < 1.35000000000000005e-103

   1. Initial program 74.1%

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

   3. Taylor expanded in x around 0 66.0%

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

   4. Taylor expanded in t around inf 48.0%

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

4. Final simplification 51.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.25 \cdot 10^{+110}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-227}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-103}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 30.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -2.5 \cdot 10^{+55}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;j \leq 0.3:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 3.5 \cdot 10^{+210}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -2.5e+55)
   (* j (* a c))
   (if (<= j 0.3)
     (* y (* x z))
     (if (<= j 3.5e+210) (* a (* c j)) (* i (* j (- y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -2.5e+55) {
		tmp = j * (a * c);
	} else if (j <= 0.3) {
		tmp = y * (x * z);
	} else if (j <= 3.5e+210) {
		tmp = a * (c * j);
	} else {
		tmp = i * (j * -y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (j <= (-2.5d+55)) then
        tmp = j * (a * c)
    else if (j <= 0.3d0) then
        tmp = y * (x * z)
    else if (j <= 3.5d+210) then
        tmp = a * (c * j)
    else
        tmp = i * (j * -y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -2.5e+55) {
		tmp = j * (a * c);
	} else if (j <= 0.3) {
		tmp = y * (x * z);
	} else if (j <= 3.5e+210) {
		tmp = a * (c * j);
	} else {
		tmp = i * (j * -y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -2.5e+55:
		tmp = j * (a * c)
	elif j <= 0.3:
		tmp = y * (x * z)
	elif j <= 3.5e+210:
		tmp = a * (c * j)
	else:
		tmp = i * (j * -y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -2.5e+55)
		tmp = Float64(j * Float64(a * c));
	elseif (j <= 0.3)
		tmp = Float64(y * Float64(x * z));
	elseif (j <= 3.5e+210)
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(i * Float64(j * Float64(-y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -2.5e+55)
		tmp = j * (a * c);
	elseif (j <= 0.3)
		tmp = y * (x * z);
	elseif (j <= 3.5e+210)
		tmp = a * (c * j);
	else
		tmp = i * (j * -y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -2.5e+55], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 0.3], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.5e+210], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(i * N[(j * (-y)), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if j < -2.50000000000000023e55

   1. Initial program 79.7%

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

   3. Taylor expanded in x around 0 75.2%

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

   4. Taylor expanded in j around inf 67.1%

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

      1. *-commutative 67.1%

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

   6. Simplified 67.1%

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

   7. Taylor expanded in c around inf 53.6%

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

   if -2.50000000000000023e55 < j < 0.299999999999999989

   1. Initial program 76.1%

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

   3. Taylor expanded in y around inf 38.2%

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

      1. +-commutative 38.2%

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

      2. mul-1-neg 38.2%

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

      3. unsub-neg 38.2%

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

      4. *-commutative 38.2%

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

   5. Simplified 38.2%

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

   6. Taylor expanded in z around inf 33.0%

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

      1. *-commutative 33.0%

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

   8. Simplified 33.0%

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

   if 0.299999999999999989 < j < 3.5e210

   1. Initial program 79.8%

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

   3. Taylor expanded in a around inf 65.3%

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

      1. +-commutative 65.3%

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

      2. mul-1-neg 65.3%

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

      3. unsub-neg 65.3%

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

   5. Simplified 65.3%

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

   6. Taylor expanded in c around inf 54.5%

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

   if 3.5e210 < j

   1. Initial program 84.0%

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

   3. Taylor expanded in y around inf 73.0%

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

      1. +-commutative 73.0%

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

      2. mul-1-neg 73.0%

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

      3. unsub-neg 73.0%

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

      4. *-commutative 73.0%

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

   5. Simplified 73.0%

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

   6. Taylor expanded in z around 0 72.3%

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

      1. associate-*r* 72.3%

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

      2. neg-mul-1 72.3%

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

   8. Simplified 72.3%

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

4. Final simplification 45.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.5 \cdot 10^{+55}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;j \leq 0.3:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 3.5 \cdot 10^{+210}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 30.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.6 \cdot 10^{+56}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;j \leq 0.3:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{+209}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -1.6e+56)
   (* j (* a c))
   (if (<= j 0.3)
     (* y (* x z))
     (if (<= j 8.5e+209) (* 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 tmp;
	if (j <= -1.6e+56) {
		tmp = j * (a * c);
	} else if (j <= 0.3) {
		tmp = y * (x * z);
	} else if (j <= 8.5e+209) {
		tmp = a * (c * j);
	} 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) :: tmp
    if (j <= (-1.6d+56)) then
        tmp = j * (a * c)
    else if (j <= 0.3d0) then
        tmp = y * (x * z)
    else if (j <= 8.5d+209) then
        tmp = a * (c * j)
    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 tmp;
	if (j <= -1.6e+56) {
		tmp = j * (a * c);
	} else if (j <= 0.3) {
		tmp = y * (x * z);
	} else if (j <= 8.5e+209) {
		tmp = a * (c * j);
	} else {
		tmp = y * (i * -j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -1.6e+56:
		tmp = j * (a * c)
	elif j <= 0.3:
		tmp = y * (x * z)
	elif j <= 8.5e+209:
		tmp = a * (c * j)
	else:
		tmp = y * (i * -j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -1.6e+56)
		tmp = Float64(j * Float64(a * c));
	elseif (j <= 0.3)
		tmp = Float64(y * Float64(x * z));
	elseif (j <= 8.5e+209)
		tmp = Float64(a * Float64(c * j));
	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)
	tmp = 0.0;
	if (j <= -1.6e+56)
		tmp = j * (a * c);
	elseif (j <= 0.3)
		tmp = y * (x * z);
	elseif (j <= 8.5e+209)
		tmp = a * (c * j);
	else
		tmp = y * (i * -j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -1.6e+56], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 0.3], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8.5e+209], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.60000000000000002e56

   1. Initial program 79.7%

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

   3. Taylor expanded in x around 0 75.2%

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

   4. Taylor expanded in j around inf 67.1%

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

      1. *-commutative 67.1%

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

   6. Simplified 67.1%

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

   7. Taylor expanded in c around inf 53.6%

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

   if -1.60000000000000002e56 < j < 0.299999999999999989

   1. Initial program 76.1%

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

   3. Taylor expanded in y around inf 38.2%

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

      1. +-commutative 38.2%

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

      2. mul-1-neg 38.2%

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

      3. unsub-neg 38.2%

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

      4. *-commutative 38.2%

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

   5. Simplified 38.2%

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

   6. Taylor expanded in z around inf 33.0%

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

      1. *-commutative 33.0%

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

   8. Simplified 33.0%

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

   if 0.299999999999999989 < j < 8.50000000000000062e209

   1. Initial program 79.8%

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

   3. Taylor expanded in a around inf 65.3%

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

      1. +-commutative 65.3%

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

      2. mul-1-neg 65.3%

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

      3. unsub-neg 65.3%

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

   5. Simplified 65.3%

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

   6. Taylor expanded in c around inf 54.5%

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

   if 8.50000000000000062e209 < j

   1. Initial program 84.0%

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

   3. Taylor expanded in y around inf 73.0%

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

      1. +-commutative 73.0%

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

      2. mul-1-neg 73.0%

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

      3. unsub-neg 73.0%

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

      4. *-commutative 73.0%

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

   5. Simplified 73.0%

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

   6. Taylor expanded in z around 0 68.7%

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

      1. neg-mul-1 68.7%

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

      2. distribute-rgt-neg-in 68.7%

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

   8. Simplified 68.7%

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

4. Final simplification 45.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.6 \cdot 10^{+56}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;j \leq 0.3:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{+209}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 30.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.65 \cdot 10^{+56}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;j \leq 1.15:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 3.8 \cdot 10^{+210}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -1.65e+56)
   (* j (* a c))
   (if (<= j 1.15)
     (* y (* x z))
     (if (<= j 3.8e+210) (* a (* c j)) (* j (* y (- 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 (j <= -1.65e+56) {
		tmp = j * (a * c);
	} else if (j <= 1.15) {
		tmp = y * (x * z);
	} else if (j <= 3.8e+210) {
		tmp = a * (c * j);
	} else {
		tmp = j * (y * -i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (j <= (-1.65d+56)) then
        tmp = j * (a * c)
    else if (j <= 1.15d0) then
        tmp = y * (x * z)
    else if (j <= 3.8d+210) then
        tmp = a * (c * j)
    else
        tmp = j * (y * -i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -1.65e+56) {
		tmp = j * (a * c);
	} else if (j <= 1.15) {
		tmp = y * (x * z);
	} else if (j <= 3.8e+210) {
		tmp = a * (c * j);
	} else {
		tmp = j * (y * -i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -1.65e+56:
		tmp = j * (a * c)
	elif j <= 1.15:
		tmp = y * (x * z)
	elif j <= 3.8e+210:
		tmp = a * (c * j)
	else:
		tmp = j * (y * -i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -1.65e+56)
		tmp = Float64(j * Float64(a * c));
	elseif (j <= 1.15)
		tmp = Float64(y * Float64(x * z));
	elseif (j <= 3.8e+210)
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(j * Float64(y * Float64(-i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -1.65e+56)
		tmp = j * (a * c);
	elseif (j <= 1.15)
		tmp = y * (x * z);
	elseif (j <= 3.8e+210)
		tmp = a * (c * j);
	else
		tmp = j * (y * -i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -1.65e+56], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.15], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.8e+210], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(j * N[(y * (-i)), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.65000000000000001e56

   1. Initial program 79.7%

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

   3. Taylor expanded in x around 0 75.2%

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

   4. Taylor expanded in j around inf 67.1%

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

      1. *-commutative 67.1%

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

   6. Simplified 67.1%

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

   7. Taylor expanded in c around inf 53.6%

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

   if -1.65000000000000001e56 < j < 1.1499999999999999

   1. Initial program 76.1%

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

   3. Taylor expanded in y around inf 38.2%

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

      1. +-commutative 38.2%

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

      2. mul-1-neg 38.2%

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

      3. unsub-neg 38.2%

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

      4. *-commutative 38.2%

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

   5. Simplified 38.2%

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

   6. Taylor expanded in z around inf 33.0%

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

      1. *-commutative 33.0%

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

   8. Simplified 33.0%

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

   if 1.1499999999999999 < j < 3.80000000000000028e210

   1. Initial program 79.8%

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

   3. Taylor expanded in a around inf 65.3%

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

      1. +-commutative 65.3%

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

      2. mul-1-neg 65.3%

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

      3. unsub-neg 65.3%

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

   5. Simplified 65.3%

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

   6. Taylor expanded in c around inf 54.5%

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

   if 3.80000000000000028e210 < j

   1. Initial program 84.0%

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

   3. Taylor expanded in x around 0 80.0%

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

   4. Taylor expanded in j around inf 84.5%

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

      1. *-commutative 84.5%

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

   6. Simplified 84.5%

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

   7. Taylor expanded in c around 0 68.6%

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

      1. neg-mul-1 68.6%

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

      2. distribute-rgt-neg-in 68.6%

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

   9. Simplified 68.6%

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

4. Final simplification 45.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.65 \cdot 10^{+56}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;j \leq 1.15:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 3.8 \cdot 10^{+210}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(y \cdot \left(-i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 30.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+90}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-227}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-102}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -6e+90)
   (* c (* a j))
   (if (<= a 4.4e-227)
     (* y (* x z))
     (if (<= a 1.85e-102) (* b (* t i)) (* j (* a c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -6e+90) {
		tmp = c * (a * j);
	} else if (a <= 4.4e-227) {
		tmp = y * (x * z);
	} else if (a <= 1.85e-102) {
		tmp = b * (t * i);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (a <= (-6d+90)) then
        tmp = c * (a * j)
    else if (a <= 4.4d-227) then
        tmp = y * (x * z)
    else if (a <= 1.85d-102) then
        tmp = b * (t * i)
    else
        tmp = j * (a * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -6e+90) {
		tmp = c * (a * j);
	} else if (a <= 4.4e-227) {
		tmp = y * (x * z);
	} else if (a <= 1.85e-102) {
		tmp = b * (t * i);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -6e+90:
		tmp = c * (a * j)
	elif a <= 4.4e-227:
		tmp = y * (x * z)
	elif a <= 1.85e-102:
		tmp = b * (t * i)
	else:
		tmp = j * (a * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -6e+90)
		tmp = Float64(c * Float64(a * j));
	elseif (a <= 4.4e-227)
		tmp = Float64(y * Float64(x * z));
	elseif (a <= 1.85e-102)
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(j * Float64(a * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -6e+90)
		tmp = c * (a * j);
	elseif (a <= 4.4e-227)
		tmp = y * (x * z);
	elseif (a <= 1.85e-102)
		tmp = b * (t * i);
	else
		tmp = j * (a * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -6e+90], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.4e-227], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.85e-102], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -5.99999999999999957e90

   1. Initial program 72.0%

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

   3. Taylor expanded in x around 0 69.8%

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

   4. Taylor expanded in j around inf 70.0%

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

      1. *-commutative 70.0%

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

   6. Simplified 70.0%

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

   7. Taylor expanded in c around inf 57.6%

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

      1. associate-*r* 55.2%

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

      2. *-commutative 55.2%

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

      3. associate-*r* 60.1%

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

   9. Simplified 60.1%

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

   if -5.99999999999999957e90 < a < 4.39999999999999962e-227

   1. Initial program 86.2%

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

   3. Taylor expanded in y around inf 52.7%

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

      1. +-commutative 52.7%

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

      2. mul-1-neg 52.7%

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

      3. unsub-neg 52.7%

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

      4. *-commutative 52.7%

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

   5. Simplified 52.7%

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

   6. Taylor expanded in z around inf 39.5%

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

      1. *-commutative 39.5%

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

   8. Simplified 39.5%

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

   if 4.39999999999999962e-227 < a < 1.8499999999999999e-102

   1. Initial program 74.1%

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

   3. Taylor expanded in x around 0 66.0%

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

   4. Taylor expanded in t around inf 48.0%

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

   if 1.8499999999999999e-102 < a

   1. Initial program 74.1%

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

   3. Taylor expanded in x around 0 60.2%

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

   4. Taylor expanded in j around inf 58.2%

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

      1. *-commutative 58.2%

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

   6. Simplified 58.2%

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

   7. Taylor expanded in c around inf 41.1%

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

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+90}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-227}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-102}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 30.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{+90}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{-228}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-93}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -2.4e+90)
   (* c (* a j))
   (if (<= a 2.05e-228)
     (* x (* y z))
     (if (<= a 6e-93) (* b (* t i)) (* j (* a c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -2.4e+90) {
		tmp = c * (a * j);
	} else if (a <= 2.05e-228) {
		tmp = x * (y * z);
	} else if (a <= 6e-93) {
		tmp = b * (t * i);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (a <= (-2.4d+90)) then
        tmp = c * (a * j)
    else if (a <= 2.05d-228) then
        tmp = x * (y * z)
    else if (a <= 6d-93) then
        tmp = b * (t * i)
    else
        tmp = j * (a * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -2.4e+90) {
		tmp = c * (a * j);
	} else if (a <= 2.05e-228) {
		tmp = x * (y * z);
	} else if (a <= 6e-93) {
		tmp = b * (t * i);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -2.4e+90:
		tmp = c * (a * j)
	elif a <= 2.05e-228:
		tmp = x * (y * z)
	elif a <= 6e-93:
		tmp = b * (t * i)
	else:
		tmp = j * (a * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -2.4e+90)
		tmp = Float64(c * Float64(a * j));
	elseif (a <= 2.05e-228)
		tmp = Float64(x * Float64(y * z));
	elseif (a <= 6e-93)
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(j * Float64(a * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -2.4e+90)
		tmp = c * (a * j);
	elseif (a <= 2.05e-228)
		tmp = x * (y * z);
	elseif (a <= 6e-93)
		tmp = b * (t * i);
	else
		tmp = j * (a * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -2.4e+90], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.05e-228], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6e-93], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.4000000000000001e90

   1. Initial program 72.0%

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

   3. Taylor expanded in x around 0 69.8%

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

   4. Taylor expanded in j around inf 70.0%

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

      1. *-commutative 70.0%

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

   6. Simplified 70.0%

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

   7. Taylor expanded in c around inf 57.6%

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

      1. associate-*r* 55.2%

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

      2. *-commutative 55.2%

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

      3. associate-*r* 60.1%

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

   9. Simplified 60.1%

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

   if -2.4000000000000001e90 < a < 2.04999999999999999e-228

   1. Initial program 86.2%

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

   3. Taylor expanded in y around inf 52.7%

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

      1. +-commutative 52.7%

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

      2. mul-1-neg 52.7%

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

      3. unsub-neg 52.7%

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

      4. *-commutative 52.7%

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

   5. Simplified 52.7%

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

   6. Taylor expanded in z around inf 37.1%

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

      1. *-commutative 37.1%

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

   8. Simplified 37.1%

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

   if 2.04999999999999999e-228 < a < 6.0000000000000003e-93

   1. Initial program 74.1%

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

   3. Taylor expanded in x around 0 66.0%

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

   4. Taylor expanded in t around inf 48.0%

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

   if 6.0000000000000003e-93 < a

   1. Initial program 74.1%

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

   3. Taylor expanded in x around 0 60.2%

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

   4. Taylor expanded in j around inf 58.2%

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

      1. *-commutative 58.2%

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

   6. Simplified 58.2%

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

   7. Taylor expanded in c around inf 41.1%

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

4. Final simplification 43.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{+90}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{-228}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-93}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 52.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.26 \cdot 10^{+61} \lor \neg \left(j \leq 0.08\right):\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -1.26e+61) (not (<= j 0.08)))
   (* j (- (* a c) (* y i)))
   (* b (- (* t i) (* z c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -1.26e+61) || !(j <= 0.08)) {
		tmp = j * ((a * c) - (y * i));
	} else {
		tmp = b * ((t * i) - (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((j <= (-1.26d+61)) .or. (.not. (j <= 0.08d0))) then
        tmp = j * ((a * c) - (y * i))
    else
        tmp = b * ((t * i) - (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -1.26e+61) || !(j <= 0.08)) {
		tmp = j * ((a * c) - (y * i));
	} else {
		tmp = b * ((t * i) - (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -1.26e+61) or not (j <= 0.08):
		tmp = j * ((a * c) - (y * i))
	else:
		tmp = b * ((t * i) - (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -1.26e+61) || !(j <= 0.08))
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	else
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -1.26e+61) || ~((j <= 0.08)))
		tmp = j * ((a * c) - (y * i));
	else
		tmp = b * ((t * i) - (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -1.26e+61], N[Not[LessEqual[j, 0.08]], $MachinePrecision]], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -1.2600000000000001e61 or 0.0800000000000000017 < j

   1. Initial program 80.2%

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

   3. Taylor expanded in j around inf 72.5%

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

   if -1.2600000000000001e61 < j < 0.0800000000000000017

   1. Initial program 76.5%

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

   3. Taylor expanded in b around inf 47.8%

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

      1. *-commutative 47.8%

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

   5. Simplified 47.8%

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

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.26 \cdot 10^{+61} \lor \neg \left(j \leq 0.08\right):\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 50.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{-76} \lor \neg \left(a \leq 1.25 \cdot 10^{-99}\right):\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -7.2e-76) (not (<= a 1.25e-99)))
   (* a (- (* c j) (* x t)))
   (* b (- (* t i) (* z c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -7.2e-76) || !(a <= 1.25e-99)) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = b * ((t * i) - (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((a <= (-7.2d-76)) .or. (.not. (a <= 1.25d-99))) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = b * ((t * i) - (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -7.2e-76) || !(a <= 1.25e-99)) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = b * ((t * i) - (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (a <= -7.2e-76) or not (a <= 1.25e-99):
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = b * ((t * i) - (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -7.2e-76) || !(a <= 1.25e-99))
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((a <= -7.2e-76) || ~((a <= 1.25e-99)))
		tmp = a * ((c * j) - (x * t));
	else
		tmp = b * ((t * i) - (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -7.2e-76], N[Not[LessEqual[a, 1.25e-99]], $MachinePrecision]], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -7.2000000000000001e-76 or 1.24999999999999992e-99 < a

   1. Initial program 75.4%

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

   3. Taylor expanded in a around inf 56.9%

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

      1. +-commutative 56.9%

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

      2. mul-1-neg 56.9%

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

      3. unsub-neg 56.9%

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

   5. Simplified 56.9%

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

   if -7.2000000000000001e-76 < a < 1.24999999999999992e-99

   1. Initial program 83.2%

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

   3. Taylor expanded in b around inf 52.2%

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

      1. *-commutative 52.2%

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

   5. Simplified 52.2%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{-76} \lor \neg \left(a \leq 1.25 \cdot 10^{-99}\right):\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 30.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -2.1 \cdot 10^{+55} \lor \neg \left(j \leq 0.0042\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -2.1e+55) (not (<= j 0.0042))) (* a (* c j)) (* b (* t i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -2.1e+55) || !(j <= 0.0042)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((j <= (-2.1d+55)) .or. (.not. (j <= 0.0042d0))) then
        tmp = a * (c * j)
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -2.1e+55) || !(j <= 0.0042)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -2.1e+55) or not (j <= 0.0042):
		tmp = a * (c * j)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -2.1e+55) || !(j <= 0.0042))
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -2.1e+55) || ~((j <= 0.0042)))
		tmp = a * (c * j);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -2.1e+55], N[Not[LessEqual[j, 0.0042]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -2.1000000000000001e55 or 0.00419999999999999974 < j

   1. Initial program 80.5%

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

   3. Taylor expanded in a around inf 56.8%

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

      1. +-commutative 56.8%

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

      2. mul-1-neg 56.8%

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

      3. unsub-neg 56.8%

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

   5. Simplified 56.8%

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

   6. Taylor expanded in c around inf 50.1%

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

   if -2.1000000000000001e55 < j < 0.00419999999999999974

   1. Initial program 76.1%

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

   3. Taylor expanded in x around 0 51.6%

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

   4. Taylor expanded in t around inf 28.5%

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

4. Final simplification 39.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.1 \cdot 10^{+55} \lor \neg \left(j \leq 0.0042\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 30.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -2.4 \cdot 10^{+55}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;j \leq 1:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -2.4e+55)
   (* j (* a c))
   (if (<= j 1.0) (* b (* t i)) (* a (* c j)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -2.4e+55) {
		tmp = j * (a * c);
	} else if (j <= 1.0) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (j <= (-2.4d+55)) then
        tmp = j * (a * c)
    else if (j <= 1.0d0) then
        tmp = b * (t * i)
    else
        tmp = a * (c * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -2.4e+55) {
		tmp = j * (a * c);
	} else if (j <= 1.0) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -2.4e+55:
		tmp = j * (a * c)
	elif j <= 1.0:
		tmp = b * (t * i)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -2.4e+55)
		tmp = Float64(j * Float64(a * c));
	elseif (j <= 1.0)
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(a * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -2.4e+55)
		tmp = j * (a * c);
	elseif (j <= 1.0)
		tmp = b * (t * i);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -2.4e+55], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.0], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -2.3999999999999999e55

   1. Initial program 79.7%

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

   3. Taylor expanded in x around 0 75.2%

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

   4. Taylor expanded in j around inf 67.1%

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

      1. *-commutative 67.1%

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

   6. Simplified 67.1%

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

   7. Taylor expanded in c around inf 53.6%

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

   if -2.3999999999999999e55 < j < 1

   1. Initial program 76.1%

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

   3. Taylor expanded in x around 0 51.6%

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

   4. Taylor expanded in t around inf 28.5%

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

   if 1 < j

   1. Initial program 81.3%

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

   3. Taylor expanded in a around inf 56.8%

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

      1. +-commutative 56.8%

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

      2. mul-1-neg 56.8%

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

      3. unsub-neg 56.8%

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

   5. Simplified 56.8%

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

   6. Taylor expanded in c around inf 48.4%

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

4. Final simplification 39.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.4 \cdot 10^{+55}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;j \leq 1:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 22.9% accurate, 5.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 78.4%

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

3. Taylor expanded in a around inf 41.3%

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

   1. +-commutative 41.3%

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

   2. mul-1-neg 41.3%

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

   3. unsub-neg 41.3%

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

5. Simplified 41.3%

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

6. Taylor expanded in c around inf 29.0%

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

Developer Target 1: 59.7% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024135 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

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

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