Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.5% → 82.3%

Time: 25.4s

Alternatives: 25

Speedup: 0.9×

• 58.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 82.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot c - y \cdot i\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right) + j \cdot t_1\\ \mathbf{if}\;t_2 \leq \infty:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;j \cdot \sqrt[3]{t_1 \cdot \left(t_1 \cdot t_1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* t c) (* y i)))
        (t_2
         (+
          (+ (* x (- (* y z) (* t a))) (* b (- (* a i) (* z c))))
          (* j t_1))))
   (if (<= t_2 INFINITY) t_2 (* j (cbrt (* t_1 (* t_1 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (t * c) - (y * i);
	double t_2 = ((x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))) + (j * t_1);
	double tmp;
	if (t_2 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = j * cbrt((t_1 * (t_1 * t_1)));
	}
	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 = (t * c) - (y * i);
	double t_2 = ((x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))) + (j * t_1);
	double tmp;
	if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = j * Math.cbrt((t_1 * (t_1 * t_1)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(t * c) - Float64(y * i))
	t_2 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(a * i) - Float64(z * c)))) + Float64(j * t_1))
	tmp = 0.0
	if (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(j * cbrt(Float64(t_1 * Float64(t_1 * t_1))));
	end
	return tmp
end

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 90.5%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in y around 0 25.8%

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

      1. sub-neg 25.8%

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

   4. Simplified 31.3%

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

   5. Taylor expanded in j around inf 49.8%

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

      1. mul-1-neg 49.8%

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

      2. distribute-lft-neg-out 49.8%

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

      3. +-commutative 49.8%

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

      4. cancel-sign-sub-inv 49.8%

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

      5. *-commutative 49.8%

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

      6. *-commutative 49.8%

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

   7. Simplified 49.8%

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

      1. add-cbrt-cube 54.9%

         \[\leadsto j \cdot \color{blue}{\sqrt[3]{\left(\left(t \cdot c - y \cdot i\right) \cdot \left(t \cdot c - y \cdot i\right)\right) \cdot \left(t \cdot c - y \cdot i\right)}} \]

   9. Applied egg-rr 54.9%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \leq \infty:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \sqrt[3]{\left(t \cdot c - y \cdot i\right) \cdot \left(\left(t \cdot c - y \cdot i\right) \cdot \left(t \cdot c - y \cdot i\right)\right)}\\ \end{array} \]

Alternative 2: 81.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 90.5%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in c around inf 53.2%

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

4. Final simplification 82.5%

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

Alternative 3: 75.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.15 \cdot 10^{+142} \lor \neg \left(c \leq 2.45 \cdot 10^{+129}\right):\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - \left(y \cdot \left(i \cdot j - x \cdot z\right) + t \cdot \left(x \cdot a - c \cdot j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -1.15e+142) (not (<= c 2.45e+129)))
   (* c (- (* t j) (* z b)))
   (-
    (* b (- (* a i) (* z c)))
    (+ (* y (- (* i j) (* x z))) (* t (- (* x 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 ((c <= -1.15e+142) || !(c <= 2.45e+129)) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = (b * ((a * i) - (z * c))) - ((y * ((i * j) - (x * z))) + (t * ((x * 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 ((c <= (-1.15d+142)) .or. (.not. (c <= 2.45d+129))) then
        tmp = c * ((t * j) - (z * b))
    else
        tmp = (b * ((a * i) - (z * c))) - ((y * ((i * j) - (x * z))) + (t * ((x * 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 ((c <= -1.15e+142) || !(c <= 2.45e+129)) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = (b * ((a * i) - (z * c))) - ((y * ((i * j) - (x * z))) + (t * ((x * a) - (c * j))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -1.15e+142) or not (c <= 2.45e+129):
		tmp = c * ((t * j) - (z * b))
	else:
		tmp = (b * ((a * i) - (z * c))) - ((y * ((i * j) - (x * z))) + (t * ((x * a) - (c * j))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -1.15e+142) || !(c <= 2.45e+129))
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	else
		tmp = Float64(Float64(b * Float64(Float64(a * i) - Float64(z * c))) - Float64(Float64(y * Float64(Float64(i * j) - Float64(x * z))) + Float64(t * Float64(Float64(x * 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 ((c <= -1.15e+142) || ~((c <= 2.45e+129)))
		tmp = c * ((t * j) - (z * b));
	else
		tmp = (b * ((a * i) - (z * c))) - ((y * ((i * j) - (x * z))) + (t * ((x * a) - (c * j))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -1.15e+142], N[Not[LessEqual[c, 2.45e+129]], $MachinePrecision]], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y * N[(N[(i * j), $MachinePrecision] - N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(x * a), $MachinePrecision] - N[(c * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.15000000000000001e142 or 2.45e129 < c

   1. Initial program 57.7%

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

   2. Taylor expanded in c around inf 76.5%

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

   if -1.15000000000000001e142 < c < 2.45e129

   1. Initial program 76.6%

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

   2. Taylor expanded in y around 0 79.5%

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

      1. sub-neg 79.5%

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

   4. Simplified 83.2%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.15 \cdot 10^{+142} \lor \neg \left(c \leq 2.45 \cdot 10^{+129}\right):\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - \left(y \cdot \left(i \cdot j - x \cdot z\right) + t \cdot \left(x \cdot a - c \cdot j\right)\right)\\ \end{array} \]

Alternative 4: 63.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right) + y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.9 \cdot 10^{+184}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -2.9 \cdot 10^{-88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 9 \cdot 10^{-123}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;j \leq 9 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* t (- (* c j) (* x a))) (* y (- (* x z) (* i j)))))
        (t_2 (* j (- (* t c) (* y i)))))
   (if (<= j -1.9e+184)
     t_2
     (if (<= j -2.9e-88)
       t_1
       (if (<= j 9e-123)
         (- (* b (- (* a i) (* z c))) (* a (* x t)))
         (if (<= j 9e+47) 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 = (t * ((c * j) - (x * a))) + (y * ((x * z) - (i * j)));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -1.9e+184) {
		tmp = t_2;
	} else if (j <= -2.9e-88) {
		tmp = t_1;
	} else if (j <= 9e-123) {
		tmp = (b * ((a * i) - (z * c))) - (a * (x * t));
	} else if (j <= 9e+47) {
		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 = (t * ((c * j) - (x * a))) + (y * ((x * z) - (i * j)))
    t_2 = j * ((t * c) - (y * i))
    if (j <= (-1.9d+184)) then
        tmp = t_2
    else if (j <= (-2.9d-88)) then
        tmp = t_1
    else if (j <= 9d-123) then
        tmp = (b * ((a * i) - (z * c))) - (a * (x * t))
    else if (j <= 9d+47) 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 = (t * ((c * j) - (x * a))) + (y * ((x * z) - (i * j)));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -1.9e+184) {
		tmp = t_2;
	} else if (j <= -2.9e-88) {
		tmp = t_1;
	} else if (j <= 9e-123) {
		tmp = (b * ((a * i) - (z * c))) - (a * (x * t));
	} else if (j <= 9e+47) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (t * ((c * j) - (x * a))) + (y * ((x * z) - (i * j)))
	t_2 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -1.9e+184:
		tmp = t_2
	elif j <= -2.9e-88:
		tmp = t_1
	elif j <= 9e-123:
		tmp = (b * ((a * i) - (z * c))) - (a * (x * t))
	elif j <= 9e+47:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) + Float64(y * Float64(Float64(x * z) - Float64(i * j))))
	t_2 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -1.9e+184)
		tmp = t_2;
	elseif (j <= -2.9e-88)
		tmp = t_1;
	elseif (j <= 9e-123)
		tmp = Float64(Float64(b * Float64(Float64(a * i) - Float64(z * c))) - Float64(a * Float64(x * t)));
	elseif (j <= 9e+47)
		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 = (t * ((c * j) - (x * a))) + (y * ((x * z) - (i * j)));
	t_2 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -1.9e+184)
		tmp = t_2;
	elseif (j <= -2.9e-88)
		tmp = t_1;
	elseif (j <= 9e-123)
		tmp = (b * ((a * i) - (z * c))) - (a * (x * t));
	elseif (j <= 9e+47)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.9e+184], t$95$2, If[LessEqual[j, -2.9e-88], t$95$1, If[LessEqual[j, 9e-123], N[(N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 9e+47], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.9000000000000001e184 or 8.99999999999999958e47 < j

   1. Initial program 70.3%

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

   2. Taylor expanded in y around 0 57.6%

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

      1. sub-neg 57.6%

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

   4. Simplified 60.1%

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

   5. Taylor expanded in j around inf 77.1%

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

      1. mul-1-neg 77.1%

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

      2. distribute-lft-neg-out 77.1%

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

      3. +-commutative 77.1%

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

      4. cancel-sign-sub-inv 77.1%

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

      5. *-commutative 77.1%

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

      6. *-commutative 77.1%

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

   7. Simplified 77.1%

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

   if -1.9000000000000001e184 < j < -2.9000000000000001e-88 or 8.99999999999999986e-123 < j < 8.99999999999999958e47

   1. Initial program 69.9%

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

   2. Taylor expanded in y around 0 76.5%

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

      1. sub-neg 76.5%

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

   4. Simplified 78.4%

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

   5. Taylor expanded in b around 0 73.8%

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

   if -2.9000000000000001e-88 < j < 8.99999999999999986e-123

   1. Initial program 73.3%

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

   2. Taylor expanded in y around 0 70.3%

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

      1. associate-*r* 70.3%

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

      2. *-commutative 70.3%

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

      3. associate-*r* 68.9%

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

      4. associate-*r* 68.9%

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

      5. associate-*r* 68.9%

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

      6. distribute-rgt-in 68.9%

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

      7. *-commutative 68.9%

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

      8. +-commutative 68.9%

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

      9. mul-1-neg 68.9%

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

      10. unsub-neg 68.9%

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

      11. *-commutative 68.9%

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

   4. Simplified 68.9%

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

   5. Taylor expanded in j around 0 69.1%

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

      1. sub-neg 69.1%

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

      2. neg-mul-1 69.1%

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

      3. +-commutative 69.1%

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

      4. unsub-neg 69.1%

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

      5. distribute-rgt-neg-in 69.1%

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

      6. neg-sub0 69.1%

         \[\leadsto b \cdot \color{blue}{\left(0 - \left(c \cdot z - a \cdot i\right)\right)} - a \cdot \left(t \cdot x\right) \]

      7. associate--r- 69.1%

         \[\leadsto b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + a \cdot i\right)} - a \cdot \left(t \cdot x\right) \]

      8. neg-sub0 69.1%

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

      9. +-commutative 69.1%

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

      10. sub-neg 69.1%

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

   7. Simplified 69.1%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.9 \cdot 10^{+184}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -2.9 \cdot 10^{-88}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;j \leq 9 \cdot 10^{-123}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;j \leq 9 \cdot 10^{+47}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 5: 49.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(i \cdot \left(-j\right)\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_3 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -5.8 \cdot 10^{+78}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -7.5 \cdot 10^{+27}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -9.5 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -4.6 \cdot 10^{-63}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq -2.7 \cdot 10^{-88}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;c \leq 1.4 \cdot 10^{-307}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 8 \cdot 10^{-254}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 8 \cdot 10^{+80}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* i (- j))))
        (t_2 (* a (- (* b i) (* x t))))
        (t_3 (* c (- (* t j) (* z b)))))
   (if (<= c -5.8e+78)
     t_3
     (if (<= c -7.5e+27)
       t_2
       (if (<= c -9.5e-11)
         t_1
         (if (<= c -4.6e-63)
           (* x (* y z))
           (if (<= c -2.7e-88)
             (* c (* t j))
             (if (<= c 1.4e-307)
               t_2
               (if (<= c 8e-254) t_1 (if (<= c 8e+80) t_2 t_3))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (i * -j);
	double t_2 = a * ((b * i) - (x * t));
	double t_3 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -5.8e+78) {
		tmp = t_3;
	} else if (c <= -7.5e+27) {
		tmp = t_2;
	} else if (c <= -9.5e-11) {
		tmp = t_1;
	} else if (c <= -4.6e-63) {
		tmp = x * (y * z);
	} else if (c <= -2.7e-88) {
		tmp = c * (t * j);
	} else if (c <= 1.4e-307) {
		tmp = t_2;
	} else if (c <= 8e-254) {
		tmp = t_1;
	} else if (c <= 8e+80) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y * (i * -j)
    t_2 = a * ((b * i) - (x * t))
    t_3 = c * ((t * j) - (z * b))
    if (c <= (-5.8d+78)) then
        tmp = t_3
    else if (c <= (-7.5d+27)) then
        tmp = t_2
    else if (c <= (-9.5d-11)) then
        tmp = t_1
    else if (c <= (-4.6d-63)) then
        tmp = x * (y * z)
    else if (c <= (-2.7d-88)) then
        tmp = c * (t * j)
    else if (c <= 1.4d-307) then
        tmp = t_2
    else if (c <= 8d-254) then
        tmp = t_1
    else if (c <= 8d+80) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (i * -j);
	double t_2 = a * ((b * i) - (x * t));
	double t_3 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -5.8e+78) {
		tmp = t_3;
	} else if (c <= -7.5e+27) {
		tmp = t_2;
	} else if (c <= -9.5e-11) {
		tmp = t_1;
	} else if (c <= -4.6e-63) {
		tmp = x * (y * z);
	} else if (c <= -2.7e-88) {
		tmp = c * (t * j);
	} else if (c <= 1.4e-307) {
		tmp = t_2;
	} else if (c <= 8e-254) {
		tmp = t_1;
	} else if (c <= 8e+80) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (i * -j)
	t_2 = a * ((b * i) - (x * t))
	t_3 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -5.8e+78:
		tmp = t_3
	elif c <= -7.5e+27:
		tmp = t_2
	elif c <= -9.5e-11:
		tmp = t_1
	elif c <= -4.6e-63:
		tmp = x * (y * z)
	elif c <= -2.7e-88:
		tmp = c * (t * j)
	elif c <= 1.4e-307:
		tmp = t_2
	elif c <= 8e-254:
		tmp = t_1
	elif c <= 8e+80:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(i * Float64(-j)))
	t_2 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	t_3 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -5.8e+78)
		tmp = t_3;
	elseif (c <= -7.5e+27)
		tmp = t_2;
	elseif (c <= -9.5e-11)
		tmp = t_1;
	elseif (c <= -4.6e-63)
		tmp = Float64(x * Float64(y * z));
	elseif (c <= -2.7e-88)
		tmp = Float64(c * Float64(t * j));
	elseif (c <= 1.4e-307)
		tmp = t_2;
	elseif (c <= 8e-254)
		tmp = t_1;
	elseif (c <= 8e+80)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * (i * -j);
	t_2 = a * ((b * i) - (x * t));
	t_3 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -5.8e+78)
		tmp = t_3;
	elseif (c <= -7.5e+27)
		tmp = t_2;
	elseif (c <= -9.5e-11)
		tmp = t_1;
	elseif (c <= -4.6e-63)
		tmp = x * (y * z);
	elseif (c <= -2.7e-88)
		tmp = c * (t * j);
	elseif (c <= 1.4e-307)
		tmp = t_2;
	elseif (c <= 8e-254)
		tmp = t_1;
	elseif (c <= 8e+80)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -5.8e+78], t$95$3, If[LessEqual[c, -7.5e+27], t$95$2, If[LessEqual[c, -9.5e-11], t$95$1, If[LessEqual[c, -4.6e-63], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.7e-88], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.4e-307], t$95$2, If[LessEqual[c, 8e-254], t$95$1, If[LessEqual[c, 8e+80], t$95$2, t$95$3]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -5.80000000000000034e78 or 8e80 < c

   1. Initial program 62.5%

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

   2. Taylor expanded in c around inf 72.2%

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

   if -5.80000000000000034e78 < c < -7.5000000000000002e27 or -2.69999999999999995e-88 < c < 1.4e-307 or 7.9999999999999993e-254 < c < 8e80

   1. Initial program 78.3%

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

   2. Taylor expanded in y around 0 81.6%

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

      1. sub-neg 81.6%

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

   4. Simplified 82.3%

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

   5. Taylor expanded in a around inf 58.6%

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

      1. +-commutative 58.6%

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

      2. mul-1-neg 58.6%

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

      3. unsub-neg 58.6%

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

      4. *-commutative 58.6%

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

      5. *-commutative 58.6%

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

   7. Simplified 58.6%

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

   if -7.5000000000000002e27 < c < -9.49999999999999951e-11 or 1.4e-307 < c < 7.9999999999999993e-254

   1. Initial program 64.1%

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

   2. Taylor expanded in y around inf 65.8%

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

      1. +-commutative 65.8%

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

      2. mul-1-neg 65.8%

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

      3. unsub-neg 65.8%

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

      4. *-commutative 65.8%

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

   4. Simplified 65.8%

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

   5. Taylor expanded in z around 0 50.3%

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

      1. mul-1-neg 50.3%

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

      2. *-commutative 50.3%

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

      3. *-commutative 50.3%

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

      4. associate-*r* 56.8%

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

      5. *-commutative 56.8%

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

      6. distribute-rgt-neg-out 56.8%

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

      7. distribute-rgt-neg-in 56.8%

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

   7. Simplified 56.8%

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

   if -9.49999999999999951e-11 < c < -4.6e-63

   1. Initial program 89.9%

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

   2. Taylor expanded in y around inf 67.3%

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

      1. +-commutative 67.3%

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

      2. mul-1-neg 67.3%

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

      3. unsub-neg 67.3%

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

      4. *-commutative 67.3%

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

   4. Simplified 67.3%

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

   5. Taylor expanded in z around inf 67.5%

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

   if -4.6e-63 < c < -2.69999999999999995e-88

   1. Initial program 75.0%

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

   2. Taylor expanded in y around 0 100.0%

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

      1. sub-neg 100.0%

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

   4. Simplified 99.2%

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

   5. Taylor expanded in j around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-lft-neg-out 100.0%

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

      3. +-commutative 100.0%

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

      4. cancel-sign-sub-inv 100.0%

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

      5. *-commutative 100.0%

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

      6. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in t around inf 75.1%

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

      1. *-commutative 75.1%

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

   10. Simplified 75.1%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.8 \cdot 10^{+78}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -7.5 \cdot 10^{+27}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq -9.5 \cdot 10^{-11}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq -4.6 \cdot 10^{-63}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq -2.7 \cdot 10^{-88}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;c \leq 1.4 \cdot 10^{-307}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 8 \cdot 10^{-254}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 8 \cdot 10^{+80}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 6: 68.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{+88} \lor \neg \left(b \leq 1.42 \cdot 10^{-27}\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -3.8e+88) (not (<= b 1.42e-27)))
   (+ (* b (- (* a i) (* z c))) (* j (- (* t c) (* y i))))
   (+ (* t (- (* c j) (* x a))) (* y (- (* x z) (* 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 ((b <= -3.8e+88) || !(b <= 1.42e-27)) {
		tmp = (b * ((a * i) - (z * c))) + (j * ((t * c) - (y * i)));
	} else {
		tmp = (t * ((c * j) - (x * a))) + (y * ((x * z) - (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 ((b <= (-3.8d+88)) .or. (.not. (b <= 1.42d-27))) then
        tmp = (b * ((a * i) - (z * c))) + (j * ((t * c) - (y * i)))
    else
        tmp = (t * ((c * j) - (x * a))) + (y * ((x * z) - (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 ((b <= -3.8e+88) || !(b <= 1.42e-27)) {
		tmp = (b * ((a * i) - (z * c))) + (j * ((t * c) - (y * i)));
	} else {
		tmp = (t * ((c * j) - (x * a))) + (y * ((x * z) - (i * j)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -3.8e+88) or not (b <= 1.42e-27):
		tmp = (b * ((a * i) - (z * c))) + (j * ((t * c) - (y * i)))
	else:
		tmp = (t * ((c * j) - (x * a))) + (y * ((x * z) - (i * j)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -3.8e+88) || !(b <= 1.42e-27))
		tmp = Float64(Float64(b * Float64(Float64(a * i) - Float64(z * c))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))));
	else
		tmp = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) + Float64(y * Float64(Float64(x * z) - Float64(i * j))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -3.8e+88) || ~((b <= 1.42e-27)))
		tmp = (b * ((a * i) - (z * c))) + (j * ((t * c) - (y * i)));
	else
		tmp = (t * ((c * j) - (x * a))) + (y * ((x * z) - (i * j)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -3.8e+88], N[Not[LessEqual[b, 1.42e-27]], $MachinePrecision]], N[(N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.7999999999999997e88 or 1.41999999999999996e-27 < b

   1. Initial program 75.5%

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

   2. Taylor expanded in x around 0 79.1%

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

      1. *-commutative 79.1%

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

   4. Simplified 79.1%

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

   if -3.7999999999999997e88 < b < 1.41999999999999996e-27

   1. Initial program 67.3%

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

   2. Taylor expanded in y around 0 68.3%

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

      1. sub-neg 68.3%

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

   4. Simplified 72.4%

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

   5. Taylor expanded in b around 0 70.9%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{+88} \lor \neg \left(b \leq 1.42 \cdot 10^{-27}\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]

Alternative 7: 60.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(x \cdot t\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -7 \cdot 10^{+35}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -3.6 \cdot 10^{-243}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - t_1\\ \mathbf{elif}\;j \leq 1.55 \cdot 10^{+32}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* x t))) (t_2 (* j (- (* t c) (* y i)))))
   (if (<= j -7e+35)
     t_2
     (if (<= j -3.6e-243)
       (- (* z (- (* x y) (* b c))) t_1)
       (if (<= j 1.55e+32) (- (* b (- (* a i) (* z c))) t_1) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (x * t);
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -7e+35) {
		tmp = t_2;
	} else if (j <= -3.6e-243) {
		tmp = (z * ((x * y) - (b * c))) - t_1;
	} else if (j <= 1.55e+32) {
		tmp = (b * ((a * i) - (z * c))) - t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (x * t)
    t_2 = j * ((t * c) - (y * i))
    if (j <= (-7d+35)) then
        tmp = t_2
    else if (j <= (-3.6d-243)) then
        tmp = (z * ((x * y) - (b * c))) - t_1
    else if (j <= 1.55d+32) then
        tmp = (b * ((a * i) - (z * c))) - t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (x * t);
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -7e+35) {
		tmp = t_2;
	} else if (j <= -3.6e-243) {
		tmp = (z * ((x * y) - (b * c))) - t_1;
	} else if (j <= 1.55e+32) {
		tmp = (b * ((a * i) - (z * c))) - t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (x * t)
	t_2 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -7e+35:
		tmp = t_2
	elif j <= -3.6e-243:
		tmp = (z * ((x * y) - (b * c))) - t_1
	elif j <= 1.55e+32:
		tmp = (b * ((a * i) - (z * c))) - t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(x * t))
	t_2 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -7e+35)
		tmp = t_2;
	elseif (j <= -3.6e-243)
		tmp = Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) - t_1);
	elseif (j <= 1.55e+32)
		tmp = Float64(Float64(b * Float64(Float64(a * i) - Float64(z * c))) - t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (x * t);
	t_2 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -7e+35)
		tmp = t_2;
	elseif (j <= -3.6e-243)
		tmp = (z * ((x * y) - (b * c))) - t_1;
	elseif (j <= 1.55e+32)
		tmp = (b * ((a * i) - (z * c))) - t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -7e+35], t$95$2, If[LessEqual[j, -3.6e-243], N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[j, 1.55e+32], N[(N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -7.0000000000000001e35 or 1.54999999999999997e32 < j

   1. Initial program 70.5%

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

   2. Taylor expanded in y around 0 62.0%

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

      1. sub-neg 62.0%

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

   4. Simplified 63.6%

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

   5. Taylor expanded in j around inf 71.6%

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

      1. mul-1-neg 71.6%

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

      2. distribute-lft-neg-out 71.6%

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

      3. +-commutative 71.6%

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

      4. cancel-sign-sub-inv 71.6%

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

      5. *-commutative 71.6%

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

      6. *-commutative 71.6%

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

   7. Simplified 71.6%

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

   if -7.0000000000000001e35 < j < -3.6000000000000001e-243

   1. Initial program 76.2%

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

   2. Taylor expanded in y around 0 79.2%

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

      1. sub-neg 79.2%

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

   4. Simplified 82.0%

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

   5. Taylor expanded in j around 0 70.3%

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

   6. Taylor expanded in z around inf 71.8%

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

   if -3.6000000000000001e-243 < j < 1.54999999999999997e32

   1. Initial program 67.4%

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

   2. Taylor expanded in y around 0 67.2%

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

      1. associate-*r* 67.2%

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

      2. *-commutative 67.2%

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

      3. associate-*r* 64.6%

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

      4. associate-*r* 64.6%

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

      5. associate-*r* 64.5%

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

      6. distribute-rgt-in 65.9%

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

      7. *-commutative 65.9%

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

      8. +-commutative 65.9%

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

      9. mul-1-neg 65.9%

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

      10. unsub-neg 65.9%

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

      11. *-commutative 65.9%

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

   4. Simplified 65.9%

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

   5. Taylor expanded in j around 0 66.0%

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

      1. sub-neg 66.0%

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

      2. neg-mul-1 66.0%

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

      3. +-commutative 66.0%

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

      4. unsub-neg 66.0%

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

      5. distribute-rgt-neg-in 66.0%

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

      6. neg-sub0 66.0%

         \[\leadsto b \cdot \color{blue}{\left(0 - \left(c \cdot z - a \cdot i\right)\right)} - a \cdot \left(t \cdot x\right) \]

      7. associate--r- 66.0%

         \[\leadsto b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + a \cdot i\right)} - a \cdot \left(t \cdot x\right) \]

      8. neg-sub0 66.0%

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

      9. +-commutative 66.0%

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

      10. sub-neg 66.0%

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

   7. Simplified 66.0%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -7 \cdot 10^{+35}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -3.6 \cdot 10^{-243}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;j \leq 1.55 \cdot 10^{+32}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 8: 52.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -7.5 \cdot 10^{+88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -8.4 \cdot 10^{-255}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-35}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+102}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a)))))
   (if (<= t -7.5e+88)
     t_1
     (if (<= t -8.4e-255)
       (* i (- (* a b) (* y j)))
       (if (<= t 4.5e-35)
         (* y (- (* x z) (* i j)))
         (if (<= t 2.8e+102) (- (* (* t a) (- x)) (* b (* z c))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -7.5e+88) {
		tmp = t_1;
	} else if (t <= -8.4e-255) {
		tmp = i * ((a * b) - (y * j));
	} else if (t <= 4.5e-35) {
		tmp = y * ((x * z) - (i * j));
	} else if (t <= 2.8e+102) {
		tmp = ((t * a) * -x) - (b * (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((c * j) - (x * a))
    if (t <= (-7.5d+88)) then
        tmp = t_1
    else if (t <= (-8.4d-255)) then
        tmp = i * ((a * b) - (y * j))
    else if (t <= 4.5d-35) then
        tmp = y * ((x * z) - (i * j))
    else if (t <= 2.8d+102) then
        tmp = ((t * a) * -x) - (b * (z * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -7.5e+88) {
		tmp = t_1;
	} else if (t <= -8.4e-255) {
		tmp = i * ((a * b) - (y * j));
	} else if (t <= 4.5e-35) {
		tmp = y * ((x * z) - (i * j));
	} else if (t <= 2.8e+102) {
		tmp = ((t * a) * -x) - (b * (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -7.5e+88:
		tmp = t_1
	elif t <= -8.4e-255:
		tmp = i * ((a * b) - (y * j))
	elif t <= 4.5e-35:
		tmp = y * ((x * z) - (i * j))
	elif t <= 2.8e+102:
		tmp = ((t * a) * -x) - (b * (z * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -7.5e+88)
		tmp = t_1;
	elseif (t <= -8.4e-255)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (t <= 4.5e-35)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (t <= 2.8e+102)
		tmp = Float64(Float64(Float64(t * a) * Float64(-x)) - Float64(b * Float64(z * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -7.5e+88)
		tmp = t_1;
	elseif (t <= -8.4e-255)
		tmp = i * ((a * b) - (y * j));
	elseif (t <= 4.5e-35)
		tmp = y * ((x * z) - (i * j));
	elseif (t <= 2.8e+102)
		tmp = ((t * a) * -x) - (b * (z * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.5e+88], t$95$1, If[LessEqual[t, -8.4e-255], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e-35], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.8e+102], N[(N[(N[(t * a), $MachinePrecision] * (-x)), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.50000000000000031e88 or 2.80000000000000018e102 < t

   1. Initial program 58.5%

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

   2. Taylor expanded in t around inf 72.2%

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

      1. +-commutative 72.2%

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

      2. mul-1-neg 72.2%

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

      3. unsub-neg 72.2%

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

      4. *-commutative 72.2%

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

   4. Simplified 72.2%

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

   if -7.50000000000000031e88 < t < -8.3999999999999999e-255

   1. Initial program 80.1%

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

   2. Taylor expanded in y around 0 83.0%

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

      1. sub-neg 83.0%

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

   4. Simplified 78.2%

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

   5. Taylor expanded in i around inf 58.7%

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

      1. +-commutative 58.7%

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

      2. mul-1-neg 58.7%

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

      3. unsub-neg 58.7%

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

      4. *-commutative 58.7%

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

   7. Simplified 58.7%

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

   if -8.3999999999999999e-255 < t < 4.5000000000000001e-35

   1. Initial program 77.7%

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

   2. Taylor expanded in y around inf 57.9%

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

      1. +-commutative 57.9%

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

      2. mul-1-neg 57.9%

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

      3. unsub-neg 57.9%

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

      4. *-commutative 57.9%

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

   4. Simplified 57.9%

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

   if 4.5000000000000001e-35 < t < 2.80000000000000018e102

   1. Initial program 73.0%

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

   2. Taylor expanded in y around 0 66.9%

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

      1. sub-neg 66.9%

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

   4. Simplified 70.1%

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

   5. Taylor expanded in j around 0 58.4%

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

   6. Taylor expanded in z around inf 61.5%

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

   7. Taylor expanded in y around 0 53.7%

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

      1. distribute-lft-out 53.7%

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

      2. associate-*r* 56.5%

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

   9. Simplified 56.5%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(a \cdot t\right) \cdot x + b \cdot \left(c \cdot z\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+88}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -8.4 \cdot 10^{-255}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-35}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+102}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]

Alternative 9: 37.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;i \leq -1.6 \cdot 10^{+234}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;i \leq -7.2 \cdot 10^{-219}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -3.55 \cdot 10^{-283}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 5.1 \cdot 10^{-89}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;i \leq 4.4 \cdot 10^{+277}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))))
   (if (<= i -1.6e+234)
     (* y (* i (- j)))
     (if (<= i -7.2e-219)
       t_1
       (if (<= i -3.55e-283)
         (* t (* c j))
         (if (<= i 5.1e-89)
           (* z (* c (- b)))
           (if (<= i 4.4e+277) t_1 (* i (* y (- j))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double tmp;
	if (i <= -1.6e+234) {
		tmp = y * (i * -j);
	} else if (i <= -7.2e-219) {
		tmp = t_1;
	} else if (i <= -3.55e-283) {
		tmp = t * (c * j);
	} else if (i <= 5.1e-89) {
		tmp = z * (c * -b);
	} else if (i <= 4.4e+277) {
		tmp = t_1;
	} else {
		tmp = i * (y * -j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((b * i) - (x * t))
    if (i <= (-1.6d+234)) then
        tmp = y * (i * -j)
    else if (i <= (-7.2d-219)) then
        tmp = t_1
    else if (i <= (-3.55d-283)) then
        tmp = t * (c * j)
    else if (i <= 5.1d-89) then
        tmp = z * (c * -b)
    else if (i <= 4.4d+277) then
        tmp = t_1
    else
        tmp = i * (y * -j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double tmp;
	if (i <= -1.6e+234) {
		tmp = y * (i * -j);
	} else if (i <= -7.2e-219) {
		tmp = t_1;
	} else if (i <= -3.55e-283) {
		tmp = t * (c * j);
	} else if (i <= 5.1e-89) {
		tmp = z * (c * -b);
	} else if (i <= 4.4e+277) {
		tmp = t_1;
	} else {
		tmp = i * (y * -j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	tmp = 0
	if i <= -1.6e+234:
		tmp = y * (i * -j)
	elif i <= -7.2e-219:
		tmp = t_1
	elif i <= -3.55e-283:
		tmp = t * (c * j)
	elif i <= 5.1e-89:
		tmp = z * (c * -b)
	elif i <= 4.4e+277:
		tmp = t_1
	else:
		tmp = i * (y * -j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (i <= -1.6e+234)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (i <= -7.2e-219)
		tmp = t_1;
	elseif (i <= -3.55e-283)
		tmp = Float64(t * Float64(c * j));
	elseif (i <= 5.1e-89)
		tmp = Float64(z * Float64(c * Float64(-b)));
	elseif (i <= 4.4e+277)
		tmp = t_1;
	else
		tmp = Float64(i * Float64(y * Float64(-j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (i <= -1.6e+234)
		tmp = y * (i * -j);
	elseif (i <= -7.2e-219)
		tmp = t_1;
	elseif (i <= -3.55e-283)
		tmp = t * (c * j);
	elseif (i <= 5.1e-89)
		tmp = z * (c * -b);
	elseif (i <= 4.4e+277)
		tmp = t_1;
	else
		tmp = i * (y * -j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.6e+234], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -7.2e-219], t$95$1, If[LessEqual[i, -3.55e-283], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5.1e-89], N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4.4e+277], t$95$1, N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -1.59999999999999996e234

   1. Initial program 66.7%

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

   2. Taylor expanded in y around inf 75.7%

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

      1. +-commutative 75.7%

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

      2. mul-1-neg 75.7%

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

      3. unsub-neg 75.7%

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

      4. *-commutative 75.7%

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

   4. Simplified 75.7%

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

   5. Taylor expanded in z around 0 60.0%

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

      1. mul-1-neg 60.0%

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

      2. *-commutative 60.0%

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

      3. *-commutative 60.0%

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

      4. associate-*r* 75.8%

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

      5. *-commutative 75.8%

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

      6. distribute-rgt-neg-out 75.8%

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

      7. distribute-rgt-neg-in 75.8%

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

   7. Simplified 75.8%

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

   if -1.59999999999999996e234 < i < -7.19999999999999947e-219 or 5.10000000000000004e-89 < i < 4.39999999999999993e277

   1. Initial program 70.6%

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

   2. Taylor expanded in y around 0 74.1%

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

      1. sub-neg 74.1%

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

   4. Simplified 73.5%

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

   5. Taylor expanded in a around inf 47.5%

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

      1. +-commutative 47.5%

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

      2. mul-1-neg 47.5%

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

      3. unsub-neg 47.5%

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

      4. *-commutative 47.5%

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

      5. *-commutative 47.5%

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

   7. Simplified 47.5%

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

   if -7.19999999999999947e-219 < i < -3.5499999999999999e-283

   1. Initial program 72.2%

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

   2. Taylor expanded in y around 0 77.8%

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

      1. sub-neg 77.8%

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

   4. Simplified 88.5%

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

   5. Taylor expanded in j around inf 49.6%

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

      1. mul-1-neg 49.6%

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

      2. distribute-lft-neg-out 49.6%

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

      3. +-commutative 49.6%

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

      4. cancel-sign-sub-inv 49.6%

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

      5. *-commutative 49.6%

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

      6. *-commutative 49.6%

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

   7. Simplified 49.6%

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

   8. Taylor expanded in t around inf 54.7%

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

      1. associate-*r* 54.8%

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

      2. *-commutative 54.8%

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

   10. Simplified 54.8%

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

   if -3.5499999999999999e-283 < i < 5.10000000000000004e-89

   1. Initial program 78.1%

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

   2. Taylor expanded in b around inf 46.7%

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

      1. *-commutative 46.7%

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

   4. Simplified 46.7%

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

   5. Taylor expanded in i around 0 44.4%

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

      1. mul-1-neg 44.4%

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

      2. *-commutative 44.4%

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

      3. *-commutative 44.4%

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

      4. associate-*r* 51.3%

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

      5. *-commutative 51.3%

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

      6. distribute-rgt-neg-out 51.3%

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

      7. *-commutative 51.3%

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

      8. distribute-rgt-neg-in 51.3%

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

   7. Simplified 51.3%

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

   if 4.39999999999999993e277 < i

   1. Initial program 50.6%

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

   2. Taylor expanded in y around inf 94.6%

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

      1. +-commutative 94.6%

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

      2. mul-1-neg 94.6%

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

      3. unsub-neg 94.6%

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

      4. *-commutative 94.6%

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

   4. Simplified 94.6%

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

   5. Taylor expanded in z around 0 94.6%

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

      1. mul-1-neg 94.6%

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

      2. *-commutative 94.6%

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

   7. Simplified 94.6%

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

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.6 \cdot 10^{+234}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;i \leq -7.2 \cdot 10^{-219}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;i \leq -3.55 \cdot 10^{-283}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 5.1 \cdot 10^{-89}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;i \leq 4.4 \cdot 10^{+277}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \]

Alternative 10: 60.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -5200000 \lor \neg \left(j \leq 1.36 \cdot 10^{+32}\right):\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - a \cdot \left(x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -5200000.0) (not (<= j 1.36e+32)))
   (* j (- (* t c) (* y i)))
   (- (* b (- (* a i) (* z c))) (* a (* x t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -5200000.0) || !(j <= 1.36e+32)) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = (b * ((a * i) - (z * c))) - (a * (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((j <= (-5200000.0d0)) .or. (.not. (j <= 1.36d+32))) then
        tmp = j * ((t * c) - (y * i))
    else
        tmp = (b * ((a * i) - (z * c))) - (a * (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -5200000.0) || !(j <= 1.36e+32)) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = (b * ((a * i) - (z * c))) - (a * (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -5200000.0) or not (j <= 1.36e+32):
		tmp = j * ((t * c) - (y * i))
	else:
		tmp = (b * ((a * i) - (z * c))) - (a * (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -5200000.0) || !(j <= 1.36e+32))
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	else
		tmp = Float64(Float64(b * Float64(Float64(a * i) - Float64(z * c))) - Float64(a * 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 <= -5200000.0) || ~((j <= 1.36e+32)))
		tmp = j * ((t * c) - (y * i));
	else
		tmp = (b * ((a * i) - (z * c))) - (a * (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -5200000.0], N[Not[LessEqual[j, 1.36e+32]], $MachinePrecision]], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -5.2e6 or 1.3599999999999999e32 < j

   1. Initial program 71.5%

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

   2. Taylor expanded in y around 0 63.3%

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

      1. sub-neg 63.3%

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

   4. Simplified 64.8%

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

   5. Taylor expanded in j around inf 71.0%

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

      1. mul-1-neg 71.0%

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

      2. distribute-lft-neg-out 71.0%

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

      3. +-commutative 71.0%

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

      4. cancel-sign-sub-inv 71.0%

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

      5. *-commutative 71.0%

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

      6. *-commutative 71.0%

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

   7. Simplified 71.0%

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

   if -5.2e6 < j < 1.3599999999999999e32

   1. Initial program 70.7%

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

   2. Taylor expanded in y around 0 66.5%

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

      1. associate-*r* 66.5%

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

      2. *-commutative 66.5%

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

      3. associate-*r* 66.3%

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

      4. associate-*r* 66.3%

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

      5. associate-*r* 66.3%

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

      6. distribute-rgt-in 67.1%

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

      7. *-commutative 67.1%

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

      8. +-commutative 67.1%

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

      9. mul-1-neg 67.1%

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

      10. unsub-neg 67.1%

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

      11. *-commutative 67.1%

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

   4. Simplified 67.1%

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

   5. Taylor expanded in j around 0 65.1%

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

      1. sub-neg 65.1%

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

      2. neg-mul-1 65.1%

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

      3. +-commutative 65.1%

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

      4. unsub-neg 65.1%

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

      5. distribute-rgt-neg-in 65.1%

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

      6. neg-sub0 65.1%

         \[\leadsto b \cdot \color{blue}{\left(0 - \left(c \cdot z - a \cdot i\right)\right)} - a \cdot \left(t \cdot x\right) \]

      7. associate--r- 65.1%

         \[\leadsto b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + a \cdot i\right)} - a \cdot \left(t \cdot x\right) \]

      8. neg-sub0 65.1%

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

      9. +-commutative 65.1%

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

      10. sub-neg 65.1%

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

   7. Simplified 65.1%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -5200000 \lor \neg \left(j \leq 1.36 \cdot 10^{+32}\right):\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - a \cdot \left(x \cdot t\right)\\ \end{array} \]

Alternative 11: 59.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.55 \cdot 10^{+151} \lor \neg \left(i \leq 2.85 \cdot 10^{+162}\right):\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) - c \cdot \left(z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -1.55e+151) (not (<= i 2.85e+162)))
   (* i (- (* a b) (* y j)))
   (- (* t (- (* c j) (* x a))) (* c (* z b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -1.55e+151) || !(i <= 2.85e+162)) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = (t * ((c * j) - (x * a))) - (c * (z * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((i <= (-1.55d+151)) .or. (.not. (i <= 2.85d+162))) then
        tmp = i * ((a * b) - (y * j))
    else
        tmp = (t * ((c * j) - (x * a))) - (c * (z * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -1.55e+151) || !(i <= 2.85e+162)) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = (t * ((c * j) - (x * a))) - (c * (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (i <= -1.55e+151) or not (i <= 2.85e+162):
		tmp = i * ((a * b) - (y * j))
	else:
		tmp = (t * ((c * j) - (x * a))) - (c * (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((i <= -1.55e+151) || !(i <= 2.85e+162))
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	else
		tmp = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) - Float64(c * Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((i <= -1.55e+151) || ~((i <= 2.85e+162)))
		tmp = i * ((a * b) - (y * j));
	else
		tmp = (t * ((c * j) - (x * a))) - (c * (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[i, -1.55e+151], N[Not[LessEqual[i, 2.85e+162]], $MachinePrecision]], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -1.5500000000000001e151 or 2.84999999999999998e162 < i

   1. Initial program 56.8%

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

   2. Taylor expanded in y around 0 55.1%

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

      1. sub-neg 55.1%

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

   4. Simplified 53.3%

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

   5. Taylor expanded in i around inf 79.8%

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

      1. +-commutative 79.8%

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

      2. mul-1-neg 79.8%

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

      3. unsub-neg 79.8%

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

      4. *-commutative 79.8%

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

   7. Simplified 79.8%

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

   if -1.5500000000000001e151 < i < 2.84999999999999998e162

   1. Initial program 75.9%

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

   2. Taylor expanded in y around 0 64.2%

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

      1. associate-*r* 64.2%

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

      2. *-commutative 64.2%

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

      3. associate-*r* 66.6%

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

      4. associate-*r* 66.6%

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

      5. associate-*r* 67.6%

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

      6. distribute-rgt-in 69.6%

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

      7. *-commutative 69.6%

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

      8. +-commutative 69.6%

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

      9. mul-1-neg 69.6%

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

      10. unsub-neg 69.6%

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

      11. *-commutative 69.6%

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

   4. Simplified 69.6%

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

   5. Taylor expanded in c around inf 61.7%

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

      1. *-commutative 61.7%

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

      2. associate-*l* 64.1%

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

      3. *-commutative 64.1%

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

   7. Simplified 64.1%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.55 \cdot 10^{+151} \lor \neg \left(i \leq 2.85 \cdot 10^{+162}\right):\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) - c \cdot \left(z \cdot b\right)\\ \end{array} \]

Alternative 12: 29.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ \mathbf{if}\;t \leq -1.26 \cdot 10^{+217}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -6.3 \cdot 10^{+162}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;t \leq -1.16 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-164}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-35}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+121}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j))))
   (if (<= t -1.26e+217)
     t_1
     (if (<= t -6.3e+162)
       (* a (* x (- t)))
       (if (<= t -1.16e+84)
         t_1
         (if (<= t -6e-164)
           (* i (* a b))
           (if (<= t 4.5e-35)
             (* y (* i (- j)))
             (if (<= t 9.5e+121) (* z (* c (- b))) (* t (* c j))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double tmp;
	if (t <= -1.26e+217) {
		tmp = t_1;
	} else if (t <= -6.3e+162) {
		tmp = a * (x * -t);
	} else if (t <= -1.16e+84) {
		tmp = t_1;
	} else if (t <= -6e-164) {
		tmp = i * (a * b);
	} else if (t <= 4.5e-35) {
		tmp = y * (i * -j);
	} else if (t <= 9.5e+121) {
		tmp = z * (c * -b);
	} else {
		tmp = t * (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) :: t_1
    real(8) :: tmp
    t_1 = c * (t * j)
    if (t <= (-1.26d+217)) then
        tmp = t_1
    else if (t <= (-6.3d+162)) then
        tmp = a * (x * -t)
    else if (t <= (-1.16d+84)) then
        tmp = t_1
    else if (t <= (-6d-164)) then
        tmp = i * (a * b)
    else if (t <= 4.5d-35) then
        tmp = y * (i * -j)
    else if (t <= 9.5d+121) then
        tmp = z * (c * -b)
    else
        tmp = t * (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 t_1 = c * (t * j);
	double tmp;
	if (t <= -1.26e+217) {
		tmp = t_1;
	} else if (t <= -6.3e+162) {
		tmp = a * (x * -t);
	} else if (t <= -1.16e+84) {
		tmp = t_1;
	} else if (t <= -6e-164) {
		tmp = i * (a * b);
	} else if (t <= 4.5e-35) {
		tmp = y * (i * -j);
	} else if (t <= 9.5e+121) {
		tmp = z * (c * -b);
	} else {
		tmp = t * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (t * j)
	tmp = 0
	if t <= -1.26e+217:
		tmp = t_1
	elif t <= -6.3e+162:
		tmp = a * (x * -t)
	elif t <= -1.16e+84:
		tmp = t_1
	elif t <= -6e-164:
		tmp = i * (a * b)
	elif t <= 4.5e-35:
		tmp = y * (i * -j)
	elif t <= 9.5e+121:
		tmp = z * (c * -b)
	else:
		tmp = t * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(t * j))
	tmp = 0.0
	if (t <= -1.26e+217)
		tmp = t_1;
	elseif (t <= -6.3e+162)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (t <= -1.16e+84)
		tmp = t_1;
	elseif (t <= -6e-164)
		tmp = Float64(i * Float64(a * b));
	elseif (t <= 4.5e-35)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (t <= 9.5e+121)
		tmp = Float64(z * Float64(c * Float64(-b)));
	else
		tmp = Float64(t * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (t * j);
	tmp = 0.0;
	if (t <= -1.26e+217)
		tmp = t_1;
	elseif (t <= -6.3e+162)
		tmp = a * (x * -t);
	elseif (t <= -1.16e+84)
		tmp = t_1;
	elseif (t <= -6e-164)
		tmp = i * (a * b);
	elseif (t <= 4.5e-35)
		tmp = y * (i * -j);
	elseif (t <= 9.5e+121)
		tmp = z * (c * -b);
	else
		tmp = t * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.26e+217], t$95$1, If[LessEqual[t, -6.3e+162], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.16e+84], t$95$1, If[LessEqual[t, -6e-164], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e-35], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e+121], N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -1.2599999999999999e217 or -6.3000000000000001e162 < t < -1.16e84

   1. Initial program 61.6%

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

   2. Taylor expanded in y around 0 70.9%

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

      1. sub-neg 70.9%

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

   4. Simplified 80.4%

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

   5. Taylor expanded in j around inf 54.6%

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

      1. mul-1-neg 54.6%

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

      2. distribute-lft-neg-out 54.6%

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

      3. +-commutative 54.6%

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

      4. cancel-sign-sub-inv 54.6%

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

      5. *-commutative 54.6%

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

      6. *-commutative 54.6%

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

   7. Simplified 54.6%

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

   8. Taylor expanded in t around inf 57.1%

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

      1. *-commutative 57.1%

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

   10. Simplified 57.1%

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

   if -1.2599999999999999e217 < t < -6.3000000000000001e162

   1. Initial program 67.3%

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

   2. Taylor expanded in y around 0 83.3%

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

      1. associate-*r* 83.3%

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

      2. *-commutative 83.3%

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

      3. associate-*r* 83.2%

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

      4. associate-*r* 83.2%

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

      5. associate-*r* 83.2%

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

      6. distribute-rgt-in 83.2%

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

      7. *-commutative 83.2%

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

      8. +-commutative 83.2%

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

      9. mul-1-neg 83.2%

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

      10. unsub-neg 83.2%

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

      11. *-commutative 83.2%

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

   4. Simplified 83.2%

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

   5. Taylor expanded in x around inf 67.1%

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

      1. neg-mul-1 67.1%

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

      2. distribute-lft-neg-in 67.1%

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

   7. Simplified 67.1%

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

   if -1.16e84 < t < -6.0000000000000002e-164

   1. Initial program 84.2%

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

   2. Taylor expanded in b around inf 51.1%

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

      1. *-commutative 51.1%

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

   4. Simplified 51.1%

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

   5. Taylor expanded in i around inf 37.8%

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

      1. associate-*r* 42.0%

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

   7. Simplified 42.0%

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

   if -6.0000000000000002e-164 < t < 4.5000000000000001e-35

   1. Initial program 75.4%

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

   2. Taylor expanded in y around inf 56.2%

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

      1. +-commutative 56.2%

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

      2. mul-1-neg 56.2%

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

      3. unsub-neg 56.2%

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

      4. *-commutative 56.2%

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

   4. Simplified 56.2%

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

   5. Taylor expanded in z around 0 38.9%

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

      1. mul-1-neg 38.9%

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

      2. *-commutative 38.9%

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

      3. *-commutative 38.9%

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

      4. associate-*r* 42.6%

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

      5. *-commutative 42.6%

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

      6. distribute-rgt-neg-out 42.6%

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

      7. distribute-rgt-neg-in 42.6%

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

   7. Simplified 42.6%

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

   if 4.5000000000000001e-35 < t < 9.49999999999999949e121

   1. Initial program 71.7%

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

   2. Taylor expanded in b around inf 40.6%

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

      1. *-commutative 40.6%

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

   4. Simplified 40.6%

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

   5. Taylor expanded in i around 0 33.4%

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

      1. mul-1-neg 33.4%

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

      2. *-commutative 33.4%

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

      3. *-commutative 33.4%

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

      4. associate-*r* 40.8%

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

      5. *-commutative 40.8%

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

      6. distribute-rgt-neg-out 40.8%

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

      7. *-commutative 40.8%

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

      8. distribute-rgt-neg-in 40.8%

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

   7. Simplified 40.8%

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

   if 9.49999999999999949e121 < t

   1. Initial program 55.9%

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

   2. Taylor expanded in y around 0 50.8%

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

      1. sub-neg 50.8%

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

   4. Simplified 72.3%

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

   5. Taylor expanded in j around inf 51.4%

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

      1. mul-1-neg 51.4%

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

      2. distribute-lft-neg-out 51.4%

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

      3. +-commutative 51.4%

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

      4. cancel-sign-sub-inv 51.4%

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

      5. *-commutative 51.4%

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

      6. *-commutative 51.4%

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

   7. Simplified 51.4%

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

   8. Taylor expanded in t around inf 42.8%

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

      1. associate-*r* 45.3%

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

      2. *-commutative 45.3%

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

   10. Simplified 45.3%

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

4. Final simplification 46.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.26 \cdot 10^{+217}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq -6.3 \cdot 10^{+162}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;t \leq -1.16 \cdot 10^{+84}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-164}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-35}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+121}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 13: 40.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;j \leq -1.75 \cdot 10^{+14}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq 8 \cdot 10^{-88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 7.2 \cdot 10^{+14}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;j \leq 2 \cdot 10^{+190}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 1.4 \cdot 10^{+229}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= j -1.75e+14)
     (* t (* c j))
     (if (<= j 8e-88)
       t_1
       (if (<= j 7.2e+14)
         (* a (- (* b i) (* x t)))
         (if (<= j 2e+190)
           t_1
           (if (<= j 1.4e+229) (* j (* t c)) (* y (* i (- j))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (j <= -1.75e+14) {
		tmp = t * (c * j);
	} else if (j <= 8e-88) {
		tmp = t_1;
	} else if (j <= 7.2e+14) {
		tmp = a * ((b * i) - (x * t));
	} else if (j <= 2e+190) {
		tmp = t_1;
	} else if (j <= 1.4e+229) {
		tmp = j * (t * c);
	} else {
		tmp = y * (i * -j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    if (j <= (-1.75d+14)) then
        tmp = t * (c * j)
    else if (j <= 8d-88) then
        tmp = t_1
    else if (j <= 7.2d+14) then
        tmp = a * ((b * i) - (x * t))
    else if (j <= 2d+190) then
        tmp = t_1
    else if (j <= 1.4d+229) then
        tmp = j * (t * c)
    else
        tmp = y * (i * -j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (j <= -1.75e+14) {
		tmp = t * (c * j);
	} else if (j <= 8e-88) {
		tmp = t_1;
	} else if (j <= 7.2e+14) {
		tmp = a * ((b * i) - (x * t));
	} else if (j <= 2e+190) {
		tmp = t_1;
	} else if (j <= 1.4e+229) {
		tmp = j * (t * c);
	} else {
		tmp = y * (i * -j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	tmp = 0
	if j <= -1.75e+14:
		tmp = t * (c * j)
	elif j <= 8e-88:
		tmp = t_1
	elif j <= 7.2e+14:
		tmp = a * ((b * i) - (x * t))
	elif j <= 2e+190:
		tmp = t_1
	elif j <= 1.4e+229:
		tmp = j * (t * c)
	else:
		tmp = y * (i * -j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (j <= -1.75e+14)
		tmp = Float64(t * Float64(c * j));
	elseif (j <= 8e-88)
		tmp = t_1;
	elseif (j <= 7.2e+14)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (j <= 2e+190)
		tmp = t_1;
	elseif (j <= 1.4e+229)
		tmp = Float64(j * Float64(t * c));
	else
		tmp = Float64(y * Float64(i * Float64(-j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (j <= -1.75e+14)
		tmp = t * (c * j);
	elseif (j <= 8e-88)
		tmp = t_1;
	elseif (j <= 7.2e+14)
		tmp = a * ((b * i) - (x * t));
	elseif (j <= 2e+190)
		tmp = t_1;
	elseif (j <= 1.4e+229)
		tmp = j * (t * c);
	else
		tmp = y * (i * -j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.75e+14], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8e-88], t$95$1, If[LessEqual[j, 7.2e+14], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2e+190], t$95$1, If[LessEqual[j, 1.4e+229], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -1.75e14

   1. Initial program 74.9%

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

   2. Taylor expanded in y around 0 67.2%

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

      1. sub-neg 67.2%

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

   4. Simplified 68.7%

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

   5. Taylor expanded in j around inf 70.3%

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

      1. mul-1-neg 70.3%

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

      2. distribute-lft-neg-out 70.3%

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

      3. +-commutative 70.3%

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

      4. cancel-sign-sub-inv 70.3%

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

      5. *-commutative 70.3%

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

      6. *-commutative 70.3%

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

   7. Simplified 70.3%

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

   8. Taylor expanded in t around inf 43.5%

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

      1. associate-*r* 47.9%

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

      2. *-commutative 47.9%

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

   10. Simplified 47.9%

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

   if -1.75e14 < j < 7.99999999999999947e-88 or 7.2e14 < j < 2.0000000000000001e190

   1. Initial program 71.5%

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

   2. Taylor expanded in b around inf 49.9%

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

      1. *-commutative 49.9%

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

   4. Simplified 49.9%

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

   if 7.99999999999999947e-88 < j < 7.2e14

   1. Initial program 69.1%

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

   2. Taylor expanded in y around 0 83.8%

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

      1. sub-neg 83.8%

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

   4. Simplified 87.7%

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

   5. Taylor expanded in a around inf 52.1%

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

      1. +-commutative 52.1%

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

      2. mul-1-neg 52.1%

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

      3. unsub-neg 52.1%

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

      4. *-commutative 52.1%

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

      5. *-commutative 52.1%

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

   7. Simplified 52.1%

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

   if 2.0000000000000001e190 < j < 1.4000000000000001e229

   1. Initial program 87.5%

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

   2. Taylor expanded in y around 0 75.0%

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

      1. sub-neg 75.0%

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

   4. Simplified 75.7%

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

   5. Taylor expanded in j around inf 75.0%

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

      1. mul-1-neg 75.0%

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

      2. distribute-lft-neg-out 75.0%

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

      3. +-commutative 75.0%

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

      4. cancel-sign-sub-inv 75.0%

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

      5. *-commutative 75.0%

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

      6. *-commutative 75.0%

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

   7. Simplified 75.0%

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

   8. Taylor expanded in t around inf 62.6%

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

      1. *-commutative 62.6%

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

   10. Simplified 62.6%

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

   if 1.4000000000000001e229 < j

   1. Initial program 42.9%

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

   2. Taylor expanded in y around inf 78.6%

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

      1. +-commutative 78.6%

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

      2. mul-1-neg 78.6%

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

      3. unsub-neg 78.6%

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

      4. *-commutative 78.6%

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

   4. Simplified 78.6%

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

   5. Taylor expanded in z around 0 79.3%

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

      1. mul-1-neg 79.3%

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

      2. *-commutative 79.3%

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

      3. *-commutative 79.3%

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

      4. associate-*r* 85.7%

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

      5. *-commutative 85.7%

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

      6. distribute-rgt-neg-out 85.7%

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

      7. distribute-rgt-neg-in 85.7%

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

   7. Simplified 85.7%

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

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.75 \cdot 10^{+14}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq 8 \cdot 10^{-88}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 7.2 \cdot 10^{+14}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;j \leq 2 \cdot 10^{+190}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.4 \cdot 10^{+229}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \]

Alternative 14: 50.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -1.1 \cdot 10^{+141}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -2.1 \cdot 10^{-107}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;i \leq 1.92 \cdot 10^{-72}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* a b) (* y j)))))
   (if (<= i -1.1e+141)
     t_1
     (if (<= i -2.1e-107)
       (* a (- (* b i) (* x t)))
       (if (<= i 1.92e-72) (* c (- (* t j) (* z b))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -1.1e+141) {
		tmp = t_1;
	} else if (i <= -2.1e-107) {
		tmp = a * ((b * i) - (x * t));
	} else if (i <= 1.92e-72) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * ((a * b) - (y * j))
    if (i <= (-1.1d+141)) then
        tmp = t_1
    else if (i <= (-2.1d-107)) then
        tmp = a * ((b * i) - (x * t))
    else if (i <= 1.92d-72) then
        tmp = c * ((t * j) - (z * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -1.1e+141) {
		tmp = t_1;
	} else if (i <= -2.1e-107) {
		tmp = a * ((b * i) - (x * t));
	} else if (i <= 1.92e-72) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((a * b) - (y * j))
	tmp = 0
	if i <= -1.1e+141:
		tmp = t_1
	elif i <= -2.1e-107:
		tmp = a * ((b * i) - (x * t))
	elif i <= 1.92e-72:
		tmp = c * ((t * j) - (z * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -1.1e+141)
		tmp = t_1;
	elseif (i <= -2.1e-107)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (i <= 1.92e-72)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((a * b) - (y * j));
	tmp = 0.0;
	if (i <= -1.1e+141)
		tmp = t_1;
	elseif (i <= -2.1e-107)
		tmp = a * ((b * i) - (x * t));
	elseif (i <= 1.92e-72)
		tmp = c * ((t * j) - (z * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.1e+141], t$95$1, If[LessEqual[i, -2.1e-107], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.92e-72], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if i < -1.1e141 or 1.92000000000000004e-72 < i

   1. Initial program 65.1%

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

   2. Taylor expanded in y around 0 64.9%

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

      1. sub-neg 64.9%

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

   4. Simplified 65.7%

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

   5. Taylor expanded in i around inf 62.5%

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

      1. +-commutative 62.5%

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

      2. mul-1-neg 62.5%

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

      3. unsub-neg 62.5%

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

      4. *-commutative 62.5%

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

   7. Simplified 62.5%

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

   if -1.1e141 < i < -2.0999999999999999e-107

   1. Initial program 75.6%

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

   2. Taylor expanded in y around 0 81.4%

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

      1. sub-neg 81.4%

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

   4. Simplified 83.4%

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

   5. Taylor expanded in a around inf 54.8%

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

      1. +-commutative 54.8%

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

      2. mul-1-neg 54.8%

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

      3. unsub-neg 54.8%

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

      4. *-commutative 54.8%

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

      5. *-commutative 54.8%

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

   7. Simplified 54.8%

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

   if -2.0999999999999999e-107 < i < 1.92000000000000004e-72

   1. Initial program 76.3%

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

   2. Taylor expanded in c around inf 58.8%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.1 \cdot 10^{+141}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -2.1 \cdot 10^{-107}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;i \leq 1.92 \cdot 10^{-72}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \]

Alternative 15: 52.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -2.1 \cdot 10^{-49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 3.8 \cdot 10^{-92}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{+32}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))))
   (if (<= j -2.1e-49)
     t_1
     (if (<= j 3.8e-92)
       (* b (- (* a i) (* z c)))
       (if (<= j 1.7e+32) (* a (- (* b i) (* x t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -2.1e-49) {
		tmp = t_1;
	} else if (j <= 3.8e-92) {
		tmp = b * ((a * i) - (z * c));
	} else if (j <= 1.7e+32) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    if (j <= (-2.1d-49)) then
        tmp = t_1
    else if (j <= 3.8d-92) then
        tmp = b * ((a * i) - (z * c))
    else if (j <= 1.7d+32) then
        tmp = a * ((b * i) - (x * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -2.1e-49) {
		tmp = t_1;
	} else if (j <= 3.8e-92) {
		tmp = b * ((a * i) - (z * c));
	} else if (j <= 1.7e+32) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -2.1e-49:
		tmp = t_1
	elif j <= 3.8e-92:
		tmp = b * ((a * i) - (z * c))
	elif j <= 1.7e+32:
		tmp = a * ((b * i) - (x * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -2.1e-49)
		tmp = t_1;
	elseif (j <= 3.8e-92)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (j <= 1.7e+32)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -2.1e-49)
		tmp = t_1;
	elseif (j <= 3.8e-92)
		tmp = b * ((a * i) - (z * c));
	elseif (j <= 1.7e+32)
		tmp = a * ((b * i) - (x * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.1e-49], t$95$1, If[LessEqual[j, 3.8e-92], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.7e+32], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if j < -2.0999999999999999e-49 or 1.69999999999999989e32 < j

   1. Initial program 72.0%

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

   2. Taylor expanded in y around 0 62.8%

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

      1. sub-neg 62.8%

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

   4. Simplified 64.9%

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

   5. Taylor expanded in j around inf 68.4%

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

      1. mul-1-neg 68.4%

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

      2. distribute-lft-neg-out 68.4%

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

      3. +-commutative 68.4%

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

      4. cancel-sign-sub-inv 68.4%

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

      5. *-commutative 68.4%

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

      6. *-commutative 68.4%

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

   7. Simplified 68.4%

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

   if -2.0999999999999999e-49 < j < 3.8000000000000001e-92

   1. Initial program 69.6%

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

   2. Taylor expanded in b around inf 52.6%

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

      1. *-commutative 52.6%

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

   4. Simplified 52.6%

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

   if 3.8000000000000001e-92 < j < 1.69999999999999989e32

   1. Initial program 72.4%

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

   2. Taylor expanded in y around 0 85.4%

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

      1. sub-neg 85.4%

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

   4. Simplified 85.7%

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

   5. Taylor expanded in a around inf 53.7%

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

      1. +-commutative 53.7%

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

      2. mul-1-neg 53.7%

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

      3. unsub-neg 53.7%

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

      4. *-commutative 53.7%

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

      5. *-commutative 53.7%

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

   7. Simplified 53.7%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.1 \cdot 10^{-49}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 3.8 \cdot 10^{-92}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{+32}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 16: 51.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -1.95 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -1.08 \cdot 10^{-240}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;i \leq 1.92 \cdot 10^{-72}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* a b) (* y j)))))
   (if (<= i -1.95e-7)
     t_1
     (if (<= i -1.08e-240)
       (* t (- (* c j) (* x a)))
       (if (<= i 1.92e-72) (* c (- (* t j) (* z b))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -1.95e-7) {
		tmp = t_1;
	} else if (i <= -1.08e-240) {
		tmp = t * ((c * j) - (x * a));
	} else if (i <= 1.92e-72) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * ((a * b) - (y * j))
    if (i <= (-1.95d-7)) then
        tmp = t_1
    else if (i <= (-1.08d-240)) then
        tmp = t * ((c * j) - (x * a))
    else if (i <= 1.92d-72) then
        tmp = c * ((t * j) - (z * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -1.95e-7) {
		tmp = t_1;
	} else if (i <= -1.08e-240) {
		tmp = t * ((c * j) - (x * a));
	} else if (i <= 1.92e-72) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((a * b) - (y * j))
	tmp = 0
	if i <= -1.95e-7:
		tmp = t_1
	elif i <= -1.08e-240:
		tmp = t * ((c * j) - (x * a))
	elif i <= 1.92e-72:
		tmp = c * ((t * j) - (z * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -1.95e-7)
		tmp = t_1;
	elseif (i <= -1.08e-240)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (i <= 1.92e-72)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((a * b) - (y * j));
	tmp = 0.0;
	if (i <= -1.95e-7)
		tmp = t_1;
	elseif (i <= -1.08e-240)
		tmp = t * ((c * j) - (x * a));
	elseif (i <= 1.92e-72)
		tmp = c * ((t * j) - (z * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.95e-7], t$95$1, If[LessEqual[i, -1.08e-240], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.92e-72], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if i < -1.95000000000000012e-7 or 1.92000000000000004e-72 < i

   1. Initial program 64.5%

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

   2. Taylor expanded in y around 0 67.1%

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

      1. sub-neg 67.1%

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

   4. Simplified 67.8%

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

   5. Taylor expanded in i around inf 60.6%

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

      1. +-commutative 60.6%

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

      2. mul-1-neg 60.6%

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

      3. unsub-neg 60.6%

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

      4. *-commutative 60.6%

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

   7. Simplified 60.6%

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

   if -1.95000000000000012e-7 < i < -1.08e-240

   1. Initial program 84.6%

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

   2. Taylor expanded in t around inf 57.0%

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

      1. +-commutative 57.0%

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

      2. mul-1-neg 57.0%

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

      3. unsub-neg 57.0%

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

      4. *-commutative 57.0%

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

   4. Simplified 57.0%

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

   if -1.08e-240 < i < 1.92000000000000004e-72

   1. Initial program 74.5%

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

   2. Taylor expanded in c around inf 64.9%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.95 \cdot 10^{-7}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -1.08 \cdot 10^{-240}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;i \leq 1.92 \cdot 10^{-72}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \]

Alternative 17: 29.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+85}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-161}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-35}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+121}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -3.8e+85)
   (* c (* t j))
   (if (<= t -1.25e-161)
     (* i (* a b))
     (if (<= t 3.5e-35)
       (* y (* i (- j)))
       (if (<= t 7.8e+121) (* z (* c (- b))) (* t (* 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 (t <= -3.8e+85) {
		tmp = c * (t * j);
	} else if (t <= -1.25e-161) {
		tmp = i * (a * b);
	} else if (t <= 3.5e-35) {
		tmp = y * (i * -j);
	} else if (t <= 7.8e+121) {
		tmp = z * (c * -b);
	} else {
		tmp = t * (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 (t <= (-3.8d+85)) then
        tmp = c * (t * j)
    else if (t <= (-1.25d-161)) then
        tmp = i * (a * b)
    else if (t <= 3.5d-35) then
        tmp = y * (i * -j)
    else if (t <= 7.8d+121) then
        tmp = z * (c * -b)
    else
        tmp = t * (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 (t <= -3.8e+85) {
		tmp = c * (t * j);
	} else if (t <= -1.25e-161) {
		tmp = i * (a * b);
	} else if (t <= 3.5e-35) {
		tmp = y * (i * -j);
	} else if (t <= 7.8e+121) {
		tmp = z * (c * -b);
	} else {
		tmp = t * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -3.8e+85:
		tmp = c * (t * j)
	elif t <= -1.25e-161:
		tmp = i * (a * b)
	elif t <= 3.5e-35:
		tmp = y * (i * -j)
	elif t <= 7.8e+121:
		tmp = z * (c * -b)
	else:
		tmp = t * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -3.8e+85)
		tmp = Float64(c * Float64(t * j));
	elseif (t <= -1.25e-161)
		tmp = Float64(i * Float64(a * b));
	elseif (t <= 3.5e-35)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (t <= 7.8e+121)
		tmp = Float64(z * Float64(c * Float64(-b)));
	else
		tmp = Float64(t * 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 (t <= -3.8e+85)
		tmp = c * (t * j);
	elseif (t <= -1.25e-161)
		tmp = i * (a * b);
	elseif (t <= 3.5e-35)
		tmp = y * (i * -j);
	elseif (t <= 7.8e+121)
		tmp = z * (c * -b);
	else
		tmp = t * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -3.8e+85], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.25e-161], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e-35], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.8e+121], N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3.79999999999999992e85

   1. Initial program 62.9%

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

   2. Taylor expanded in y around 0 70.0%

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

      1. sub-neg 70.0%

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

   4. Simplified 77.3%

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

   5. Taylor expanded in j around inf 46.2%

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

      1. mul-1-neg 46.2%

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

      2. distribute-lft-neg-out 46.2%

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

      3. +-commutative 46.2%

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

      4. cancel-sign-sub-inv 46.2%

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

      5. *-commutative 46.2%

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

      6. *-commutative 46.2%

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

   7. Simplified 46.2%

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

   8. Taylor expanded in t around inf 48.2%

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

      1. *-commutative 48.2%

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

   10. Simplified 48.2%

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

   if -3.79999999999999992e85 < t < -1.25e-161

   1. Initial program 84.2%

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

   2. Taylor expanded in b around inf 51.1%

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

      1. *-commutative 51.1%

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

   4. Simplified 51.1%

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

   5. Taylor expanded in i around inf 37.8%

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

      1. associate-*r* 42.0%

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

   7. Simplified 42.0%

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

   if -1.25e-161 < t < 3.49999999999999996e-35

   1. Initial program 75.4%

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

   2. Taylor expanded in y around inf 56.2%

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

      1. +-commutative 56.2%

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

      2. mul-1-neg 56.2%

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

      3. unsub-neg 56.2%

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

      4. *-commutative 56.2%

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

   4. Simplified 56.2%

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

   5. Taylor expanded in z around 0 38.9%

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

      1. mul-1-neg 38.9%

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

      2. *-commutative 38.9%

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

      3. *-commutative 38.9%

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

      4. associate-*r* 42.6%

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

      5. *-commutative 42.6%

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

      6. distribute-rgt-neg-out 42.6%

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

      7. distribute-rgt-neg-in 42.6%

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

   7. Simplified 42.6%

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

   if 3.49999999999999996e-35 < t < 7.79999999999999967e121

   1. Initial program 71.7%

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

   2. Taylor expanded in b around inf 40.6%

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

      1. *-commutative 40.6%

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

   4. Simplified 40.6%

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

   5. Taylor expanded in i around 0 33.4%

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

      1. mul-1-neg 33.4%

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

      2. *-commutative 33.4%

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

      3. *-commutative 33.4%

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

      4. associate-*r* 40.8%

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

      5. *-commutative 40.8%

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

      6. distribute-rgt-neg-out 40.8%

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

      7. *-commutative 40.8%

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

      8. distribute-rgt-neg-in 40.8%

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

   7. Simplified 40.8%

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

   if 7.79999999999999967e121 < t

   1. Initial program 55.9%

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

   2. Taylor expanded in y around 0 50.8%

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

      1. sub-neg 50.8%

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

   4. Simplified 72.3%

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

   5. Taylor expanded in j around inf 51.4%

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

      1. mul-1-neg 51.4%

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

      2. distribute-lft-neg-out 51.4%

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

      3. +-commutative 51.4%

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

      4. cancel-sign-sub-inv 51.4%

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

      5. *-commutative 51.4%

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

      6. *-commutative 51.4%

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

   7. Simplified 51.4%

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

   8. Taylor expanded in t around inf 42.8%

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

      1. associate-*r* 45.3%

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

      2. *-commutative 45.3%

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

   10. Simplified 45.3%

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

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+85}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-161}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-35}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+121}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 18: 30.2% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{+84}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-255}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-157}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-26}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -8.6e+84)
   (* c (* t j))
   (if (<= t -9e-255)
     (* a (* b i))
     (if (<= t 6.5e-157)
       (* y (* x z))
       (if (<= t 3.4e-26) (* b (* a i)) (* j (* t 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 (t <= -8.6e+84) {
		tmp = c * (t * j);
	} else if (t <= -9e-255) {
		tmp = a * (b * i);
	} else if (t <= 6.5e-157) {
		tmp = y * (x * z);
	} else if (t <= 3.4e-26) {
		tmp = b * (a * i);
	} else {
		tmp = j * (t * 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 (t <= (-8.6d+84)) then
        tmp = c * (t * j)
    else if (t <= (-9d-255)) then
        tmp = a * (b * i)
    else if (t <= 6.5d-157) then
        tmp = y * (x * z)
    else if (t <= 3.4d-26) then
        tmp = b * (a * i)
    else
        tmp = j * (t * 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 (t <= -8.6e+84) {
		tmp = c * (t * j);
	} else if (t <= -9e-255) {
		tmp = a * (b * i);
	} else if (t <= 6.5e-157) {
		tmp = y * (x * z);
	} else if (t <= 3.4e-26) {
		tmp = b * (a * i);
	} else {
		tmp = j * (t * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -8.6e+84:
		tmp = c * (t * j)
	elif t <= -9e-255:
		tmp = a * (b * i)
	elif t <= 6.5e-157:
		tmp = y * (x * z)
	elif t <= 3.4e-26:
		tmp = b * (a * i)
	else:
		tmp = j * (t * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -8.6e+84)
		tmp = Float64(c * Float64(t * j));
	elseif (t <= -9e-255)
		tmp = Float64(a * Float64(b * i));
	elseif (t <= 6.5e-157)
		tmp = Float64(y * Float64(x * z));
	elseif (t <= 3.4e-26)
		tmp = Float64(b * Float64(a * i));
	else
		tmp = Float64(j * Float64(t * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -8.6e+84)
		tmp = c * (t * j);
	elseif (t <= -9e-255)
		tmp = a * (b * i);
	elseif (t <= 6.5e-157)
		tmp = y * (x * z);
	elseif (t <= 3.4e-26)
		tmp = b * (a * i);
	else
		tmp = j * (t * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -8.6e+84], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -9e-255], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.5e-157], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.4e-26], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -8.5999999999999992e84

   1. Initial program 62.9%

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

   2. Taylor expanded in y around 0 70.0%

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

      1. sub-neg 70.0%

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

   4. Simplified 77.3%

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

   5. Taylor expanded in j around inf 46.2%

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

      1. mul-1-neg 46.2%

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

      2. distribute-lft-neg-out 46.2%

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

      3. +-commutative 46.2%

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

      4. cancel-sign-sub-inv 46.2%

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

      5. *-commutative 46.2%

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

      6. *-commutative 46.2%

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

   7. Simplified 46.2%

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

   8. Taylor expanded in t around inf 48.2%

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

      1. *-commutative 48.2%

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

   10. Simplified 48.2%

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

   if -8.5999999999999992e84 < t < -8.99999999999999959e-255

   1. Initial program 79.1%

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

   2. Taylor expanded in b around inf 49.0%

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

      1. *-commutative 49.0%

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

   4. Simplified 49.0%

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

   5. Taylor expanded in i around inf 36.1%

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

   if -8.99999999999999959e-255 < t < 6.5000000000000002e-157

   1. Initial program 80.0%

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

   2. Taylor expanded in y around inf 61.9%

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

      1. +-commutative 61.9%

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

      2. mul-1-neg 61.9%

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

      3. unsub-neg 61.9%

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

      4. *-commutative 61.9%

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

   4. Simplified 61.9%

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

   5. Taylor expanded in z around inf 31.1%

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

      1. associate-*r* 31.1%

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

      2. *-commutative 31.1%

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

      3. associate-*r* 35.5%

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

   7. Simplified 35.5%

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

   if 6.5000000000000002e-157 < t < 3.40000000000000013e-26

   1. Initial program 76.6%

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

   2. Taylor expanded in b around inf 44.7%

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

      1. *-commutative 44.7%

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

   4. Simplified 44.7%

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

   5. Taylor expanded in i around inf 25.6%

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

      1. *-commutative 25.6%

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

   7. Simplified 25.6%

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

   if 3.40000000000000013e-26 < t

   1. Initial program 62.1%

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

   2. Taylor expanded in y around 0 55.0%

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

      1. sub-neg 55.0%

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

   4. Simplified 69.4%

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

   5. Taylor expanded in j around inf 48.7%

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

      1. mul-1-neg 48.7%

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

      2. distribute-lft-neg-out 48.7%

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

      3. +-commutative 48.7%

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

      4. cancel-sign-sub-inv 48.7%

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

      5. *-commutative 48.7%

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

      6. *-commutative 48.7%

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

   7. Simplified 48.7%

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

   8. Taylor expanded in t around inf 34.2%

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

      1. *-commutative 34.2%

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

   10. Simplified 34.2%

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

4. Final simplification 36.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{+84}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-255}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-157}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-26}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \]

Alternative 19: 30.4% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+85}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-254}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{-157}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-25}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -1.1e+85)
   (* c (* t j))
   (if (<= t -1.7e-254)
     (* i (* a b))
     (if (<= t 7.6e-157)
       (* y (* x z))
       (if (<= t 4.5e-25) (* b (* a i)) (* j (* t 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 (t <= -1.1e+85) {
		tmp = c * (t * j);
	} else if (t <= -1.7e-254) {
		tmp = i * (a * b);
	} else if (t <= 7.6e-157) {
		tmp = y * (x * z);
	} else if (t <= 4.5e-25) {
		tmp = b * (a * i);
	} else {
		tmp = j * (t * 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 (t <= (-1.1d+85)) then
        tmp = c * (t * j)
    else if (t <= (-1.7d-254)) then
        tmp = i * (a * b)
    else if (t <= 7.6d-157) then
        tmp = y * (x * z)
    else if (t <= 4.5d-25) then
        tmp = b * (a * i)
    else
        tmp = j * (t * 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 (t <= -1.1e+85) {
		tmp = c * (t * j);
	} else if (t <= -1.7e-254) {
		tmp = i * (a * b);
	} else if (t <= 7.6e-157) {
		tmp = y * (x * z);
	} else if (t <= 4.5e-25) {
		tmp = b * (a * i);
	} else {
		tmp = j * (t * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -1.1e+85:
		tmp = c * (t * j)
	elif t <= -1.7e-254:
		tmp = i * (a * b)
	elif t <= 7.6e-157:
		tmp = y * (x * z)
	elif t <= 4.5e-25:
		tmp = b * (a * i)
	else:
		tmp = j * (t * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -1.1e+85)
		tmp = Float64(c * Float64(t * j));
	elseif (t <= -1.7e-254)
		tmp = Float64(i * Float64(a * b));
	elseif (t <= 7.6e-157)
		tmp = Float64(y * Float64(x * z));
	elseif (t <= 4.5e-25)
		tmp = Float64(b * Float64(a * i));
	else
		tmp = Float64(j * Float64(t * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -1.1e+85)
		tmp = c * (t * j);
	elseif (t <= -1.7e-254)
		tmp = i * (a * b);
	elseif (t <= 7.6e-157)
		tmp = y * (x * z);
	elseif (t <= 4.5e-25)
		tmp = b * (a * i);
	else
		tmp = j * (t * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -1.1e+85], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.7e-254], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.6e-157], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e-25], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.1000000000000001e85

   1. Initial program 62.9%

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

   2. Taylor expanded in y around 0 70.0%

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

      1. sub-neg 70.0%

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

   4. Simplified 77.3%

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

   5. Taylor expanded in j around inf 46.2%

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

      1. mul-1-neg 46.2%

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

      2. distribute-lft-neg-out 46.2%

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

      3. +-commutative 46.2%

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

      4. cancel-sign-sub-inv 46.2%

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

      5. *-commutative 46.2%

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

      6. *-commutative 46.2%

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

   7. Simplified 46.2%

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

   8. Taylor expanded in t around inf 48.2%

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

      1. *-commutative 48.2%

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

   10. Simplified 48.2%

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

   if -1.1000000000000001e85 < t < -1.69999999999999996e-254

   1. Initial program 79.1%

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

   2. Taylor expanded in b around inf 49.0%

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

      1. *-commutative 49.0%

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

   4. Simplified 49.0%

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

   5. Taylor expanded in i around inf 36.1%

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

      1. associate-*r* 39.1%

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

   7. Simplified 39.1%

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

   if -1.69999999999999996e-254 < t < 7.60000000000000041e-157

   1. Initial program 80.0%

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

   2. Taylor expanded in y around inf 61.9%

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

      1. +-commutative 61.9%

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

      2. mul-1-neg 61.9%

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

      3. unsub-neg 61.9%

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

      4. *-commutative 61.9%

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

   4. Simplified 61.9%

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

   5. Taylor expanded in z around inf 31.1%

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

      1. associate-*r* 31.1%

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

      2. *-commutative 31.1%

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

      3. associate-*r* 35.5%

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

   7. Simplified 35.5%

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

   if 7.60000000000000041e-157 < t < 4.5000000000000001e-25

   1. Initial program 76.6%

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

   2. Taylor expanded in b around inf 44.7%

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

      1. *-commutative 44.7%

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

   4. Simplified 44.7%

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

   5. Taylor expanded in i around inf 25.6%

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

      1. *-commutative 25.6%

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

   7. Simplified 25.6%

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

   if 4.5000000000000001e-25 < t

   1. Initial program 62.1%

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

   2. Taylor expanded in y around 0 55.0%

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

      1. sub-neg 55.0%

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

   4. Simplified 69.4%

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

   5. Taylor expanded in j around inf 48.7%

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

      1. mul-1-neg 48.7%

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

      2. distribute-lft-neg-out 48.7%

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

      3. +-commutative 48.7%

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

      4. cancel-sign-sub-inv 48.7%

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

      5. *-commutative 48.7%

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

      6. *-commutative 48.7%

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

   7. Simplified 48.7%

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

   8. Taylor expanded in t around inf 34.2%

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

      1. *-commutative 34.2%

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

   10. Simplified 34.2%

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

4. Final simplification 37.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+85}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-254}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{-157}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-25}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \]

Alternative 20: 29.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+83}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{-161}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+54}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -6.5e+83)
   (* c (* t j))
   (if (<= t -6.8e-161)
     (* i (* a b))
     (if (<= t 1.4e+54) (* i (* y (- j))) (* t (* 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 (t <= -6.5e+83) {
		tmp = c * (t * j);
	} else if (t <= -6.8e-161) {
		tmp = i * (a * b);
	} else if (t <= 1.4e+54) {
		tmp = i * (y * -j);
	} else {
		tmp = t * (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 (t <= (-6.5d+83)) then
        tmp = c * (t * j)
    else if (t <= (-6.8d-161)) then
        tmp = i * (a * b)
    else if (t <= 1.4d+54) then
        tmp = i * (y * -j)
    else
        tmp = t * (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 (t <= -6.5e+83) {
		tmp = c * (t * j);
	} else if (t <= -6.8e-161) {
		tmp = i * (a * b);
	} else if (t <= 1.4e+54) {
		tmp = i * (y * -j);
	} else {
		tmp = t * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -6.5e+83:
		tmp = c * (t * j)
	elif t <= -6.8e-161:
		tmp = i * (a * b)
	elif t <= 1.4e+54:
		tmp = i * (y * -j)
	else:
		tmp = t * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -6.5e+83)
		tmp = Float64(c * Float64(t * j));
	elseif (t <= -6.8e-161)
		tmp = Float64(i * Float64(a * b));
	elseif (t <= 1.4e+54)
		tmp = Float64(i * Float64(y * Float64(-j)));
	else
		tmp = Float64(t * 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 (t <= -6.5e+83)
		tmp = c * (t * j);
	elseif (t <= -6.8e-161)
		tmp = i * (a * b);
	elseif (t <= 1.4e+54)
		tmp = i * (y * -j);
	else
		tmp = t * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -6.5e+83], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6.8e-161], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e+54], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.5000000000000003e83

   1. Initial program 62.9%

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

   2. Taylor expanded in y around 0 70.0%

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

      1. sub-neg 70.0%

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

   4. Simplified 77.3%

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

   5. Taylor expanded in j around inf 46.2%

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

      1. mul-1-neg 46.2%

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

      2. distribute-lft-neg-out 46.2%

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

      3. +-commutative 46.2%

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

      4. cancel-sign-sub-inv 46.2%

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

      5. *-commutative 46.2%

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

      6. *-commutative 46.2%

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

   7. Simplified 46.2%

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

   8. Taylor expanded in t around inf 48.2%

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

      1. *-commutative 48.2%

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

   10. Simplified 48.2%

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

   if -6.5000000000000003e83 < t < -6.79999999999999964e-161

   1. Initial program 84.2%

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

   2. Taylor expanded in b around inf 51.1%

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

      1. *-commutative 51.1%

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

   4. Simplified 51.1%

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

   5. Taylor expanded in i around inf 37.8%

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

      1. associate-*r* 42.0%

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

   7. Simplified 42.0%

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

   if -6.79999999999999964e-161 < t < 1.40000000000000008e54

   1. Initial program 75.4%

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

   2. Taylor expanded in y around inf 51.6%

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

      1. +-commutative 51.6%

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

      2. mul-1-neg 51.6%

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

      3. unsub-neg 51.6%

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

      4. *-commutative 51.6%

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

   4. Simplified 51.6%

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

   5. Taylor expanded in z around 0 37.5%

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

      1. mul-1-neg 37.5%

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

      2. *-commutative 37.5%

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

   7. Simplified 37.5%

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

   if 1.40000000000000008e54 < t

   1. Initial program 59.1%

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

   2. Taylor expanded in y around 0 51.8%

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

      1. sub-neg 51.8%

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

   4. Simplified 69.0%

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

   5. Taylor expanded in j around inf 46.6%

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

      1. mul-1-neg 46.6%

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

      2. distribute-lft-neg-out 46.6%

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

      3. +-commutative 46.6%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t + \left(-i\right) \cdot y\right)} \]

      4. cancel-sign-sub-inv 46.6%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t - i \cdot y\right)} \]

      5. *-commutative 46.6%

         \[\leadsto j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      6. *-commutative 46.6%

         \[\leadsto j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   7. Simplified 46.6%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot c - y \cdot i\right)} \]

   8. Taylor expanded in t around inf 36.9%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 38.7%

         \[\leadsto \color{blue}{\left(c \cdot j\right) \cdot t} \]

      2. *-commutative 38.7%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j\right)} \]

   10. Simplified 38.7%

       \[\leadsto \color{blue}{t \cdot \left(c \cdot j\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 40.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+83}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{-161}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+54}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 21: 30.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+85}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{-162}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-13}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -1.4e+85)
   (* c (* t j))
   (if (<= t -6.8e-162)
     (* i (* a b))
     (if (<= t 2.4e-13) (* (* y i) (- j)) (* j (* t 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 (t <= -1.4e+85) {
		tmp = c * (t * j);
	} else if (t <= -6.8e-162) {
		tmp = i * (a * b);
	} else if (t <= 2.4e-13) {
		tmp = (y * i) * -j;
	} else {
		tmp = j * (t * 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 (t <= (-1.4d+85)) then
        tmp = c * (t * j)
    else if (t <= (-6.8d-162)) then
        tmp = i * (a * b)
    else if (t <= 2.4d-13) then
        tmp = (y * i) * -j
    else
        tmp = j * (t * 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 (t <= -1.4e+85) {
		tmp = c * (t * j);
	} else if (t <= -6.8e-162) {
		tmp = i * (a * b);
	} else if (t <= 2.4e-13) {
		tmp = (y * i) * -j;
	} else {
		tmp = j * (t * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -1.4e+85:
		tmp = c * (t * j)
	elif t <= -6.8e-162:
		tmp = i * (a * b)
	elif t <= 2.4e-13:
		tmp = (y * i) * -j
	else:
		tmp = j * (t * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -1.4e+85)
		tmp = Float64(c * Float64(t * j));
	elseif (t <= -6.8e-162)
		tmp = Float64(i * Float64(a * b));
	elseif (t <= 2.4e-13)
		tmp = Float64(Float64(y * i) * Float64(-j));
	else
		tmp = Float64(j * Float64(t * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -1.4e+85)
		tmp = c * (t * j);
	elseif (t <= -6.8e-162)
		tmp = i * (a * b);
	elseif (t <= 2.4e-13)
		tmp = (y * i) * -j;
	else
		tmp = j * (t * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -1.4e+85], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6.8e-162], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.4e-13], N[(N[(y * i), $MachinePrecision] * (-j)), $MachinePrecision], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.4e85

   1. Initial program 62.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in y around 0 70.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(c \cdot \left(j \cdot t\right) + y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   3. Step-by-step derivation

      1. sub-neg 70.0%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(c \cdot \left(j \cdot t\right) + y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)\right)\right) + \left(-b \cdot \left(c \cdot z - a \cdot i\right)\right)} \]

   4. Simplified 77.3%

      \[\leadsto \color{blue}{\left(t \cdot \left(j \cdot c - a \cdot x\right) + y \cdot \left(z \cdot x - i \cdot j\right)\right) + b \cdot \left(i \cdot a - c \cdot z\right)} \]

   5. Taylor expanded in j around inf 46.2%

      \[\leadsto \color{blue}{j \cdot \left(-1 \cdot \left(i \cdot y\right) + c \cdot t\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 46.2%

         \[\leadsto j \cdot \left(\color{blue}{\left(-i \cdot y\right)} + c \cdot t\right) \]

      2. distribute-lft-neg-out 46.2%

         \[\leadsto j \cdot \left(\color{blue}{\left(-i\right) \cdot y} + c \cdot t\right) \]

      3. +-commutative 46.2%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t + \left(-i\right) \cdot y\right)} \]

      4. cancel-sign-sub-inv 46.2%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t - i \cdot y\right)} \]

      5. *-commutative 46.2%

         \[\leadsto j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      6. *-commutative 46.2%

         \[\leadsto j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   7. Simplified 46.2%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot c - y \cdot i\right)} \]

   8. Taylor expanded in t around inf 48.2%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   9. Step-by-step derivation

      1. *-commutative 48.2%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

   10. Simplified 48.2%

       \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if -1.4e85 < t < -6.8e-162

   1. Initial program 84.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in b around inf 51.1%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 51.1%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

   4. Simplified 51.1%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

   5. Taylor expanded in i around inf 37.8%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 42.0%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot i} \]

   7. Simplified 42.0%

      \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot i} \]

   if -6.8e-162 < t < 2.3999999999999999e-13

   1. Initial program 76.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in y around 0 82.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(c \cdot \left(j \cdot t\right) + y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   3. Step-by-step derivation

      1. sub-neg 82.0%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(c \cdot \left(j \cdot t\right) + y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)\right)\right) + \left(-b \cdot \left(c \cdot z - a \cdot i\right)\right)} \]

   4. Simplified 73.7%

      \[\leadsto \color{blue}{\left(t \cdot \left(j \cdot c - a \cdot x\right) + y \cdot \left(z \cdot x - i \cdot j\right)\right) + b \cdot \left(i \cdot a - c \cdot z\right)} \]

   5. Taylor expanded in j around inf 41.1%

      \[\leadsto \color{blue}{j \cdot \left(-1 \cdot \left(i \cdot y\right) + c \cdot t\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 41.1%

         \[\leadsto j \cdot \left(\color{blue}{\left(-i \cdot y\right)} + c \cdot t\right) \]

      2. distribute-lft-neg-out 41.1%

         \[\leadsto j \cdot \left(\color{blue}{\left(-i\right) \cdot y} + c \cdot t\right) \]

      3. +-commutative 41.1%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t + \left(-i\right) \cdot y\right)} \]

      4. cancel-sign-sub-inv 41.1%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t - i \cdot y\right)} \]

      5. *-commutative 41.1%

         \[\leadsto j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      6. *-commutative 41.1%

         \[\leadsto j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   7. Simplified 41.1%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot c - y \cdot i\right)} \]

   8. Taylor expanded in t around 0 39.3%

      \[\leadsto j \cdot \color{blue}{\left(-1 \cdot \left(i \cdot y\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 39.3%

         \[\leadsto j \cdot \color{blue}{\left(-i \cdot y\right)} \]

      2. *-commutative 39.3%

         \[\leadsto j \cdot \left(-\color{blue}{y \cdot i}\right) \]

      3. distribute-rgt-neg-in 39.3%

         \[\leadsto j \cdot \color{blue}{\left(y \cdot \left(-i\right)\right)} \]

   10. Simplified 39.3%

       \[\leadsto j \cdot \color{blue}{\left(y \cdot \left(-i\right)\right)} \]

   if 2.3999999999999999e-13 < t

   1. Initial program 60.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in y around 0 51.4%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(c \cdot \left(j \cdot t\right) + y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   3. Step-by-step derivation

      1. sub-neg 51.4%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(c \cdot \left(j \cdot t\right) + y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)\right)\right) + \left(-b \cdot \left(c \cdot z - a \cdot i\right)\right)} \]

   4. Simplified 67.0%

      \[\leadsto \color{blue}{\left(t \cdot \left(j \cdot c - a \cdot x\right) + y \cdot \left(z \cdot x - i \cdot j\right)\right) + b \cdot \left(i \cdot a - c \cdot z\right)} \]

   5. Taylor expanded in j around inf 49.2%

      \[\leadsto \color{blue}{j \cdot \left(-1 \cdot \left(i \cdot y\right) + c \cdot t\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 49.2%

         \[\leadsto j \cdot \left(\color{blue}{\left(-i \cdot y\right)} + c \cdot t\right) \]

      2. distribute-lft-neg-out 49.2%

         \[\leadsto j \cdot \left(\color{blue}{\left(-i\right) \cdot y} + c \cdot t\right) \]

      3. +-commutative 49.2%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t + \left(-i\right) \cdot y\right)} \]

      4. cancel-sign-sub-inv 49.2%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t - i \cdot y\right)} \]

      5. *-commutative 49.2%

         \[\leadsto j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      6. *-commutative 49.2%

         \[\leadsto j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   7. Simplified 49.2%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot c - y \cdot i\right)} \]

   8. Taylor expanded in t around inf 36.6%

      \[\leadsto j \cdot \color{blue}{\left(c \cdot t\right)} \]
   9. Step-by-step derivation

      1. *-commutative 36.6%

         \[\leadsto j \cdot \color{blue}{\left(t \cdot c\right)} \]

   10. Simplified 36.6%

       \[\leadsto j \cdot \color{blue}{\left(t \cdot c\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 40.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+85}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{-162}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-13}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \]

Alternative 22: 30.2% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+83}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq -1.95 \cdot 10^{-163}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+54}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -1.65e+83)
   (* c (* t j))
   (if (<= t -1.95e-163)
     (* i (* a b))
     (if (<= t 1.4e+54) (* y (* i (- j))) (* t (* 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 (t <= -1.65e+83) {
		tmp = c * (t * j);
	} else if (t <= -1.95e-163) {
		tmp = i * (a * b);
	} else if (t <= 1.4e+54) {
		tmp = y * (i * -j);
	} else {
		tmp = t * (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 (t <= (-1.65d+83)) then
        tmp = c * (t * j)
    else if (t <= (-1.95d-163)) then
        tmp = i * (a * b)
    else if (t <= 1.4d+54) then
        tmp = y * (i * -j)
    else
        tmp = t * (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 (t <= -1.65e+83) {
		tmp = c * (t * j);
	} else if (t <= -1.95e-163) {
		tmp = i * (a * b);
	} else if (t <= 1.4e+54) {
		tmp = y * (i * -j);
	} else {
		tmp = t * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -1.65e+83:
		tmp = c * (t * j)
	elif t <= -1.95e-163:
		tmp = i * (a * b)
	elif t <= 1.4e+54:
		tmp = y * (i * -j)
	else:
		tmp = t * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -1.65e+83)
		tmp = Float64(c * Float64(t * j));
	elseif (t <= -1.95e-163)
		tmp = Float64(i * Float64(a * b));
	elseif (t <= 1.4e+54)
		tmp = Float64(y * Float64(i * Float64(-j)));
	else
		tmp = Float64(t * 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 (t <= -1.65e+83)
		tmp = c * (t * j);
	elseif (t <= -1.95e-163)
		tmp = i * (a * b);
	elseif (t <= 1.4e+54)
		tmp = y * (i * -j);
	else
		tmp = t * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -1.65e+83], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.95e-163], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e+54], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.64999999999999992e83

   1. Initial program 62.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in y around 0 70.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(c \cdot \left(j \cdot t\right) + y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   3. Step-by-step derivation

      1. sub-neg 70.0%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(c \cdot \left(j \cdot t\right) + y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)\right)\right) + \left(-b \cdot \left(c \cdot z - a \cdot i\right)\right)} \]

   4. Simplified 77.3%

      \[\leadsto \color{blue}{\left(t \cdot \left(j \cdot c - a \cdot x\right) + y \cdot \left(z \cdot x - i \cdot j\right)\right) + b \cdot \left(i \cdot a - c \cdot z\right)} \]

   5. Taylor expanded in j around inf 46.2%

      \[\leadsto \color{blue}{j \cdot \left(-1 \cdot \left(i \cdot y\right) + c \cdot t\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 46.2%

         \[\leadsto j \cdot \left(\color{blue}{\left(-i \cdot y\right)} + c \cdot t\right) \]

      2. distribute-lft-neg-out 46.2%

         \[\leadsto j \cdot \left(\color{blue}{\left(-i\right) \cdot y} + c \cdot t\right) \]

      3. +-commutative 46.2%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t + \left(-i\right) \cdot y\right)} \]

      4. cancel-sign-sub-inv 46.2%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t - i \cdot y\right)} \]

      5. *-commutative 46.2%

         \[\leadsto j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      6. *-commutative 46.2%

         \[\leadsto j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   7. Simplified 46.2%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot c - y \cdot i\right)} \]

   8. Taylor expanded in t around inf 48.2%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   9. Step-by-step derivation

      1. *-commutative 48.2%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

   10. Simplified 48.2%

       \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if -1.64999999999999992e83 < t < -1.9500000000000001e-163

   1. Initial program 84.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in b around inf 51.1%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 51.1%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

   4. Simplified 51.1%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

   5. Taylor expanded in i around inf 37.8%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 42.0%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot i} \]

   7. Simplified 42.0%

      \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot i} \]

   if -1.9500000000000001e-163 < t < 1.40000000000000008e54

   1. Initial program 75.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in y around inf 51.6%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   3. Step-by-step derivation

      1. +-commutative 51.6%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 51.6%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 51.6%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 51.6%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   4. Simplified 51.6%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   5. Taylor expanded in z around 0 37.5%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 37.5%

         \[\leadsto \color{blue}{-i \cdot \left(j \cdot y\right)} \]

      2. *-commutative 37.5%

         \[\leadsto -\color{blue}{\left(j \cdot y\right) \cdot i} \]

      3. *-commutative 37.5%

         \[\leadsto -\color{blue}{\left(y \cdot j\right)} \cdot i \]

      4. associate-*r* 40.5%

         \[\leadsto -\color{blue}{y \cdot \left(j \cdot i\right)} \]

      5. *-commutative 40.5%

         \[\leadsto -y \cdot \color{blue}{\left(i \cdot j\right)} \]

      6. distribute-rgt-neg-out 40.5%

         \[\leadsto \color{blue}{y \cdot \left(-i \cdot j\right)} \]

      7. distribute-rgt-neg-in 40.5%

         \[\leadsto y \cdot \color{blue}{\left(i \cdot \left(-j\right)\right)} \]

   7. Simplified 40.5%

      \[\leadsto \color{blue}{y \cdot \left(i \cdot \left(-j\right)\right)} \]

   if 1.40000000000000008e54 < t

   1. Initial program 59.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in y around 0 51.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(c \cdot \left(j \cdot t\right) + y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   3. Step-by-step derivation

      1. sub-neg 51.8%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(c \cdot \left(j \cdot t\right) + y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)\right)\right) + \left(-b \cdot \left(c \cdot z - a \cdot i\right)\right)} \]

   4. Simplified 69.0%

      \[\leadsto \color{blue}{\left(t \cdot \left(j \cdot c - a \cdot x\right) + y \cdot \left(z \cdot x - i \cdot j\right)\right) + b \cdot \left(i \cdot a - c \cdot z\right)} \]

   5. Taylor expanded in j around inf 46.6%

      \[\leadsto \color{blue}{j \cdot \left(-1 \cdot \left(i \cdot y\right) + c \cdot t\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 46.6%

         \[\leadsto j \cdot \left(\color{blue}{\left(-i \cdot y\right)} + c \cdot t\right) \]

      2. distribute-lft-neg-out 46.6%

         \[\leadsto j \cdot \left(\color{blue}{\left(-i\right) \cdot y} + c \cdot t\right) \]

      3. +-commutative 46.6%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t + \left(-i\right) \cdot y\right)} \]

      4. cancel-sign-sub-inv 46.6%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t - i \cdot y\right)} \]

      5. *-commutative 46.6%

         \[\leadsto j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      6. *-commutative 46.6%

         \[\leadsto j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   7. Simplified 46.6%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot c - y \cdot i\right)} \]

   8. Taylor expanded in t around inf 36.9%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 38.7%

         \[\leadsto \color{blue}{\left(c \cdot j\right) \cdot t} \]

      2. *-commutative 38.7%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j\right)} \]

   10. Simplified 38.7%

       \[\leadsto \color{blue}{t \cdot \left(c \cdot j\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 42.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+83}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq -1.95 \cdot 10^{-163}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+54}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 23: 30.4% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+83} \lor \neg \left(t \leq 3.8 \cdot 10^{-35}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -1.65e+83) (not (<= t 3.8e-35))) (* c (* t j)) (* a (* b 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 ((t <= -1.65e+83) || !(t <= 3.8e-35)) {
		tmp = c * (t * j);
	} else {
		tmp = a * (b * 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 ((t <= (-1.65d+83)) .or. (.not. (t <= 3.8d-35))) then
        tmp = c * (t * j)
    else
        tmp = a * (b * 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 ((t <= -1.65e+83) || !(t <= 3.8e-35)) {
		tmp = c * (t * j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -1.65e+83) or not (t <= 3.8e-35):
		tmp = c * (t * j)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -1.65e+83) || !(t <= 3.8e-35))
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -1.65e+83) || ~((t <= 3.8e-35)))
		tmp = c * (t * j);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -1.65e+83], N[Not[LessEqual[t, 3.8e-35]], $MachinePrecision]], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.64999999999999992e83 or 3.8000000000000001e-35 < t

   1. Initial program 63.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in y around 0 62.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(c \cdot \left(j \cdot t\right) + y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   3. Step-by-step derivation

      1. sub-neg 62.5%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(c \cdot \left(j \cdot t\right) + y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)\right)\right) + \left(-b \cdot \left(c \cdot z - a \cdot i\right)\right)} \]

   4. Simplified 73.5%

      \[\leadsto \color{blue}{\left(t \cdot \left(j \cdot c - a \cdot x\right) + y \cdot \left(z \cdot x - i \cdot j\right)\right) + b \cdot \left(i \cdot a - c \cdot z\right)} \]

   5. Taylor expanded in j around inf 46.5%

      \[\leadsto \color{blue}{j \cdot \left(-1 \cdot \left(i \cdot y\right) + c \cdot t\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 46.5%

         \[\leadsto j \cdot \left(\color{blue}{\left(-i \cdot y\right)} + c \cdot t\right) \]

      2. distribute-lft-neg-out 46.5%

         \[\leadsto j \cdot \left(\color{blue}{\left(-i\right) \cdot y} + c \cdot t\right) \]

      3. +-commutative 46.5%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t + \left(-i\right) \cdot y\right)} \]

      4. cancel-sign-sub-inv 46.5%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t - i \cdot y\right)} \]

      5. *-commutative 46.5%

         \[\leadsto j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      6. *-commutative 46.5%

         \[\leadsto j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   7. Simplified 46.5%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot c - y \cdot i\right)} \]

   8. Taylor expanded in t around inf 38.6%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   9. Step-by-step derivation

      1. *-commutative 38.6%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

   10. Simplified 38.6%

       \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if -1.64999999999999992e83 < t < 3.8000000000000001e-35

   1. Initial program 78.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in b around inf 42.9%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 42.9%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

   4. Simplified 42.9%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

   5. Taylor expanded in i around inf 30.3%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 34.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+83} \lor \neg \left(t \leq 3.8 \cdot 10^{-35}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 24: 30.5% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{+83}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-35}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -4.3e+83)
   (* c (* t j))
   (if (<= t 2.8e-35) (* a (* b i)) (* j (* t 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 (t <= -4.3e+83) {
		tmp = c * (t * j);
	} else if (t <= 2.8e-35) {
		tmp = a * (b * i);
	} else {
		tmp = j * (t * 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 (t <= (-4.3d+83)) then
        tmp = c * (t * j)
    else if (t <= 2.8d-35) then
        tmp = a * (b * i)
    else
        tmp = j * (t * 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 (t <= -4.3e+83) {
		tmp = c * (t * j);
	} else if (t <= 2.8e-35) {
		tmp = a * (b * i);
	} else {
		tmp = j * (t * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -4.3e+83:
		tmp = c * (t * j)
	elif t <= 2.8e-35:
		tmp = a * (b * i)
	else:
		tmp = j * (t * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -4.3e+83)
		tmp = Float64(c * Float64(t * j));
	elseif (t <= 2.8e-35)
		tmp = Float64(a * Float64(b * i));
	else
		tmp = Float64(j * Float64(t * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -4.3e+83)
		tmp = c * (t * j);
	elseif (t <= 2.8e-35)
		tmp = a * (b * i);
	else
		tmp = j * (t * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -4.3e+83], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.8e-35], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.3e83

   1. Initial program 62.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in y around 0 70.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(c \cdot \left(j \cdot t\right) + y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   3. Step-by-step derivation

      1. sub-neg 70.0%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(c \cdot \left(j \cdot t\right) + y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)\right)\right) + \left(-b \cdot \left(c \cdot z - a \cdot i\right)\right)} \]

   4. Simplified 77.3%

      \[\leadsto \color{blue}{\left(t \cdot \left(j \cdot c - a \cdot x\right) + y \cdot \left(z \cdot x - i \cdot j\right)\right) + b \cdot \left(i \cdot a - c \cdot z\right)} \]

   5. Taylor expanded in j around inf 46.2%

      \[\leadsto \color{blue}{j \cdot \left(-1 \cdot \left(i \cdot y\right) + c \cdot t\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 46.2%

         \[\leadsto j \cdot \left(\color{blue}{\left(-i \cdot y\right)} + c \cdot t\right) \]

      2. distribute-lft-neg-out 46.2%

         \[\leadsto j \cdot \left(\color{blue}{\left(-i\right) \cdot y} + c \cdot t\right) \]

      3. +-commutative 46.2%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t + \left(-i\right) \cdot y\right)} \]

      4. cancel-sign-sub-inv 46.2%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t - i \cdot y\right)} \]

      5. *-commutative 46.2%

         \[\leadsto j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      6. *-commutative 46.2%

         \[\leadsto j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   7. Simplified 46.2%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot c - y \cdot i\right)} \]

   8. Taylor expanded in t around inf 48.2%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   9. Step-by-step derivation

      1. *-commutative 48.2%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

   10. Simplified 48.2%

       \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if -4.3e83 < t < 2.8e-35

   1. Initial program 78.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in b around inf 42.9%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 42.9%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

   4. Simplified 42.9%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

   5. Taylor expanded in i around inf 30.3%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

   if 2.8e-35 < t

   1. Initial program 63.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in y around 0 56.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(c \cdot \left(j \cdot t\right) + y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   3. Step-by-step derivation

      1. sub-neg 56.9%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(c \cdot \left(j \cdot t\right) + y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)\right)\right) + \left(-b \cdot \left(c \cdot z - a \cdot i\right)\right)} \]

   4. Simplified 70.7%

      \[\leadsto \color{blue}{\left(t \cdot \left(j \cdot c - a \cdot x\right) + y \cdot \left(z \cdot x - i \cdot j\right)\right) + b \cdot \left(i \cdot a - c \cdot z\right)} \]

   5. Taylor expanded in j around inf 46.8%

      \[\leadsto \color{blue}{j \cdot \left(-1 \cdot \left(i \cdot y\right) + c \cdot t\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 46.8%

         \[\leadsto j \cdot \left(\color{blue}{\left(-i \cdot y\right)} + c \cdot t\right) \]

      2. distribute-lft-neg-out 46.8%

         \[\leadsto j \cdot \left(\color{blue}{\left(-i\right) \cdot y} + c \cdot t\right) \]

      3. +-commutative 46.8%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t + \left(-i\right) \cdot y\right)} \]

      4. cancel-sign-sub-inv 46.8%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot t - i \cdot y\right)} \]

      5. *-commutative 46.8%

         \[\leadsto j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      6. *-commutative 46.8%

         \[\leadsto j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   7. Simplified 46.8%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot c - y \cdot i\right)} \]

   8. Taylor expanded in t around inf 32.9%

      \[\leadsto j \cdot \color{blue}{\left(c \cdot t\right)} \]
   9. Step-by-step derivation

      1. *-commutative 32.9%

         \[\leadsto j \cdot \color{blue}{\left(t \cdot c\right)} \]

   10. Simplified 32.9%

       \[\leadsto j \cdot \color{blue}{\left(t \cdot c\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 34.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{+83}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-35}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \]

Alternative 25: 22.4% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(b \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* b i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (b * i);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = a * (b * i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (b * i);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (b * i)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(b * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (b * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 71.1%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

2. Taylor expanded in b around inf 37.3%

   \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
3. Step-by-step derivation

   1. *-commutative 37.3%

      \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

4. Simplified 37.3%

   \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

5. Taylor expanded in i around inf 21.6%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

6. Final simplification 21.6%

   \[\leadsto a \cdot \left(b \cdot i\right) \]

Developer target: 68.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ t_2 := x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{if}\;t < -8.120978919195912 \cdot 10^{-33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t < -4.712553818218485 \cdot 10^{-169}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t < -7.633533346031584 \cdot 10^{-308}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t < 1.0535888557455487 \cdot 10^{-139}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
          (/
           (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0)))
           (+ (* c t) (* i y)))))
        (t_2
         (-
          (* x (- (* z y) (* a t)))
          (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))
   (if (< t -8.120978919195912e-33)
     t_2
     (if (< t -4.712553818218485e-169)
       t_1
       (if (< t -7.633533346031584e-308)
         t_2
         (if (< t 1.0535888557455487e-139) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (pow((c * t), 2.0) - pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ** 2.0d0) - ((i * y) ** 2.0d0))) / ((c * t) + (i * y)))
    t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
    if (t < (-8.120978919195912d-33)) then
        tmp = t_2
    else if (t < (-4.712553818218485d-169)) then
        tmp = t_1
    else if (t < (-7.633533346031584d-308)) then
        tmp = t_2
    else if (t < 1.0535888557455487d-139) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (Math.pow((c * t), 2.0) - Math.pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (math.pow((c * t), 2.0) - math.pow((i * y), 2.0))) / ((c * t) + (i * y)))
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
	tmp = 0
	if t < -8.120978919195912e-33:
		tmp = t_2
	elif t < -4.712553818218485e-169:
		tmp = t_1
	elif t < -7.633533346031584e-308:
		tmp = t_2
	elif t < 1.0535888557455487e-139:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(Float64(j * Float64((Float64(c * t) ^ 2.0) - (Float64(i * y) ^ 2.0))) / Float64(Float64(c * t) + Float64(i * y))))
	t_2 = Float64(Float64(x * Float64(Float64(z * y) - Float64(a * t))) - Float64(Float64(b * Float64(Float64(z * c) - Float64(a * i))) - Float64(Float64(Float64(c * t) - Float64(y * i)) * j)))
	tmp = 0.0
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ^ 2.0) - ((i * y) ^ 2.0))) / ((c * t) + (i * y)));
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	tmp = 0.0;
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[Power[N[(c * t), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(i * y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * t), $MachinePrecision] + N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(c * t), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -8.120978919195912e-33], t$95$2, If[Less[t, -4.712553818218485e-169], t$95$1, If[Less[t, -7.633533346031584e-308], t$95$2, If[Less[t, 1.0535888557455487e-139], t$95$1, t$95$2]]]]]]

Reproduce

herbie shell --seed 2023297 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< t -8.120978919195912e-33) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -4.712553818218485e-169) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (if (< t -7.633533346031584e-308) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 1.0535888557455487e-139) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))